Studies of Liquid-Liquid Two-Phase Flows Using Laser-Based … · 2019. 11. 11. · co-current...

Studies of Liquid-Liquid Two-Phase

Flows Using Laser-Based Methods

Rhys Gareth Morgan

March 2012

Department of Chemical Engineering and Chemical Technology

Imperial College London

South Kensington Campus

London SW7 2AZ

A thesis submitted to Imperial College London in partial fulfilment of the requirements

of the degree of Doctor of Philosophy and for the Diploma of Membership of the

Imperial College

“I have no idols. I admire work, dedication and competence.”

Ayrton Senna da Silva

Declaration

This thesis is a description of the work carried out in the Department of Chemical Engineering,

Imperial College London, between October 2007 and March 2012, under the supervision of

Emeritus Professor Geoffrey F. Hewitt and Dr Christos Markides. Except where acknowledged,

the material is the original work of the author and no part of it has been submitted for a degree

at any other university.

Abstract

The research described in this thesis has been focused on the detailed investigation of horizontal

co-current liquid-liquid two-phase flows. The experiments were carried out in channels of

square and circular cross section and involved the use of two immiscible liquids of matched

refractive index; namely an oil (ExxolTMD80) and a 81.7 wt% glycerol-water solution. The

experiments were carried out in a refurbished liquid-liquid flow facility (TOWER) and the focus

was on examining the flows using high-speed laser-based visualisation methods which allowed

both qualitative evaluation of the nature of the flows (i.e. the flow patterns) and quantitative

measurements of parameters such as drop size and velocity distribution. The laser-based

techniques used included Planar Laser Induced Fluorescence (PLIF), Particle Tracking

Velocimetry (PTV) and Particle Image Velocimetry (PIV). Using these techniques, it was

possible to obtain high spatial and temporal resolution measurements of velocity and phase

distribution of liquid-liquid flows which enabled the detailed diagnostic inspection to an extent

that has not been previously possible. 144 experiments were carried out in three experimental

campaigns. In the first campaign, a square cross section channel was used in order to avoid

image distortion by the channel walls. In the second and third campaigns, a circular tube was

employed and a graticule correction method was used to correct the distortion to the PLIF and

PTV/PIV images which occurs when the circular cross-section visualisation cell is used. In the

two circular tube experiments, two methods of injection of the phases were used: (1) the heavier

(glycerol solution) phase was injected in its natural location at the bottom of the channel, and

(2) in the second case the heavier phase was injected at the top of the channel.

The PLIF images gave a clear indication of the distribution of the phases at the channel centre

line and have been used qualitatively in obtaining information about the flow patterns occurring.

The PLIF images have also been used quantitatively in generating data on phase distribution, in-

situ phase fraction, interface level and drop size distribution. Much of the data on in-situ phase

fraction and interface level fits well with a simple laminar-laminar stratified flow model. The

PTV/PIV method provided extensive data on velocity profiles; in the lower (aqueous glycerol

solution) phase, the profile usually showed the curved shape characteristic of laminar flow and

in the upper (ExxolTMD80) phase, the velocity profile often showed the flattened form

characteristic of turbulent flow.

Acknowledgements

I feel extremely fortunate to have been surrounded by some truly great people while I have

undertaken this PhD. The following attempts to articulate the gratitude and thanks I have for

their involvement in this work, whether it be of an academic nature or otherwise. Firstly, I

would like to thank my supervisors, Professor Geoffrey F. Hewitt and Dr Christos Markides.

It’s difficult to concisely convey the appreciation I have for all the guidance, encouragement

and teaching that I have had from them. I would like to express my thanks and appreciation for

the help I have had from Dr Ivan Zadrazil and Dr Colin Hale. Also, I would like to thank the

Chemical Engineering Workshop for the help in refurbishing the TOWER facility to enable my

experimental work to be conducted. There are a few friends that I would like to thanks, these

being Patrick Wray, Kat Fu and Henry Morris. Finally, I would like to extend a massive thank

you to my mother, father and the rest of my family for their love, support and encouragement

during not just this PhD but all of my educational endeavours that led to this point.

Ta

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2.1

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APTER 1: INT

Backgrou1

Objective2

Research3

Thesis St4

APTER 2: LIT

Introduct1

Flow Reg2

Phase Inv3

Emulsion4

Concludi5

APTER 3: EX

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Introduct1

The TOW2

Compo3.2.1

Laser Equ3

Coppe3.3.1

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3.8

3.9

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4.3

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Fluoresce6

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APTER 4: LA

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Conclusio9

APTER 5: LA

UID FLOWS

Introduct1

Experime2

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3

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Conclu10

APTER 6: INV

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Introduct1

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4

6.7

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7.1

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Conclusio9

APTER 7: CO

Conclusio1

Suggestio2

ERENCES ...

ENDIX 1: ST

ENDIX 2: D

nd Hewitt (1

Size Distribu

Profiles.......

Regime Anal

ct Angle Ana

ons ..............

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ons ..............

ons for Futur

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ERIVATION

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NS AND SU

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NS FOR FUT

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OCEDURE ..

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5

6

ListofFigures

FIGURE 2-1: FLOW PATTERNS IN OIL-WATER PIPE FLOW FOR SUPERFICIAL WATER VELOCITIES,

UM OF: (A) 0.287 FT/SEC; (B) 1.79 FT/SEC, AND; (C) 3.55 FT/SEC AT DIFFERENT INLET OIL-

WATER RATIOS, (WHERE, O/ W), RUSSELL ET AL. (1959) ................................ 34

FIGURE 2-2: FLOW PATTERNS OBSERVED FOR THE OIL 16.8 MPA. S OIL FLOWING IN THE

PRESENCE OF WATER AT WATER SUPERFICIAL VELOCITIES OF UM OF: (A) 0.10 FT/SEC; (B)

0.682 FT/SEC, AND; (C) 2.04 FT/SEC, CHARLES ET AL. (1961) .............................................. 35

FIGURE 2-3: FLOW REGIME MAPS FOR TWO-PHASE OIL-WATER FLOWS FOR OIL VISCOSITIES OF

(A) OIL 6.29 AND 16.8 MPA. S (B) OIL 65 MPA. S (WHERE, OIL 988 KG. M 3),

CHARLES ET AL. (1961) ........................................................................................................ 36

FIGURE 2-4: FLOW PATTERNS OBSERVED FOR EQUAL DENSITY TWO-PHASE DISTILLED WATER

( OIL 0.82 MPA. S) AND KEROSENE-PERCHLOROETHYLENE SOLUTION ( OIL 1.0 MPA. S)

FLOWS: (A) DISPERSIONS; (B) SLUGS; (C) STRATIFIED LAYERS; (D) ANNULAR FLOW, AND; (E)

MIXED. HASSON ET AL. (1970) ............................................................................................ 38

FIGURE 2-5: FLOW PATTERNS OBSERVED FOR A TWO-PHASE KEROSENE-PERCHLORETHYLENE

AND DISTILLED WATER SYSTEM, HASSON ET AL. (1970) ..................................................... 39

FIGURE 2-6: FLOW PATTERN MAP FOR THE FLOW OF OIL (WHERE OIL 21.7 MPA. S) AND

WATER IN A 39.4 MM ID PIPE (GUZHOV ET AL., 1973) ......................................................... 40

FIGURE 2-7: FLOW PATTERN MAP FOR TWO-PHASE OIL-WATER FLOW IN A 41MM INTERNAL

DIAMETER PIPE, WITH OIL VISCOSITY OIL 84.0 MPA. S, OGLESBY ET AL. (1979) ............ 41

FIGURE 2-8: FLOW PATTERN MAP, ARIRACHAKARAN ET AL. (1989) ......................................... 42

FIGURE 2-9: TWO PHASE FLOW PATTERNS OBSERVED BY NÄDLER & MEWES (1995). .............. 44

FIGURE 2-10: OIL-WATER FLOW REGIME MAP FOR A HORIZONTAL PIPELINE OF 59MM ID AS

IDENTIFIED BY NÄDLER & MEWES (1995) ........................................................................... 45

7

FIGURE 2-11: TWO-PHASE OIL-WATER FLOW PATTERN CLASSIFICATIONS: (A) OIL IN WATER

EMULSION (O/W); (B) DISPERSION OF WATER IN OIL AND OIL IN WATER (DW/O & DO/W); (C)

WATER IN OIL EMULSION (W/O); (D) STRATIFIED FLOW (ST); (E) STRATIFIED FLOW WITH

MIXING AT THE INTERFACE (ST & MI), AND; (F) DISPERSION OF OIL IN WATER AND WATER

(DO/W & W), TRALLERO (1995) ........................................................................................... 46

FIGURE 2-12: FLOW PATTERNS BY ANGELI & HEWITT (2000A) IN THE (A) STAINLESS STEEL

TEST SECTION, (B) ACRYLIC RESIN TEST SECTION. ○, STRATIFIED WAVY (SW); ▬, THREE

LAYERS (3L); ∆, STRATIFIED MIXED/OIL (SM/OIL); - - - , PHASE CONTINUITY BOUNDARIES;

▲, STRATIFIED WAVY/DROPS (SWD); ●, STRATIFIED MIXED/WATER (SM/WATER); +,

MIXED (M) ............................................................................................................................ 47

FIGURE 2-13: FLOW REGIME MAP CONSTRUCTED BY NADLER & MEWES (1997) FOR TWO-

PHASE OIL-WATER FLOW BASED ON INPUT WATER FRACTION. ............................................ 48

FIGURE 2-14: FLOW PATTERN MAP FOR THE STAINLESS STEEL TEST SECTION OF THE TOWER

FACILITY, SOLEIMANI (1999) ............................................................................................... 49

FIGURE 2-15: FLOW PATTERNS MAP WITHOUT MIXER AT THE TUBE INLET, HUSSAIN (2004) .... 51

FIGURE 2-16: FLOW PATTERNS MAP WITH A 5-ELEMENT KENICS™ MIXER AT THE TUBE INLET,

HUSSAIN (2004) ................................................................................................................... 51

FIGURE 2-17: FLOW PATTERN MAPS PREDICTION FOR TRANSITIONS TO DISPERSED OIL IN WATER

AND TRANSITION TO DISPERSED WATER IN OIL AND COMPARISON WITH EXPERIMENTAL

DATA OF GUZHOV ET AL (1973) IN HORIZONTAL OIL-WATER SYSTEM, BRAUNER (2001) ... 52

FIGURE 2-18: THE BRAUNER (2001) PREDICTIONS FOR TRANSITIONS TO DO/W (BOUNDARY 4)

AND TRANSITION TO DW/O (BOUNDARY 5) IN A HORIZONTAL OIL-WATER SYSTEM

(TRALLERO (1995)) .............................................................................................................. 53

FIGURE 2-19: SCHEMATIC DIAGRAM OF DUAL CONTINUOUS FLOW, LOCK & ANGELI (2004) ... 54

FIGURE 2-20: FLOW PATTERN MAP (LOVICK & ANGELI (2004)) WITH THE RESULTS FROM

LAFLIN & OGLESBY (1976) (SOLID LINES. (I) DUAL CONTINUOUS FLOW; (II) DISPERSION OF

8

OIL IN WATER AND WATER; (III) DISPERSION OF OIL IN WATER; (IV) DISPERSION OF WATER

IN OIL .................................................................................................................................... 55

FIGURE 2-21: GRAPHICAL REPRESENTATION OF THE AMBIVALENT RANGE, YEO ET AL. (2002) 56

FIGURE 2-22: PHASE INVERSION PROCESS FOR AN OIL-WATER DISPERSION SYSTEM,

ARIRACHAKARAN ET AL (1989) ........................................................................................... 59

FIGURE 2-23: PHASE INVERSION POINT CORRELATION, ARIRACHAKARAN ET AL. (1989) ......... 60

FIGURE 2-24: MIXTURE VISCOSITY AGAINST INPUT WATER FRACTION FOR LOW VISCOSITY OIL,

ARIRACHAKARAN ET AL. (1989) .......................................................................................... 62

FIGURE 2-25: PRESSURE GRADIENT IN TWO-PHASE LIQUID-LIQUID FLOWS, SOLEIMANI (1999) 63

FIGURE 2-26: PRESSURE DROP FOR OIL-WATER FLOW (NADLER AND MEWES, 1995) ............... 63

FIGURE 3-1: SCHEMATIC DIAGRAM OF THE TOWER FACILITY ................................................. 77

FIGURE 3-2: PHOTOGRAPH SHOWING THE ARRANGEMENT OF THE SEPARATOR AND THE

STORAGE TANKS ................................................................................................................... 78

FIGURE 3-3: PHOTOGRAPH OF THE FLOW CONTROL PANEL ....................................................... 80

FIGURE 3-4: PHOTOGRAPH ILLUSTRATING THE FLOW CONTROL PANEL OF THE TOWER

FACILITY ............................................................................................................................... 81

FIGURE 3-5: PHOTOGRAPH SHOWING THE ORIENTATION AT THE PIPE TEST SECTION INLET ...... 82

FIGURE 3-6: 1.5 MM TYPE K THERMOCOUPLE ............................................................................ 83

FIGURE 3-7: ILLUSTRATION OF THE LASER SHEET, SQUARE CROSS-SECTION VISUALISATION

CELL AND CAMERA ORIENTATION ........................................................................................ 86

FIGURE 3-8: LASER-CAMERA SYNCHRONISATION EQUIPMENT .................................................. 88

FIGURE 3-9: DIAGRAM ILLUSTRATING STOKES SHIFT ................................................................ 90

FIGURE 3-10: COMPARISON OF THE EXCITATION SPECTRUM OF EOSIN Y WITH THE OUTPUT

SPECTRUM OF THE COPPER VAPOUR LASER ........................................................................ 93

FIGURE 3-11: REFRACTIVE INDICES OF (A) EXXSOL D80 AND WATER-GLYCEROL SOLUTIONS AS

A FUNCTION OF A TEMPERATURE AND COMPOSITION AND (B) EXXSOL D80 AND WATER-

GLYCEROL-DYE (0.2ML/L OF EOSIN Y) AT 20°C ................................................................. 95

9

FIGURE 3-12: DENSITY AS A FUNCTION OF TEMPERATURE FOR (A) 81.7WT% WATER-GLYCEROL

SOLUTION WITH DIFFERENT CONCENTRATIONS OF EOSIN Y AND (B) EXXSOL D80 OIL ...... 97

FIGURE 3-13: VISCOSITY AS A FUNCTION OF TEMPERATURE FOR (A) 81.7WT% WATER-

GLYCEROL SOLUTION WITH DIFFERENT CONCENTRATIONS OF EOSIN Y AND (B) EXXSOL

D80 OIL ................................................................................................................................ 99

FIGURE 3-14: SHEAR STRESS, Τ, AGAINST STRAIN RATE, Γ, FOR (A) 81.7WT% WATER-GLYCEROL

SOLUTION WITH 0.4 ML/L OF EOSIN Y AND (B) EXXSOL D80 OIL ..................................... 100

FIGURE 3-15: VARIATION IN GLYCEROL SOLUTION-OIL INTERFACIAL TENSION AS A FUNCTION

OF EOSIN Y CONCENTRATION ............................................................................................ 101

FIGURE 3-16: DIAGRAM ILLUSTRATING THE REFRACTION OF LIGHT AT THE INTERFACE

BETWEEN TWO MEDIA ........................................................................................................ 103

FIGURE 3-17: SQUARE CROSS SECTION VISUALISATION SECTION ............................................ 105

FIGURE 3-18: CIRCULAR CROSS SECTION VISUALISATION SECTION ........................................ 107

FIGURE 3-19: GRATICULE CALIBRATION PIECE ........................................................................ 109

FIGURE 3-20: DEMONSTRATION OF THE GRATICULE IMAGE CORRECTION TECHNIQUE. .......... 109

FIGURE 3-21: DIAGRAM TO SHOW MATLAB IMAGE PROCESSING TECHNIQUE TO GENERATE

PHASE DISTRIBUTION DATA ................................................................................................ 112

FIGURE 3-22: INVESTIGATION OF THE EFFECT OF THRESHOLDING AND BINARISATION ON THE

INSTANTANEOUS IMAGE PRESENTED IN FIGURE 3-23: (A) VARIATIONS IN THE

IDENTIFICATION OF THE INTERFACE LOCATION, AND (B) VARIATIONS IN THE IMAGE-

AVERAGED INSTANTANEOUS IN-SITU OIL FRACTION ΦY,T (AS DEFINED IN EQUATION 2), IN

BOTH CASES DUE TO THE USE OF DIFFERENT THRESHOLDING PARAMETERS Α, FROM 2% TO

50%. OUR SELECTED VALUE WAS Α 5% ........................................................................ 113

FIGURE 3-23: INTERFACE LEVEL IMAGE PROCESSING, SHOWING IMPORTANT DEFINITIONS .... 114

FIGURE 3-24: PROCESS FOR DETERMINING THE VELOCITY OF THE WAVES AT THE LIQUID –

LIQUID INTERFACE, SPECIFICALLY: (A) INTERFACE LEVEL PROFILES FOR TWO SUCCESSIVE

10

IMAGES; (B) THE TWO SUCCESSIVE IMAGES SHOWN IN FIGURE 3-26(A) AFTER HAVING

UNDERGONE PRE-PROCESSING; (C) THE CORRELATION BETWEEN THE PRE-PROCESSED

INTERFACE LEVELS SHOWN IN FIGURE 3-26(B), INCLUDING A 0.99 ACCEPTABILITY

THRESHOLD, AND; (D) ILLUSTRATION THAT THE PEAK VALUE CORRESPONDS TO THE

INTERFACE DISPLACEMENT BETWEEN THE TWO SUCCESSIVE IMAGES .............................. 118

FIGURE 3-25: THE PIV-PTV PROCESS FOR ACQUIRING VELOCITY VECTORS BETWEEN TWO

IMAGES SEPARATED BY A KNOWN TIME INTERVAL: (A) A DISTORTION-CORRECTED LIF

IMAGE; (B) SHOWS THE IMAGE IN FIGURE 3-25(A) AFTER IT HAS UNDERGONE PRE-

PROCESSING (I.E., SUBTRACTION OF SLIDING MINIMUM PIXEL INTENSITY); (C) A VELOCITY

VECTOR MAP CALCULATED USING THE PIV TECHNIQUE BETWEEN TWO SUCCESSIVE

IMAGES, AND; (D) A PTV VECTOR MAP WHICH IS CALCULATED FROM THE PIV VECTOR MAP

SHOWN IN FIGURE 3-25(C). IN (C) AND (D) THE SIZE OF THE VECTORS (ARROWS) REFERS TO

THE VELOCITY .................................................................................................................... 120

FIGURE 3-26: AGGREGATED PTV VECTORS FOR A GIVEN TIME SERIES OF LIF IMAGES AT A

FIXED SUPERFICIAL VELOCITY UM AND INPUT OIL FRACTION ΦIN COMBINATION ............ 122

FIGURE 3-27: FLOW VELOCITY PROFILE. THE DOTTED RED LINE INDICATES THE AVERAGE

INTERFACE LEVEL FOR THE PARTICULAR FLOW RUN (SUPERFICIAL VELOCITY UM AND

INPUT OIL FRACTION ΦIN COMBINATION) ANALYSED ........................................................ 122

FIGURE 4-1: IMAGES OF THE 8 DISTINCT FLOW REGIMES OBSERVED IN THE SQUARE CROSS

SECTION CAMPAIGN ........................................................................................................... 126

FIGURE 4-2: FLOW REGIME MAP .............................................................................................. 129

FIGURE 4-3: SECONDARY DISPERSIONS OF (A) OIL-IN-GLYCEROL SOLUTION-IN OIL DROPLETS

AT AN OIL INPUT FRACTION OF ΦIN = 0.13, AND (B) OIL-IN-GLYCEROL SOLUTION-IN OIL AND

GLYCEROL SOLUTION-IN-OIL-IN-GLYCEROL SOLUTION DROPLETS AT AN OIL INPUT

FRACTION OF ΦIN = 0.87, BOTH AT A SUPERFICIAL MIXTURE VELOCITY UM OF 0.29 M.S-1 132

11

FIGURE 4-4: (A) SECONDARY DISPERSIONS OIL-IN-GLYCEROL SOLUTION-IN OIL DROPLETS AT

AN OIL INPUT FRACTION OF ΦIN = 0.13, AND (B) SECONDARY AND TERNARY DISPERSIONS

OF OIL-IN-GLYCEROL SOLUTION-IN OIL AND GLYCEROL SOLUTION-IN-OIL-IN-GLYCEROL

SOLUTION DROPLETS AT AN OIL INPUT FRACTION OF ΦIN = 0.87, BOTH AT A SUPERFICIAL

MIXTURE VELOCITY UMOF 0.29 M.S-1 ................................................................................ 132

FIGURE 4-5: VERTICAL OIL PHASE FRACTION PROFILES Φ(Y) AT DIFFERENT INPUT OIL

FRACTIONS ΦIN FOR A SUPERFICIAL MIXTURE VELOCITY UM OF: (A) 0.07 M.S-1; (B) 0.14 M.S-

1; (C) 0.21 M.S-1, AND; (D) 0.29 M.S-1 ................................................................................... 134

FIGURE 4-6: VERTICAL OIL PHASE FRACTION PROFILES Φ(Y) FOR DIFFERENT SUPERFICIAL

MIXTURE VELOCITIES UM AT AN INPUT OIL FRACTION ΦIN OF: (A) 0.25, (B) 0.50, AND (C)

0.75 .................................................................................................................................... 135

FIGURE 4-7: SCHEMATIC ZONE CATEGORISATION OF LIQUID-LIQUID FLOWS BASED UPON PHASE

DISTRIBUTION ..................................................................................................................... 136

FIGURE 4-8: INSTANTANEOUS FLOW IMAGES FOR AN OIL INPUT PHASE FRACTION ΦIN 0.26

AND SUPERFICIAL MIXTURE VELOCITY UM 0.07 M.S-1 AT: (A) 0 SECONDS; (B) 1

S, AND; 2 S ................................................................................................................... 136

FIGURE 4-9: (A) SINE WAVE PROFILE, AND; (B) THE ASSOCIATED PHASE DISTRIBUTION PROFILE

........................................................................................................................................... 137

FIGURE 4-10: HEIGHT OF INTERFACE ZONE FOR AS A FUNCTION OF (A) SUPERFICIAL MIXTURE

VELOCITIES UM FOR CONSTANT INPUT OIL FRACTION ΦIN; (B) INPUT OIL FRACTION ΦIN FOR

CONSTANT SUPERFICIAL MIXTURE VELOCITIES UM ........................................................... 138

FIGURE 4-11: INSTANTANEOUS FLOW IMAGES HIGHLIGHT THE PRESENCE OF AN OIL DROPLET

LAYER BELOW THE INTERFACE FOR UM 0.29 M.S-1 AT: (A) ΦIN 0.13, AND; (B)

ΦIN 0.25 ......................................................................................................................... 139

FIGURE 4-12: IN-SITU FRACTION ΦY,T AS A FUNCTION OF INPUT OIL FRACTION ΦIN FOR

DIFFERENT SUPERFICIAL MIXTURE VELOCITIES UM........................................................... 141

12

FIGURE 4-13: STRATIFIED LIQUID-LIQUID FLOW MODEL CONSTRUCTION ............................... 142

FIGURE 4-14: EXPERIMENTAL RESULTS AND CORRELATIONS FOR: (A) SLIP RATIO S AS A

FUNCTION OF INPUT OIL FRACTION ΦIN, AND: (B) IN-SITU OIL PHASE FRACTION ΦY,T AS A

FUNCTION OF INPUT OIL FRACTION ΦIN ............................................................................. 146

FIGURE 4-15: SLIP RATIO S AS A FUNCTION OF INPUT OIL FRACTION ΦIN FOR DIFFERENT

SUPERFICIAL MIXTURE VELOCITIES UM PLIF DATA IS PRESENTED IN BLUE AND THE

RESULTS FROM LOVICK AND ANGELI (2004) ARE PRESENTED IN RED) ............................. 149

FIGURE 4-16: IN-SITU FRACTION ΦY,T AS A FUNCTION OF INPUT OIL FRACTION ΦIN COMPARED

WITH DATA FROM LOVICK AND ANGELI (2004) AND RUSSELL ET AL. (1959) ................... 150


DIFFERENT SUPERFICIAL MIXTURE VELOCITIES UM FOR DATA BY LOVICK AND ANGELI

(2004) AND RUSSELL ET AL. (1959) ................................................................................... 151

FIGURE 4-18: IN-SITU PHASE FRACTION ENVELOPE ................................................................. 152

FIGURE 4-19: THE MEAN (Μ) AND UPPER (Μ + 2Σ) AND LOWER (Μ – 2Σ) LIMITS FOR THE

INTERFACE LEVEL H AS A FUNCTION OF INPUT OIL FRACTION ΦIN FOR SUPERFICIAL

MIXTURE VELOCITIES UM OF: (A) 0.07 M.S-1, (B) 0.14 M.S-1, (C) 0.21 M.S-1, AND (D) 0.29 M.S-1

........................................................................................................................................... 153


INTERFACE LEVEL H AS A FUNCTION OF SUPERFICIAL MIXTURE VELOCITY UM FOR INPUT

OIL FRACTIONS ΦIN OF: (A) 0.25, (B) 0.50, AND (C) 0.75. POINTS A, B, C; K, L, M; AND X, Y, Z

CORRESPOND TO THE EXAMPLE IMAGES AND PROBABILITY HISTOGRAMS IN FIGURES 4-23,

4-24 AND 4-25 RESPECTIVELY ............................................................................................ 154

FIGURE 4-21: INTERFACE LEVEL H AS A FUNCTION OF INPUT OIL FRACTION ΦIN FOR DIFFERENT

SUPERFICIAL MIXTURE VELOCITIES UM ............................................................................. 156


SUPERFICIAL MIXTURE VELOCITIES UM FEATURING INTERFACE LEVEL MODELS PRESENTED

13

BY HALL AND HEWITT (1993) FOR: (A) STRATIFIED LIQUID-LIQUID FLOW, AND (B)

STRATIFIED GAS-LIQUID FLOW ........................................................................................... 157

FIGURE 4-23: FLOW IMAGES WITH SUPERFICIAL MIXTURE VELOCITIES UM OF: (A1) 0.07 M.S-1,

(B1) 0.14 M.S-1, (C1) 0.29 M.S-1, ALL AT AN INPUT OIL FRACTION ΦIN 0.25; (A2), (B2) AND

(C2) SHOW THE PROBABILITY HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY.

DATA CORRESPONDS TO POINTS A, B AND C, AS LABELLED IN FIGURE 4-20(A) ................ 158

FIGURE 4-24: FLOW IMAGES WITH SUPERFICIAL MIXTURE VELOCITIES UM OF: (K1) 0.07 M.S-1,

(L1) 0.14 M.S-1, (M1) 0.29 M.S-1, ALL AT AN INPUT OIL FRACTION ΦIN 0.50; (K2), (L2) AND

(M2) SHOW THE PROBABILITY HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY.

DATA CORRESPONDS TO POINTS K, L AND M, AS LABELLED IN FIGURE 4.23(B) ................ 159

FIGURE 4-25: FLOW IMAGES WITH SUPERFICIAL MIXTURE VELOCITIES UM OF: (X1) 0.07 M.S-1,

(X1) 0.14 M.S-1, (X1) 0.29 M.S-1, ALL AT AN INPUT OIL FRACTION ΦIN 0.75; (X2), (Y2) AND

(Z2) SHOW THE PROBABILITY HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY.

DATA CORRESPONDS TO POINTS X, Y AND Z, AS LABELLED IN FIGURE 4-20(C) ................ 160

FIGURE 4-26: DIMENSIONLESS INTERFACE DEPTH 1 CORRELATED WITH IN-SITU PHASE

FRACTION ΦY,T ................................................................................................................... 161

FIGURE 4-27: MEAN DROPLET DIAMETER ΜD FOR: (A) VARYING INPUT OIL FRACTION ΦIN AND

CONSTANT SUPERFICIAL MIXTURE VELOCITIES UM 0.14 M.S-1, 0.22 M.S-1 AND 0.29 M.S-1,

AND (B) VARYING SUPERFICIAL MIXTURE VELOCITY UM AND A CONSTANT INPUT OIL

FRACTION OF ΦIN 0.5. POINTS A, B AND C CORRESPOND TO THE PROBABILITY

HISTOGRAMS IN FIGURES 4-28 (FOR OIL) AND 4-29 (FOR GLYCEROL-WATER). RED

SYMBOLS REPRESENT GLYCEROL-SOLUTION DROPLETS AND BLUE SYMBOLS FOR OIL

DROPLETS ........................................................................................................................... 162


(B1) 0.22 M.S-1, (C1) 0.29 M.S-1, ALL AT AN INPUT OIL FRACTION ΦIN 0. 5; (A2), (B2) AND

(C2) SHOW THE OIL DROPLET SIZE DISTRIBUTION PROBABILITY HISTOGRAMS FOR THE SAME

14

CONDITIONS RESPECTIVELY. DATA CORRESPONDS TO POINTS A, B AND C, AS LABELLED IN

FIGURE 4-27(B) .................................................................................................................. 164


(B1) 0.22 M.S-1, (C1) 0.29 M.S-1, ALL AT AN INPUT OIL FRACTION ΦIN 0. 5; (A2), (B2) AND

(C2) SHOW THE GLYCEROL SOLUTION DROPLET SIZE DISTRIBUTION PROBABILITY

HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY. DATA CORRESPONDS TO POINTS

A, B AND C, AS LABELLED IN FIGURE 4-27(B) .................................................................... 165

FIGURE 4-30: OIL PHASE FRACTION AS A FUNCTION OF INPUT OIL PHASE FRACTION ΦIN FOR

DIFFERENT SUPERFICIAL MIXTURE VELOCITY UM: (A) ABOVE THE INTERFACE LEVEL, AND

(B) BELOW THE INTERFACE LEVEL ..................................................................................... 167

FIGURE 4-31: OIL PHASE FRACTION AS A FUNCTION OF SUPERFICIAL MIXTURE VELOCITY UM

FOR DIFFERENT INPUT OIL PHASE FRACTION ΦIN: (A) ABOVE THE INTERFACE LEVEL, AND

(B) BELOW THE INTERFACE LEVEL ..................................................................................... 167


SUPERFICIAL MIXTURE VELOCITIES UM: (A) 0.07 M.S-1; (B) 0.14 M.S-1; (C) 0.21 M.S-1, AND;

(D) 0.29 M.S-1 ...................................................................................................................... 169

FIGURE 5-1: IMAGES OF THE 8 DISTINCT FLOW REGIMES OBSERVED IN THE CIRCULAR CROSS

SECTION EXPERIMENTAL CAMPAIGN .................................................................................. 177

FIGURE 5-2: FLOW REGIME MAP ............................................................................................... 178


MIXTURE VELOCITIES UM AT AN INPUT OIL FRACTION ΦIN OF: (A) 0.25; (B) 0.50, AND; (C)

0.75 .................................................................................................................................... 181


FRACTIONS ΦIN FOR A SUPERFICIAL MIXTURE VELOCITY UM OF: (A) 0.11 M.S-1; (B) 0.17 M.S-

1; (C) 0.22 M.S-1; (D) 0.28 M.S-1; (E) 0.34 M.S-1, AND; (F) 0.42 M.S-1 ..................................... 182

15

FIGURE 5-5: INSTANTANEOUS FLOW IMAGES FOR AN OIL INPUT PHASE FRACTION ΦIN 0.12

AND SUPERFICIAL MIXTURE VELOCITY UM 0.22 M.S-1 AT: (A) 0 S; (B) 1 S, AND;

2 S ............................................................................................................................... 183






FIGURE 5-8: STRATIFIED LIQUID-LIQUID FLOW MODEL CONSTRUCTION ................................. 187




FIGURE 5-10: COMPARISON OF THE CORRELATIONS FOR IN-SITU OIL PHASE FRACTION ΦY,T AS

A FUNCTION OF INPUT OIL FRACTION ΦIN FOR THE SQUARE CROSS-SECTION VISUALISATION

CELL PLIF RESULTS (EQUATION 4.16) SHOWN IN BLUE AND THE CIRCULAR CROSS-SECTION

VISUALISATION CELL PLIF RESULTS (EQUATION 5.8) SHOWN IN RED ............................... 190

FIGURE 5-11: SLIP RATIO S AS A FUNCTION OF INPUT OIL FRACTION ΦIN FOR DIFFERENT

SUPERFICIAL MIXTURE VELOCITIES UM PLIF DATA IS PRESENTED IN BLUE AND THE

RESULTS FROM LOVICK AND ANGELI (2004) ARE PRESENTED IN RED) ............................. 191


DIFFERENT SUPERFICIAL MIXTURE VELOCITIES UM COMPARED WITH DATA FROM LOVICK

AND ANGELI (2004) AND RUSSELL ET AL. (1959) .............................................................. 193

FIGURE 5-13: IN-SITU PHASE FRACTION ENVELOPE ................................................................. 194

FIGURE 5-14: THE MEAN (Μ) AND UPPER (Μ + 2Σ) AND LOWER (Μ A2Σ) LIMITS FOR THE


16

MIXTURE VELOCITIES UM OF: (A) 0.11 M.S-1; (B) 0.17 M.S-1; (C) 0.22 M.S-1, AND (D) 0.28 M.S-

1 .......................................................................................................................................... 195

FIGURE 5-15: THE MEAN (Μ) AND UPPER (Μ + 2Σ) AND LOWER (Μ A2Σ) LIMITS FOR THE



CORRESPOND TO THE EXAMPLE IMAGES AND PROBABILITY HISTOGRAMS IN FIGURES 5-16,

5-17 AND 5-18 RESPECTIVELY ............................................................................................ 196

FIGURE 5-16: FLOW IMAGES WITH INPUT OIL FRACTION ΦIN OF (A1) 0.25, (B1) 0.50, (C1) 0.75,

ALL AT A SUPERFICIAL MIXTURE VELOCITIES UM = 0.11 M.S-1; (A2), (B2) AND (C2) SHOW THE

PROBABILITY HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY. DATA

CORRESPONDS TO POINTS A, B AND C, AS LABELLED IN FIGURE 5-14(A) .......................... 198

FIGURE 5-17: FLOW IMAGES WITH INPUT OIL FRACTION ΦIN OF (X1) 0.25 M.S-1, (Y1) 0.50, (Z1)

0.75, ALL AT A SUPERFICIAL MIXTURE VELOCITIES UM = 0.28 M.S-1; (X2), (Y2) AND (Z2)

SHOW THE PROBABILITY HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY. DATA

CORRESPONDS TO POINTS A, B AND C, AS LABELLED IN FIGURE 5-14(D) .......................... 199








DATA CORRESPONDS TO POINTS K, L AND M, AS LABELLED IN FIGURE 5-14(B) ............... 201



17







BY HALL AND HEWITT (1993) FOR: (A) STRATIFIED LIQUID-LIQUID FLOW, AND (B)

STRATIFIED GAS-LIQUID FLOW ........................................................................................... 204

FIGURE 5-23: MEAN GLYCEROL SOLUTION DROPLET DIAMETER ΜD,GS FOR: (A) VARYING INPUT

OIL FRACTION ΦIN AND CONSTANT SUPERFICIAL MIXTURE VELOCITIES UM 0.22 M.S-1,

AND; (B) VARYING SUPERFICIAL MIXTURE VELOCITY UM AND A CONSTANT INPUT OIL

FRACTION OF ΦIN 0.25. POINTS A, B AND C CORRESPOND TO THE INSTANTANEOUS

IMAGES A1 → C1 AND PROBABILITY HISTOGRAMS A2 → C2 IN FIGURE 5-24. POINTS X, Y

AND Z CORRESPOND TO THE INSTANTANEOUS IMAGES X1 → Z1 AND PROBABILITY

HISTOGRAMS X2 → Z2 IN FIGURE 5-25 ................................................................................ 206

FIGURE 5-24: FLOW IMAGES WITH A SUPERFICIAL MIXTURE VELOCITY UM = 0.22 M.S-1 AT OIL

INPUT FRACTIONS ΦIN OF: (A1) 0.25, (B1) 0.50 AND, (C1) 0.87; (A2), (B2) AND (C2) SHOW THE

GLYCEROL SOLUTION DROPLET SIZE DISTRIBUTION PROBABILITY HISTOGRAMS FOR THE

SAME CONDITIONS RESPECTIVELY. DATA CORRESPONDS TO POINTS A, B AND C, AS

LABELLED IN FIGURE 5-23(A) ............................................................................................ 208

FIGURE 5-25: FLOW IMAGES WITH AN OIL INPUT FRACTION FRACTIONS ΦIN = 0.25 AT

SUPERFICIAL MIXTURE VELOCITIES UM OF (X1) 0.22, (Y1) 0.28 AND, (Z1) 0.42; (X2), (Y2) AND

(Z2) SHOW THE GLYCEROL SOLUTION DROPLET SIZE DISTRIBUTION PROBABILITY

HISTOGRAMS FOR THE SAME CONDITIONS RESPECTIVELY. DATA CORRESPONDS TO POINTS

X, Y AND Z, AS LABELLED IN FIGURE 5-23(B) .................................................................... 209

18

FIGURE 5-26: NORMALISED VELOCITY PROFILES M FOR DIFFERENT SUPERFICIAL MIXTURE

VELOCITIES UM AT AN INPUT OIL FRACTION ΦIN OF: (A) 0.25; (B) 0.50, AND; (C) 0.75 ..... 212

FIGURE 5-27: VELOCITY PROFILES FOR: (A) LAMINAR FLOW, AND; (B) TURBULENT FLOW,

TAKEN FROM SELLENS (2008) ............................................................................................ 213

FIGURE 5-28: VELOCITY PROFILES (A1 → A2) AND INSTANTANEOUS IMAGES (B1 → B2) FOR: (1) UM

= 0.17 M.S-1 AND ΦIN = 0.17, AND; (2) UM = 0.28 M.S-1 AND ΦIN = 0.38 ............................ 214

FIGURE 5-29: VELOCITY PROFILE (A) AND INSTANTANEOUS FLOW IMAGE (B) FOR STRATIFIED

FLOW WITH DROPLETS AT UM = 0.42 M.S-1 AND ΦIN = 0.50 .............................................. 216

FIGURE 5-30: VELOCITY PROFILE (A) AND INSTANTANEOUS FLOW IMAGE (B) FOR THREE-LAYER

FLOW WITH DROPLETS AT UM = 0.84 M.S-1 AND ΦIN = 0.50 .............................................. 217

FIGURE 5-31: VELOCITY PROFILES (A1 → A2) AND INSTANTANEOUS IMAGES (B1 → B2) FOR: (1)

UM = 0.67 M.S-1 AND ΦIN = 0.75, AND; (2) UM = 0.56 M.S-1

AND ΦIN = 0.75 ..................... 218

FIGURE 5-32: VELOCITY PROFILES (A1 → A2) AND INSTANTANEOUS IMAGES (B1 → B2) FOR

DISPERSED FLOWS, AT: (1) UM = 0.84 M.S-1 AND ΦIN = 0.25, AND; (2) UM = 0.83 M.S-1 AND

ΦIN = 0.90 .......................................................................................................................... 219

FIGURE 5-33: INTERFACE LEVEL AS A FUNCTION NORMALISED INTERFACE LEVEL VELOCITY

( M)............................................................................................................................... 220

FIGURE 6-1: (A) DEFINITIONS FROM DIMONTE AND SCHNEIDER (2000), AND; (B) SIMULATIONS

FROM GLIMM ET AL., (2000) .............................................................................................. 227

FIGURE 6-2: INLET ORIENTATION FOR (A) THE “NORMAL” CONFIGURATION AS USED IN

CHAPTER 5, AND; (B) THE “INVERTED” INLET CONFIGURATION AS USED IN THE CURRENT

(CHAPTER 6) PLIF STUDY. ................................................................................................. 231

FIGURE 6-3: IMAGES OF THE 8 DISTINCT FLOW REGIMES OBSERVED IN THE CIRCULAR CROSS

EXPERIMENTAL CAMPAIGN WITH AN “INVERTED” INLET CONFIGURATION ....................... 233

FIGURE 6-4: FLOW REGIME MAP ............................................................................................... 234

19


MIXTURE VELOCITIES UM AT AN INPUT OIL FRACTION ΦIN OF: (A) 0.25, (B) 0.50, AND (C)

0.75 .................................................................................................................................... 236


FRACTIONS ΦIN FOR A SUPERFICIAL MIXTURE VELOCITY UM OF: (A) 0.11 M.S-1, (B) 0.17 M.S-

1, (C) 0.22 M.S-1, (D) 0.28 M.S-1, (C) 0.33 M.S-1, (D) 0.42 M.S-1 ............................................. 237

FIGURE 6-7: INSTANTANEOUS FLOW IMAGES FOR: (1) M 0.17 M.S-1 FOR IN 0.17; (2);

M 0.22 M.S-1 FOR IN 0.12; (3) M 0.28 M.S-1 FOR IN 0.25, AND; (4) M 0.33

M.S-1 FOR IN 0.25; “A” REFERS TO THE “NORMAL” INLET CONFIGURATION AND “B” TO

THE “INVERTED” INLET CONFIGURATION. .......................................................................... 239

FIGURE 6-8: INSTANTANEOUS FLOW IMAGES FOR A SUPERFICIAL MIXTURE VELOCITY M

0.28 M.S-1 AND AN OIL INPUT PHASE FRACTION IN 0.1 FOR: (A) THE “NORMAL” INLET

CONFIGURATION, AND; (B) THE “INVERTED” INLET CONFIGURATION ............................... 240









FIGURE 6-12: (A) SLIP RATIO S AS A FUNCTION OF INPUT OIL FRACTION ΦIN FOR ALL THREE

PLIF EXPERIMENTAL CAMPAIGNS, AND; (B) SLIP RATIO S AS A FUNCTION OF INPUT OIL

FRACTION ΦIN FOR DIFFERENT SUPERFICIAL MIXTURE VELOCITIES UM, WHERE “A”

DENOTES THE “NORMAL” INLET CONFIGURATION AND “B” THE “INVERTED” INLET

CONFIGURATION ................................................................................................................. 247

20

FIGURE 6-13: (A) IN-SITU PHASE FRACTION EXPERIMENTAL RESULTS, AND; (B) IN-SITU PHASE

FRACTION CORRELATIONS FOR THE SQUARE CROSS-SECTION VISUALISATION SECTION

(BLACK) AND THE CIRCULAR CROSS SECTION VISUALISATION SECTION WITH THE

“NORMAL” INLET CONFIGURATION (RED) AND “INVERTED” INLET CONFIGURATION (BLUE)

........................................................................................................................................... 248



MIXTURE VELOCITIES UM OF: (A) 0.11 M.S-1, (B) 0.17 M.S-1, (C) 0.22 M.S-1, AND (D) 0.28 M.S-1

........................................................................................................................................... 249




CORRESPOND TO THE EXAMPLE IMAGES AND PROBABILITY HISTOGRAMS IN FIGURES 4.12,

4.13 AND 4.14 RESPECTIVELY. ........................................................................................... 250

FIGURE 6-16: FLOW IMAGES WITH INPUT OIL FRACTION ΦIN OF (A1) 0.25, (B1) 0.50, (C1) 0.75,

ALL AT A SUPERFICIAL MIXTURE VELOCITIES UM = 0.11 M.S-1; (A2), (B2) AND (C2) SHOW THE


CORRESPONDS TO POINTS A, B AND C, AS LABELLED IN FIGURE 6-14(A) .......................... 251

FIGURE 6-17: FLOW IMAGES WITH INPUT OIL FRACTION ΦIN OF (X1) 0.25, (Y1) 0.50, (Z1) 0.75,

ALL AT A SUPERFICIAL MIXTURE VELOCITIES UM = 0.17 M.S-1; (X2), (Y2) AND (Z2) SHOW THE


CORRESPONDS TO POINTS X, Y AND Z, AS LABELLED IN FIGURE 6-14(C) .......................... 252





21




DATA CORRESPONDS TO POINTS K, L AND M, AS LABELLED IN FIGURE 6-15(B) ............... 254









BY HALL AND HEWITT (1993) FOR: (A) STRATIFIED GAS-LIQUID FLOW, AND; (B) STRATIFIED

LIQUID-LIQUID FLOW .......................................................................................................... 257

FIGURE 6-23: MEAN DROPLET DIAMETER ΜD AS A FUNCTION OF INPUT OIL PHASE FRACTION

ΦIN AND A CONSTANT SUPERFICIAL MIXTURE VELOCITY OF UM 0.28 M.S-1, FOR

GLYCEROL SOLUTION DROPLETS (BLUE CIRCLES) AND OIL DROPLETS (RED SQUARES) .... 259

FIGURE 6-24: NORMALISED VELOCITY PROFILES M FOR DIFFERENT SUPERFICIAL MIXTURE

VELOCITIES UM AT AN INPUT OIL FRACTION ΦIN OF: (A) 0.25; (B) 0.50, AND; (C) 0.75 ..... 260

FIGURE 6-25: VELOCITY PROFILES (A) AND INSTANTANEOUS IMAGES (B) FOR A SUPERFICIAL

MIXTURE VELOCITY OF UM = 0.11 M.S-1 AND AN INPUT OIL PHASE FRACTION ΦIN = 0.50 262

FIGURE 6-26: VELOCITY PROFILES (A) AND INSTANTANEOUS IMAGES (B) FOR A SUPERFICIAL

MIXTURE VELOCITY OF UM = 0.84 M.S-1 AND AN INPUT OIL PHASE FRACTION ΦIN = 0.50 263

FIGURE 6-27: VELOCITY PROFILES (A1 → A2) AND INSTANTANEOUS IMAGES (B1 → B2) FOR: (1)

UM = 0.84 M.S-1 AND ΦIN = 0.10, AND; (2) UM = 0. 83 M.S-1 AND ΦIN = 0.90 .................... 264

22

FIGURE 6-28: THE GEOMETRY AND COORDINATES OF THE FLOW SYSTEMS, SHOWING: (A)

AXIAL, AND; (B) SIDE VIEWS, NG (2002) ............................................................................ 266

FIGURE 6-29: CONTACT ANGLE MEASUREMENT TECHNIQUE ................................................... 266

FIGURE 6-30: INTERFACE SHAPES FOR A BOND NUMBER BO 250 AND CONTACT ANGLES: (A)

0.1 ; (B) 0.3 ; (C) 0.5 , AND; (D) 0.7 , ALL FOR 0.1, 0.2, … , 0.9

COMPUTATIONAL RESULTS BY NG (2002) .......................................................................... 268

FIGURE 6-31: INTERFACE LEVEL AS A FUNCTION NORMALISED INTERFACE LEVEL VELOCITY

( H M). ............................................................................................................................. 269

FIGURE 6-32: VARIATION OF THE DIMENSIONLESS FLOW RATE WITH HOLD-UP AND BOND

NUMBER, BO 0.1, 1, 10, 25, 50 AND 100 WITH A CONTACT ANGLE 3, TAKEN FROM

NG (2002) ........................................................................................................................... 270

FIGURE 6-33: VARIATION OF THE DIMENSIONLESS INTERFACIAL VELOCITY PROFILE FOR HOLD-

UP VALUES 0.25, 0.5 AND 0.75 (BO 50 AND 3), TAKEN FROM NG (2002) ...... 270

FIGURE 6-34: VELOCITY PROFILE ACROSS THE PIPE CROSS SECTION FOR A HOLD-UP OF 0.3,

CONTACT ANGLE OF 3 AND A BOND NUMBER OF BO 10 FOR: (A) M 1.6, AND; (B)

M 45 WHERE M A B WHERE A IS THE LESS DENSE PHASE, NG (2002) ..................... 271

23

List of Tables

TABLE 2-1: CORRESPONDING FLOW CLASSIFICATIONS FOR RUSSELL ET AL. (1959) AND

CHARLES ET AL. (1961) ........................................................................................................ 33

TABLE 3-1: PHYSICAL PROPERTIES OF THE SELECTED TEST FLUIDS AT 20°C .......................... 101

TABLE 4-1: CATEGORISATION OF OBSERVED FLOW REGIMES .................................................. 127

TABLE 5-1: INTERFACE WAVE VELOCITY INT RESULTS ........................................................ 210

TABLE 6-1: REYNOLDS NUMBERS FOR THE CURRENT EXPERIMENTAL MATRIX ....................... 228

TABLE 6-2: FLOW INSTABILITY SCENARIOS ............................................................................. 230

CH

Int

1.1

The r

co-cu

encou

chem

reacto

2006)

micro

most

subse

wellh

result

Thou

Introd

subje

flows

oils (

HAPT

troduc

Backgro

research activ

urrent flows

untered in a

mical process

ors for conti

), as well a

oreactors are

notable and

ea pipelines

head contain

t from water

ugh a more de

duction, to p

ect area. Inv

s with the ai

(Russell and

TER 1

ction

ound

vities presen

of two imm

host of diffe

sing (CFCP)

inuous produ

as in the fi

e used to imp

d pertinent to

from petrole

water whic

injection int

etailed review

place the pr

vestigation in

im of impro

Charles, 19

nted in this th

miscible liqui

erent setting

) on microc

uction in th

fine chemica

prove heat an

o the current

eum producti

h can either

to the reservo

w of relevan

resent work

nto liquid-liq

ving the pum

959). This is

hesis focused

ds. The co-

s and indust

chips (Toske

e pharmaceu

als industry

nd mass tran

investigatio

ion facilities

r occur natur

oir to increas

nt literature is

in the conte

quid flows b

mping requi

s still a pert

d on the detai

-current flow

trial processe

eshi et al.,

utical indust

where liqu

nsfer (Kashid

on is the tran

, where the

rally in the r

se pressure a

s given in Ch

ext of the hi

began with t

rements whe

inent issue b

Cha

iled investiga

w of two imm

es, such as in

2000), micr

try (Wegman

uid-liquid slu

d and Agar,

nsportation o

production f

reservoir (“c

and in turn oi

hapter 2, it is

istory of dev

the injection

en transporti

but the scop

apter 1: Introd

ation of horiz

miscible liqu

n continuous

rochannel tu

nn and von

ug flow cap

2007). How

of hydrocarbo

flowlines fro

connate wate

il recovery.

s important, i

velopment o

n of water in

ing viscous

e of the wor

duction

zontal

uids is

s-flow

ubular

Rohr,

pillary

wever,

ons in

om the

er”) or

in this

of this

nto oil

heavy

rk has

24

Chapter 1: Introduction

25

significantly developed in the intervening 50 years. Multiphase pumping for subsea boosting

from oil wells enables the cost-efficient development of marginal and previously inaccessible

fields. Enhanced oil recovery from ultra-deep wells, such as those in the oil fields of the Santos

Basin, Brazil and the Gulf of Mexico, has benefited from the development of multiphase

pumping, as has the recovery from more remote oil reservoirs (Bell et al., 2005). However, in

these applications, it is often necessary to pass the multiphase mixtures along long distance

subsea flowlines to a central processing facility. The design of the subsea infrastructure, such as

flowline sizing, hinges on being able to predict the hydrodynamic behaviour of the flows they

contain. An improved understanding of the rheological behaviour and flow dynamics of such

multiphase flows can lead to significant advancements in empirical and phenomenological

models capable of the accurate prediction of these flows, and in turn to better designs and

operation of related industrial facilities. Obtaining a comprehensive mechanistic understanding

and being able to develop such models hinges crucially on being able to visualise the flows and

to provide detailed and high-quality experimental data. Since Russell et al. (1959) embarked on

investigating oil-water flows, considerable effort has been focused on the characterisation of

liquid-liquid flows (Charles et al., 1961; Hasson et al., 1970; Guzhov et al., 1973; Arirachakaran

et al., 1989; Hussain, 2004; Liu, 2005). However, in contrast to the case of gas-liquid flows

(see for instance Taitel and Dukler, 1976), only limited work has been done on developing

predictive tools for the transition between liquid-liquid flow regimes. Modelling endeavours for

liquid-liquid flows have focused on the transition from oil-continuous flows to water-continuous

flows (“phase inversion”) (Arirachakaran et al., 1989; Chen, 2001; Yeo et al., 2002) and

pressure gradient prediction (Malinowsky, 1975).

Most horizontal liquid-liquid flow visualisation studies have employed high-speed photography

(Soleimani 1999) or high-speed photography coupled with an endoscopic technique (Angeli and

Hewitt, 2000a,b). However, one of the most powerful tools for the study of fluid flow and

mixing is laser-induced fluorescence (LIF). Liu (2005) used LIF to visualise co-current vertical

down

the tw

here,

liquid

1.2

The t

visua

flows

applic

of the

situ p

veloc

1.3

This

induc

detail

flows

exper

meas

existi

nwards liquid

wo phases.

namely the

d-liquid flow

Objectiv

two main ob

alisation tech

s, and; (2) to

cation of the

e behaviour o

phase fractio

city, and; (vii

Researc

thesis prese

ced fluoresce

led spatiotem

s. The prim

rimental fac

urements, an

ing correlatio

d-liquid flow

The studies

application o

ws.

ves

bjectives for

hnique to yi

o enhance u

e developed t

of: (i) liquid-

on; (iv) the in

i) velocity pr

h Overvie

ents what is

ence (PLIF)

mporally reso

mary undertak

ility; (2) de

nd; (3) the P

on algorithm

ws and produc

s by Liu (20

of LIF and r

the work co

eld high spa

understanding

technique. S

-liquid flow

nterface leve

rofiles.

ew

believed to

and particle

olved measu

kings of thi

eveloping th

PLIF and PT

ms were empl

ced images w

005) provided

related techn

ontained in t

atial and tem

g of the flow

Specifically,

regimes; (ii)

el; (v) the dr

o be the firs

e tracking an

urement and c

s work were

he optical sy

TV/PIV imag

oyed).

with a strong

d encourage

niques to the

this thesis w

mporal resol

ws of two im

the work aim

) the vertical

oplet size di

st application

nd image ve

characterisat

e focused on

ystem for th

ge processing

Cha

g and clear d

ement to the

study of co-

were: (1) the

lution image

mmiscible li

med to deve

phase distrib

istribution; (v

n of high-sp

elocimetry (P

tion of horiz

n: (1) the de

he laser-indu

g methodolo

apter 1: Introd

istinction be

project desc

-current horiz

developmen

es of liquid-

quids throug

elop understa

bution; (iii) t

vi) interface

peed planar

PTV/PIV) fo

ontal liquid-

evelopment o

uced fluores

ogy (for the

duction

tween

cribed

zontal

nt of a

-liquid

gh the

anding

the in-

wave

laser-

for the

-liquid

of the

scence

latter,

26

The l

was n

and c

here

with

areas

of sui

the ex

peak;

(inclu

visua

PLIF

devel

the P

techn

In to

indep

techn

1.4

In wh

resea

litera

pheno

liquid-liquid

necessary to

control and m

was the intr

time. Deve

: (1) test flui

itable physic

xcitation spe

; (2) the opt

uding the ne

alisation sect

and PTV/PI

loped can be

PLIF images

nique that com

tal three exp

pendent expe

nique.

Thesis S

hat follows

arch that has

ature pertaini

omena, and;

flow experim

carry out ex

measurement

roduction of

elopment of

id selection,

cal properties

ectrum of wh

tical system,

ecessary filte

ions and a g

IV images. F

e divided into

s, from whic

mbines both

perimental c

erimental run

Structure

in this thes

been condu

ing to: (1) f

; (3) the em

mental rig u

xtensive refu

t of the indep

f electronic m

f the laser-in

based upon

s with one te

hich is over t

i.e., the las

ers) and thei

graticule (prin

Finally and a

o two main c

ch, several

PIV and PT

campaigns w

ns using the

is, Chapter

ucted by prev

flow phenom

mulsion visco

used was bas

urbishment o

pendent varia

measuremen

nduced fluor

establishing

est fluid seed

the same wav

er (and asso

ir synchroni

nted grid) te

although mul

categories: (1

forms of an

V to calculat

were underta

e high spatio

2, provides

vious investi

menology an

osity of liqui

ed on an exi

of the facility

ables of the r

nt systems w

rescence tech

g a pair of ref

ded with a flu

velength ban

ociated optic

isation, and;

chnique to c

ltifaceted, th

1) a computa

nalysis have

te the velocit

aken, which

otemporal re

an overview

igators. Spe

nd regime m

id – liquid

Cha

isting facility

y in order to

rig. An impo

whose output

hnique was

fractive inde

uorescent dy

nd as the lase

s) and the h

; (3) the des

correct for th

e image proc

ational code w

e been perfo

ty profile of

collectively

esolution opt

w of the liq

ecifically, att

maps; (2) the

systems. C

apter 1: Introd

y (TOWER)

o acquire acc

rtant develop

t could be lo

focused on

ex matched li

yestuff, the pe

er output spe

high speed ca

sign of the o

he distortion

cessing techn

written to bi

ormed, and:

the flow.

comprise o

tical measure

quid – liquid

tention is giv

e phase inve

hapter 3 pro

duction

but it

curate

pment

ogged

three

iquids

eak in

ectrum

amera

optical

to the

niques

narise

(2) a

of 144

ement

d flow

ven to

ersion

ovides

27


28

details of the experimental facility and methods that have been used, to firstly, acquire images

of flows containing two immiscible liquids using the LIF technique, and secondly, to process

these images to generate quantitative results. Chapter 3 begins by providing details of the Two-

Phase Oil–Water Experimental Rig (TOWER); TOWER is a multiphase flow facility at

Imperial College London, designed for the investigation of liquid-liquid flows. Considerable

improvement and development of this facility was necessary to carry out the work described

here. Chapter 3 continues by presenting information pertaining to the pulsed laser system, the,

high-speed camera system and the methods used to synchronise these two systems.

Synchronisation of the laser produced pulses with camera exposures allowed capturing of

successive laser-induced fluorescence images. Chapter 3 also provides details on the test fluids,

including their physical properties and the basis for their selection, i.e., refractive index

matching. Information is also provided on the design of the two visualisation cells (one with a

square cross-section, the other with a circular cross-section) that that have been used in the PLIF

experimental campaigns. It is necessary to correct the distortion to the PLIF and PTV/PIV

images which occurs when the circular cross-section visualisation cell is used and details of the

graticule correction methodology are presented (together with the image binarisation technique

and the methods used to generate results) are also provided in Chapter 3.

The results of the experimental campaigns are presented in Chapters 4, 5 and 6. Chapter 4

presents LIF results acquired using a square cross-section visualisation cell placed in a square

cross section horizontal duct; the use of this duct geometry avoided the image distortion which

occurs with circular channel geometry. Though the results obtained using the square section

duct were very interesting, it is clear that a duct of circular cross-section would be more

representative of industrial pipe systems. In order to obtain results with circular cross section

ducts, a method employing photography of a graticule within the duct was developed. Knowing

the positions of locations on the graticule, it was possible to correct the images obtained for the

circular tube cross section. In the studies on circular tubes, the experiments were extended to


29

include velocity measurements using PTV/PIV (Particle Tracking Velocimetry / Particle Image

Velocimetry). Chapters 5 presents the results of the PLIF and PTV/PIV study performed when

using the circular cross-section visualisation cell; in this study, the (heavier) aqueous phase was

injected below the lighter (oil) phase at the test section entrance (i.e. in its natural location).

Chapter 6 presents the results of a second PLIF and PTV/PIV study performed using the circular

cross-section visualisation section. In this second study, the fluids were introduced to the test

section such that the denser fluid is above the lighter fluid at the inlet. This was done to

investigate the influence that entrance effects have on liquid-liquid flows.

Each of the studies presented in Chapters 4, 5 and 6 consist of two parts. Firstly, the observed

flows are described qualitatively and classified into flow regimes and a flow regime map is

presented. Secondly, the quantitative measurements are presented; for all the studies, these

measurements included phase distribution, in-situ phase fraction, interface level and droplet size

distribution. For the circular tube experiments (Chapters 5 and 6) interface wave velocity and

velocity profile measurements were also made and are reported.

Finally, the conclusions of the investigations and recommendations for future work are

summarised in Chapter 7.

CH

Lit

2.1

This

flows

confi

impo

phase

Sectio

pheno

pertai

is the

mode

2.2

One

(1959

horiz

super

HAPT

teratu

Introduc

Chapter rev

s in horizon

guration of t

rtant transiti

e changes fr

on 2.3. Tho

omenon has

ining to pipe

e emulsion

els is present

Flow R

of the first

9) who inves

ontal pipe o

rficial water

TER 2

ure Rev

ction

views the res

ntal pipeline

the flowing

ion in disper

rom one flui

ough a con

been focuse

e flows. A k

viscosity; an

ted in Section

Regimes a

studies into

stigated flow

of 25.4 mm i

velocity (

view

search and s

es. Section

fluids) in liq

sed liquid-liq

id to the oth

nsiderable pr

d on agitated

key paramete

n overview

n 2.4.

nd Maps

o two-phase

w patterns of

internal diam

) and the r

significant d

2.2 review

quid-liquid fl

quid flows i

her and the l

roportion of

d vessels, the

er needed for

of liquid-liq

liquid-liquid

f oil-water f

meter. Russe

ratio of inlet

evelopments

ws the flow

lows and the

s phase inve

literature in

f the resear

e work prese

r the closure

quid emulsi

d flows was

flows in a sm

ell et al. (195

t oil and wa

Chapter 2

s in the stud

regimes (i.

e associated

ersion in whi

this transiti

rch into the

ented herein

of phase inv

on viscosity

s conducted

mooth transp

59) investiga

ater velocitie

2: Literature R

dy of liquid-

e., the geom

regime maps

ich the conti

on is review

e phase inve

is exclusivel

version predi

y correlation

by Russell

parent 8.0 m

ated the effe

s ( / ) o

Review

-liquid

metric

s. An

nuous

wed in

ersion

ly that

ctions

ns and

et al.

m long

ects of

on the

30

Chapter 2: Literature Review

31

flow pattern and the nature of the liquid-liquid interface (see Figure 2-1). Thirteen different

values (ranging from 0.116 ft/sec to 3.55 ft/sec) were used with oil-water inlet velocity ratios

(U /U ) ranging from 0.1 to 10. The oil used in the research had a viscosity of 18 mPa. s and

a density of 834 kg.m‐ . Russell et al. (1959) observed three main flow patterns which are

categorised as:

1. Stratified flow – oil and water travel along the pipe in two separate layers.

2. Mixed flow – oil and water phases are completely mixed; this occurred at high flow rates.

3. Bubble flow – oil drops (called “bubbles” in this investigation) travel along the top of the

pipe.

The flow was found to be stratified (1 from the above list) for low flowrates. For stratified

flow, the experimental results of Russell et al. (1959) conform to the findings of a theoretical

analysis which shows that for laminar flow the hold-up (i.e., interface level) was independent of

the superficial water velocity and is only a function of viscosity and the phase input ratio. Phase

break-up and droplet formation were observed at higher flowrates i.e., this regime was termed

mixed flow (pattern 2 from the above list). The third flow regime, “bubble flow” occurred at the

lowest oil-water velocity ratios investigated, typically / 1.4 to 1.5. In summary, the

Russell et al. (1959) observations reveal that increasing the mixture flowrate leads to an increase

in the turbulence in the flow resulting in fingering and ligament formation that in turn results in

droplet formation and ultimately a droplet layer i.e., mixed flow.

Charles et al. (1961) investigated flow patterns in horizontal two-phase oil-water flows in a

8.78 m long pipe with a 25.4 mm internal diameter using oil phases of three different

viscosities, namely: oil 6.29, 16.8 and 65.0mPa. s. The densities of the oil phases were

adjusted to values close to that of the water ( oil 988 kg.m ) by the addition of carbon


32

tetrachloride (Liu, 2004). Experimental runs were performed for a decreasing oil phase flowrate

at a constant water flowrate for each of the three oil phases. The range of oil phase-water

velocity ratio and the ranges of superficial velocity for each of the test liquids were similar to

those studies by Russell et al. (1959). Charles et al. (1961) observed the following flow patterns

as the input oil phase-water ratio was decreased;

1. concentric oil-in-water

2. oil-slugs-in-water

3. oil-bubbles-in-water

4. oil-drops-in-water

Here, a distinction was made between “drops” and “bubbles” of the oil phase in that the

“bubbles” were much larger that the “drops”. The results obtained by Charles et al. (1961) are

shown in Figure 2-2 and are somewhat similar to the observations by Russell et al. (1959),

though Charles et al. (1961) did not observe stratified flow. Though (in terms of superficial

mixture velocity and flowrate ratios) Charles et al. (1961) did operate in the regime in which

Russell et al. (1959) observed stratified flow, it has to be recalled that the phase densities were

made nearly equal in the Charles et al. (1961) study. The degree of stratification of two

immiscible liquids when flowing in a pipeline will depend on the density ratio (R) between the

oil and water phases. In the Charles et al. (1961) study, 0.99 and stratified flows were not

observed. On the other hand, Russell et al. (1959) used phases for which 0.83 and the

density difference was sufficient to promote stratified flow. The corresponding flow pattern

terminologies adopted by Russell et al. (1959) and Charles et al. (1961) are tabulated in Table 2-

1.


33

Charles et al. (1961) concluded the oil-water flow pattern is “largely independent” of the oil

viscosity. The flow patterns observed for the different viscosity oils are the same apart for the

most viscous oil (65.0 mPa. s), which at high oil-water input ratios yielded different results, as

seen by comparing Figures 2-2(a) and 2-2(b) with Figure 2-2(c). Charles et al. (1961) attributed

the difference in behaviour to surface forces which may become significant enough for the

higher viscosity fluids to affect the flow pattern. It was also postulated by Charles et al. (1961)

that the more viscous oil wetted the pipe wall more than the other oils. From the findings

presented pictorially in Figure 2.2, Charles et al (1961) constructed two flow regime maps, one

for the lower viscosity oils ( 6.29 mPa. s and 16.8 mPa. s) and another for the higher

viscosity oil ( 65.0 mPa. s ). From this, Charles et al. (1961) identified the conditions

under which an oil-continuous flow pattern inverts to a water-continuous flow pattern. This is

represented by the line PQ in Figure 2-3(b). This phenomenon has subsequently been termed

phase inversion and is discussed in Section 2.3.

Table 2-1: Corresponding flow classifications for Russell et al. (1959) and Charles et al. (1961)

Corresponding flow pattern terminologies

Russell et al (1959) classification Charles et al (1961) classification

Bubble flow Oil-drops-in-water

Oil-bubbles-in-water

Oil-slugs-in-water

Mixed flow Water-drops-in-oil

Stratified flow Not observed

Not observed Concentric oil-in-water

Figur

0.287

re 2-1: Flow

7 ft/sec; (b)

/ ), Ru

(a)

w patterns in

1.79 ft/sec,

ussell et al. (

n oil-water p

and; (c) 3.5

(1959)

(c)

pipe flow fo

5 ft/sec at d

or superficial

different inle

Chapter 2

(b)

l water veloc

et oil-water r

2: Literature R

cities, Um o

ratios, (w

Review

of: (a)

where,

34

Figur

water

ft/sec

re 2-2: Flow

r at water su

c, Charles et

(a)

w patterns ob

uperficial ve

al. (1961)

bserved for t

elocities of U

(c)

the 1

Um of: (a) 0

6.8 mPa. s o

0.10 ft/sec; (

Chapter 2

(b)

oil flowing i

(b) 0.682 ft/

2: Literature R

in the presen

sec, and; (c)

Review

nce of

) 2.04

35

Figur

(1961

An im

visco

in the

secon

the br

water

The t

identi

Charl

re 2-3: Flo

6.29 and 1

1)

mportant reg

ous (water) p

e core of the

nd), Hasson

reak-up mec

r ( 0.8

1.0 mPa. s

two phases h

ified four flo

les et al. (196

(a)

ow regime m

16.8 mPa. s

gime in two-

hase flows a

e pipe. Usin

et al. (1970)

hanisms of c

82 mPa. s) a

s) were studi

had equal den

ow patterns w

61). These ar

maps for tw

(b) 6

-phase liquid

as a film at th

g high speed

) studied cor

core-annular

and an oil

ed in a 2.7 m

nsities of 10

which were

re listed belo

wo-phase oi

5 mPa. s (w

d-liquid flow

he tube wall

d cine photo

re-annular flo

flow and the

phase (a k

m long pipel

20 kg.m .

similar to th

ow and are sh

il-water flow

where,

ws is core-an

with the mo

ography (at 1

ow mechanis

e resultant fl

kerosene-per

line with an

At lower fl

hose observe

hown in Figu

Chapter 2

(b)

ws for oil v

988 kg.m

nnular flow

ore viscous p

1250 to 2300

sms of two im

ow patterns.

rchlorethylen

internal diam

low rates, Ha

d by Russell

ure 2-4.

2: Literature R

viscosities o

), Charles

in which th

phase (oil) flo

0 fps, frame

mmiscible li

Flows of di

ne solution,

meter of 12.6

asson et al. (

l et al. (1959

Review

of (a)

et al.

he less

owing

es-per-

quids,

stilled

with

6 mm.

(1970)

9) and

36


37

1. Dispersions – oil-in-water and water-in-oil dispersions; this corresponds to the flow

regimes termed water-drops-in-oil and oil-drops-in-water

2. Slugs – water slugs in oil and oil slugs in water

3. Stratified layers

4. Annular flow

Hasson et al. (1970) found that the flow patterns that follow annular flow as the velocity is

increased depend on three main factors:

1. The break-up mechanism of the annulus core

2. The liquid flow rates

3. The wetting properties of the pipe wall (as was observed by Charles et al., 1961)

Hasson et al. (1970) experimented with hydrophobic and hydrophilic pipelines and found that

the different wetting properties of the wall can affect the break-up mechanism of the annular

core and the flow pattern that it develops into. It was found that in hydrophobic pipes the flow

pattern tends to be water-continuous and the wall film break-up mechanism did not occur. In

contrast, in a hydrophilic pipeline both water-continuous and oil-continuous flow regimes were

identified after annular flow break-up. Annular core break-up was found to be a high flowrate

phenomenon, caused when the amplitude of interfacial waves reached the centre of the core,

which give rise to slug flow. Conversely, wall film rupture is a low flowrate phenomenon.

Hasson et al. (1970) constructed flow pattern maps of oil flowrate against water flowate for: (1)

hydrophobic; (2) hydrophilic, and; (3) an intermediate pipeline at 200 cm from the pipe inlet.

These flow regime maps can be seen in Figure 2-5 below.

The annular flow break-up mechanisms that Hasson et al. (1970) observed can be categorised

into two groups: (1) wall film rupture, and; (2) annular core break-up due to interfacial waves.


38

(a)

(b)

(c)

(d)

(e)

Figure 2-4: Flow patterns observed for equal density two-phase distilled water

( 0.82 mPa. s) and kerosene-perchloroethylene solution ( 1.0 mPa. s) flows: (a)

dispersions; (b) slugs; (c) stratified layers; (d) annular flow, and; (e) mixed. Hasson et al.

(1970)

Figur

water

Guzh

water

39.4 m

re 2-5: Flow

r system, Ha

hov et al. (19

r system (w

mm internal

w patterns o

sson et al. (1

973) investig

where,

diameter. G

observed for

1970)

gated horizo

21.7 mPa. s

Guzhov et al.

a two-phas

ontal two-pha

s and

(1973) cons

e kerosene-p

ase liquid-liq

896 kg.m

structed a flo

Chapter 2

perchlorethy

quid flow pa

m at 20°C)

ow pattern m

2: Literature R

ylene and di

atterns for o

) in a pipeli

map of their re

Review

stilled

il and

ine of

esults,

39

plotti

Figur

simila

Arira

(1979

oil (

pipeli

Figur

mm I

Ogles

patter

patter

stratif

annul

ing superfici

re 2-6. The f

ar to that u

achakaran et

9) produced

21.7 m

ine.

re 2-6: Flow

ID pipe (Guz

sby et al. (1

rns using oil

rns were ge

fied, dispers

lar flow with

ial mixture v

flow pattern

used by Ar

al. (1989), G

a revised ve

mPa. s,

w pattern map

zhov et al., 19

1979) also i

ls of viscosit

enerally sim

ed and interm

h a water cor

velocity Um

n classificatio

rirachakaran

Guzhov et al

ersion of the

896 kg.m

p for the flow

973)

investigated

ty 58.

milar to tho

mittent flow.

re and oil an

against inp

on terminolo

et al. (198

l. (1973) did

Guzhov et a

m ) and wa

w of oil (whe

the effect o

0, 84.0 and

se observed

. However, i

nnulus. The

put water fra

ogy adopted

89) (see Fig

d not observe

al. (1973) flo

ater flows in

ere 21

of viscosity

115.0 mPa. s

d by previo

in addition, O

observation

Chapter 2

action ,

by Guzhov

gure 2-7).

e annular flo

ow pattern m

a 39.4 mm

1.7 mPa. s) a

on horizont

s at 20°C. T

ous research

Oglesby et a

of this flow

2: Literature R

; this is sho

et al. (1973

However, u

w. Oglesby

map for two-

internal dia

and water in a

tal oil-water

The observed

ers and inc

l. (1979) obs

regime seem

Review

wn in

3) was

unlike

y et al.

-phase

ameter

a 39.4

r flow

d flow

cluded

served

mingly

40

contr

and J

‘In a

visco

If it

visco

integr

Ogles

seen

Figur

with

radicts the m

Joseph et al. (

pipe flow of

sity liquid w

is postulate

osity) and the

rity of the pr

sby et al. (19

in their flow

re 2-7: Flow

oil viscosity

inimum visc

(1984), whic

f two liquids w

would tend to

ed that the w

e oil annulus

rinciple still h

979) identifie

w pattern map

w pattern ma

84.0

cous dissipat

ch has been d

with differen

encapsulate

water core e

flow is lami

holds (Liu, 2

ed a phase in

p (Figure 2-7

ap for two-ph

mPa. s, Ogle

ion principle

described by

nt viscosities

e the high vis

exhibits turb

inar, analysis

2005).

nversion regi

) as a narrow

hase oil-wate

esby et al. (1

e adopted in

Liu (2005) a

under an ap

cosity liquid

bulent flow

s of the appa

on (discusse

w vertical ban

er flow in a

979)

Chapter 2

the work of

as:

pplied pressu

d.”

Liu (

(which has

arent viscosit

d in Section

nd.

41mm intern

2: Literature R

f MacLean (

ure drop, the

(2005, p.38)

a high turb

ties shows th

2.3) which c

nal diameter

Review

(1973)

low-

bulent

hat the

can be

r pipe,

41

Arira

of vi

38.1 m

from

al. (1

expla

sustai

water

over

Oil-a

achakaran et

iscosities

mm internal

Um 0.45 t

970), Arirac

ained by sug

in an oil-cor

r-continuous

which oil-an

annulus annu

al. (1989) st

4.7, 58

diameter. S

to 3.6 m.s-1 a

chakaran et a

ggesting that

re for this flo

. It was con

nnulus annu

lar was not o

Figure 2-8

tudied two-p

.0, 84.0 and

Superficial m

and in,w

al. (1989) di

the oils use

ow regime.

ncluded by A

lar flow is o

observed for

8: Flow patte

phase oil-wa

d 115.0 mP

mixture veloc

0.05 to 0.90

id not observ

ed in the stud

Thus the flo

Arirachakaran

observed dim

the 4.7 mPa

ern map, Arir

ter flow patt

a. s) in hori

cities and inp

, respectively

ve water-ann

dy were not

ow patterns

n et al. (1989

minishes as t

a. s (lowest vi

rachakaran e

Chapter 2

terns (using

izontal pipel

put water fra

y. However

nulus annula

viscous and

observed we

9) that the ra

the oil visco

iscosity) oil.

et al. (1989)

2: Literature R

four differen

lines of 25.4

action were v

r, unlike Has

ar flow. Thi

d heavy enou

ere predomin

ange of cond

osity is decre

Review

nt oils

4 and

varied

son et

is was

ugh to

nantly

ditions

eased.

42


43

Arirachakaran et al. (1989) found that when water is the continuous phase the oil viscosity has

little effect on the flow pattern. This is in agreement with the observations made by Charles et

al. (1961). Arirachakaran et al. (1989) revised the flow pattern map of Guzhov et al. (1973)

using earlier flow pattern classifications and found good agreement with their own map. The

definitions used in Figure 2-8 are as follows: Stratified flow (S); Mixture flow (MO, MW;

Annular Flow (AO); Intermittent flow (IO, IW), and; Dispersed flow (DO, DW).

Nädler & Mewes (1995) used conductivity probes to investigate two-phase oil-water flow

patterns in a horizontal Perspex pipeline with a 59 mm internal diameter. In this work,

20 mPa. s and 841 kg.m . Nädler & Mewes (1995) observed 7 flow patterns

and constructed flow regime maps of their findings; these are shown in Figures 2-9 and 2-10,

respectively. It should be noted that they did not observe annular flow. Nädler & Mewes

(1995) identified regions between oil and water continuous dispersed flow (regions II and V

respectively in Figure 2-10) where oil and water occurred in continuous layers simultaneously,

regions IIIa and IIIb in Figure 2-10.

One key development they made was to distinguish between dispersions and emulsions. Nadler

and Mewes (1995) identified a flow as an emulsion when one phase is uniformly dispersed in

nearly equal sized droplets in the other, continuous, phase. Conversely, they identified a flow as

a dispersion when:

“Layers of one continuous phase in which the other phase is nonuniformly dispersed.”

Nädler & Mewes (1995)

Tralle

listed

S

D

Figure

ero (1995) r

d below and i

Segregated fl

Dispersed flo

e 2-9: Two ph

eclassified tw

illustrated in

ow: -

a.

b.

ow: - Wate

a.

b.

Oil d

a.

b.

hase flow pa

wo-phase oil

n Figure 2-11

Stratified fl

Stratified fl

er dominated

Dispersion

Oil in wate

dominated: -

Dispersions

Water in oi

atterns observ

l-water flow

.

low (ST)

low with mix

d: -

of oil in wat

r dispersions

s of water in

il dispersion

ved by Nädle

w patterns int

xing at the in

ter and water

s (o/w)

oil and oil in

(w/o)

Chapter 2

er & Mewes

to three cate

nterface (ST&

r (Do/w&w)

n water (Dw

2: Literature R

(1995).

gories. The

&MI)

w/o&Do/w)

Review

se are

44


45

Figure 2-10: Oil-water flow regime map for a horizontal pipeline of 59mm ID as identified by

Nädler & Mewes (1995)

Figur

(b) di

(d) st

dispe

Ange

(wher

Expe

re 2-11: Tw

ispersion of

tratified flow

ersion of oil i

eli (1996) an

re, 1.

rimental Rig

o-phase oil-w

water in oil

w (ST); (e)

in water and

nd Angeli &

6 mPa. s and

g) facility a

water flow p

and oil in w

stratified flo

water (Do/w

Hewitt (200

d 801

at Imperial

(a)

(b)

(c)

(d)

(e)

(f)

pattern classi

water (Dw/o

ow with mix

w & w), Trall

00a) investig

1 kg.m ) u

College Lon

ifications: (a

& Do/w); (c

xing at the i

lero (1995)

gated two-ph

using the TO

ndon (which

Chapter 2

a) oil in wate

c) water in o

interface (ST

ase oil-water

OWER (Two

h is detailed

2: Literature R

er emulsion (

il emulsion (

T & MI), an

r co-current

o-Phase Oil-W

d in Section

Review

(o/w);

(w/o);

nd; (f)

flows

Water

n 3.2)

46

focus

ID =

rough

determ

imped

contin

flow

input

acryli

and 2

that m

acryli

condi

rough

contin

noted

Figur

acryli

sing on dro

25.4 mm), o

hness and w

mine the flo

dance probe

nuous phase

patterns wer

t volume frac

ic resin test

2.14(b) respe

mixed flow p

ic resin pip

itions. Ang

hness but the

nuous phase

d that Arirach

re 2-12: Flow

ic resin test

oplet size d

one of stainle

wetting prop

ow pattern A

es were used

e in disperse

re made for

ctions ,

sections con

ectively. Com

patterns appe

e, where oil

geli (1996) f

e wetting pro

. On compa

hakaran et al

(a)

w patterns by

section. ○, s

distribution.

ess steel, the

erties on th

Angeli (1996

d to establis

ed flows a c

mixture velo

0.14 to 0

nstructed by

mparing the

ear at lower m

l remains th

found that th

operties of th

arison with th

l. (1989) did

y Angeli & H

stratified wav

Angeli

e other of acr

he flow patt

6) used high

sh the local

onductivity

ocities, rangi

.96. The flo

Angeli & He

maps for the

mixture velo

he continuou

he flow patt

he pipe could

he flow regim

not observe

Hewitt (2000

vy (SW); ▬

(1996) used

rylic resin to

ern. To vi

h speed pho

phase fracti

needle prob

ing from Um

ow regime m

ewitt (2000a

e respective t

ocities in the

us phase for

tern was lar

d affect the

me map by A

three-layer f

0a) in the (a)

▬, three layer

Chapter 2

d two test

o investigate

isualise the

otography an

ion, ⟨φ⟩y,t.

e was used.

m 0.2 to 3.9

maps for the

a) are shown

test section m

stainless ste

r a wider ra

rgely indepen

flow pattern

Arirachakaran

flow.

(b)

stainless ste

rs (3L); ∆, st

2: Literature R

sections (w

the effect o

flow and in

nd high freq

To determin

Observatio

9 m.s-1 and f

stainless stee

n in Figure 2-

materials it i

el pipe than

ange of ope

ndent of the

n when oil w

n et al. (1989

eel test sectio

tratified mix

Review

where

of wall

n turn

quency

ne the

ons of

for oil

el and

-12(a)

s seen

in the

erating

e pipe

was the

9) it is

on, (b)

xed/oil

47

(SM/

mixed

Nadle

emul

mixtu

perfo

achie

regim

occur

betwe

dispe

Figur

flow

/oil); - - - ,

d/water (SM

er & Mewes

sification an

ures, in a 48m

ormed using

eved by chan

me map from

rring within

een regions

ersion above

re 2-13: Flow

based on inp

phase conti

M/water); +, m

(1997) cont

nd phase inv

m long horiz

oil viscositi

nging the li

m their result

the dispersio

IIIa (water

an oil-in-wa

w regime ma

put water frac

inuity bound

mixed (M)

inued their m

version on p

zontal test se

ies of

quid temper

s which is p

on layer. In

r-in-oil disp

ater dispersio

ap constructe

ction.

daries; ▲, st

multiphase fl

pressure drop

ection with a

22, 27 and

rature. Nad

presented in F

n Figure 2-13

persion abov

on, above wat

ed by Nadler

tratified wav

low research

p for differe

a 59mm inte

35 mPa. s;

dler & Mew

Figure 2-13

3 this is repr

ve a water

ter).

r & Mewes (

Chapter 2

vy/drops (SW

by investiga

ent flow reg

ernal diamete

the differen

es (1997) co

and observe

resented by

layer) and

(1997) for tw

2: Literature R

WD); ●, stra

ating the effe

gimes of oil-

er. The stud

nt viscosities

onstructed a

ed phase inve

the boundar

IIIb (water-

wo-phase oil-

Review

atified

ects of

-water

dy was

s were

a flow

ersion

ry line

-in-oil

-water

48

Solei

exper

imped

fracti

imme

shape

mixer

14) b

result

Arira

Um

concl

obser

Figur

Solei

mani (1999

rimental fac

dance probe

ions respect

ediately dow

ed and hone

rs was also i

based on obs

ts are in goo

achakaran et

1.25 m.s-1

luded that st

rved.

re 2-14: Flo

mani (1999)

9) continued

cility (TOW

es were aga

tively. Sol

wnstream of t

eycomb flow

investigated.

ervation mad

od agreemen

al., 1989, N

1 region in

tratified flow

ow pattern m

d the resear

WER) and fl

ain used to

leimani (19

the inlet had

w straightene

. Soleimani

de when an

nt with the f

Nadler & Mew

which Ange

w of oil and

map for the

rch conduct

luids. A h

visualise th

99) studied

d on the two-

ers [used to

(1999) cons

entrance mix

findings of p

wes, 1995 an

eli (1996) o

d water disp

stainless st

ted by Ang

high speed

e flow and

d the effect

-phase flow

reduce swir

structed a flo

xer and/or st

previous rese

nd Angeli, 1

observed 3-l

ersions occu

teel test sec

Chapter 2

geli (1996)

camera and

to establish

ts that helic

patterns. Th

rl] placed do

ow regime m

traightener w

earchers (Gu

996). When

layer flow,

ur and no 3-

tion of the

2: Literature R

using the

d high freq

h the local

cal static m

he effect of

ownstream o

map (see Figu

was not used

uzhov et al.,

n re-evaluatin

Soleimani (

-layer flows

TOWER fa

Review

same

quency

phase

mixers

cross-

of the

ure 2-

. The

1973,

ng the

(1999)

were

acility,

49


50

Hussain (2004) extended the research by Angeli (1996) and Soleimani (1999) using the same

experimental facility and fluids which have been detailed earlier in this section of this report.

Hussain (2004) conducted two different experimental campaigns; a case with a 5-element

Kenic™ element kinetic mixer placed immediately downstream of the tube inlet and another

without a mixer at the inlet. Flow regime maps for each of these cases were constructed and are

presented in Figures 2-15 and 2-16. The results obtained are consistent with findings of Angeli

(1996) and Soleimani (1999). There is a noticeable difference between the flow patterns

Hussain (2004) observed with and without a mixer present. Without a mixer present Hussain

observed 6 flow regimes:

1. Stratified wavy [SW]

2. Stratified wavy / drops [SWD]

3. Stratified mixed / oil layer [SM/O layer]

4. Three-layer [3L]

5. Stratified mixer / water layer [SM/W layer]

6. Dispersed-flow [DF]

When the mixer was in used Hussain (2004) only observed 4 flow regimes;

1. Wavy-flow

2. Dispersed oil-in-water

3. Dispersed water-in-oil

4. Fully dispersed flow

Figur

(2004

Braun

patter

Figure 2

re 2-16: Flo

4)

ner (2001) p

rns in liqui

2-15: Flow pa

ow patterns m

proposed a

id-liquid sys

atterns map w

map with a

unified appr

stems. She

without mixe

5-element K

roach for pr

e revised th

er at the tube

Kenics™ mi

rediction the

he Kolmogo

Chapter 2

e inlet, Hussa

xer at the tu

e transition t

orov (1949)

2: Literature R

ain (2004)

ube inlet, Hu

to dispersed

– Hinze (

Review

ussain

d flow

(1955)

51

pheno

consi

Braun

bubbl

Hinze

17 an

Tralle

Figur

to dis

horiz

omenologica

iderations ca

ner (2001) e

le size large

e (1955). Th

nd Figure 2

ero (1995) re

re 2-17: Flow

spersed wate

ontal oil-wat

al model for

an be employ

employed the

er than 0.1D

he flow patte

-18 in comp

espectively, w

w pattern ma

er in oil and

ter system, B

r droplet br

yed to help d

e Hughmark

D due to the

ern transition

parison with

where good a

aps predictio

d compariso

Brauner (200

reak-up in tu

determine the

(1971) – Ku

limitation im

n predictions

h the flow p

agreement is

n for transiti

on with expe

01)

urbulent flo

e maximal dr

ubie & Gard

mposed by t

by Brauner

pattern data

s observed.

ions to disper

erimental da

Chapter 2

ow and prop

rop size in a

dner (1977) m

the turbulenc

(2001) are s

of Guzhov

rsed oil in w

ta of Guzho

2: Literature R

posed that e

a dense dispe

model for dr

ce model us

shown in Fig

et al. (1973

water and tran

ov et al (197

Review

energy

ersion.

rop or

sed by

gure 2-

3) and

nsition

73) in

52

Figur

to Dw

Sotgi

resea

from

densi

duct,

1

2

3

4

Lovic

exper

visco

Um

(2003

re 2-18: The

w/o (boundar

ia and Tartar

arch. They u

3 to 28mm

ity ratios from

which are in

) smooth-in

2) wavy-inte

3) wavy-inte

4) core-annu

ck (2003) in

rimental rig w

osity of

0.8 to 3 m

3) observed 3

e Brauner (20

ry 5) in a hor

rini (2001) c

used an exper

m and a rang

m 0.8 to 0.9.

n good agree

nterface strat

erface stratif

erface stratif

ular flow

nvestigated

with a 38.8m

6 mPa. s a

m.s-1 and an o

3 flow patter

001) predicti

rizontal oil-w

conducted ex

rimental rig

ge of oils to

Sotgia and

ment with pr

tified flow

fied flow – ty

fied flow – ty

oil-water fl

mm internal d

and a density

oil input vol

rns, namely:

ons for trans

water system

xperimental

with numero

achieve vis

Tartarini (20

revious resea

ype 1

ype 2

lows in the

diameter stai

y of 8

lume fraction

sitions to Do/

m (Trallero (1

and theoret

ous horizonta

scosity ratio

001) observe

arch:

dual contin

inless steel, t

828 kg.m .

n range of 0

Chapter 2

/w (boundary

995))

ical two-pha

al ducts that

s from

ed 4 flow pat

nuous flow

test section, u

. A mixture

0.1 to 0.9 w

2: Literature R

y 4) and tran

ase oil-water

range in dia

10 to 1300

tterns for a 2

regime usin

using an oil w

e velocity ran

were used. L

Review

nsition

r flow

ameter

0, and

21 mm

ng an

with a

nge of

Lovick

53

1

2

3

Expe

Lovic

retain

degre

Figur

Using

dual

map

onset

interm

input

) stratified

2) dual cont

3) dispersed

rimental res

ck & Angeli

n their contin

ees, into the

re 2-19.

Figure 2-

g the same fl

continuous f

of mixture v

t of dual con

mediate mixt

t volume frac

wavy – at lo

tinuous flow

d flow – at hi

earch into d

i (2004), wh

nuity at the to

continuum

-19: Schemat

fluids, ranges

flow pattern

velocity again

ntinuous flo

ture velocitie

ctions.

ow lower vel

– up to a mi

igher mixture

dual continuo

ho classified

op and botto

of the other

tic diagram o

s of condition

boundaries.

nst oil input

w occurs at

es between s

ocities

ixture velocit

e velocities

ous flow patt

a regime as

om of the pip

r. The dual

of dual contin

ns and equip

. Lovick &

volume frac

t a mixture v

stratified and

ty of 1.5 m.s

terns in oil-w

s dual contin

pe while each

l continuous

nuous flow,

pment as Lov

Angeli (200

ction (see Fig

velocity of

d dispersed f

Chapter 2

-1

water flows

nuous flow w

h phase is dis

s flow regim

Lock & Ang

vick (2003) t

04) construct

gure 2-20) a

Um 0.8 m

flow patterns

2: Literature R

was continu

when both p

spersed, at va

me is illustrat

geli (2004)

they identifie

ted a flow re

and establishe

m.s-1 and occ

s for a range

Review

ued by

phases

arious

ted in

ed the

egime

ed the

curs at

of oil

54

Figur

Ogles

(III) d

As ha

liquid

of the

tensio

Induc

of flo

in the

2.3

Phase

defin

(disco

water

re 2-20: Flo

sby (1976) (

dispersion of

as be seen fro

d-liquid flow

e phases but

on and wetti

ced Fluoresc

ow structure

e future.

Phase I

e inversion i

ned as a tra

ontinuous) p

r dispersion t

ow pattern m

(solid lines. (

f oil in water

om the abov

ws. The flow

t also on the

ing angle ha

ence (LIF) i

but it is clea

Inversion

is a phenom

ansition in

phase to bein

to a water-in

map (Lovick

(I) dual cont

r; (IV) disper

e discussion

pattern depe

e wetting pr

ave not so fa

n the presen

ar that a muc

n

menon that oc

which one

g the continu

n-oil dispersio

k & Angeli

tinuous flow

rsion of wate

, a wide vari

ends not only

roperties of t

ar been syste

nt work has a

ch wider rang

ccurs in disp

of the pha

uous phase,

on.

(2004)) wi

; (II) dispers

er in oil

iety of flow p

y on the flow

the flow cha

ematically in

allowed muc

ge of conditi

persions of t

ases change

for example

Chapter 2

th the resul

sion of oil in

patterns have

w rates and p

annel. The r

nvestigated.

h more obje

ons remains

two immisci

es from bei

e the transiti

2: Literature R

ts from Laf

n water and w

e been observ

physical prop

roles of inter

The use of

ctive observ

to be investi

ible liquids a

ing the disp

ion from an o

Review

flin &

water;

ved in

perties

rfacial

Laser

ations

igated

and is

persed

oil-in-

55

Soun

effect

espec

consi

Most

the w

Centr

the co

point

which

hyste

either

called

From

in-wa

nd understand

t it has on pr

cially near th

ideration in t

t phase inver

will be on pha

ral to develo

oncepts of in

t is defined a

h phase inv

eresis effect

r of the two

d the ambiva

Figure 2-

m Figure 2-21

ater dispersio

ding and pre

roperties suc

he pipe wal

the process in

sion literatur

ase inversion

oping a comp

nversion poin

as the critica

ersion occur

which is ma

immiscible l

alent range (Y

-21: Graphic

1 it can be se

ons to water-

ediction of t

ch as viscosi

ll (Lang and

ndustries wh

re relates to l

n in two-phas

prehensive u

nt and the am

al phase com

rs (Yeh et a

anifested by

liquid compo

Yeo et al., 20

al representa

een that the c

-in-oil disper

this phenom

ity, pressure

d Auracher,

here fluid tran

liquid-liquid

se liquid-liqu

understandin

mbivalent ran

mposition (vo

al., 1964).

a range of

onents can be

002).

ation of the a

critical dispe

rsions are mu

menon is imp

drop, heat tr

1996). Pha

nsport and h

d dispersions

uid channel f

g of the pha

nge (range of

olume per c

Associated

conditions (

e the dispers

ambivalent ra

ersed phase h

uch higher th

Chapter 2

perative due

ransfer and p

ase inversion

heating or coo

in agitated v

flows.

ase inversion

f ambivalenc

ent of the di

with the inv

volume frac

sed phase (Fi

ange, Yeo et

holdups for in

han for the re

2: Literature R

to the signi

phase distrib

n is an imp

oling are req

vessels. How

n phenomeno

ce). The inve

ispersed pha

version poin

tions) over w

igure 2-21);

al. (2002)

nversion from

everse invers

Review

ificant

bution,

portant

quired.

wever,

on are

ersion

ase) at

nt is a

which

this is

m oil-

ion.

56


57

Yeh et al. (1964) developed an equation to predict the phase inversion point of two immiscible

liquids based upon the viscosities of the two components:

1

/ 2.1

Where is the volume fraction of the dispersed phase at the inversion point, is the

dynamic viscosity of the dispersed phase and is the dynamic viscosity of the continuous

phase.

Yeh et al. (1964) found that phase inversion predictions from Equation 2.1 were poor for some

experimental systems, including water–cyclohexanol, water–oleic acid, water–n-octyl alcohol

and also for most of the ternary systems they investigated. Yeh et al. (1964) found agreement

with experimental results was greatly improved when the bulk-phase viscosity (viscosity of the

continuous phase, ) is replaced with the interfacial viscosity (μ ). Thus equation 2.1

becomes;

1

/

2.2

Clayton (1935) calculated that the volume fraction of the dispersed phase could not exceed

74.02%. This maximum value represents the point as which uniform spheres touch each other

and coalescence occurs (Yeh et al., 1964). This value represents the Ostwald Ratio for the

maximum packing efficiency of a rhombohedral face centred cubic structure. The volume

fraction of the dispersed phase can exceed this value because the dispersed phase is not limited

to uniform spheres i.e., the dispersed phase drops need not be spherical or uniform in size.


58

Arashmid & Jeffreys (1980) established that the collision frequency and coalescence frequency

of agitated dispersions can be combined to accurately predict the ambivalent range and the

phase inversion concentration. They found that the volume percentage of the dispersed phase

can range from 20% to 90% and the extent of the ambivalent range depends on how the

dispersion was produced. A series of other factors have been identified that affect phase

inversion including the physical properties of the liquids, the process conditions, wettability

characteristics, the pipe materials and the associated geometry and orientation (McClarey &

Mansoori, 1978). An alternative theory for the occurrence of phase inversion was presented by

Efthimiadu and Moore (1993) who proposed that it is a form of instability with regard to the

type of dispersion and it can occur whenever the equilibrium between coalescence and re-

dispersion shifts towards coalescence.

Arirachakaran et al. (1989) investigated the phase inversion phenomenon in an oil-water system,

researching the effects of input water fraction, oil viscosity, mixture viscosity and laminar flow

regime on the process. Although they did not investigate the effects of droplet size, droplet size

distribution and flow regime on phase inversion they did identify them as influential factors.

Arirachakaran et al. (1989) presented a mechanism for the phase inversion process in an oil-

water system, which is shown in Figure 2-22. Their mechanism shows there is a range of

volume fractions over which either component can form the dispersed phase; the ambivalent

range.

Figur

(1989

Arira

(Guzh

assum

betwe

show

devel

where

Brock

re 2-22: Pha

9)

achakaran et

hov et al., 1

med that the

een oil visco

ws the relatio

loped shown

e φ , is in

ks and Richm

0.2 mPa. s

ase inversion

al. (1989) co

973; Russel

ere exists a

osity and the

onship that A

n below:

, 0.5

nput water fr

mond (1994)

s. However

n process fo

ombined the

ll et al., 195

logarithmic

e input wate

Arirachakara

500 0.110

fraction requi

) reported a c

r, the experi

or an oil-wat

ir phase inve

9; Charles e

c relationshi

er fraction re

an et al. (19

08 log 10

ired to inver

constant valu

ments of Br

ter dispersion

ersion data w

et al., 1964 a

ip in the fu

equired to in

989) identifi

rt the system

ue of ,

rocks and R

Chapter 2

n system, A

with those of

and Oglesby

ully laminar

nvert the syst

ied, with the

m and is

0.15 for oil

Richmond (1

2: Literature R

Arirachakaran

f other resear

y et al., 1969

oil phase r

tem. Figure

e correlation

2.3

s the oil visc

l viscosities

994) incorpo

Review

n et al

rchers

9) and

region

e 2-23

n they

cosity.

above

orated

59

some

differ

Since

inver

shoul

inver

inver

argue

being

a fun

Luhn

and M

e cases with

rent from tha

Figure

e Arirachaka

rsion. They m

ld invert at

rsion occurs

rsion should

ed that the m

g that if the c

nction of the

ning & Sawis

McClarey &

surfactants a

at in a system

e 2-23: Phase

aran et al. (1

made an assu

an input w

to reduce int

occur at an

magnitude of

converse wer

curvature o

stowski (197

& Mansoori

and, in this c

m with pure l

e inversion p

1989) did no

umption that

water fraction

terfacial ene

n input water

the interfaci

re the case, it

f the interfac

71) and are n

(1978) affir

case, the mec

iquids. (Xu e

point correlat

ot consider

for an oil w

n of 0.5, wh

rgy by reduc

r fraction of

ial tension ca

t would infer

ce. Both of

not supported

rmed that, if

chanism of p

et al., 2007).

tion, Arirach

the effect of

with a viscosi

hich is base

cing interfac

f 0.5. Selke

annot affect

r interfacial t

f these propo

d by experim

f no other f

Chapter 2

phase invers

hakaran et al.

f interfacial

ity 1 m

ed on the co

ial area, and

er & Sleiche

phase invers

tension betw

osals have be

mental data.

forces are p

2: Literature R

ion is found

(1989)

tension on

mPa. s, the s

oncept that

d as a result,

er (1965) how

sion. Their r

ween two liqu

een discount

Yeh et al. (

present, inter

Review

d to be

phase

ystem

phase

phase

wever

reason

uids is

ted by

(1964)

rfacial

60


61

tension would cause phase inversion to occur at 50%. However, other factors need to be taken

into account. Yeo et al. (2002) presented a simple equation (based on the criterion of interfacial

energy minimisation) to predict the limits of the ambivalence region:

,

1 ,

/

/

2.4

where φ , is the holdup of the organic phase at phase inversion and d is the Sauter mean

diameter which is defined as the diameter of a sphere that has the same volume to surface area

ratio as the object of interest. The subscripts o/w and w/o denote oil-in-water and water-in-oil

dispersions respectively. The predictions of this equation were in good agreement with

experimental results obtained by Selker and Sleicher (1965).

The Yeo et al (2002) model does not, however, account for wetting effects which further

accentuate the hysteresis effect (ambivalent range). The wetting effects (interfacial energy

associated with the solid surface) only become significant when the surface area to volume ratio

is large enough or when the drops are large which is the case with pipe flow but is not the case

with agitated vessels hence its omission from the model in this case (Tidhar et al., 1986).

One of the key observations from the experimental work by Arirachakaran et al. (1989) is that

the mixture viscosity exhibits a peak at the phase inversion point, shown in Figure 2-24; here,

the viscosity is calculated from the pressure gradient which also shows a peak at the phase

inversion location. Arirachakaran et al. (1989) conclude that the magnitude of this peak depends

predominantly on the flow regime of the mixture when inversion takes place. Martinez et al.

(1988) and Pal (1993) also observed that for an oil-water system the viscosity increases as water

fraction is increased until it reaches a maximum at the phase inversion point, and then begins to

drop. In earlier studies, Falco et al. (1974) also observed a peak in viscosity for a water-in-oil

emul

dispe

Figur

et al.

Ogles

increa

drop.

decre

Solei

volum

(1999

can b

the tw

sion at the i

ersed water p

re 2-24: Mix

(1989)

sby (1979) o

asing mixtur

Oglesby (1

eased as the o

mani (1999)

me percentag

9) found that

be explained

wo liquids ar

inversion poi

phase from a

xture viscosit

observed a si

re velocity an

1979) also o

oil viscosity

) observed a

ge caused b

t phase inver

by the fact t

re more homo

int. They at

lamellae stru

ty against in

gnificant cha

nd oil viscos

observed that

increased.

a peak in pr

by phase inv

rsion occurs

that at higher

ogeneously m

ttributed this

ucture to a co

nput water fra

ange in press

sity increase

t the input w

ressure grad

version, as s

at lower wat

r mixture ve

mixed.

s peak to a

ontinuous ph

action for lo

sure drop at

d the magnit

water fraction

dient betwee

shown in Fi

ter-cuts for h

locities the d

Chapter 2

change in th

hase.

w viscosity

the phase inv

tude of the c

n at the pha

n 34% and

gure 2-25 b

higher mixtur

degree of mi

2: Literature R

he structure

oil, Ariracha

version poin

change in pre

se inversion

37% input

below. Sole

re velocities.

xing is highe

Review

of the

akaran

nt. An

essure

point

water

eimani

. This

er and

62

Nadle

is sho

dispe

that f

Figure 2-2

er & Mewes

own in Figu

ersion to a re

flow regime t

Figur

25: Pressure

s (1995) obse

ure 2-26. Th

egion of strat

to an oil-in-w

re 2-26: Pres

gradient in t

erved two pr

hey associate

tified/dispers

water dispers

ssure drop fo

two-phase liq

ressure gradi

ed the first p

sed flow and

sion.

r oil-water fl

quid-liquid fl

ient peaks fo

peak to the

d the second p

low (Nadler

Chapter 2

flows, Soleim

or oil-water p

transition fr

peak being t

and Mewes,

2: Literature R

mani (1999)

pipeline flow

rom a water-

the transition

1995)

Review

w; this

-in-oil

n from

63


64

Nadler and Mewes (1997) developed a simplified phase inversion model based upon the

momentum equations for two-phase liquid-liquid stratified flow. They modelled phase

inversion in terms of the critical water cut (φ ) at which phase inversion occurs (Equation 2.5).

1

1′′

1

2.5

In Equation 2.5, and are the oil and water density respectively, and are the oil and

water viscosity respectively, and are the pipe diameter and the total liquid velocity

respectively and ′ , ′ , and are the parameters of the Blasius friction factor equation

which is given as;

′Re 2.6

where Re is the Reynolds number.

Nadler & Mewes (1995a) reported that for a well-mixed two-phase liquid-liquid flow where

both layers are in the same flow regime – for example in slug flow, is equivalent to ,

inferring that the liquid velocity does not affect the critical water cut.

Decarre and Fabre (1997) proposed the following correlation to predict the dispersed phase

concentration ( ) at the phase inversion point based on the dispersed and continuous phase

properties:

1/ /

2.7


65

Chen (2001) proposed the following correlation to predict the critical water fraction based on

the Arirachakaran et al. (1989) model.

w

ow

w

ow

w

ow

4841.26533.9log1108.03788.0 10 2.8

Although Chen (2001) accounted for the oil-water density ratio the correlation did not take into

account the mixture velocity (Xu et al., 2007). The scope of the Chen correlation is limited

because it was developed with reference to a configuration of laminar flow in stratified layers.

Brauner and Ullmann (2002) developed a model for phase inversion based on the free energy of

the dispersion; the dispersion (oil-in –water or water-in-oil, say) showing the minimum free

energy was the stable one. This model is reviewed in detail by Xu et al. (2007). To develop a

correlation for the critical water fraction, Brauner and Ullmann (2002) made the following

assumptions:

1) The composition of the oil phase and water phase and the system temperature are

invariant with phase inversion.

2) Wall-liquid wettability effects can be neglected.

3) The free energy of the oil phase and water phase remains the same.

4) Only the free energies of the interfaces have to be considered.

Where wo /~

(density ratio) and wo /~

(kinematic viscosity ratio). Xu et al. (2007)

reported that the Brauner and Ullmann (2002) correlation performed well when compared with

available data on the critical holdup for phase inversion. Although phase inversion in stirred

4.0~~

4.0~~

1

w 2.9

tanks

exam

Tsour

the sy

2.4

It is

dispe

Sectio

calcu

obvio

visco

An al

follow

Howe

predi

phase

s is not the

mple, the effe

ris & Dong

ystem the sys

Emulsi

evident from

ersions behav

on, the litera

ulating the vi

ous approach

osities of the

lternative app

ws:

ever, adoptin

cts a viscosi

e inversion p

focus of thi

ect of an ele

(2000). The

stem would i

ion Viscos

m the work

ves in an an

ature on disp

iscosity of a

h is to use, to

pure compon

proach is to u

ng linear or

ity maximum

phenomena (d

is report the

ctric field on

ey observed

invert from a

sity

on phase inv

nomalous ma

persion visco

a liquid-liqui

o calculate m

nents:

.

use reciproca

reciprocal in

m as a functi

discussed in

e research co

n phase inve

that when a

a water-in-oi

version desc

anner near t

osity is revie

id mixture h

mixture visco

1 .

al interpolati

1

nterpolation

ion of volum

Section 2.3)

onducted in

ersion in stir

a sudden volt

il dispersion

cribed in Sec

the phase in

ewed. A num

have been di

osity , a lin

ion as sugges

is not appro

me fraction i

.

Chapter 2

this field is

rred tanks wa

tage increase

to an oil-in-w

ction 2.3 tha

nversion poin

mber of sim

iscussed in t

near interpol

sted by Bing

opriate since

i.e., the fail t

2: Literature R

s of interest.

as investigat

e was impos

water dispers

at the viscos

nt. In this p

mple approach

the literature

lation betwee

2.10

gham (1916)

2.11

e neither app

to account f

Review

. For

ted by

sed on

sion.

sity of

resent

hes to

e. One

en the

0

as

1

proach

for the

66


67

The principle factors affecting the viscosity of an emulsion μ are: (i) the volume fraction of the

dispersed phase , and; (ii) the temperature T . Farah et al (2005) listed nine other minor

factors that influence the effective viscosity of a water-in-oil emulsion, these being the:

1. viscosity of the continuous phase,

μ

2. viscosity of the dispersed phase, μ

3. shear rate, γ 4. average droplet size, μ

5. droplet size distribution 6. density of the continuous phase, ρ

7. density of the dispersed phase, ρ 8. nature and concentration of emulsifying

agents

9. presence of solids

There are essentially two groupings of emulsion viscosity models (i) those at constant

temperature, and; (ii) those that account for the influence of temperature changes on effective

viscosity. Following an investigation in to the effect of temperature on the test fluids used in

the experimental campaigns detailed in Chapters 4, 5 and 6 (i.e., Exxsol D80 and a water-

glycerol-dyestuff solution) which is presented in Section 3.8, a thermocouple was inserted

directly upstream of the test section inlet (see Figure 3.5) to monitor the temperature of the

fluids. Many of the existing models define the relative emulsion viscosity μ as a ratio of the

emulsion viscosity μ to that of the continuous phase μ :

2.12

Einstein (1906) developed a viscosity prediction model for infinitely dilute suspension systems

in which the volume fraction of the dispersed phase is less than 2% in a solid-liquid

dispersion. The model is limited to rigid spheres and owing to the diluteness of the suspension


68

there is no appreciable interaction between the dispersed spheres. The model proposed is as

follows:

1 . 2.13

where is 2.5 and is the volume fraction of the dispersed phase, or more precisely it is the

volume of dispersed phase spheres in unit volume of suspension.

Numerous researchers have used the work by Einstein (1906) as a basis from which to develop

models for concentrated emulsions, non-spherical and polydisperse liquid-liquid systems.

Taylor (1932) presented a model for the relative emulsion viscosity μ that accounts for the

influence of the dispersed phase viscosity as well the continuous phase viscosity .

The model, which is valid for emulsions with a low concentration of dispersed spherical drops,

is given as:

1 2.50.41

2.14

where is the ratio of the dispersed phase viscosity to that of the continuous phase :

2.15

For dispersions of spherical solid particles K tends to infinity and Equation 2.14 reduced the

Einstein viscosity model (Equation 2.13) i.e., the Taylor (1932) equation is a modified form of

the Einstein (1906) viscosity model for emulsions where K is given as:


69

2.50.4

2.16

Eiler (1943) presented a relative emulsion viscosity μ correlation for Newtonian systems using

bitumen emulsions. This is given as:

11.25

1

2.17

where, 1.28 α 1.30.

Hatschek (1928) obtained the following relationship:

1

1

2.18

Mooney (1950) extended Einstein’s viscosity model to predict the relative emulsion viscosity

μ of finite concentration monodisperse systems i.e., systems in which the dispersed particles

having the same shape, size and mass. In order to do so the interaction between the dispersed

spheres must be taken into account. Mooney (1950) described this interaction as a crowding

effect. The equation is given as:

2.5

1 .

2.19

where 2.5 was selected to give correspondence with the Einstein (1906) viscosity model for

very dilute suspensions when the volume fraction approaches zero. The constant k is a self-

crowding factor.


70

Mooney (1950) also presented a model com for polydisperse systems, those being systems

wherein the dispersed phase particles have a broad range of size, shape and mass characteristics.

These systems involve a variable factor, , which measures the crowding of spheres of radius

by spheres of radius . For a suspension comprised of groups of spheres of different

diameters Mooney (1950) presented the following equation:

ln 2.51∑

2.20

Based on a geometric argument, Mooney presented the following limits for the crowding factor:

1.35 λ 1.91. On comparison with data obtained by Vand (1950) 1.43 was presented as a

suitable value for λ .

Brinkman (1952) considered the impact to the relative emulsion viscosity of adding a single

dispersed particle to a system already containing n dispersed particles. It was assumed that the

relative emulsion viscosity would increase by the factor given by the Einstein (1906)

viscosity equation. Brinkman (1952) derived the following expression for the relative emulsion

viscosity :

1

1.

2.21

Roscoe (1952) investigated the effect of the of the size distribution of the dispersed droplets on

the relative emulsion viscosity μ and found that when the spherical droplets have a wide

spectrum of sizes, the Brinkman (1952) viscosity model works well for all dispersed phase

fraction φ values. However, when the dispersed phase is comprised of uniform sized


71

spheres, Roscoe (1952) found the Einstein (1906) model is limited to dispersed phase fractions

0.05. For medium and high dispersed phase fractions φ Roscoe (1952) proposed a

modified form of the Brinkman (1952) model in which the phase fraction of the dispersed phase

is multiplied by 1.35, i.e.:

1

1 1.35.

2.22

Pal and Rhodes (1989) developed the correlation presented by Brinkman (1952) into model for

both Newtonian and non-Newtonian emulsions which accounts for hydrate effects and the

flocculation of dispersed droplets:

1

1.

2.23

Where, is a hydration factor that depends on the nature of any emulsifying agents that may

be present and, accounts for flocculation and only used in non-Newtonian emulsions.

Phan-Thein & Pham (1997) presented a different equation for the effective viscosity for a

droplet suspension model for which they used the model by Taylor (1932) as a starting point.

The model, in which the particles are of a size where Brownian motion is unimportant, is given

as:

.2 52 5

1 2.24

For rigid droplets (μ → ∞ ) the effective viscosity reduces to:


72

1.

2.25

Equation 2.25 reduces to the Einstein (1906) model (Equation 2.13) in the limit of small volume

fractions of the dispersed phase.

Pal (2000) reviewed the model proposed by Phan-Thein & Pham (1997) and found that it under

predicts the relative viscosity for concentrated emulsions by a large amount and fails to account

for the presence of surfactants. Pal (2000) presented a modified form of Equation 2.26 to

describe the viscosity-concentration relationship of emulsions of nearly spherical droplets. This

model showed good predictive ability when compared to experimental data. The correlation is

given as:

.2 52 5

1 . 2.26

where, is a constant that factors for the presence of absorbed surfactants on the surface of

droplets. It is a constant for a given emulsion, but varies between systems.

Krieger – Dougherty (1959) presented an equation for concentrated solid-in-liquid suspensions

which is given as:

1 2.27

where, μ is the intrinsic viscosity and has a theoretical value of 2.4 for rigid spheres,

is the maximum packing concentration and represents an effective fluidity limit at which the

system loses liquid characteristics and becomes an elastic solid. A difficulty arises when

calculating emulsion viscosity due to problems associated with measuring for emulsions.


73

Chong et al. (1971) presented a graphical extrapolation technique to determine for solid-

in-liquid suspensions. Unlike soild-in-liquid suspensions, emulsion viscosities do not tend to

infinity as φ approaches . Furthermore, for emulsions can exceed , when

the droplets of the dispersed phases can no longer remain spherical and undergo

deformation. Due to these reasons extrapolation methods to determine μ are unsuitable.

A limitation of the Krieger-Doughtery (1959) model is that it is confined to Newtonian systems.

However, Barnes (1994) postulated that the system could be adopted for use with non-

Newtonian fluids by making dependent on shear-rate.

Aoamari et al. (1998) presented shear viscosity data for water-in-oil systems using a Crude

Arabian Light (CAL) which, showed the existence of not only but also , the critical

water volume fraction which represents the onset of physical contact between water droplets.

Ronningsen (1995) presented a model for predicting the viscosity of water-in-crude oil (w/o)

emulsions based on experimental results from eight different North Sea crude oils. The model

is a development of the exponential model proposed by Richardson (1933). The exponential

relationship between viscosity and the volume fraction of the dispersed phase represents the fact

that the emulsion becomes increasingly more non-Newtonian and that such emulsions exhibit a

non-linear relationship. The model is given as:


74

. 2.28

where K is a constant.

A modified form of this model was presented by Broughton & Squires (1938) as follows:

. 2.29

Equation 2.29 was the basis for the Ronningsen (1995) model who postulated that A and K

could be expressed as linear function of temperature such that:

. 2.30

. 2.31

which can be substituted into Equation 2.29 to give:

ln . . . . 2.32

where , , and are constants.

Pal (1998) correlated emulsion viscosity μ data using experimental data for mineral oil-in-

water and kerosene-in-water emulsions. In the correlation presented emulsion viscosity is a

function of particle Reynolds number Re , the volume fraction of the dispersed phase φ , the

maximum packing concentration of the dispersed phase and intrinsic viscosity μ ]. The

model assumes that the emulsion droplets are large enough to neglect the influence of Brownian

motio

numb

2.5

In th

(Sect

2.4).

that t

inver

area

mode

exper

on and there

ber (Ca) sma

/ 1

Conclu

e above dis

tion 2.2), on

Though it is

the topics co

rsion and flow

not dealt wi

elling metho

rimental resu

efore the Pec

all. The corre

/

uding rem

cussion, atte

phase inver

s convenient

overed are clo

w regimes a

ith in this ch

ods will be i

ults presented

clet number

elation is giv

marks

ention has b

rsion phenom

t to divide th

osely connec

and between

hapter is tha

introduced a

d in Chapters

is disregarde

ven as:

. log Re

been focusse

mena (Sectio

he material u

cted. Thus, t

apparent vis

at of modelli

and describe

s 4, 5 and 6.

ed. The mo

log

d on flow r

on 2.3) and

under these h

there is a clo

scosity and p

ing methods

ed in the co

Chapter 2

del assumes

Re

regimes in li

on mixture

headings, it s

ose relationsh

phase inversi

for liquid-l

ontext of int

2: Literature R

that the cap

2.34

iquid-liquid

viscosity (Se

should be str

hip between

ion. A major

iquid flows.

erpretation o

Review

pillary

flows

ection

ressed

phase

r topic

Such

of the

75

CH

Ex

Liq

3.1

The e

proce

using

3.2)

exper

liquid

patter

liquid

exper

equip

system

Sectio

Sectio

physi

visua

metho

HAPT

xperim

quid-L

Introdu

experimental

essing metho

g the PLIF a

with a desc

riments carri

d-liquid flow

rns and phas

ds has been

rimental bac

pment, and c

ms is describ

on 3.6 and th

on 3.7. The

ical propertie

alisation sect

odology and

TER 3

mental

Liquid

uction

l facility and

odology used

and PTV/PIV

cription of

ied out in th

ws has been

se distributio

carefully m

kground to t

camera syste

bed in Sectio

he principles

e selection o

es are detaile

tions for us

d the means o

Appa

d Flow

d procedure,

d to conduct

V technique

the generic

he work desc

on the app

on in a liquid

matched and

these studies

ems respectiv

on 3.5. The b

s of the laser

of the test f

ed in Section

se in the L

of obtaining q

aratus

w Studi

as well as t

the studies o

are describe

liquid-liqui

cribed in thi

plication of P

d-liquid flow

the remaini

s. Sections

vely and the

bases of the

r-induced flu

fluids (includ

ns 3.8 and 3.9

LIF experim

quantitative

C

and M

ies

the visualisat

of co-current

ed below. Th

id flow faci

s thesis. Th

PLIF and PT

w in which th

ing Sections

3.3 and 3.4

e synchronis

fluorescence

uorescence (L

ding refracti

9, respective

ments and, fi

data are disc

Chapter 3: Exp

Method

tion equipme

t horizontal l

his Chapter b

ility (TOWE

he main focu

TV/PIV to t

he refractive

in this Cha

give descrip

ation of the

e phenomeno

LIF) method

ve index ma

ely. Section

finally, the

cussed in Sec

perimental M

ds for

ent and the i

liquid-liquid

begins (in Se

ER) used fo

us of the wo

the study of

e index of th

apter describ

ptions of the

laser and ca

on are describ

d are outlined

atching) and

3.10 describ

image proce

ction 3.11.

Methods

image

flows

ection

or the

ork on

f flow

he two

be the

e laser

amera

bed in

d in in

d their

bes the

essing

76

3.2

The e

which

pheno

was o

of the

3.2.1

two l

separ

the en

respe

The TO

experiments

h is a multip

omena occur

originally bu

e facility for

below. A s

liquid phases

rately enterin

nd of the tes

ective storage

OWER Fa

were carried

phase flow fa

rring in co-cu

uilt around 20

r the present

schematic dia

s is pumped

ng the test se

st section to

e tanks.

Figure 3-

acility

d out in the

acility at Imp

urrent horizo

0 years ago, i

work and th

agram of the

from the res

ection where

the separato

-1: Schemati

Two-Phase

perial College

ontal liquid-l

it has been n

he details of

e facility is sh

spective stor

they flow in

or vessel fro

ic Diagram o

C

Oil-Water

e London de

liquid flows.

necessary to c

this refurbis

hown in Figu

rage tanks an

n contact; th

om which the

of the TOWE

Chapter 3: Exp

Experimenta

esigned for th

Though the

conduct a ma

shment are o

ure 3-1. Bas

nd through fl

e mixture is

e two fluids

ER facility

perimental M

al Rig (TOW

he investigat

e TOWER fa

ajor refurbish

outlined in Se

sically, each

flow meters b

passed back

are passed

Methods

WER),

tion of

acility

hment

ection

of the

before

k from

to the

77

3.2.1

3.2.1

The l

positi

0.5 m

impro

comp

strand

togeth

theref

F

Compon1

Separat1.1

liquid – liqu

ioned above

m diameter, 0

ove separatio

pared with co

ds of two m

her. These

fore collect e

Figure 3-2: P

nents of th

tor

uid separator

the storage

0.3 m long K

on efficiency

onventional

materials (met

two materia

either fluid in

Photograph s

he TOWER

r is a vessel

tanks. The

KnitMeshTM

y of the tes

separators.

tal and plast

als, metal a

n a continuum

showing the

R Facility

l constructed

vessel is 1.

coalescer.

st fluids and

The KnitMe

tic) with hig

and plastic h

m of the othe

arrangement

C

d from PVC

94 m long a

The KnitMe

d enable a sm

eshTM coales

ghly different

have differen

er.

t of the separ

Chapter 3: Exp

C reinforced

and 0.54 m I

eshTM coales

maller vesse

scer consists

t surface fre

nt wetting p

rator and the

perimental M

with steel a

ID and cont

scer is includ

el size to be

of a mesh p

e energies k

properties an

storage tank

Methods

and is

ains a

ded to

e used

pad of

knitted

nd can

ks

78

3.2.1

The f

Fluid

as pa

mean

flow

3-1 &

and th

for th

the lo

throu

flowm

FM4

for ea

rates

meas

full s

Flow M1.2

flow rates ar

d Well FllQ-X

art of the refu

ns of a 4-20 m

meters. The

& 3-3, FM1

he oil phase

he aqueous p

ow range flow

ugh FM2 BV

meter (FM3)

valve BV12

ach phase w

and phase

urement of t

cale value, w

Metering

re measured

X LCD digit

urbishment o

mA linear cu

orientation o

and FM3 ar

respectively

phase and the

wmeter FM1

V10 is closed

) valve BV12

2 is to be ope

was to allow

fractions,

the flow rate

while their re

by means o

tal display; t

of the facility

urrent output

of this arrang

re the low ra

y and FM2 &

e oil phase re

1 valve BV10

and BV11 is

2 is opened

en and BV12

experimenta

whilst mini

es. The accur

epeatability is

of four NB L

these new flo

y. The flow r

. Each fluid

gement is illu

ange (2-20 L

& FM4 are th

espectively.

0 is opened a

s open. To o

and BV13 i

2 closed. T

al runs to be

imising the

racy of the N

s ±0.1% of fu

C

Liquid Turbi

ow meters w

rates can be

can be direct

ustrated in F

L.min-1) flow

he high range

To direct th

and BV11 is

orientate the

is closed wh

The reason fo

e conducted

overall un

NB Liquid F

full scale.

Chapter 3: Exp

ine Flow Me

were fitted on

time-logged

ted through o

igures 3-1 an

wmeters for t

e (14-140 L.

he aqueous p

closed, whe

oil flow thro

ereas to dire

or providing

over a broa

certainty in

Flow Turbine

perimental M

eters, fitted w

n the present

on a compu

one of two tu

nd 3-3. In Fi

the aqueous

.min-1) flowm

hase flow th

reas to direc

ough the low

ect the oil th

g two flow m

ader range of

n the setting

es is ±0.5%

Methods

with a

t work

uter by

urbine

igures

phase

meters

hrough

ct flow

range

hrough

meters

f flow

g and

of the

79

3.2.1

Two

these

work

each

Figur

Pumps 1.3

Grundfos CR

pumps wer

k. The pump

have a rated

re 3-4 below

Figur

RN 10-5 pum

re fitted to t

p for the oil

d flowrate of

:

re 3-3: Photo

mps with thr

the facility a

phase is fitt

f 2.788 L.s-1 a

ograph of the

ee phase sup

as part of th

ted with dou

and a rated h

C

flow contro

pplies were u

he refurbishm

uble back to

head of 361 k

Chapter 3: Exp

l panel

used, one for

ment conduct

back shaft s

kPa. The pu

perimental M

r each fluid;

ted in the p

seals. The p

umps are sho

Methods

again,

resent

pumps

own in

80

3.2.1

Each

Wilfo

The i

Of th

3.2.1

The i

botto

keros

the g

Figure 3-

Tanks 1.4

of the test

ord Plastics L

inlet streams

he outlet strea

Inlet Se1.5

inlet to the t

m of the test

sene-like oil

glycerol solut

4: Photograp

fluids is sto

Ltd. Each t

s are from th

ams from eac

ection

test section i

t section, see

(EXXOL D

tion valves B

ph illustrating

ored in a 0.6

tank has two

he separator

ch tank one l

is configured

e Figure 3-5.

D80) and an

BV15 and B

g the flow co

681 m3 tank

o inlet and tw

and the recy

leads to the p

d so that eith

. In the LIF

aqueous gly

BV16 are ope

C

ontrol panel

constructed

wo outlet str

ycle stream f

pump and the

her test fluid

experiments

ycerol solutio

ened wherea

Chapter 3: Exp

of the TOWE

from fibreg

reams as sho

from the corr

e other is a d

d can be inje

s, the two liq

on. To introd

as valves BV

perimental M

ER facility

glass and res

own in Figur

responding p

drainage line.

ected at the t

quids used w

duce oil on t

V14 and BV1

Methods

sin by

re 3-1.

pump.

.

top or

were, a

top of

17 are

81

close

BV16

are op

3.2.1

The r

const

test s

sectio

d. Converse

6 are closed

pen.

Figure

Test Se1.6

rig has a 7.

tructed from

section is 7.

on inlet. The

ely, to introd

and valves B

3-5: Photog

ction

30 m long,

stainless ste

30 m long,

visualisation

duce the aqu

BV14 and BV

graph showin

1-inch (D =

el (SCH 80)

with the vi

n sections ar

ueous phase

V17 are ope

ng the orienta

= 25.4 mm)

and mounte

isualisation s

re discussed i

C

on top of th

n. For both

ation at the p

nominal bo

d in a precis

sections pos

in Section 3.

Chapter 3: Exp

he oil phase

cases valves

pipe test secti

ore stainless

ely horizonta

sitioned 6.20

10.

perimental M

valves BV1

s BV18 and

ion inlet

steel test se

al orientation

0 m from th

Methods

5 and

BV19

ection

n. The

he test

82

3.2.1

There

press

Figur

3.2.1

A 1.5

tempe

sectio

seen

3.3

In the

a she

liquid

laser

Pressur1.7

e are two pr

ure measure

re 3-1.

Thermo1.8

5 mm type K

erature durin

on inlet, fitti

in Figure 3-5

Laser E

e Laser Indu

et of light de

d two phase

sheet passes

re Gauges

ressure gaug

ement. The p

ocouple

K thermocoup

ng experime

ing into the

5.

Fi

Equipmen

ced Fluoresc

erived from

flow is pas

s through th

es; one for w

pressure gaug

ple (Figure 3

ental runs.

exposed thre

igure 3-6: 1.

nt

cence (LIF) t

a laser is pas

sing. Since t

he test sectio

water pressu

ges are conn

3.6) can be fi

When being

ead of drain

5 mm type K

technique, as

ssed through

the refractiv

on without d

C

ure measurem

ected to the

itted to the T

g used, it is

age value B

K thermocoup

s applied in t

h the test sec

ve index of t

distortion at

Chapter 3: Exp

ment and the

pump outlet

TOWER facil

located ups

V20. The p

ple

the current ex

tion through

the two fluid

the fluid-flu

perimental M

e other for t

t pipe as sho

lity to monit

stream of th

positioning c

xperimental

h which the l

ds is matche

uid interfaces

Methods

the oil

own in

tor the

he test

can be

work,

iquid-

ed, the

s. By

83

addin

determ

sheet

flows

(Chap

cause

3.3.1

An O

green

peake

intern

by us

8) wh

range

expla

3.3.2

A Fi

sheet

sheet

outpu

orien

ng a fluoresc

mine the pos

t is passing.

s in a square

pters 5 and

ed by the circ

Copper 1

Oxford Laser

n light source

ed at 510.6

nal clock freq

se of an exter

hich override

e of the laser

ained in secti

Laser Sh2

ibre Optic L

t and is conn

t has a thickn

ut lens and t

ntation of the

cent dyestuff

sition of the

This Plana

cross section

6); in the la

cular channe

Vapour L

rs LS20-10

e for the lase

nm and the

quency of 10

rnal frequenc

es the interna

r. The ability

ion 3-5.

heet Gene

Light Sheet G

nected to the

ness of less

the position

laser sheet a

f to the aque

oil-aqueous

ar Laser Ind

n channel (se

atter case it w

l wall.

Laser

20 W nomin

er-induced flu

e laser has a

0 kHz. Other

cy source an

al clock freq

y is utilised i

rator

Generator pro

e copper vap

than 1 mm

of the mini

and test secti

eous phase it

s phase interf

duced Fluore

ee Chapter 4

was necessar

nal output p

uorescence (

a pulse ener

r Pulse Repe

nd setting the

quency when

in synchronis

oduced by O

pour laser by

and a throw

imum thickn

ion visualisat

C

t is possible

faces in the

escence (PLI

4) and also in

ry to correct

pulsed coppe

(LIF) experim

rgy of appro

etition Freque

e frequency s

n the external

sing the lase

Oxford Laser

y means of a

w distance (th

ness of the l

tion section i

Chapter 3: Exp

to visualise

plane throug

IF) system w

n a round cro

t the images

er vapour las

ments. The o

oximately 2

encies (PRFs

switch to “au

l source is w

er and camera

rs is used to

a fibre optic

he distance

laser sheet)

is illustrated

perimental M

that phase a

gh which the

was used to

oss section ch

for the dist

ser was used

output spectr

mJ/pulse wi

s) can be ach

uto” (see Fig

within the ope

a systems. T

generate the

cable. The

between the

of 155 mm.

in Figure 3-

Methods

and to

e laser

study

hannel

tortion

d as a

rum is

ith an

hieved

ure 3-

erable

This is

e laser

e laser

e main

The

7.

84

3.4

For th

The

synch

Sectio

is illu

3.4.1

The i

1,280

This

exper

Chap

3.4.2

A Ph

laser

sectio

of 1,2

Instru

High S

he LIF exper

specification

hronisation o

on 3.5. The o

ustrated in Fi

Olympu1

i-SPEED 3

0 × 1024 pix

camera syst

rimental stud

pter 5 and Ch

Phantom2

hantom V710

illumination

on visualisati

280 × 800 at

ument Loan P

Speed Ima

rimental cam

ns of these

of the came

orientation o

igure 3-7.

us iSPEED

monochroma

xels at which

tem was use

dies using th

hapter 6.

m V710 M

0 Monochrom

n of the test

ion cell; this

which the fr

Pool.

agers

mpaigns deta

cameras ar

eras with th

of the camera

D 3 System

atic system

the highest

ed to record

he circular c

Monochrom

matic System

t section in

s is presented

rame rate is 7

ailed in this t

re detailed b

e copper va

a relative to t

m

produced by

attainable fr

the laser illu

cross-section

matic Syste

m produced b

the PLIF ex

d in Chapter

7,530 fps. T

C

thesis, two h

below in se

apour laser

the visualisat

y Olympus h

rame rate is 2

umination o

n visualisatio

em

by Vision Re

xperimental

4. The cam

The camera w

Chapter 3: Exp

high speed ca

ections 3.4.1

(Section 3.3

tion section a

has a maxim

2,000 frames

f the test se

on cell; these

esearch was

study using

mera has a ma

was borrowed

perimental M

ameras were

1 and 3.4.2

3) is explain

and the laser

mum resoluti

s per second

ection in the

e are presen

used to reco

the square

aximum reso

d from the EP

Methods

used.

. The

ned in

r sheet

ion of

(fps).

PLIF

nted in

ord the

cross-

olution

PSRC

85

Figur

orien

3.4.3

A Ma

used

evalu

re 3-7: Illus

ntation

Camera3

acro 105mm

in the LIF

uation of its M

stration of th

as Len and

m F2.8 EX D

experimenta

MTF (Modul

he laser shee

d Filter

DG medium

al campaign

lation Transf

et, square cr

telephoto le

ns. The sui

fer Function)

C

ross-section

ens produced

itability of t

) against Ima

Chapter 3: Exp

visualisation

d by Sigma

the lens was

age Height ch

perimental M

n cell and ca

Imaging Ltd

s confirmed

hart, which r

Methods

amera

d was

from

relates

86

the le

of the

f is th

resolu

in a

arran

of the

diame

3.5

As th

came

captu

below

pulse

The

impli

at the

outsid

came

betwe

When

Out”

ens’ ability to

e distance fro

he focal len

ution was 42

shallow dep

ngement to g

e acquired P

eter 50 mm w

Laser-C

he copper va

era system to

ures the laser

w. A trigger

e falls within

importance

ications of no

e same frequ

de the camer

era exposure

een the liquid

n the camera

output to th

o distinguish

om the centre

gth of the c

2 μm per pix

pth of field,

enerate well

PLIF signals

was placed in

Camera S

apour laser d

o ensure the

r-induced flu

r box is used

a single exp

of camera

ot having suc

uency the si

ra exposures

es. Thus, wi

d phases.

a is triggered

he trigger box

h and resolve

e of the imag

camera) to m

xel. Howeve

hence consi

l focused ima

by the lase

n front of the

Synchron

delivers a pu

laser pulses

uorescence e

d to synchron

posure of the

– laser syn

ch synchroni

ignals could

s and a cons

ithout synch

it sends a T

x. The TTL

e fine details

ge. The aper

maximise ima

er, a large ap

iderable care

ages. Finall

r excitation

e lens during

isation

ulsed output

during an e

effect. This

nise the lase

camera.

nchronisation

isation. Eve

be out of p

equent failur

hronisation,

TL (transisto

L output is a

C

between ligh

rture was opt

age sharpnes

perture size a

e was taken

ly, in order t

light, a 525

g the PLIF m

it is necessa

exposure of t

is demonstr

er with the c

n is recogni

en if the laser

phase resulti

re to illumin

one could n

or-transistor

binary electr

Chapter 3: Exp

ht and dark a

timised to se

ss. The resu

and close foc

in configur

to eliminate

nm longpas

measurements

ary to synch

the camera s

rated pictoria

amera such

ised when o

r and camera

ing in the la

nate the targe

not see, let

logic) signal

rical signal w

perimental M

areas as a fun

etting of f/8 (w

ulting spatial

cal distance r

ring the app

the contamin

ss optical fil

s.

hronise it wi

so that the ca

ally in Figur

that a single

one consider

a are set to op

aser pulses f

et field durin

alone distin

l via its “Exp

which has a

Methods

nction

where

pixel

results

aratus

nation

lter of

ith the

amera

re 3-8

e laser

rs the

perate

falling

ng the

nguish

posure

“low”

87

voltag

durat

“high

rate a

with

frequ

set to

ge level and

tion of the e

h” at the start

at which the

the camera s

uency of the l

o until the cam

a “high” vo

exposure, at

t of the next

camera is se

signal albeit

laser from its

mera stops c

Figure 3

oltage level w

the end of w

frame and so

et to. From

it via a freq

s internal clo

apturing ima

3-8: Laser-ca

which becom

which the si

o on. This s

the trigger b

quency reade

ock frequenc

ages.

amera synchr

C

me “high” at

ignal returns

ignal is sent

box the sign

er. The sign

y of 10 kHz

ronisation eq

Chapter 3: Exp

the start of e

to the “low

to the trigge

al is sent to

al reduces th

to the freque

quipment

perimental M

each frame f

w” level, retu

er box at the

the laser in

he pulse repe

ency the cam

Methods

for the

urning

frame

phase

etition

mera is

88

3.6

The

electr

forms

Phosp

chara

those

appro

which

energ

in exc

energ

fluore

relati

to flu

wave

a suit

the q

photo

Fluore

LIF techni

romagnetic r

s of photolu

phorescence

acterised by

e absorbed.

oximately 10

h lasts for ap

gy is emitted

cess of the lo

gy, i.e. there

escent mater

ve effectiven

uoresce and

elengths of el

table fluoresc

quantum yiel

ons emitted t

scence

ique is bas

radiation, wh

uminescence

is character

the rapid em

In fluores

0-15 seconds,

pproximately

as a photon

ower vibratio

e is a Stok

rial has two

ness of differ

secondly, it

lectromagnet

cent dyestuff

ld which de

to the numbe

Φ

sed upon p

hich in turn r

e, fluorescen

rised by the

mission of p

scence, elec

which cause

y 10-4 second

of light. How

on energy is

kes shift. Th

characterist

rent wavelen

ts emission

tic radiation

f; this is disc

enotes the e

er of photons

photolumines

results in the

nce (on whi

delayed emi

hotons of lo

ctromagnetic

es the excitat

ds. When th

wever, when

dissipated a

his process

tic spectra, i

ngths of elect

spectrum wh

emitted. Thi

cussed in Sec

fficiency of

absorbed. T

C

scence, in

e emission of

ich LIF is b

ission of pho

ower energy

radiation

ion of an ele

he electron re

n when the el

and the the em

is illustrated

its absorption

tromagnetic

hich shows

is is an impo

ction 3.8. An

f the fluores

This is given

Chapter 3: Exp

which a su

f photons. Th

based) and

otons where

(i.e. longer

(a photon)

ectron to a hi

elaxes to its

lectron is ex

mitted photo

d in Figure

n spectrum,

radiation to

the relative

ortant factor

nother param

cence, or ra

below:

perimental M

ubstance ab

here are two

phosphoresc

as fluorescen

wavelength)

is absorbe

igher energy

ground state

cited some e

on will be of

3-9. Thus,

which show

cause the ma

intensities o

when establi

meter to consi

ather, the ra

(3.1)

Methods

bsorbs

o main

cence.

nce is

) than

ed in

level,

e, the

energy

lower

each

ws the

aterial

of the

ishing

ider is

atio of

89

3.7

There

multi

main

categ

thesis

the f

dyest

fluore

sensit

per te

where

with

there

are a

Princip

e are a mu

iphase flows

categories,

gory. PLIF i

s because it

flow of two

tuff; when t

escent emiss

tive visualis

en billion, a

eas tracer m

Particle Ima

is a caveat t

multitude o

Figu

ples of La

ultitude of fl

(Hewitt et a

tracer and o

s a spectrosc

can be used

immiscible

the laser she

sion can be c

ation techniq

and has very

ethods that i

age Velocim

to the effecti

of factors tha

ure 3-9: Dia

aser-Induc

flow visualis

al., 1990; Ba

optical meth

copic techniq

to visualise

e liquids. O

eet passes t

captured by

que; it can d

y good speci

involve the in

metry, PIV) c

iveness of LI

at have to be

agram illustra

ced Fluor

sation techn

arbosa et al.,

hods, of whi

que that has

the complex

One fluid, th

through this

the camera.

detect substa

ificity. Furt

njection of a

can result in

IF; to achiev

e accounted f

C

ating Stokes

rescence

niques that c

2001; Liu, 2

ch planar LI

been applied

x interfacial

he aqueous

phase, this

LIF has th

ances in conc

thermore, it

a solid tracer

changes to

e clear distin

for such as t

Chapter 3: Exp

shift

can be adop

2005). Of th

IF (PLIF) fa

d in the work

configuratio

phase conta

dyestuff flu

he advantage

centrations a

is a non-in

r into the flow

the flow pa

nction betwe

the attenuatio

perimental M

pted for stu

hese, there ar

alls into the

k described i

ons which oc

ains a fluore

uoresces and

es of being a

as low as on

ntrusive techn

w (such as is

atterns. How

een the fluids

on mechanis

Methods

udying

re two

latter

in this

ccur in

escent

d this

a very

ne part

nique,

s used

wever,

s there

sms of

90

light,

be m

select

3.8

When

mean

mech

refrac

witho

walls

transp

from

absor

distan

imper

3.8.1

For th

was o

respe

which large

mitigated thro

tion of the fl

Fluid S

n a parallel b

ns, namely: a

hanisms, whi

ctive indices

out distortion

s of the cont

parent to bot

the fluoresc

rbing photon

nce along th

rative; the fu

Selection1

he experime

of prime im

ectively.

ely pertain to

ough careful

luids and dye

Selection &

beam of ligh

absorption, d

ich can colle

s of the two

ns arising fro

taining duct

th the activat

cence proces

ns from the ac

he laser shee

ull extent of t

n Criteria

ents describe

mportance. T

o the liquids

l selection o

estuffs is disc

& Refrac

ht strikes a di

diffraction, re

ectively be t

liquid phase

om changes

t. To preve

ting light (th

ss). Howeve

ctivating lase

et. Thus op

the fluid sele

a

d here, prop

he criteria a

used. The ef

of the test f

cussed in Sec

ctive Index

ispersed syst

efraction and

termed scatte

es. This allo

in refractiv

nt attenuatio

he laser sheet

er, the LIF p

er sheet so in

tical transpa

ection criteria

per selection

applying are

C

ffects of suc

fluids and th

ction 3.8.

x Matchin

tem its inten

d reflection.

ering, can b

ws the plane

e index in th

on via absor

t) and the gen

process hinge

ntensity of th

arency and m

a is discussed

of the test f

listed below

Chapter 3: Exp

h attenuation

he fluoresce

ng

nsity can be a

Attenuation

e eliminated

e of illumina

he flow field

rption the te

nerated light

es on the flu

he fluorescen

matched refr

d in Section

fluids and flu

w for the fl

perimental M

n mechanism

nt dyestuff.

attenuated by

n via the last

d by matchin

ation to be v

d and throug

est fluids mu

t (the light em

uorescent dy

nce decrease

ractive indice

3.8.1.

uorescent dy

luids and dy

Methods

ms can

The

y four

t three

ng the

viewed

gh the

ust be

mitted

yestuff

s with

es are

yestuff

yestuff

91

Chapter 3: Experimental Methods

92

1 SelectionCriteriafortheTestFluids

A Transparent (colourless or pale) liquids.

B Matched Refractive Indices

C One phase (the organic phase) to be able to dissolve the fluorescent dyestuff (Eosin Y).

D Suitable physical properties - importance of density and viscosity with regards to

pumping.

A Transparent (colourless or pale) liquids.

B Matched Refractive Indices

C One phase (the organic phase) to be able to dissolve the fluorescent dyestuff (Eosin Y).

D Suitable physical properties - importance of density and viscosity with regards to

pumping.

E Low toxicity

F Low flammability

G Low corrosiveness

H Economic considerations require the fluid to be of low cost

2 SelectionCriteriafortheFluorescentDyestuff

A Soluble in either the oil phase (Exxsol 080) or the aqueous solution (water-glycerol

solution).

B The absorption spectrum of the dye should be between wavelengths 500-520nm and

the emission spectrum should be in the range of visible light.

C The interfacial surface behaviour is not changed by the addition of the dye.

D The disturbances to the flow due to localised heating due to the LIF process should be

minimal.

E The dye should have a minimal effect on the refractive index of the test fluids.

F Stable i.e., does not form a precipitation.

3.8.2

Eosin

camp

criter

select

at the

extinc

wave

Eosin

Figur

Copp

Fluoresc2

n Y (C20H8B

paigns includ

ria, see Sect

tion was bas

e laser output

ction coeffic

elength. The

n Y has a qua

re 3-10: Com

per Vapour L

cent Dyest

Br4O5) has be

ded in this th

ion 3.8.1. T

sed, the absor

t spectrum p

cient is a me

concentratio

antum yield,

mparison of t

Laser

tuff Select

een selected

hesis after e

The suitabilit

rption spectr

peak wavelen

asure of how

on of the dye

Ф, of 0.67.

the excitation

ion

d as the fluor

evaluating its

ty of Eosin Y

rum of the dy

ngth (510.6nm

w strongly lig

estuff used is

n spectrum o

C

rescent dyes

s performanc

Y against th

yestuff havin

m), is illustra

ght is absorb

s discussed in

of Eosin Y w

Chapter 3: Exp

stuff for the

ce against th

he main crit

ng a high exc

ated in Figur

bed by a sub

n Section 3.8

with the outpu

perimental M

LIF experim

he aforement

erion upon w

citation coeff

re 3-11. The

bstance for a

8.4. Additio

ut spectrum

Methods

mental

tioned

which

ficient

molar

given

onally,

of the

93

3.8.3

The m

prelim

comp

are a

(1.33

range

mixtu

a refr

refrac

poten

comp

water

prelim

this r

An A

refrac

brom

moun

prese

No li

be to

noted

Test Flu3

methodology

minarily sele

position. The

a large selec

3) and glyce

e 1.333 to 1

ure. The crite

ractive index

ctive index

ntial fluids th

positions wer

r-glycerol so

minarily iden

ange.

Abbe 60 Ref

ctive indices

monaphthalen

nted in a te

ented in Figu

terature coul

each other t

d that Liu (2

uid Selectio

y used to es

ecting a wat

e basis for th

ction of oils

erol (1.473).

.473, with th

eria for this s

x between tha

and physica

he refractive

re measured

olutions publ

ntified for in

fractometer m

s of the liqu

ne, 98% (C1

emperature-c

ure 3-11(a).

ld be found t

o ensure LIF

2005) had m

on Method

stablish a ref

ter - glycero

his is that gly

with refrac

A mixture o

he value dep

selection of t

at of water a

al properties

indices of E

at different

lished by Do

nvestigation

manufactured

uid samples,

10H7Br) used

ontrolled w

that detailed

F images of s

matched the

dology

fractive inde

ol solution a

ycerol is sol

ctive indices

of water and g

pending on t

the oil centre

and glycerol.

requirement

Exxsol D80

temperature

ow Chemica

and the refr

d by Belling

with Bellin

d to calibra

ater bath. T

how closely

sufficiently h

refractive in

C

ex matched p

as one phase

luble in wate

between th

glycerol will

the proportio

ed on the phy

Exxsol D80

ts. Followin

and water -

es. Consideri

als, the rang

ractometer m

gham & Stan

ngham & Sta

ate the equip

These refract

y the refractiv

high clarity a

ndices to thr

Chapter 3: Exp

pair of test

e, but witho

er in all prop

he refractive

l have a refra

ons of each

ysical proper

0 was found

ng the ident

glycerol solu

ing refractive

e 75 to 85 w

measurement

nley was use

anley Part N

pment and

tive index m

ve indices of

are produced

ree decimal

perimental M

fluids began

out specifyin

portions and

indices of

active index

component o

rties and that

to satisfy bo

tification of

utions of dif

e index valu

wt% glycero

s were focus

ed to measu

No. 10-43, i

the test cel

measurement

f the fluids n

. However,

places in he

Methods

n with

ng the

d there

water

in the

of the

t it has

oth the

these

fferent

ues for

ol was

sed in

ure the

.e., 1-

l was

ts are

eed to

it was

er LIF

94


95

experiments. This was taken a preliminary guide to how closely matched the refractive indices

needed to be. Prior to loading the matched fluids into the TOWER facility offline LIF tests

were performed to establish whether the fluids identified were sufficiently well matched to

produce images of an acceptable clarity.

(a) (b)

Figure 3-11: Refractive indices of (a) Exxsol D80 and water-glycerol solutions as a function of

a temperature and composition and (b) Exxsol D80 and water-glycerol-dye (0.2mL/L of

Eosin Y) at 20°C

Once a narrower band of glycerol-water solutions had been identified (79 to 81wt%), the

refractive indices of water-glycerol solutions with Eosin Y were measured to establish the effect

of adding the dyestuff and a composition that matched with the refractive index of Exxsol D80.

These results are shown in Figure 3-11(b) above. From Figure 3-11(b) it can be seen that the

refractive index of Exxsol D80 matches that of a 81.5 wt.% glycerol solution with 0.2 ml per

litre of a 5 wt.% solution of Eosin Y.

74 76 78 80 82 84 861.425

1.43

1.435

1.44

1.445

1.45

1.455

Glycerol wt%

Ref

ract

ive

Inde

x, n

T=20C

T=25C

T=30C

81 81.2 81.4 81.6 81.8 82 82.21.441

1.442

1.443

1.444

1.445

1.446

1.447

Glycerol wt%

Ref

ract

ive

Inde

x, n

oilgs

Matched

refractive

gs oil

3.8.4

Initia

This

Howe

betwe

dyest

prepa

The P

high

grey)

pixel

respe

was m

match

soluti

water

signif

Altho

glyce

Eosin

an es

Follo

estab

Fluoresc4

ally, 0.2 ml o

concentratio

ever, it was

een the phas

tuff. Water-g

ared and offl

Phantom V7

speed camer

) to be record

s correspond

ectively. The

monitored to

hed. It was

ion was the

r-dye mixtur

ficant figures

ough the sele

erol solution

n Y starts to

sential requi

owing the in

lish the temp

cent Dye C

of a 5 wt% s

on was adop

found that t

ses. An inves

glycerol solu

line tests we

710 camera s

ra, which me

ded. The ima

ding to the

e effect of in

o ensure tha

found that 0

optimum co

re was 1.7 ×

s.

ected concen

become satu

colour the a

rement for b

nstallation o

perature of th

Concentra

solution of E

pted as a st

this did not

stigation was

utions (81.5

ere conducte

system used

eans it allow

ages obtaine

water-glyce

ncreasing the

at the refract

0.4 ml of a 5

oncentration.

× 10-5 and t

ntration is w

urated with li

aqueous phas

being able to

f the therm

he fluids in t

ation Optim

Eosin Y per

tarting point

provide an

s conducted

wt%) with

d to analyse

d in this prel

ws 256 differ

d were analy

erol-Eosin Y

e Eosin Y co

tive indices o

5% wt. Solut

. The result

the correspo

well below th

ight, if the co

se resulting i

visualise the

mocouple det

the rig durin

C

misation

litre of wate

t as it was t

adequate lev

to establish

differing con

e the image c

liminary stud

rent intensitie

ysed by mea

Y solution a

oncentration

of the test f

tion of Eosin

ting mass fra

onding mola

he level at w

oncentration

in it no long

e plane at wh

tailed in Sec

ng operation.

Chapter 3: Exp

er-glycerol s

the one use

vel of bright

the optimum

ncentrations

clarity that r

dy is an 8-b

es of light (i

asuring the in

and the Exx

in the water

fluids remain

n Y per litre

action of dy

ar fraction is

which the pix

is higher the

ger being opt

hich the dyes

ction 3.2.1.9

This inform

perimental M

solution was

ed by Liu (2

tness and co

m concentrat

of Eosin Y

results from

bit monochro

i.e., 256 shad

ntensity of li

xsol D80 re

r-glycerol so

n sufficiently

of water-gly

ye in the gly

s 1.4 × 10-5

xels for the w

e opaque nat

tically transp

stuff is activa

9, it was us

mation was u

Methods

used.

2005).

ontrast

ion of

Y were

them.

omatic

des of

ight in

egions

olution

y well

ycerol

ycerol-

, to 2

water-

ture of

parent;

ated.

sed to

sed to

96

estab

tempe

It wa

by ov

shoul

in the

tempe

3.9

A co

Firstl

below

Anton

a Min

Figur

differ

1.18

1.

1.19

1

1.20

1.2

1.2

1.2

1.22

1.2

Den

sity

, (

g.cm

-3)

lish whethe

erature.

as found that

ver 20°C. Th

ld avoid prol

e refractive

erature on vi

Physica

omprehensive

ly, the tempe

w. The den

n Paar. For

nichiller prod

re 3-12: Den

rent concentr

10 2085

19

95

1.2

05

21

15

22

25

23

er the fluids

t the continu

he rate of tem

longed opera

indices and

iscosity and d

al Proper

e analysis o

erature depen

nsities were

both the den

duced by Bu

(a)

nsity as a fun

rations of Eo

30

Temperature, T

s still have

ed operation

mperature in

ation of the p

physical pr

density of th

rties of the

of the physic

ndence of the

measured u

nsity and visc

uber.

nction of tem

osin Y and (b

40 50

T (C)

0.0 0.1 0.2 0.4 0.8 1.6

e a close r

n of the pum

ncrease is sig

pumps to pre

roperties (i.e

he test fluids

e Test Flu

cal propertie

e densities of

using a DMA

cosity measu

mperature for

b) Exxsol D8

60

mL/LmL/LmL/LmL/LmL/LmL/L

10.77

0.78

0.79

0.8

0.81

0.82

0.83

Den

sity

, (

g.cm

-3)

C

efractive in

mps can resul

gnificantly hi

event the flui

e., viscosity)

is presented

uids

es of the tes

f the test flui

A 5000M d

urements tem

r (a) 81.7wt%

80 oil

10 207

8

9

8

2

Chapter 3: Exp

dex match

ts in the test

igher at high

ids heating a

of the fluid

in Section 3

st fluids has

ids is presen

densitometer

mperature wa

(b)

% water-glyc

30 4

Temperature, T (

perimental M

at the ope

t fluids heati

her flowrates.

and hence ch

ds. The eff

.9.

s been perfo

nted in Figure

manufactur

as controlled

cerol solution

0 50

(C)

Methods

erating

ing up

. One

hanges

fect of

ormed.

e 3-12

ed by

using

n with

60

97


98

From Figure 3-12(a) it is seen that the concentration of Eosin Y has little effect on the density of

the glycerol solution. Attention has been drawn to the densities at 15°C and 35°C because these

temperatures were found to be the upper and lower limits encountered during operation of the

TOWER facility. Hence, these are the upper and lower density limits of the test fluids

encountered during experimental operation. An 81.7wt% glycerol-solution with 0.4mL/L of

Eosin Y has a density of 1204.1 kg.m to 1216.4kg.m , whereas that of Exxsol D80 is

792.1 kg.m to 806 kg.m across this temperature range.

It should be noted that the samples used to construct Figures 3-12(a) and 3-13(a) have a glycerol

weight percentage of 81.7wt% opposed to 81.5wt% as identified in Figure 3-11(b). This is

because upon completion of loading the glycerol-solution into the storage tank (see Section

3.2.1.4) – due to the batch nature of the loading process – was 81.7wt%. Upon measuring the

refractive index of this glycerol-solution it was found to still be matched (to three decimal

places) to Exxsol D80 so was not altered.

Viscosity values were measured using a Physica MCR301 viscometer produced by Anton Paar.

The temperature dependence of the viscosities of the test fluids are presented graphically in

Figure 3-13 below. The values at 15°C and 35°C have been highlighted for the aforementioned

reason.


99

(a) (b)

Figure 3-13: Viscosity as a function of temperature for (a) 81.7wt% water-glycerol solution

with different concentrations of Eosin Y and (b) Exxsol D80 oil

An 81.7wt% glycerol-solution with 0.4mL/L of Eosin Y has a viscosity of 109.8 mPa. s at

15°C, which reduces to 40.8 mPa. s at 35°C; a range of almost 70 mPa. s. Whereas, Exxsol

D80 has a viscosity from 2.1 mPa. s to 1.4 mPa. s across this temperature range, which,

although much more stable than the glycerol-solution, still represents a reduction of over 30%.

Hence, the importance of temperature monitoring (and ideally, regulation) during experimental

runs is evident.

Figure 3-14 demonstrates that shear stress versus strain rate graph is linear and passes through

the origin, where the constant of proportionality is viscosity, i.e., the tests fluids obey

Newtonian fluid behaviour as defined in Equation 3.1 below.

. . (3.1)

0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200

Temperature, T (C)

Vis

cosi

ty,

(m

Pa.

s)

0.0 mL/L0.1 mL/L0.2 mL/L0.4 mL/L0.8 mL/L1.6 mL/L

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

3

3.5

4

Vis

cosi

ty,

(m

Pa.

s)

Temperature, T (C)


100

(a) (b)

Figure 3-14: Shear stress, τ, against strain rate, γ, for (a) 81.7wt% water-glycerol solution with

0.4 mL/L of Eosin Y and (b) Exxsol D80 oil

Furthermore, direct measurements were made of the interfacial tension between the glycerol

solution and oil phases at varying concentrations of Eosin Y dye in the glycerol solution phase.

This was done in order to ascertain whether, and if so to what degree, the addition of the Eosin

Y dye (whose addition was necessary for the fluorescence measurements) affected this

important property of the two-phase system. A significant modification of the interfacial

tension could lead to altered observations of interfacial phenomena and, consequently, for the

system to be non-representative of normal liquid-liquid flows. Figure 3-15 shows the results

from these measurements. The abscissa shows the concentration of Eosin Y in mL of 5% wt.

aqueous solution per litre of glycerol solution. Error bars signify the total relative experimental

uncertainty in the measurements at a 95% confidence level (2 standard deviations), which was

estimated by showing that the repeatability of the measurements was ±4%. The result implies

that, within our ability to measure interfacial tension to this stated accuracy and certainly within

the variability in this fluid property over a range of water-oil combinations (typically oil-water

interfacial tension is from 10 to 50 mN.m-1, with most values around 17 – 30 mN.m-1), the

interfacial tension is not altered significantly from its value at zero dye concentration, giving

0 50 100 150 200 2500

5

10

15

20

25

30

35

40

Strain Rate, (s-1)

She

ar S

tres

s,

(P

a)

10C

15C

20C

25C

30C

35C

40C

45C

50C

55C

60C

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

Strain Rate, (s-1)

She

ar S

tres

s,

(P

a)

10C

15C

20C

25C

30C

35C

40C

45C

50C

55C

60C


101

confidence that the results shown here are representative of a liquid-liquid flow in the absence

of the fluorescent dyestuff.

Figure 3-15: Variation in glycerol solution-oil interfacial tension as a function of Eosin Y

concentration

The properties of the fluids are summarised in Table 3-1 below:

Table 3-1: Physical properties of the selected test fluids at 20°C

Oil Phase Aqueous Phase Composition Exxsol D80 81.7wt% w/ 0.4 mL/L Eosin YDensity ( . ) 802.7 1213.3Viscosity ( . ) 1.9 82.3Refractive Index 1.444 1.444

It is interesting to compare the physical properties of the fluids used in the present tests to those

employed in previous liquid-liquid flow studies. The oil has identical physical properties to

those of the oils used by Soleimani (1999), Hussain (2004) and Liu (2005) and has similar

property values to those of the oils used by Angeli (1996) and Angeli and Hewitt (2000). The

density ratio of the test fluids (glycerol solution to oil) is 1.5 and is comparable to the density

ratio (1 to 1.5) applicable in many previous studies (Russell et al., 1959; Charles and Lilleleht,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

Inte

rfac

ial T

ensi

on,

(mN

/m)

Eosin Y Concentration, C (mL/L)


102

1966; Simmons and Azzopardi, 2001; Ioannou et al., 2005). In the present work, the fluids have

a viscosity ratio (glycerol solution to oil) of approximately 20. Though this viscosity ratio is

comparable to that in some of the earlier work (Charles and Lilleleht, 1966 and Guzhov et al.,

1973) it should be noted that, in contrast to the earlier work (where the oil is the less dense and

more viscous fluid), in the current study the oil is the less dense and also the less viscous fluid.

This interesting difference to the previous studies needs to be recognised clearly in considering

the present results.

It is emphasised at this point that the two liquids under investigation are immiscible and that

there is no diffusion of one phase into the other. As such, the purpose here is not the recovery of

instantaneous concentration information that would be necessary in diffusive flows (as done

elsewhere, for example, by Markides and Mastorakos (2006)). Indeed, in the flows presented in

Chapters 4, 5 and 6 the normalised concentration of the two phases is at all times either locally

zero or unity. Instead, the key measurement of interest relates to the correct identification of the

interface between the two phases, where this exists in the flow. Towards this end, the PLIF

measurement methodology employed is purely concerned with the presence or absence of

fluorescent dye, which (given that the dye is only soluble in the glycerol/water phase and

insoluble in oil) signifies the local, unique presence of glycerol solution. This is dissimilar to

PLIF-based concentration measurements (e.g., those by Markides and Mastorakos, 2006), where

the local concentration of dye and light intensity are crucial in recovering concentration

information from the emitted fluorescent light. As long as adequate laser light is present in the

entire measurement plane our ability to determine the presence of dye does not depend on a

uniform light illumination, or if this is not possible, on corrections for light intensity variations.

Details of the procedure used to determine the local on/off presence of glycerol solution are

given below in Section 3.11.

3.10

Two

thesis

cross

3.10

Adop

wall

perpe

Snell

Fig

Thus

can b

to tra

Visuali0

designs of v

s, namely a

section visu

Square.1

pting a squar

material wit

endicular to

’s law and F

gure 3-16: D

, when a ligh

be seen that t

avel along the

isation Se

visualisation

square cross

ualisation sec

e Cross Se

e cross sectio

th that of th

its surface, i

igure 3-16.

Diagram illus

ht sheet trave

the light doe

e normal.

ection Des

section hav

s section vis

ction (see Sec

ction Visu

on cell elimi

he test fluids

i.e. the laser

strating the re

els along the

s not get refr

sign

e been empl

sualisation se

ction 3.10.2)

ualisation S

inates the nec

s, provided

r light travel

efraction of l

normal (i.e.

fracted, .i.e. a

C

loyed in the

ection (see S

).

Section

cessity to ma

the laser sh

s along the

light at the in

θi = 0°) from

angle θr = 0°,

Chapter 3: Exp

experiments

Section 3.10

atch the refra

heet strikes t

normal. Th

nterface betw

m Snell’s law

, thus the lig

perimental M

s described i

0.1) and a ci

active index

the square se

is is explain

ween two me

w (Equation

ght sheet con

Methods

in this

ircular

of the

ection

ned by

edia

3.2) it

ntinues

103


104

sinsin

(3.2)

A square cross section duct was used in the vertical flow LIF experiments of Liu (2005) and the

use of a similar duct was a natural starting point in the current horizontal flow studies. The use

of a square cross section duct does, of course, compromise the geometric similarity of the duct

with subsea pipelines. However, as a means to mitigate the hydrodynamic disparity,

visualisation is focused in the centre line of the cell. An important consideration that needs to

be factored into the design of the visualisation cell is the optical clarity of the build material.

Selection of the wall material was based on analysis of the transmittance spectra of potential

materials. On this basis a square cross section quartz cuvette with the ends cut off was selected.

The quartz cell has the following dimensions; 18 mm internal length sides, 2 mm wall thickness

and 48 mm long. The quartz cell is housed in a brass casing which has windows cut out of it to

allow one to view the quartz cell (see Figure 3-17). In these experiments, the aqueous glycerol

solution and the Exxsol-D80 were introduced into the normal inlet zone of the 25.4 mm

diameter circular stainless steel horizontal test line with the Exxsol-D80 being fed in at the top

of the tube. The mixture then flowed for 6.20 m along the circular test line before reaching a

circular-to-square smooth transition piece. Following this transition piece, the fluid flowed

through a 360 mm long, 18x18 mm square cross section brass duct before reaching the quartz

cell (of the same cross section) where the LIF measurements were made. Following the quartz

cell, the mixture passed through a further 200 mm length of square cross section duct before

reaching a square-to-circular transition piece and passing into the normal outlet line for

transmission to the separator. The orientation of the square visualisation section relative to the

laser sheet and the camera is shown in Figure 3-7. The square geometry reduces laser light

intensity non-uniformity in the measurement plane and image distortion due to the effects of

reflection, refraction and absorption.

3.10

Thou

intere

indus

walls

index

made

plana

a trip

mater

the ad

both

with

was b

close

Furth

had a

Anoth

Round.2

ugh, as will

esting, it is o

strial pipelin

s of the flow

x identical to

e from this m

ar outer walls

ply refractive

rial have the

dded constra

the laser lig

the test fluid

borosilicate

enough mat

hermore, it w

a refractive i

her material

Figure 3

d Cross Sec

be seen, the

obvious that

e systems. T

tube. If a so

the (matche

material with

s to minimis

e index match

e same refrac

aint of establ

ght and the f

ds. It was f

glass; howe

tch to that o

was not found

index close

l considered

3-17: Square

ction Visu

e results obt

a duct of c

The problem

olid transpare

ed) refractive

h the cell hav

se image dist

hed system,

ctive indices.

lishing a wal

fluorescence

found that th

ver, the refr

of the fluids

d possible to

enough to th

d was ECTF

cross section

alisation S

tained with

ircular cross

is that of im

ent material

e indices of th

ving a circul

tortion. Cons

i.e. one in w

. However,

ll material of

e light, suffic

he material m

ractive index

used in the

find another

hat of borosi

FE (Ethylen

C

n visualisatio

Section

the square

s section wo

mage distorti

could be ide

he fluids, the

lar hole at it

siderable effo

which both te

this task is p

f suitable cha

cient strengt

most closely

x of this ma

square cross

r refractive in

ilicate glass

ne Chlorotri

Chapter 3: Exp

on section

cross sectio

uld be more

ion by the (n

entified whic

en an observa

ts centre to c

fort was plac

est fluids and

particularly c

aracteristics

th and rigidi

y matching th

aterial is 1.47

s section duc

ndex matche

to allow use

fluorotheyle

perimental M

n duct were

e representat

normally cir

ch had a refr

ation cell cou

carry the flow

ed on establi

d the pipeline

challenging d

i.e., transpar

ity and unre

hese require

74 which is

ct studies (1

ed fluid pair w

e of this ma

ne) but this

Methods

e very

ive of

rcular)

ractive

uld be

w and

ishing

e wall

due to

rent to

active

ments

not a

.444).

which

aterial.

s was

105


106

dismissed due its milky translucent appearance meaning it is not sufficiently transparent to the

laser and fluorescence light. Though it is still possible that a suitable triply matched refractive

index system could ultimately be found, efforts to do so in the present study were abandoned

and an alternative approach to using LIF in circular tube geometries was pursued.

The alternative approach to using LIF in circular tubes was to accept that the images initially

produced would be distorted due to lack of refractive index matching between the fluids and the

flow tube walls and to correct for this distortion using an image processing technique. Basically,

a short length of circular cross section transparent tube was inserted concentrically into the main

(circular) test section. As a precursor to the experiments, a graticule was mounted in the short

transparent tube such that its surface was in the same position as that traversed by the planar

laser sheet. Points on the graticule were in a known position and these could be related to their

apparent position in the (distorted) image. This allowed the image to be corrected for the

distortion effect.

The circular cross-section visualisation cell design adopted is shown in Figure 3-18 and

comprises of an LS 100 mm long (or, 3.6 equivalent diameters, LS/HT = 3.6) length of

borosilicate glass pipe with an internal diameter of HT = 27.6 mm housed in a Perspex box. The

void between the pipe section and the internal walls of the box are filled with the test fluid that

is not seeded with fluorescent dye (i.e., Exxsol D80). The cell is located LE = 6.20 m

downstream of the inlet of the 25.4 mm diameter test section pipe (such that LE/D = 244) which

was used to set up the flows. The borosilicate glass tube had a slightly larger diameter than the

test section pipe but the effect of this is expected to be small. As was stated above, the

difference in refractive index between the wall material and the fluids causes a distortion of the

image; this distortion was minimised by the choice of wall material and the use of a planar

fluid-

3.11.

3.11

This

both

result

cross

circul

result

under

visua

-filled box o

1.

Image 1

section outl

the square a

ts of this ana

sectional te

lar cross-sec

ts-generating

rwent a corr

alisation cell.

outside the tu

Figure 3-

Processin

ines the pro

and circular

alysis are pre

st pieces, res

ction visuali

g processes

rection proce

This correc

ube, Details

-18: Circular

ng Method

ocessing that

cross sectio

esented in Ch

spectively. H

isation cell (

(detailed in

ess to correc

ction process

of the imag

r cross sectio

dology an

is performe

n visualisati

hapters 4 and

However, for

(see Section

n Sections 3

ct for the di

s is described

C

ge correction

on visualisati

nd Results

ed on the raw

ion section e

d Chapters 5

r the PLIF st

n 3.10.2), pr

3.11.2 to 3.

stortion arisi

d in Section 3

Chapter 3: Exp

n method are

on section

s Generat

w generated

experimental

5 & 6 for the

tudies involv

rior to perfo

11.7), the r

ing from the

3.11.1 below

perimental M

e given in Se

tion

d PLIF imag

l campaigns.

e square and

ving the use

rming any o

raw PLIF im

e curvature o

w.

Methods

ection

es for

. The

round

of the

of the

mages

of the

107

3.11

The g

cross

so tha

which

7. It

used

the g

detac

Once

and s

displa

3-20(

Thus

gratic

20(a)

produ

instan

techn

image

liquid

in Fi

neces

the ch

a pla

Graticu.1

graticule cal

es of known

at it aligns w

h the laser li

should be no

to illuminate

graticule cali

ching the do

e the graticul

spacing of th

acement and

(a) shows a

, one can d

cule to restor

) after it has

uced by La

ntaneous ima

nique underg

es can be ap

d – liquid flo

igure 3-20(c

ssary one, it

hoice of the

anar walled

ule Correc

libration pie

n size and sp

with the centr

ight sheet pe

oted that dur

e the visuali

ibration piec

ownstream c

le had been

he crosses on

d distortion o

raw image

etermine the

re the crosse

undergone c

aVision. T

ages. Since

go the same

pplied to the

ow image an

c) after the

should be no

wall materia

cell filled w

ction Tech

ece (see Figu

acing are pri

ral vertical p

netrates the

ring the calib

sation cell.

ce was insert

onnection b

inserted, the

n the graticu

of them when

of the grati

e manipulati

es to their ac

correction. T

The resulting

e the images

distortion t

flow images

nd Figure 3-2

manipulation

oted that the

al in the visu

with Exxsol-

hnique

ure 3-19) co

inted. Durin

plane of the v

visualisation

bration no la

Prior to, and

ted into the

etween the

e test section

ule are know

n it is viewe

icule when v

ion that nee

ctual size and

This operatio

g correction

of the liqui

the same ma

s to remove t

20(d) shows

n has been

e distortion i

ualisation sec

-D80 to sur

C

ontains a fla

ng the calibr

visualisation

n cell during

aser light was

d after each

visualisation

visualisation

n was filled w

wn, one can u

d through th

viewed thro

ds to be pe

d spacing, Fi

on is perform

n was based

id – liquid fl

anipulation a

the distortion

the correcte

undertaken.

s small in th

ction (i.e. bor

rround the v

Chapter 3: Exp

at planar sur

ation this su

n cell; i.e. the

PLIF operat

s used; only

set of PLIF

n section. T

n cell and th

with Exxsol

use the valu

he visualisati

ugh the visu

rformed on

igure 3-20(b

med using th

d upon the

flows obtaine

as that used

n. Figure 3-2

d image corr

. Though th

he case illust

rosilicate gla

visualisation

perimental M

rface on to w

urface is orien

e same plane

tion, see Fig

ambient ligh

experimenta

This was do

he main pip

D80. As th

ues to measu

on section, F

ualisation se

the image o

b) shows Figu

he DaVis sof

average of

ed using the

d for the gra

20(c) shows

responding t

he correction

trated; this re

ass) and the u

section. A

Methods

which

ntated

e as to

ure 3-

ht was

al runs

one by

peline.

he size

ure the

Figure

ection.

of the

ure 3-

ftware

f 500

PLIF

aticule

a raw

to that

n is a

eflects

use of

As the

108


109

correction is only applicable to liquid – liquid flow images if the cell has not moved,

considerable care was taken to immobilise the test section and adjoining visualisation section.

A permissibility limit of 1 pixel was imposed on the movement of the visualisation cell when

compared with the calibration images.

Figure 3-19: Graticule calibration piece

(a) (b)

(c) (d)

Figure 3-20: Demonstration of the graticule image correction technique.

3.11

The

in Se

black

inform

is pre

regio

In the

interf

soluti

inten

may

depth

in Fig

soluti

sheet

distin

zones

attenu

signif

succe

seen

Binaris.2

phase distrib

ections 4.4, 5

k and white

mation of the

esented in F

ns represent

e image sho

face. Below

ion region t

sity of the f

be conclude

h are due to a

gure 3-21(a)

ion and this

t within glyc

nguish betwe

s. However,

uation is low

fies the com

essful binaris

clearly at the

sation and

bution (speci

5.4 and 6.4,

e equivalents

e resulting im

Figure 3-21 i

the glycerol

own in Figur

these dropl

that appears

fluorescence

ed, therefore

absorption of

give a local

gives rise t

erol solution

een the (non

as long as th

w enough to

mplete absen

sation of the

e top of the im

d Phase Di

ifically, verti

has been pe

s by using

mage using M

in which the

l solution pha

re 3-21(a), tw

lets, we not

at the botto

decreases w

e, that both t

f the inciden

l increase in

to the shadow

n layer was e

n-fluorescing

he spatial dec

ensure that t

nce of dye

signal can b

mage, indica

stribution

ical profile) a

rformed by

a threshold

MATLAB.

e black regio

ase (which c

wo droplets

te two ‘shad

om of the c

with distance

the “shadow

nt laser light s

the penetrati

wing effect.

excessive the

g) oil zones

cay of the flu

the signal re

and therefo

be achieved.

ating unambi

C

n Profile

analysis, the

converting t

ding approac

An example

ons represen

ontains the f

of glycerol

dow’ region

channel. It s

e down into

wing” effect

sheet in the g

ion depth of

Obviously,

en it may ha

s and the (f

uorescent sig

emains high r

ore the pres

The dark s

iguously that

Chapter 3: Exp

results of wh

the flow ima

ch and proc

of the thresh

nt the oil pha

fluorescent d

solution in o

ns in the co

should be no

the glycerol

and the fall

glycerol solu

f the laser sh

if the absor

ave become d

fluorescing)

gnal into the

relative to th

sence of the

ignal in Figu

t only oil is p

perimental M

hich are pres

ages into bin

cessing the

holding proc

ase and the

dye).

oil are seen

ontinuous gly

oted also th

l solution lay

l in intensity

ution. The dr

eet in the gly

rption of the

difficult to a

glycerol so

e image due t

he dark signa

e oil phase,

ure 3-21(a) c

present.

Methods

sented

narised

pixel

cedure

white

at the

ycerol

at the

yer. It

y with

roplets

ycerol

e laser

always

olution

to this

al that

, then

can be

110


111

The post-processing procedure involved, firstly, the identification of a typical decay profile into

the fluorescent glycerol solution phase, which was found to be well approximated by a first

order decay. A normalised correction profile was then defined as the inverse of this decay.

Each vertical instantaneous image was then corrected by multiplying all vertical (y-direction)

intensity profiles, i.e., at each horizontal position x, by the correction profile. This was done

from the location of the interface into the regions of presence of fluorescent signal, based on the

intensity value at the interface location.

In a second stage, following this correction, the image was binarised by applying an adaptive

threshold that was selected to be at the 5% rise height between the minimum (dark) single in the

image and maximum (bright) signal, corresponding to the pure oil and pure glycerol solution

phases respectively. Figure 3-21(b) demonstrates the ability of the correction and thresholding

procedures to eliminate the attenuation of the incident light and then to convert this image into

black and white, corresponding to the instantaneous presence of pure oil and pure glycerol

solution respectively. The threshold value was chosen as a compromise between smaller values

that were more sensitive in identifying the exact location of the interface and larger values

which were more robust to noise.

Figure 3-22 demonstrates the effect of varying levels of thresholding. Here, the thresholding

parameter α is the rise height from the dark background, as a % relative to the image maximum.

Specifically, Figure 3-22(a) shows the effect of α on the identification of the interface shown in

Figure 3-21, while Figure 3-22(b) shows the effect of α on the calculation of the instantaneous

image-averaged in-situ phase fraction ⟨φ⟩y(t) from the image in Figure 3-21 (this variable is

defined below, in Equation 3-3). The resulting relative uncertainty that is introduced by the

choice of the threshold value α in the result for the interface locations and consequently the

instantaneous vertical phase fraction profiles, as in Figure 3-21(c), has been estimated from


112

measurements to be about ±10% at a 95% confidence level, with a corresponding (systematic)

uncertainty in the result for the instantaneous phase fraction of ±4%.

Figure 3-21(c) shows an example (from Figure 3-21(b)) of instantaneous phase fraction

(horizontal axis) φ y,t ≡φ y i against the height inside the visualisation cell y for the processed

image, zero being the bottom of the channel/cell (vertical axis). The vertical phase profiles φ(y)

reported in Chapters 4, 5 and 6 refer to aggregated (i.e., time-averaged) phase profiles over a

number of instantaneous profiles n (such as that in Figure 3-21(c)) for a given flow condition:

1 (3.3)

At least 1,000 frames were used to evaluate the time-averaged vertical profile of (oil) phase

fraction from Equation 3.3 for each condition. As with all other flow parameters calculated

from the raw images, the number of pixels was converted to a length by using the known

dimensions of the height of visualisation cell. The relative experimental uncertainty in the

estimation of the time-averaged profiles amounts to less than ±1% at a 95% confidence level.

(a) Raw PLIF image (b) Binarised image, from (a) (c) Instantaneous vertical phase

fraction profile, from (b)

Figure 3-21: Diagram to show MATLAB image processing technique to generate phase

distribution data

Visualisation Section Width (mm)

Vis

ua

lisa

tion

Se

ctio

n H

eig

ht (

mm

)

5.0 10.0 15.0 20.0 25.0 30.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

Visualisation Section Width (mm)

Vis

ualis

atio

n S

ect

ion H

eight

(m

m)

5.0 10.0 15.0 20.0 25.0 30.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

0 0.2 0.4 0.6 0.8 1

2.5

5.0

7.5

10.0

12.5

15.0

17.5

Oil fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t (m

m)

Figur

image

(b) v

Equa

50%.

3.11

The i

meas

single

initia

result

flow

0

2

4

6

8

10

12

14

16

18

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

re 3-22: Inv

e presented i

variations in

ation 2), in b

Our selecte

In-Situ.3

instantaneou

ured instanta

e image. Th

al steps as tho

ting vertical

condition, su

0 0.1 0.2 00

2

4

6

8

0

2

4

6

8

(a)

vestigation o

in Figure 3-2

the image-

both cases du

ed value was

u Phase Fr

us in-situ oil

aneous volum

he in-situ ph

ose detailed

phase profile

uch that from

0.3 0.4 0.5 0Oil Fraction

f the effect

23: (a) Varia

-averaged in

ue to the us

α 5%

raction

phase fracti

metric ratio

hase fraction

for the phas

es to obtain a

m n images:

⟨ ⟩

0.6 0.7 0.8n,

======

of threshold

ations in the i

nstantaneous

e of differen

ion ⟨φ⟩y(t)≡

of oil, which

data ⟨φ⟩y,t h

e distribution

a mean oil co

1

0.9 1

=2%=3%=5%=10%=30%=50%

00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

In-S

itu O

il P

hase

Fra

ctio

n, y,

t

C

ding and bina

identification

in-situ oil

nt thresholdi

≡⟨φ⟩yi in a s

h is equal to

has been acq

n analysis, a

ontent in the

,

0 5 10 15

Chapter 3: Exp

(b)

arisation on

n of the inter

fraction ⟨φ⟩

ing paramete

single image

o the fraction

quired by em

and then by t

measuremen

5 20 25 30Threshold Value

perimental M

the instanta

rface location

⟩y,t (as defin

ers α, from 2

e is defined

n of dark are

mploying the

time-averagin

nt section for

(3.4)

0 35 40 45e,

Methods

aneous

n, and

ned in

2% to

as the

ea in a

same

ng the

r each

5 50

113

The u

phase

3.11

The i

from

thirty

and b

Figur

The e

the in

The m

determ

uncertainty i

e fraction dat

Interfa.4

instantaneou

the bottom

y images of

by recording

re 3-23 below

experimental

nstantaneous

Figure

mean μH (Eq

mined for ea

in the instan

ta ⟨φ⟩y,t is pr

ace Level

us interface l

of the chann

maximum te

g height H a

w. Thus, fo

l uncertainty

interface loc

3-23: Interfa

quation 3.6)

ach run (i.e.,

⟨ ⟩

ntaneous in-

resented in S

level H x,t

nel. The int

emporal spa

at five points

r each flow

y in the insta

cation, i.e. ±

ace level ima

and the stan

set of condit

⟩ ,1

⟨

situ oil phas

ection 4.5, 5

is defined a

terface level

cing (by 100

s (x position

condition 15

antaneous int

10%.

age processin

dard deviatio

tions):

C

⟩

se fraction a

.5 and 6.5.

as the heigh

analysis has

0 frames) to

ns) in each im

50 interface

terface level

ng, showing i

on σH (Equa

Chapter 3: Exp

amounts to ±

ht of the oil-

s been perfo

o ensure sam

mage, as sho

height value

H x,t is th

important de

ation 3.7) of

perimental M

(3.5)

±4%. The i

-glycerol inte

rmed by sele

mple indepen

own pictoria

es were gene

e same as th

efinitions

this data has

Methods

in-situ

erface

ecting

ndence

ally in

erated.

hat for

s been

114

In th

value

limits

estim

0.6%

3.11

Final

the a

binar

select

dropl

The r

e interface l

es are plotted

s of the 95

mation of the

%, respectively

Drople.5

ly, the dropl

area Ad of a

rised images.

ted and aver

let diameter μ

relative unce

level results

d. Assuming

% confidenc

mean and st

y).

et Size Dist

et size analy

a number of

. For each s

raged. Equa

μd:

rtainty in the

that follow

g a normal d

ce interval.

andard devia

tribution

ysis (see Sect

f droplets, af

set of condit

ations (3.8) a

e statistical e

1

11

(see Section

distribution, t

The resulti

ation of the h

tion 4.7, 5.7

fter converti

tions approx

and (3.9) we

2 ⁄

1

estimation of

C

n 4.6, 5.6 an

these values

ing relative

height H are

and 6.7) has

ing the PLIF

ximately 20 i

ere used then

⁄

f the mean of

Chapter 3: Exp

nd 6.6) the

represent the

uncertainties

both less tha

been perform

F images to

images and

n to evaluate

f the droplet

perimental M

(3.6)

(3.7)

μ+2σ and μ

e upper and

s in the stat

an ±1% (0.8%

med by meas

o black and

100 droplets

e a mean eff

(3.8)

(3.9)

size d is ±1%

Methods

μ–2σ

lower

tistical

% and

suring

white

s were

fective

%.

115

3.11

The i

Matla

locati

techn

from

every

φin co

analy

show

the fl

Firstl

secon

visua

is don

this

afore

perfo

using

been

of the

image

deem

disca

displa

Interfa.6

interface wav

ab. The step

ion of the gl

nique outline

the bottom

y frame in a g

ombination.

ysed. Follow

wn for two su

flow and the

ly, the avera

ndly, the pr

alisation cell

ne by subtra

profile is s

mentioned p

ormed. The

g Matlab. Fi

used to cons

e interface p

es, this bein

med to be poo

arded. The p

acement of th

ace Wave V

ve velocity h

ps to the proc

lycerol solut

ed in Section

surface of th

given run, i.e

It should b

wing identifi

uccessive ima

interface le

age interface

ofile is scal

for a given

cting the lin

shown for t

pre-processin

cross correla

igure 3-24(c)

struct Figure

profile. A th

ng 0.99,

or and the in

point on the

he interface

Velocity

has been calc

cedure as out

tion – oil int

n 3.11.2 and

he cell. This

e., for a fixed

e noted that

fication of th

ages in Figu

evel is on th

e level for a

led so that

a given insta

ear profile b

two success

ng was neces

ation process

) shows a plo

es 3-24(a) an

hreshold wa

, if the corre

nterface wav

abscissa tha

wave (see Fi

culated using

tlined in wha

terface, this h

d then calcu

s was done f

d superficial

runs contain

he interface

ure 3-24(a), w

he ordinate a

a given inst

the interfac

antaneous im

between the e

ive instanta

ssary for the

s between tw

ot of the corr

d 3-24(b), w

s imposed o

elation peak

ve velocity b

at correspond

igure 3-24(d

C

g an algorith

at follows. T

has been per

ulating the v

for every axi

mixture velo

ning droplets

level for an

where the ab

axis) the ima

tantaneous im

ce level at t

mage occupy

ends from th

aneous imag

cross-correl

wo successiv

relation betw

where the abs

on the correl

was below

between thos

ds to the corr

d)). This, cou

Chapter 3: Exp

hm that has b

The first task

rformed usin

erticle heigh

ial position i

ocity Um and

s above the i

n instantaneo

bscissa is the

age undergoe

mage is sub

the entrance

y the same ve

he actual prof

ges in Figur

ation proces

ve images wa

ween the two

cissa is the a

ation betwee

this level th

se two succe

relation peak

upled with the

perimental M

been develop

k is identifyin

ng the binari

ht of the inte

in a frame an

d input oil fr

interface we

ous image (t

e axial direct

es pre-proce

btracted and

e and exit o

ertical plain.

file. The res

re 3-24(b).

s in MatLab

as then perfo

o images that

axial displace

en two succe

he correlation

essive image

k is the horiz

e time durati

Methods

ped in

ng the

sation

erface

nd for

action

re not

this is

ion of

essing.

then,

of the

This

sult of

The

b to be

ormed

t have

ement

essive

n was

es was

zontal

ion ∆

116


117

between the images (which is known though the frame rate), enables the interface velocity

between two successive images to be calculated via Equation 3.10. It should be noted that for a

given run the sampled images were selected such that the time interval between them was

sufficient to provide an interface wave displacement of at least 15 pixels.

∆

(3.10)

For a give run (i.e., a fixed mixture velocity Um and input oil fraction φin combination) a series

of Uint values are generated for successive images. From these, a time-average interface wave

velocity ⟨ ⟩ and corresponding standard deviation can be computed. These are shown in

Equations 3.11 and 3.12.

⟨ ⟩1

(3.11)

11 , (3.12)

For a given run, the interface wave velocity Uint between two successive images that lie outside

the range ⟨ ⟩ 4 are discarded. From the data set that remains, new values for the

average interface wave velocity ⟨ ⟩ and associated standard deviation are calculated

and the interface wave velocity Uint values that lie outside the 95% confidence interval (i.e.,

⟨ ⟩ 2 ) are discarded. It is the data set that remains that has been used to compute the

average interface wave velocity ⟨ ⟩ for a given run.


118

(a) (b)

(c) (d)

Figure 3-24: Process for determining the velocity of the waves at the liquid – liquid interface,

specifically: (a) interface level profiles for two successive images; (b) the two successive

images shown in Figure 3-26(a) after having undergone pre-processing; (c) the correlation

between the pre-processed interface levels shown in Figure 3-26(b), including a 0.99

acceptability threshold, and; (d) illustration that the peak value corresponds to the interface

displacement between the two successive images

0 10 20 30 4020

21

22

23

24

25

Visualisation Section Length, Ls (mm)

Inte

rfac

e L

evel

, H

(m

m)

Image 1Image 2

0 10 20 30 40-1

-0.5

0

0.5

1

Visualisation Section Length, Ls (mm)

Proc

esse

d In

terf

ace

Lev

el,

H (

mm

)

Image 1Image 2

-40 -20 0 20 40-1

-0.5

0

0.5

1

Interface Displacement, Dint

(mm)

Cor

rela

tion,

C

-1 0 1 2 3 40.9

0.92

0.94

0.96

0.98

1

Interface Displacement, Dint (mm)

Cor

rela

tion,

C

3.11

The

softw

Partic

proce

studie

was p

proce

detail

stated

with

subtra

comp

time

by im

backg

proce

PTV

the m

windo

using

64

summ

of the

prese

Velocit.7

velocity pro

ware produce

cle Image V

esses ordinar

es presented

possible fro

edure first in

ls of the gra

d here that th

the use of

acting a slid

pared with th

series and th

mproving the

ground. A p

essing the ve

process is pe

movement of

ows within t

g the same p

64 interroga

mate to the v

e output from

ented in Fig

ty Profiles

ofiles of the

ed by LaVisi

Velocimetry (

rily require t

d in Chapters

om the prese

nvolves pre-p

aticule corre

he velocity p

the circular

ding minimu

he intensity o

he minimum

e signal-to-n

pre-processe

locity vector

erformed bet

f the fluid b

the whole im

pixel size int

ation window

alue of the 1

m the PIV st

gure 3-25(c)

e glycerol-so

ion. The pr

(PIV) and P

the presence

s 4, 5 and 6

ence of mic

processing th

ction metho

profile analy

r cross-secti

um over time

of the corresp

value of the

noise ratio, i

ed image is s

rs are initiall

tween succes

between them

mage were es

terrogation w

ws; in which

128 128 in

ep of the ov

; note that

olution phase

rocess is con

article Track

e of seeded p

– determini

cro-bubbles o

he distortion

d), see Figu

ysis was only

ion visualisa

e, i.e., for an

ponding pixe

e three is sub

i.e., the con

shown in Fi

y calculated

ssive images

m. Initially

stablished, th

windows. T

the vectors o

nterrogation

erall procedu

the velocity

C

e have been

nducted usin

king Velocim

particles – w

ing the veloc

of the oil in

n-corrected im

ure 3-27(a) f

y performed

ation cell.

ny pixel in a

el in both the

btracted. Th

ntrast betwee

gure 3-25(b)

via a multi-p

s and the resu

y, the vector

hese vectors

The subseque

of the four 6

windows int

ure for deter

y vectors th

Chapter 3: Exp

n calculated

ng a techniqu

metry (PTV)

which were n

city profiles

n the glycer

mages (see S

for an examp

d on the flow

The pre-pro

a given imag

e image befo

his improves

en the micro

). On comp

pass PIV alg

ultant velocit

s of 128

were refined

ent pass was

64 64 inter

to which they

rmining the v

hat it contai

perimental M

using the D

ue involving

). Although

not utilised

via this app

rol-solution.

Section 3.11

ple. It shou

w images obt

ocessing inv

ge, its intens

ore and after

the image q

o-bubbles an

pletion of the

gorithm. The

ty vectors rel

128 interrog

d in a second

s performed

rrogation win

y fit. An exa

velocity prof

ins are base

Methods

DaVis

g both

these

in the

proach

The

1.1 for

uld be

tained

volves

sity is

in the

quality

nd the

e pre-

e PIV-

late to

gation

d pass

using

ndows

ample

files is

ed on

119


120

interrogation windows of 64 64 pixels. The final velocity vectors are calculated using a PTV

approach in which individual micro-bubbles are tracked. The 64 64 interrogation windows

are split into sixty four 8 8 interrogation windows. A size restriction on the micro-bubbles

was imposed, a range of 3 to 5 pixels. This was in order to prevent over sampling of individual

micro-bubbles. Figure 3-27(d) presents an example of the velocity vectors that are generated

between two successive images.

(a) (b)

(c) (d)

Figure 3-25: The PIV-PTV process for acquiring velocity vectors between two images

separated by a known time interval: (a) a distortion-corrected LIF image; (b) shows the image in

Figure 3-25(a) after it has undergone pre-processing (i.e., subtraction of sliding minimum pixel

intensity); (c) a velocity vector map calculated using the PIV technique between two successive

images, and; (d) a PTV vector map which is calculated from the PIV vector map shown in

Figure 3-25(c). In (c) and (d) the size of the vectors (arrows) refers to the velocity

0.5 m/s0.5 m/s


121

For a given run, i.e., time series of images, the vectors can be aggregated into a single image

(shown in Figure 3-26). Such an image (i.e., time-averaged PTV velocity vector map) may

contain spurious velocity vectors due to the fact no filter was applied on the instantaneous PTV

velocity vector maps (see Figure 3-25(d)) due to the low vector density in those maps.

However, this constraint does not apply to the time-averaged PTV maps (Figure 3-26) and

filtering can be applied at this stage to remove the spurious vectors. This was done by

employing a permissibility range on the velocity vectors in both the abscissa and ordinate

directions. Vectors outside the ranges 10 10 m.s-1 and 10 10 m.s-1 were

removed. As a next step, a median filter was used. In this step, velocity vectors in the time-

average PTV vector map were removed if they were larger than 1.8 times the RMS (root mean

square) of their neighbouring velocity vectors. An individual velocity vector is based upon the

correlation peak between corresponding interrogation windows in successive images. If a

velocity vector is removed due to the aforementioned criterion, it is replaced by another vector,

that relates to the next highest peak in the correlation, if, it is less than 2.2 times the RMS of the

neighbouring velocity vectors. If the second highest peak does not fit the third highest peak is

tested and so on. From the aggregated PTV velocity vector map (Figure 3-26), a velocity

profile can be generated (see Figure 3-27). The velocity profiles presented in Chapter 5 and

Chapter 6 have been curve-fitted using the TableCurve 2D software package produced by Systat

Software.


122

Figure 3-26: Aggregated PTV vectors for a given time series of LIF images at a fixed

superficial velocity Um and input oil fraction φin combination

Figure 3-27: Flow velocity profile. The dotted red line indicates the average interface level

for the particular flow run (superficial velocity Um and input oil fraction φin combination)

analysed

0 0.05 0.1 0.15 0.2 0.25 0.30

4

8

12

16

20

24

28

Streamwise Velocity, Ux (m/s)

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

CH

La

Ho

Cr

4.1

The P

This

detail

techn

ducts

the sq

with

it wa

and 6

In wh

exper

are pr

regim

HAPT

aser-In

orizon

ross Se

Introdu

Planar Laser

technique y

led diagnost

nique was fir

s are clearly

quare cross s

circular tube

s necessary t

6.

hat follows,

riments. Qua

resented in S

me observati

TER 4

nduced

ntal Liq

ection

uction

r Induced Flu

yields high s

tic inspectio

rst applied to

less typical

section test s

es. Work wa

to correct the

Section 4.2

alitative anal

Section 4.3,

ons. In the

d Fluo

quid-L

Duct

uorescence (

spatial and t

on of co-cur

o flow in a s

of applicatio

section geom

s pursued als

e images for

describes th

lysis of the r

which also i

e succeeding

orescen

Liquid

(PLIF) techn

temporal res

rrent liquid-

square cross

ons than are

metry avoids

so with chan

r distortion. T

e experimen

results, includ

includes a flo

g sections th

Chapte

nce St

d Flow

nique was de

solution mea

liquid flows

section duct

ducts of cir

the distortio

nnels of circu

This latter w

ntal bases for

ding images

ow regime m

he quantitati

er 4: Square S

udies

ws in a

scribed in de

asurements,

s. In the c

t. Though sq

rcular cross s

on of the ima

ular cross sec

work is descri

r the square

of the flow

map construc

ive analysis

Section PLIF R

of

Squar

etail in Chap

thus allowin

current work

quare cross se

section, the u

ages which o

ction; in that

ibed in Chap

cross section

regimes obs

cted from the

of the imag

Results

re

pter 3.

ng the

k, this

ection

use of

occurs

t case,

pters 5

n duct

served

e flow

ges is

123

prese

by re

distri

in Se

4.2

The e

(Sect

exper

speed

such

3.5).

been

Flow

48 ru

of the

cross

the p

QT at

const

flow

exper

quant

0.30

ented. In Sec

esults for in-s

bution (Sect

ction 4.8 and

Experi

experiments

tion 3.2) usin

riments, the

d video Syst

that the oil p

Specific de

obtained are

w conditions a

uns: (i) the su

e two liquids

-sectional ar

ipe φin, defin

t the inlet of

tant during e

rates of eac

rimental con

titative resul

m.s-1). In a

ction 4.4 the

situ phase fr

ion 4.7). Ap

d the conclus

imental O

on the squ

ng a square c

PLIF system

tem (see Sec

phase was inj

etails on the

e outlined in

are defined v

uperficial mix

s (oil and gly

rea of the pip

ned as the vo

the pipe sect

ach run (i.e.,

ch phase (i.e

nditions span

ts in this cha

addition, φin

e vertical pha

raction (Sect

pplication of

sions of the w

Operation

are cross se

cross section

m was synch

ction 3.4.2).

jected at the

operation o

Appendix 1.

via two inde

xture velocit

ycerol soluti

pe A = πD2/4

olumetric flo

tion. The tw

, each set of

e., the oil Q

nned a rang

apter focus o

n was varied

ase distributi

tion 4.5), int

f predictive m

work are pres

ection duct w

n quartz visu

hronised wit

The test flu

top and the

of the TOWE

.

ependent par

ty Um, define

ion) in the pi

4; and (ii) th

ow rate of oi

wo impendent

conditions)

Qoiland glyce

ge of Um fro

on the regime

d between 0

Chapte

ion profiles r

erface level

methods to th

sented in Sec

were carried

ualisation sec

th a Phantom

uids were in

glycerol solu

ER facility f

ameters that

ed as the sum

ipe section Q

he inlet volum

il Qoil divide

t inlet flow v

and were set

erol Qgs) by

om 0.07 to

es observed i

0.1 and 0.9.

er 4: Square S

results are pr

(Section 4.6

he results obt

ction 4.9.

d out on the

ction (Section

m V710 Mo

ntroduced int

ution at the b

from which t

t were varied

m of the volu

QT = Qoil + Q

metric phase

ed by the tota

variables Um

t by controlli

y means of g

1.46 m.s-1,

in the lower

The matrix

Section PLIF R

resented, foll

6) and drople

tained is disc

TOWER fa

n 3.10.1). In

onochromatic

to the test se

bottom (see F

these results

d independen

umetric flow

Qgs divided b

e fraction of

al volumetric

and φin wer

ing the volum

globe valves

though the

Um range (0

x of experim

Results

lowed

et size

cussed

facility

n these

c high

ection

Figure

s have

ntly in

w rates

by the

f oil in

c flow

e kept

metric

s, The

main

0.07 to

mental

124

condi

those

4.3

In th

chara

rigoro

accur

press

latter

condi

Eight

philo

Nadle

Exam

4-1 b

flow;

dropl

unmi

these

on tw

Um.

are in

itions was se

e by Soleiman

Flow R

he co-curren

acteristics th

ous two-pha

rate quantita

ure drop acro

r being a p

itions of the

t distinct flo

sophy is ak

er and Mew

mples of each

below. Thes

; (2) mixed

lets in each;

xed region;

four groups

wo important

A flow regim

ndicated expl

elected base

ni (1999) and

Regimes a

nt flow of t

hat define th

ase phenome

ative predicti

oss a multiph

primary con

pipeline) for

ow regimes h

in to that of

wes 1995;

h of these 8 f

e can be gro

flow, which

(3) two-laye

and (4) disp

s is presented

flow parame

me map corr

licitly, is pre

d upon cons

d Hussain (2

nd Flow R

two liquids,

hem is desir

enological m

ions of the f

hase oil prod

nsideration (

r evaluating w

have been o

f previous r

Angelia and

flow regimes

ouped into fo

h is characte

er flow, whi

persed flows

d in Table 4-

eters: the inp

responding to

esented in Fig

sultation of p

2004), see Ch

Regime M

, the accura

rable. Such

models to be

flow. Of par

duction pipel

(when coup

whether hydr

observed in t

researchers (

d Hewitt, 2

s are provide

our, more ge

erised by tw

ch comprise

s. The cate

1. This cate

put oil fractio

o this flow c

g. 4-2.

Chapte

previous flow

hapter 2.

Maps

ate predictio

flow regime

e created th

rticular impo

line and the l

pled with th

rates will for

the present P

(Russell et a

2000; Solem

ed by instant

eneral flow t

wo distinct co

ed of a dispe

gorisation o

egorisation of

on φin; and th

characterisati

er 4: Square S

w regime m

on of flow

e predictions

hat in turn c

ortance are p

local in-situ p

he thermody

rm in the pip

PLIF study;

al. 1959; Ch

mani, 1999;

taneous flow

types, which

ontinuous ph

ersed region

of the eight f

f the flow ph

he superficia

ion, in which

Section PLIF R

maps, most no

regimes an

s can allow

can provide

predictions o

phase fractio

ynamic ope

pelines.

the classific

harles et al.

Hussain, 2

w images in F

h are: (1) stra

hase regions

and a contin

flow regime

henomena is

al mixture ve

h these param

Results

otably

nd the

more

more

of the

on, the

erating

cation

1961;

2004).

Figure

atified

s with

nuous,

es into

based

elocity

meters

125

(g)

Figur

(a)

(c)

(e)

Oil flow ove

with g

re 4-1: Imag

) Stratified fl

Oil droplet l

Three layer

er glycerol so

glycerol solut

ges of the 8 d

flow

layer

flow

olution dispe

tion film

distinct flow

(f

ersion

regimes obse

Chapte

(b) Stratif

(d) Glycero

f) Oil dispers

(h) Glycer

with gly

erved in the

1 mm

er 4: Square S

fied flow wit

ol solution dr

sion over gly

rol solution d

ycerol soluti

square cross

Section PLIF R

th droplets

roplet layer

ycerol solutio

dispersion

ion film

s section cam

Results

on

mpaign

126

Chapter 4: Square Section PLIF Results

127

Table 4-1: Categorisation of observed flow regimes

Flow Regime Categories Flow Regimes

Stratified Flow Stratified flow

Stratified flow with droplets

Mixed Flow

Oil droplet layer

Glycerol solution droplet layer

Three-layer flow

Two-Layer, Dispersed

Over/Under Continuous Flow

Oil dispersion over glycerol solution flow

Oil flow over glycerol solution dispersion

Dispersed Flow

Oil continuous dispersed flow

Glycerol solution continuous dispersed

flow

The observed flow regimes are in good general agreement with previous observations

(Soleimani, 1999; Lovick and Angeli, 2003; Hussain, 2004). However, some regimes observed

in previous investigations were not seen in the current study. Some investigators reported the

establishment of oil-annulus annular flows (Russell et al. 1959; Charles et al. 1961; Hasson et

al. 1970; Arirachakaran et al. 1989). In addition, Charles et al. (1961) and Hasson et al. (1970)

reported the presence of water-annulus annular flow and oil-slugs-in-water. Neither annular or

slug flow were observed in the current experimental campaign.

The absence of oil-annulus annular flow in the current campaign aligns with the findings and

conclusions of Arirachakaran et al. (1989) who attributed the presence of annular flow to the

physical properties of the oil phase. Specifically, that as the oil viscosity decreases the range of

conditions (the input oil phase fraction φin and the superficial mixture velocity Um) over which

oil-annulus flow is observed diminishes, i.e., the oil is not dense and viscous enough to sustain a

water core. Arirachakaran et al. (1989) reached this conclusion following an experimental

campaign involving four different oils, each with a different viscosity; for the lowest viscosity


128

oil ( 4.7 mPa. s) oil-annulus annular flow was not observed. Angeli (1995), Nadler and

Mewes (1995), Soleimani (1999) and Hussain (2004) did not observe the existence of annular

flows but their results are consistent with those of Arirachakaran et al. (1989) as they all used

oils with viscosity values below the oil viscosity value ( 4.7 mPa.s) for which

Arirachakaran et al. (1989) did not observe annular flow.

However, several investigators observed annular flow when using oils with viscosities

4.7mPa. s. For example, Hasson et al. (1970) used an oil viscosity 21.7mPa. s;

Charles et al. (1961) used oils of viscosity 6.27mPa. s and 65mPa. s, and;

Oglesby et al. (1979) used an oil of viscosity 84mPa. s. Hasson et al. (1970) attributed

the presence of water-annulus annular flow to the preferential wetting properties of water. The

absence of annular flows has also been attributed to the effect of relative densities of the two

test fluids. Those who observed the regime (Hasson et al. 1970; Charles et al. 1961) employed

fluids of similar densities, i.e., ⁄ 1. Investigators who used fluids with density ratios

dissimilar to unity, e.g. ⁄ 0.8 (Kurban 1997, Angeli,1996, Soleimani, 1999 and

Hussain,2004) did not observe annular flow. The density ratio of the fluids used in the present

study is ⁄ 0.66.


129

Figure 4-2: Flow regime map

The locations of the flow patterns observed in the present experiments are shown in Figure 4-2

as a function of total mixture superficial velocity and input oil fraction. From the flow regime

map (Figure 4-2) it can be seen that the smooth stratified flow regime is observed for all

investigated oil input phase fractions (φin 0.25 to 0.75) at superficial mixture velocities of

Um 0.07 m.s-1. As the total superficial velocity increases, different arrangements of stratified

flow with droplets were observed up to the onset of three-layer flow at a superficial mixture

velocity of Um 0.36 m.s-1. As the superficial mixture velocity increases further, the range of

oil input phase fractions over which three-layer flow is observed diminishes and dispersed flows

are seen to cover a boarder range of oil input phase fractions. Oil dispersions are found at

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.3

0.6

0.9

1.2

1.5

Sup

erfi

cial

Mix

ture

Vel

ocity

, Um

(m

/s)

Input Oil Fraction, in

Stratified FlowStratified Flow with DropletsOil Droplet LayerThree Layer FlowStratified Flow with Glycerol Solution Droplet LayerOil Dispersion over Glycerol SolutionOil Flow over Glycerol Solution Dispersion with FilmGlycerol Solution Dispersion with Film


130

increasingly higher oil input phase fractions and glycerol solution dispersions at increasingly

lower oil input phase fractions as the superficial mixture velocity increases.

A notable finding in the present work has been the positive identification of three-layer flows

(e.g., see Figure 4.1(e)). Three-layer flow is characterised by distinct continuous oil and

glycerol solution phase regions at the top and bottom of the pipe respectively with a highly

mixed zone between them. There have been some reports of such flows (Angeli and Hewitt,

2000a,b; Soleimani, 1999; Hussain, 2004), but the present investigation sheds further light onto

their nature. Lovick and Angeli (2004) reported a dual continuous flow regime that is

characterised by both phases retaining their continuity at the top and bottom of the pipe while

each phase is dispersed, at various degrees, into the continuum of the other (see Figure 2-18).

This description has a large degree of commonality with three layer flow. The flow regime map

constructed from the PLIF images is presented in Figure 4-2.

An earlier version of the experimental facility employed in this study was used in the liquid-

liquid flow studies by Soleimani (1999) and Hussain (2004). Hence, one can make direct

comparisons with the flow regime maps of these investigators. The fundamental modification

has involved the replacement of the water phase used in the previous investigations with a

glycerol solution containing a small concentration of a fluorescent dye. The use of the glycerol

solution allows matching of the refractive indices of the two fluids; an essential requirement for

the generation of PLIF images free of distortion arising from refraction. In the present

experiments, the heavier (glycerol solution) had a density somewhat higher than water

(1213.3kg.m ) and a viscosity much higher than water (82.3 mPa. s). It is interesting to

observe the effect of these changes in physical properties on the resulting flow regimes.

Hussain (2004) reported stratified wavy flow at higher superficial mixture velocities (up to

Um 3 m.s-1), whereas in the current campaign the limit for stratified flow is Um 0.3 m.s-1.

Furthermore, Hussain (2004) reported three layer flow in the oil fraction range φin 0.2 to 0.5


131

which is different to the range observed in the current experiments, namely φin 0.3 to 0.7.

Soleimani (1999) found the onset of stratified wavy flow with droplets and the onset of three

layer flows occur at lower superficial mixture velocities than found in the present experiments.

There is a significant overlap in the superficial mixture velocity and oil fraction combinations

between the three layer flow regime observed in the present study with the dual continuous flow

regime reported by Lovick and Angeli (2004). Lovick and Angeli (2004) reported the onset of

dual continuous at Um 0.80 m.s-1 and that, as the superficial mixture velocity increases, the

range of oil input fractions over with the regime is observed diminishes; this behaviour is

similar to that for three layer flows in the present experiments.

Another pertinent finding of the present campaign has been the positive identification of

secondary and multiple dispersions. Such dispersions have been widely reported in agitated

vessels (Luhning and Sawistowski, 1971; Pacek and Nienow, 1995 and Liu et al, 2005).

However, their presence in two-phase dispersed flows has been reported less widely. Pal (1993)

observed secondary dispersions in pipeline flow exclusively around the transition from water-

in-oil (w/o) to oil-in-water (o/w) dispersions. However, in the current campaign secondary

dispersions were not limited to the ambivalent range (see Section 2.3 for details). This is

illustrated in Figures 4-3(a) and 4-3(b) in which oil-in-glycerol solution-in-oil (i.e. o/w/o) and

glycerol solution-in-oil-in-glycerol solution droplets (i.e. w/o/w) are observed at φin 0.13 and

φin 0.87, respectively.

The results are in agreement with the findings of Liu (2005) who found that both water-in-oil-

in-water (w/o/w) and oil-in-water-in-oil (o/w/o) droplets could appear under the same

experimental conditions. This is shown in Figures 4.3(b) and 4.4(a) in which both oil-in-

glycerol solution-in-oil (i.e. o/w/o) and glycerol solution-in-oil-in-glycerol solution (i.e. w/o/w)

droplets can be seen. Multiple dispersions were also observed, Figure 4.4(b) shows a ternary

dispersion of glycerol solution-in-oil-in-glycerol solution-in-oil (w/o/w/o).

Figur

fracti

glyce

veloc

Figur

fracti

and g

both

4.4

The v

techn

re 4-3: Seco

ion of φin =

erol solution

city Um of 0.2

re 4-4: (a)

ion of φin = 0

glycerol solu

at a superfic

Vertica

vertical distr

nique detailed

(a)

ondary dispe

= 0.13, and

droplets at

29 m.s-1

(a)

Secondary d

0.13, and (b)

ution-in-oil-in

ial mixture v

al Phase D

ribution of

d in Section

rsions of (a)

(b) oil-in-gly

an oil input

dispersions o

secondary a

n-glycerol so

velocity Umo

Distributi

the phases i

3.11.2. An

) oil-in-glyce

ycerol soluti

t fraction of

oil-in-glycero

and ternary d

olution drop

of 0.29 m.s-1

ion Profil

in the PLIF

n additional q

Chapte

erol solution

ion-in oil an

f φin = 0.87,

ol solution-i

dispersions of

plets at an oi

es

pictures ha

quantifiable o

er 4: Square S

(b)

n-in oil dropl

nd glycerol

both at a su

(b)

n oil drople

f oil-in-glyce

il input fract

as been dete

output of the

Section PLIF R

lets at an oil

solution-in-o

uperficial m

ets at an oil

erol solution

tion of φin =

ermined usin

e work detai

Results

input

oil-in-

mixture

input

-in oil

= 0.87,

ng the

iled in

132


133

this section is the phase fraction of the dispersed phase φdisp above and below the interface i.e.,

the glycerol solution phase fraction entrained in the oil above the interface and the oil entrained

in the glycerol solution below the interface. This has been achieved by coupling the phase

distribution profiles with the respective interface level H measurements as detailed in Section

4.6. Measurements of the entrained fraction can be used to determine effective viscosity of

each layer (aqueous phase continuous and oil phase continuous) by accounting for the presence

of droplets in the respective layers. This in turn yields a revised viscosity ratio (of the fluid

above the interface to that of the fluid below the interface), which is a key input required for the

closure of predictive techniques to predict the in-situ phase fraction (Section 4.5).

Figure 4-5 shows vertical oil phase fraction profiles φ(y) (defined in Equation 3.3) for the full

range of oil fractions φin and with selected superficial mixture velocities Um of: (a) 0.07 m.s-1,

(b) 0.14 m.s-1, (c) 0.21 m.s-1 and (d) 0.29 m.s-1. Figure 4.6 shows vertical phase profiles φ(y) for

the full range of superficial mixture velocities Um and selected input oil fractions φin of: (a)

0.25, (b) 0.50 and (c) 0.75.


134

(a) (b)

(c) (d)

Figure 4-5: Vertical oil phase fraction profiles φ(y) at different input oil fractions φin for a

superficial mixture velocity Um of: (a) 0.07 m.s-1; (b) 0.14 m.s-1; (c) 0.21 m.s-1, and; (d)

0.29 m.s-1

From inspection of Figures 4-5 and 4-6 one can infer that there are three distinct regions in the

flow; an oil zone at the top of the channel, an aqueous phase zone at the bottom of the channel

and a mixed region between them. This zone categorisation of the flow is illustrated in Figure

4-7.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

in

=0.26

in

=0.51

in

=0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

in

=0.25

in

=0.50

in

=0.74

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

in

=0.17

in

=0.33

in

=0.50

in=0.66

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

in=0.13

in=0.25

in=0.38

in=0.49

in=0.63

in=0.74

in=0.87

a b


135

(a) (b)

(c)

Figure 4-6: Vertical oil phase fraction profiles φ(y) for different superficial mixture velocities

Um at an input oil fraction φin of: (a) 0.25, (b) 0.50, and (c) 0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

Um

=0.07 m/s

Um

=0.14 m/s

Um=0.29 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

Um

=0.07 m/s

Um

=0.14 m/s

Um

=0.22 m/s

Um

=0.29 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (

mm

)

Um=0.07 m/s

Um=0.14 m/s

Um=0.29 m/s

Figu

At lo

the tr

vertic

Figur

smoo

flow

image

Figur

mixtu

ure 4-7: Sche

ower superfic

ransition from

cal distance

re 4-5(a) for

oth flow regi

is not signi

es of the flow

(a)

re 4-8: Insta

ure velocity

ematic zone

cial flow vel

m the glycer

and the inte

r φin 0.26

me and the f

ificantly wav

w taken at di

)

antaneous flo

Um 0.07 m

categorisatio

locities, the m

rol zone to t

rface is near

and Um 0

fluctuations

vy. This is

ifferent times

ow images fo

m.s-1 at: (a)

on of liquid-l

mixed zone

the oil zone

rly horizonta

0.07 m.s-1.

in the interf

supported b

s for these lo

(b)

or an oil inpu

0 second

Chapte

liquid flows b

covers a nar

(i.e. φ 0 t

al, as exemp

In this case

face height w

y Figure 4-

ow superficia

ut phase fract

ds; (b) 1

er 4: Square S

based upon p

rrow vertica

to φ 1) oc

plified by the

e, the flow i

with time are

8 which sho

al flow veloc

tion φin 0.

s, and;

Section PLIF R

phase distrib

l range and

ccurs over a

e results sho

is in the stra

e minimal, i.e

ows instanta

city condition

(c)

.26 and supe

2 s

Results

bution

hence

small

own in

atified

e., the

aneous

ns.

rficial

136


137

A constant gradient transition from the glycerol zone to the oil zone (i.e. φ 0 to φ 1), such

as that for φin 0.74 and Um 0.14 m.s-1 shown in Figure 4-5(b), can be explained by the

presence of waves at the interface of regular frequency and constant amplitude , such as the

case of a sine wave at the interface, see Figure 4-9(a). When time-averaged, results for such an

interface configuration have the form shown in Figure 4-9(b).

(a) (b)

Figure 4-9: (a) Sine wave profile, and; (b) the associated phase distribution profile

Figure 4-5 shows that as the input oil fraction increases the height of the glycerol zone

decreases. In addition, one can observe from Figures 4-5 and 4-6 that as the superficial mixture

velocity increases the height of the mixed zone increases, i.e., the gradient of the transition

between the glycerol zone the oil zone increases; this is more clearly seen in Figure 4-10(a). If

one looks beyond the scope of the superficial mixture velocities analysed in this study to those

investigated by Soleimani (1999) it can be seen that this trend would be expected to continue all

the way to fully dispersed flows in which there the phase fraction is constant along the vertical

axis of the channel. From Figure 4-10(b) it can be seen that for a low superficial mixture

velocities, the height of the mixed zone has a maximum at an oil input phase fraction of

φin 0.50. Furthermore, as the total superficial velocity increases (such as for Um 0.29 m.s-

0

2

4

6

8

10

12

14

16

18

Vis

ualis

atio

n Se

ctio

n H

eigh

t (m

m)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Vis

ualis

atio

n Se

ctio

n H

eigh

t (m

m)

Oil Fraction,

A

A

2A


138

1) the aforementioned trend continues, though peaks in the mixed zone height are also seen at

low and high oil input phase fractions.

(a) (b)

Figure 4-10: Height of Interface Zone for as a function of (a) superficial mixture velocities Um

for constant input oil fraction φin; (b) input oil fraction φin for constant superficial mixture

velocities Um

The presence of droplets and the non-uniform wave characteristics of dual continuous flow give

rise to more complex features in the vertical phase distribution profiles, such as seen at the

points labelled “a” and “b” in Figure 4-5(d), both for a superficial mixture velocity of

Um 0.29 m.s-1 and oil input phase fraction of φin 0.13 and φin 0.25, respectively. This

“S” shape in the mixed region (see Figure 4-7) can be explained by the presence of an oil

droplet layer below the interface. Figures 4-11(a) and 4-11(b) present instantaneous images of

the flow for both of these conditions showing that there is an oil-droplet layer below the

interface.

0 0.05 0.1 0.15 0.2 0.25 0.30

2

4

6

8

10

12

14

16

18

Superficial Mixture Velocity, Um (m/s)

Mix

ed Z

one

Hei

ght,

Hm

z (m

m)

in

=0.25

in

=0.50

in

=0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Input Oil Phase Fraction, in

Mix

ed Z

one

Hei

ght,

Hm

z (m

m)

Um

=0.07 m/s

Um

=0.14 m/s

Um

=0.22 m/s

Um

=0.29 m/s

Figur

interf

The a

distri

4.6) t

i.e., t

entrai

allow

such

4.5

An a

funda

as the

mode

transi

re 4-11: Ins

face for Um

analysis pres

bution profi

to determine

the glycerol

ined in the g

ws calculation

flows.

In-Situ

ability to ac

amental impo

e two-phase

els for predic

itions, both o

(a)

stantaneous f

0.29 m.s-1

sented in thi

les are coup

the phase fr

solution ph

glycerol solu

n of the effe

u Phase Fr

ccurately cha

ortance. It a

density and

cting multip

of which are

flow images

at: (a) φin

is section is

pled with the

raction of the

hase fraction

ution below

ective viscosi

raction

aracterise th

allows the de

viscosity wh

phase flow b

dependent o

highlight the

0.13, and; (b

developed f

e respective

e dispersed φ

n entrained i

the interfac

ity of the tw

he in-situ ph

etermination

hich are key

behaviour, pa

on the in-situ

Chapte

e presence of

b) φin 0.25

further in Se

interface le

φdisp phases

n the oil ab

e. As will b

wo layers for

hase fraction

n of numerou

requirements

articularly pr

phase fracti

er 4: Square S

(b)

f an oil dropl

5

ection 4.8 in

vel H measu

above and b

bove the inte

be shown in

incorporatio

ns in two-p

us other flow

s for the clos

ressure drop

on.

Section PLIF R

let layer belo

n which the

urements (Se

below the inte

erface and th

n Section 4.8

on into mode

phase flows

w parameters

sure of multi

p and flow p

Results

ow the

phase

ection

erface

he oil

8, this

els for

is of

, such

iphase

pattern

139


140

One key liquid-liquid flow phenomenon which is dependent on the in-situ phase fraction is

phase inversion (see Section 2.3). This phenomenon, i.e., the transition from an oil-in-water

dispersion to a water-in-oil dispersion, is associated with a sharp peak in the mixture viscosity

(see Figure 2-23), and thus in turn, a sharp peak in the pressure drop. If one considers

multiphase flow production lines from oil wells, there can be significant ramifications from

operating in this region. The higher viscosity can increase the pumping requirements and

furthermore, result in pressure surges that risk exceeding the maximum arrival pressure of the

facility the oil lines feed into. Thus with accurate prediction of the in-situ phase fractions one

can set and monitor the input conditions so as to ensure they do not encounter the issues

associated with phase inversion and continue to operate in a preferred flow regime. The sound

prediction of in-situ phase fraction is also a key parameter for predicting heat transfer from flow

lines. A comprehensive grasp of the heat dissipation from flow lines is essential as it allows the

prediction of the in-situ fluid temperature, which is the controlling parameter in the formation of

solid phases such as waxes and hydrates. Knowledge of the fluid temperature in these cases is a

key factor in designing systems for the mitigation of solid formation.

This section presents the in-situ phase fraction experimental results and assesses the suitability

of various prediction techniques for characterising it. In addition, comparison of the results

obtained for in-situ phase fraction ⟨φ⟩y,t, as a function of the input phase fraction φin, with

results obtained for other systems is evaluated as a means to gain insight in the influence the

physical properties of the test fluids.

The results for the in-situ oil phase fraction ⟨φ⟩y,t (from Equation 3.5) are shown in Figure 4-12.

It can be seen that the in-situ phase fraction ⟨φ⟩y,t is lower than the input oil fraction φin for

almost all flow conditions, indicated by the data points in the figure lying below the straight line

with unity gradient that passes through the origin (denoted as S = 1).

Figur

mixtu

4.5.1

Firstl

which

stratif

gradi

1 It sh

re 4-12: In-s

ure velocities

Lamina1

ly, the in-situ

h are given

fied flow an

ents for the

hould be acknow

. howeve

situ fraction

s Um

r Drag Mo

u phase fract

in Appendix

nd the pressu

th phase ma

wledged that the

er, the results o

00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

In-s

itu O

il Ph

ase

Frac

tion

,

y, t

⟨φ⟩y,t as a fu

odel

tion ⟨φ⟩y,t wa

x 2. In this

ure gradients

ay be calcula

Δ12

4

e recommended

obtained for φm

0.1 0.2 0Inpu

Um

= 0.07

Um

= 0.14

Um

= 0.22

Um

= 0.29

mod,1

mod,1b

mod,2

S = 1

unction of inp

as calculated

model, the t

s in the two

ted from the

416

d form of the Fa

mod,1 are indepe

.3 0.4 0.5ut Oil Phase F

7 m/s

4 m/s

2 m/s

9m/s

Chapte

put oil fracti

using a lam

two phases a

phases are

friction fact

anning friction

endent of the nu

0.6 0.7 0Fraction,

in

er 4: Square S

ion φin for di

minar drag mo

are assumed

assumed equ

tor relationsh

factor for flow

umerator in Equ

0.8 0.9 1

Section PLIF R

ifferent supe

odel, the deta

d to be flowi

ual. The pre

hip1:

(4.1)

in a square cha

uation 4.1.

Results

rficial

ails of

ing in

essure

annel is

141

where

Re

phase

where

The h

value

Comp

those

mode

exper

e D i is the eq

⁄

es and, after

e:

. ;

height of the

es.

parisons of t

e measured i

el is denoted

rimental data

quivalent dia

is the Reyno

equating pre

4

; 1

Figure 4-13

e interface c

the values of

in the presen

d as φmod,1)

a points relat

ameter of pha

olds number

essure drops

4

;

3: Stratified l

an be calcul

f in situ pha

nt experimen

); excellent

ting to the low

ase i (taking

for phase i.

Δp/L, Equati

4 4

liquid-liquid

lated from E

se fraction c

nts are show

agreement

w-velocity st

Chapte

g account of t

Thus there a

ion 4.1 reduc

1 0

; 4

flow model

Equation 4.2

calculated by

wn in Figure

is obtained

tratified flow

er 4: Square S

the interfacia

are two equat

ces to a quint

;

construction

and compar

y the laminar

4-12 (here,

between th

w (Um 0.07

Section PLIF R

al area) and

tions for the

tic:

(4.2)

(4.3)

n

red with mea

r drag mode

the laminar

he model an

7 m.s-1).

Results

two

asured

l with

r drag

nd the

142

In ca

conta

which

contr

squar

9y12

12 by

are al

Final

4.5.2

A sec

Figur

arran

al., 20

occur

in-sit

(Yoil

in-sit

lculating the

act area was

h the interfa

ribution to th

re channel.

6y1 1

y the dashed

lmost identic

ly, the mode

Differen2

cond form o

re 4-12. This

ngement of tw

001). The m

r i.e., the inte

tu oil fractio

Ygs H

tu oil fraction

e equivalent

included in

acial contact

he equivalent

In this case

0. The resul

bold curve;

cal.

elled in-situ o

,

ntial Mom

of analysis w

s is based up

wo immiscib

model assume

erface remai

on ⟨φ⟩y,t 0

HT/2 in Fi

n (i.e., ⟨φ⟩y,t

diameter of

the wetted p

t area betwe

t diameter. I

e Equation 4

lts obtained u

it is clear fr

oil phase frac

⟨φ⟩y,t

entum Ba

was also perf

pon the avera

ble liquids, d

es that the flu

ins exactly p

.5, i.e., when

igure 4-13).

0.5) is giv

the two flow

perimeter. A

en the two

In this case D

4.2 is modif

using this mo

rom Figure 4

ction ⟨φ⟩y,t pr

lance Mod

formed, the r

age velocities

derived from

uids are flow

planar. It is a

n the interfa

The input o

ven by:

Chapte

w regions (aq

similar mod

fluid stream

Di4YoilW

2Yoil W

fied to the f

odified form

4-12 that the

resented in F

1

del

result from w

s of each liqu

a differentia

wing sufficien

applicable to

ace level H i

oil fraction φ

er 4: Square S

queous and o

del can be de

ms is neglecte

, where W i

form Xy15

mulation are s

results from

Figure 4-6 is

which is den

uid flow in th

al momentum

ntly slowly th

o the special

is at the mid

φin that resul

Section PLIF R

oil), the inter

erived (φmod

ed in terms

is the width

6Xy14 9X

shown in Fig

m the two ana

defined as:

(4.4)

noted by φmo

he co-curren

m balance (B

hat no instab

case in whic

dpoint of the

lts in this va

Results

rfacial

d,1b) in

of its

of the

Xy13

gure 4-

alyses

od,2 in

nt flow

Bird et

bilities

ch the

e pipe

alue of

143


144

, 1 (4.5)

where y2

Qoil

Qgs. Now, bearing in mind that Yoil Ygs HT/2 we obtain:

⟨ ⟩

⟨ ⟩

(4.6)

Hence, φmod,2 φin can be evaluated from the ratio of the average/bulk velocities of each liquid

in the co-current flow, which is derived from differential momentum balances:

⟨ ⟩2

48

/ 7

(4.7)

⟨ ⟩2

48/

7

(4.8)

After substituting Equation 4.7 and 4.8 into Equation 4.6 we obtain,

⟨ ⟩

⟨ ⟩ (4.9)

and finally from Equation 4.5:

, (4.10)

where mμgs

μoil is the ratio of the dynamic viscosities of the two fluids.

Figur

sugge

cause

soluti

For e

4.5.3

In the

ratio

an as

slip r

betwe

where

utilise

oil fra

where

re 4-12 show

esting that th

ed by the hig

ion layer at

example, see

Homoge3

e homogenou

S, i.e. the ve

ssessment is

ratio criterion

een the phase

e and

ed to obtain

action φin:

e:

ws that this

he interface

gher viscosit

the bottom o

Figure 4-25(

eneous Flo

us model of t

elocity ratio

made of the

n, compared

es:

are the a

an expressio

s prediction

level is adj

ty of the gly

of the pipe s

(a1) and note

ow Model

two phase fl

of the fluids

e suitability

with separat

average velo

on for the in

⟨ ⟩ ,

is also in g

justing in or

ycerol soluti

section to th

e the value of

and Slip R

ow the centr

s (defined in

of a homoge

ted flow mod

ocities of the

-situ oil pha

⟨ ⟩ ,

Chapte

good agreem

rder to satisf

on. Specific

icken with r

f φin 0.75

Ratio

ral tenet and

n Equation 4

enous flow m

dels which ac

e oil and gl

se fraction ⟨

.⟨

φin

1 φi

er 4: Square S

ment with th

fy the increa

cally, this ca

respect to the

.

key assumpt

.11) is unity

model appro

ccount for th

ycerol solut

φ⟩y,t as a fun

⟨ ⟩ ,

⟨ ⟩ ,

in

Section PLIF R

he measurem

ased viscous

auses the gly

e oil layer o

tion is that th

. In what fo

oach, based o

he existence o

(4.11)

ion. This c

nction of the

(4.12)

(4.13)

Results

ments,

s drag

ycerol

n top.

he slip

ollows

on the

of slip

can be

e input

145


146

Hence the following expression is obtained for the slip ratio:

φin

φin.

⟨ ⟩ ,

⟨ ⟩ , (4.14)

One can see that under homogenous flow conditions, i.e., when S = 1, Equation 4.14 reduces to

φin⟨φ⟩y,t. The homogenous flow model is denoted by the thin sold line labelled S = 1 in

Figure 4-12.

It is seen that this approach over-predicts the in-situ phase fraction, with the extent of the over-

prediction increasing with an increasing oil input fraction (this will be accounted for and

explained to a large extent for in the further analysis below). Hence, a slip ratio of S = 1 does

not adequately characterise the experimental results contained herein.

In a bid to address the predictive shortcoming of this approach, Figure 4-14 investigates whether

a single S value, or alternatively an expression, can be used to characterise these flows.

(a) (b)

Figure 4-14: Experimental results and correlations for: (a) slip ratio S as a function of input oil

fraction φin, and: (b) in-situ oil phase fraction ⟨φ⟩y,t as a function of input oil fraction φin

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6


Slip

Rat

io, S

S = 1

S = 5.8251in

-0.1448

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

y, t

= 0.4111in

+0.1099

y, t

= in

/[(5.8251in

-0.1448)(1-in

)+in

]


147

It can be seen in Figure 4-14(a) that the fluids do not have a slip ratio of S = 1 except at the low

end of input oil phase fractions φin. This observation gives further confirmation of the

inadequacy of the homogeneous flow model to characterise the results presented in this chapter.

From Figure 4-14(a) a “best fit” correlation for the slip ratio is shown, the equation for which is:

5.8251 0.1448 (4.15)

From Figure 4-14(b) it can be seen that using the above correlation for the slip ratio coupled

with Equation 4.14 offers a better correlation between the input oil phase fraction φin and the in-

situ phase fraction ⟨φ⟩y,t compared with a simple linear relationship. The plot presented in

Figure 4-14(b) (given by the solid blue line) is of the relation:

⟨φ⟩y,t 5.8251 0.1448 1 (4.16)

One significant shortcoming of Figure 4-14(a) and ultimately of Equation 4.16 is that the

superficial mixture velocity is not accounted for, and as seen in Figure 4-12, the in-situ phase

fraction is a function of this the superficial mixture velocity.

Figure 4-15 examines the effect of the input oil phase fraction φin on the slip ratio S at constant

superficial mixture velocities Um. The figure includes a comparison with the experimental data

acquired by Lovick and Angeli (2004) for an oil-water system.

4.5.4

From

mixtu

(2004

the su

descr

impli

such

that

Solei

3.00

Howe

corre

decre

pursu

PVT

Model A4

m Figure 4-1

ure velocity

4) data plotte

uperficial m

ribed via the

ication that th

that the fluid

at Um 3.0

mani (1999)

m.s-1; the fl

ever, at a su

sponding re

ease in the s

ued in Chapt

techniques a

Application

5 it can be

increases th

ed for Um

mixture veloc

e homogenou

he flow is w

d is travelling

0 m.s-1, Lov

) reported a s

flow regime

uperficial mix

egime was t

lip ratio as t

ter 5 and Ch

are also cons

n and Com

seen that fo

he slip ratio

3.00 m.s-1 th

city increases

us flow mod

well mixed an

g at approxim

vick and A

slip ratio of S

at both thes

xture velocit

three-layer f

the superfici

hapter 6 in w

idered.

mparison

or a given o

decreases.

he slip ratio

s beyond a c

del. Coupled

nd has a turbu

mately the sa

Angeli (2004

S ≈ 1 at supe

se superficia

ty of Um

flow. Furth

ial mixture v

which results

Chapte

oil input pha

On inspecti

is S ≈ 1. He

critical poin

d with the ho

ulent velocit

ame velocity

) reported t

rficial mixtu

al mixture v

1.25 m.s-1 th

hermore, Hu

velocity incr

s obtained fo

er 4: Square S

ase fraction,

ion of the L

ence, it can b

t, the flow c

omogenous

ty profile (se

y. This is sup

the flow as

ure velocities

velocities wa

he slip ratio w

ussain (2004

eases. This

or velocity p

Section PLIF R

as the supe

Lovick and A

be deduced t

can be adequ

flow model

ee Figure 5-2

pported by th

being disp

s of Um 2.1

as dispersed

was S 1 an

) also repor

line of inqu

rofile by PIV

Results

rficial

Angeli

that as

uately

is the

27(b)),

he fact

persed.

10 and

flow.

nd the

rted a

uiry is

V and

148


149

Figure 4-15: Slip ratio S as a function of input oil fraction φin for different superficial mixture

velocities Um PLIF data is presented in blue and the results from Lovick and Angeli (2004) are

presented in red)

Figures 4-16 and 4-17 compare the in-situ phase fraction results of Russell et al. (1959) and

Lovick and Angeli (2004) with the present PLIF results and examine the ability of φmod,1 to

predict their data using the revised form of Equations 4.1 to 4.4 for flow in a circular cross-

sectional pipeline, given in Equation 5.6 in Chapter 5. It should be noted that Figure 4-16 does

not distinguish between the different constant superficial mixture velocities investigated.

However, this distinction is made in Figure 4-17.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6


Slip

Rat

io, S

S = 1Um = 0.07 m/s

Um = 0.14 m/s

Um = 0.22 m/s

Um = 0.14 m/s

Um = 0.80 m/s (Lovick and Angeli, 2004)



150

Figure 4-16: In-situ fraction ⟨φ⟩y,t as a function of input oil fraction φin compared with data

from Lovick and Angeli (2004) and Russell et al. (1959)

The first notable observation is that the φmod,1 predictive curves for the Russell et al. (1959) and

Lovick and Angeli (2004) data (red and black lines) occupy the opposite side of the S = 1 line

(i.e., the ⟨φ⟩y,t φin region) than that occupied by the φmod,1b predictive curve for the present

PLIF data (blue line), i.e., ⟨φ⟩y,t φin. This can be attributed to the viscosity ratio of the fluids.

The laminar drag model predicts that the in-situ oil phase fraction will be less than the input oil

phase fraction when the oil viscosity is less than that of the other fluid (in this case, glycerol

solution) and the oil density is less than that of the other fluid. Whereas, the laminar drag model

predicts that the in-situ oil phase fraction will be greater than the input oil phase fraction when

the oil viscosity is greater than that of the other phase and again, has the lower density of the

two fluids. This is observed in the experimental results. In the current campaign,

μoil μaq 0.04 whereas for Lovick and Angeli (2004) and Russell et al. (1959), the ratio values

were μoil μw

6 and μoil μw

18, respectively. It can be seen from Figure 4-16 that the

predictive φmod,1 curve for Lovick and Angeli (2004) is closer to the S = 1 line compared with

the predictive curve for Russell et al. (1959) data. The viscosity ratio for the fluids used by

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu

Oil

Pha

se F

ract

ion,

y,

t

PLIF ResultsLovick and Angeli (2004)Russell et al. (1959)

mod,1b(PLIF Data)

mod,1(Lovick and Angeli, 2004)

mod,1(Russell et al. (1959))

mod,2

(PLIF Data)

mod,2

(Lovick and Angeli, 2004)

mod,2(Russell et al. (1959))


151

Lovick and Angeli (2004) is closer to unity than those used by Russell et al. (1959). Hence, as

μoil μaq→ 1, S → 1 and a flow in which ⟨φ⟩y,t tends to φin occurs.

Figure 4-17 presents the data of Lovick and Angeli (2004) and Russell et al. (1959) for a range

of constant superficial mixture velocities. It can be seen that the trend observed in Figure 4-14

– that as the superficial mixture velocity increases the in-situ oil phase fraction ⟨φ⟩y,t tends

towards the input oil phase fraction φin and hence, towards homogenous flow – is again seen

from the data plotted in this form.

Figure 4-17: In-situ fraction ⟨φ⟩y,t as a function of input oil fraction φin for different superficial

mixture velocities Um for data by Lovick and Angeli (2004) and Russell et al. (1959)

Consideration of Figures 4-12, 4-16 and 4-17 together leads to the observation that at low

superficial mixture velocities a laminar drag model provides excellent agreement with the

experimental results, and as the superficial mixture velocity increases the flow becomes

sufficiently well mixed (i.e., it is in the dispersed flow regime) that φin⟨φ⟩y,t can be evaluated

via the homogenous flow model (i.e. S = 1).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu

Oil

Pha

se F

ract

ion,

y,

t


mod,1(Russell et al. 1959)



Um = 0.22 m/s (Russell et al. 1959)



152

These two conditions, i.e., smooth stratified flow and dispersed flow, present the extreme

conditions of an envelope in which the in-situ phase fraction can be found. This is presented in

Figure 4-18. The complexity arises in predicting the in-situ phase fraction at intermediate flow

regimes, i.e., the flow regime termed dual continuous flow by Lovick and Angeli (2004) and

three-layer flows in the current study. Here, both phases are dispersed at various degrees into

the continuum of the other. This underpins the need for a modified form of the two-fluid model

that accounts for the entrainment of one phase in a continuum of the other in dual continuous

flows. The information on phase distribution detailed in Section 4.4 can begin to provide an

insight into phase entrainment to make these developments.

Figure 4-18: In-situ phase fraction envelope

Section 4.8 presents a revised approach for the laminar drag model to account for the

entrainment of one phase in a continuum of the other to enable the prediction of the in-situ

phase fraction beyond the smooth stratified flow regime.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

Stratified FlowDispersed Flow

Dual Continuous Flow

Region

Increasing Um

4.6

This

on th

of the

as Eq

Figur

as a f

0.14 m

00

2

4

6

8

10

12

14

16

18

Inte

rfac

e L

evel

, H (

mm

)

00

2

4

6

8

10

12

14

16

18

Inte

rfac

e L

evel

, H (

mm

)

Interfa

section pres

he PLIF imag

e laminar dra

quation 4.4 a

re 4-19: The

function of in

m.s-1, (c) 0.2

0 0.2

0 0.2

ace Level

ents measure

ges and com

ag model. Th

s detailed in

(a)

(c)

e mean (μ) an

nput oil frac

21 m.s-1, and

0.4Oil Input Fracti

0.4Oil Input Fracti

ements of th

mpares these m

he prediction

Appendix 2

nd upper (μ +

tion φin for s

(d) 0.29 m.s

0.6 0.8ion,

in

0.6 0.8ion,

in

he position o

measuremen

n is denoted b

.

+ 2σ) and low

superficial m

s-1

1

-2+2

00

2

4

6

8

10

12

14

16

18

Inte

rfac

e L

evel

, H (

mm

)

1

-2+2

00

2

4

6

8

10

12

14

16

18

Inte

rfac

e L

evel

, H (

mm

)

Chapte

f the liquid-

nts with pred

by Hmod,1b an

wer (μ – 2σ)

mixture veloc

0.2

0.2

er 4: Square S

liquid interfa

dictions using

nd follows th

(b)

(d)

limits for the

cities Um of:

0.4 0Oil Input Fractio


Section PLIF R

face analysis

g a modified

he same deriv

e interface le

(a) 0.07 m.s

0.6 0.8on,

in

0.6 0.8on,

in

Results

made

d form

vation

evel H

s-1, (b)

1

-2+2

1

-2+2

153


154

Figure 4-19 shows the interface level H as a function of input oil fraction φin for fixed

superficial mixture velocities from Um 0.07 to 0.29 m.s-1, while Figure 4-20 shows the

interface level H as a function of superficial mixture velocities Um for given oil fractions

ranging from φin 0.25 to 0.75. The results presented are for the mean values and for the 95%

confidence limits of the mean value ± 2σ where σ is the standard deviation.

(a) (b)

(c)

Figure 4-20: The mean (μ) and upper (μ + 2σ) and lower (μ – 2σ) limits for the interface level H

as a function of superficial mixture velocity Um for input oil fractions φin of: (a) 0.25, (b) 0.50,

and (c) 0.75. Points a, b, c; k, l, m; and x, y, z correspond to the example images and

probability histograms in Figures 4-23, 4-24 and 4-25 respectively

0 0.1 0.2 0.30

2

4

6

8

10

12

14

16

18

Superficial Mixture Velocity, Um

(m/s)

Inte

rfac

e L

evel

, H (

mm

)

-2+2

0 0.1 0.2 0.30

2

4

6

8

10

12

14

16

18

Superficial Mixture Velocity, Um (m/s)

Inte

rfac

e L

evel

, H (

mm

)

-2+2

0 0.1 0.2 0.30

2

4

6

8

10

12

14

16

18


(m/s)

Inte

rfac

e L

evel

, H (

mm

)

-2+2

a b c

x

k l

m

z

y

These

super

interf

confi

level

oil fra

4.6.1

Figur

Hmod

is in

flow

the in

veloc

and d

e figures rev

rficial mixtur

face level is

dence interv

H fluctuates

action φin.

Lamina1

re 4-21 show

,1b) predicts

excellent ag

(Um 0.07

nterface leve

city increases

droplet forma

veal that, for

re velocity U

greater for

val (μ – 2σ →

s, increases

r Drag Mo

ws that the

the lowering

greement wit

m.s-1) in wh

el H decrea

s. This can

ation.

a given inpu

Um increases

higher inpu

→ μ + 2σ), wh

as the super

odel

modified fo

g of the inter

th the exper

hich the flow

ses for a gi

be attribute

ut oil fraction

s. It can als

ut oil fraction

hich indicate

ficial mixtur

rm of the la

rface level H

rimental data

contains no

iven oil inpu

d to the fact

Chapte

n φin, the inte

so be seen th

ns φin. Mor

s a height ran

re velocity U

aminar drag

H as the oil in

a points rela

droplets. H

ut fraction φ

t the model

er 4: Square S

erface level H

hat the rate o

reover, the e

nge within w

Um increases

model equa

nput fraction

ating to low-

However, it fa

φin as the su

does consid

Section PLIF R

H decreases

of decrease

extent of the

which the inte

s for a given

ation (denot

n φin increase

-velocity stra

ails to captur

uperficial m

er phase bre

Results

as the

in the

e 95%

erface

n input

ted by

es and

atified

re that

mixture

eak-up

155

Figur

mixtu

4.6.2

Hall

flows

gas-li

that t

Lock

liquid

flowi

prese

re 4-21: Inte

ure velocities

Hall and2

and Hewitt

s based upon

iquid flows t

the holdup (

khart and Ma

d flows, this

ing much fa

ented by Hall

erface Level

s Um

d Hewitt (1

(1993) prese

n the Taitel a

that assumes

(and thus, th

artinelli (1949

s assumption

aster than th

l and Hewitt

2

00

2

4

6

8

10

12

14

16

18

Inte

rfac

e L

evel

, H (

mm

)

l H as a fun

1993) Pred

ented models

and Dukler (

a flat gas-liq

he interface

9) parameter

n is extended

he liquid.

(1993) given

1 2

0.2O

Hmod,1b

Um

= 0.07 m

Um

= 0.14 m

Um

= 0.22 m

Um

= 0.29 m

ction of inpu

dictive Tec

s for the inte

(1976) 1D tw

quid interfac

level) for st

r under the

d to

The two-flu

n by:

0.4Oil Input Fract

m/s

m/s

m/s

m/s

Chapte

ut oil fractio

chniques

erface level i

wo-fluid mod

ce. Taitel an

tratified flow

e assumption

owing to th

uid model f

0

0.6 0tion,

in

er 4: Square S

on φin for di

in gas-liquid

del for the h

nd Dukler (19

w is a uniqu

n that ≅ c

he assumptio

for stratified

.8 1

Section PLIF R

ifferent supe

d and liquid-

holdup in stra

976) demons

ue function o

constant. Fo

on that the

d oil-water

(4.16)

Results

rficial

-liquid

atified

strated

of the

or gas-

gas is

flows

156


157

where is the Martinelli parameter given by oil oil

w w and is the dimensionless

interface height .

For gas-liquid flow a revised version of Equation 4.16 was presented:

12

1 0 (4.17)

Predicted interface level curves based on Equations 4.16 and 4.17 are plotted along with the

experimental results in Figures 4-22(a) and 4-22(b), respectively. The Hall and Hewitt liquid-

liquid flow model over-predicts the observed liquid levels, the over-prediction increasing with

increasing superficial velocity and oil input fraction. This over-prediction probably arises

because the interface is disturbed (and hence rough) whereas the model assumes a flat interface.

Surprisingly, better agreement is observed with the Hall and Hewitt gas-liquid model, but this is

probably coincidental.

(a) (b)

Figure 4-22: Interface Level H as a function of input oil fraction φin for different superficial

mixture velocities Um featuring interface level models presented by Hall and Hewitt (1993) for:

(a) stratified liquid-liquid flow, and (b) stratified gas-liquid flow

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

18

Oil Input Fraction, in

Inte

rfac

e L

evel

, H (

mm

)

Hall (1993)liquid-liquid

Um

= 0.07 m/s

Um

= 0.14 m/s

Um

= 0.22 m/s

Um

= 0.29 m/s

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

18


Inte

rfac

e L

evel

, H (

mm

)

Hall (1993)gas-liquid

Um

= 0.07 m/s

Um

= 0.14 m/s

Um

= 0.22 m/s

Um

= 0.29 m/s

4.6.3

Figur

used

respe

(a2 →

an in

fluctu

the fl

Figur

0.14 m

proba

c, as

00

0.2

0.4

0.6

0.8

1

Prob

abili

ty

Probabi3

res 4-23 to 4

to construc

ectively. Fro

→ c2, k2 → m

ncreasing su

uation range

low is stratifi

(a1)

(a2)

re 4-23: Flo

m.s-1, (c1) 0

ability histog

labelled in F

2 4 6 8Interface L

ility Histog

-25 present f

ct the mean

om inspection

m2 and x2 → z

uperficial mi

widens. We

ied, that the i

)

)

ow images

.29 m.s-1, al

grams for the

Figure 4-20(a

10 12 14 16Level (mm)

grams

frames and th

n interface

n of the imag

z2), one can c

ixture veloc

e would expe

interface lev

with superfi

ll at an inpu

e same condi

a)

18 0 20

0.2

0.4

0.6

0.8

1

Pro

babi

lity

he probabilit

level plots

ges (a1 → c1,

conclude tha

ity Um whi

ect that at a l

el would be

(b1)

(b2)

ficial mixtur

ut oil fraction

tions respect

4 6 8 10 1Interface Level (m

Chapte

ty histogram

shown in

, k1 → m1 an

at the mean in

ile at the sa

low superfic

flat and stab

e velocities

n φin 0.25

tively. Data

12 14 16 18mm)

Prob

abili

ty

er 4: Square S

ms for the poi

Figures 4-2

nd x1 → z1) a

nterface leve

ame time th

ial mixture v

ble H (Shaha,

Um of: (a1

5; (a2), (b2) a

corresponds

0 2 4 60

0.2

0.4

0.6

0.8

1

Interf

Section PLIF R

ints that have

20(a) to 4-

and the histog

el μH decreas

he interface

velocity Um,

, 1999).

(c1)

(c2)

) 0.07 m.s-1

and (c2) sho

s to Points a,

8 10 12 14face Level (mm)

Results

e been

-20(c),

grams

ses for

level

when

1, (b1)

ow the

b and

16 18

158


159

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 4-24: Flow images with superficial mixture velocities Um of: (k1) 0.07 m.s-1, (l1) 0.14

m.s-1, (m1) 0.29 m.s-1, all at an input oil fraction φin 0.50; (k2), (l2) and (m2) show the

probability histograms for the same conditions respectively. Data corresponds to Points k, l and

m, as labelled in Figure 4.23(b)

From inspection of Figures 4-23 to 4-25 it is seen that at low superficial mixture velocities the

interface is found only over a narrow vertical range i.e., as seen in Figure 4-23(a2), thus fits with

the classification of smooth stratified flow. As the superficial mixture velocity increases, it is

seen that the range of vertical heights over which it is found widens, with the flow first

transitioning into stratified wavy flow, and then, as the superficial mixture velocity continues to

increases the flow becomes increasingly disturbed resulting in droplet formation, i.e., the flow

regime being mixed flow (see Table 4-1). This is coupled with a further widening of the range

of interface level heights; see Figures 4-24(c2) and 4-25(z2).

0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Prob

abili

ty

Interface Level (mm)0 2 4 6 8 10 12 14 16 18

0

0.2

0.4

0.6

0.8

1

Prob

abili

ty

Interface Level (mm)0 2 4 6 8 10 12 14 16 18

0

0.2

0.4

0.6

0.8

1

Prob

abili

ty

Interface Level (mm)

Figur

m.s-1,

proba

and z

4.6.4

Final

chann

seen

low s

a con

the

encou

4-25(

00

0.2

0.4

0.6

0.8

1

Prob

abil

ity

(x1)

(x2)

re 4-25: Flo

, (x1) 0.29

ability histog

z, as labelled

Interfac4

ly, Figure 4-

nel, where

that the dime

superficial m

ntinuum of th

1 ≅ ⟨φ

untered as th

(z1). For low

2 4 6 8Interface L

)

)

ow images w

m.s-1, all at

grams for th

in Figure 4-

ce Depth

-26 below rel

is the dimen

ensionless in

mixture veloc

he other is n

φ⟩y,t relation

he superficia

wer oil input

10 12 14 16Level (mm)

with superfici

t an input o

he same cond

20(c)

lates the dim

nsionless int

nterface heig

ities i.e., for

ot present. H

nship break

al mixture ve

t phase frac

18 0 20

0.2

0.4

0.6

0.8

1

Prob

abili

ty

(y1)

(y2)

ial mixture v

oil fraction φ

ditions respe

mensionless in

terface heigh

ght equates w

stratified flo

However, as

s down.

elocity is inc

tions the en

4 6 8 10Interface Level (m

Chapte

velocities Um

φin 0.75;

ectively. Da

nterface dept

ht) to the in-

well with the

ows for whic

s the superfic

This can b

reased, see F

ntrainment is

12 14 16 18mm)

Prob

abili

ty

er 4: Square S

m of: (x1) 0.0

(x2), (y2) a

ata correspon

th 1 (f

situ phase fr

in-situ phase

ch entrainme

cial mixture

be attributed

Figures 4-25

seen to be

0 2 4 60

0.2

0.4

0.6

0.8

1

Inter

Section PLIF R

(z1)

(z2)

07 m.s-1, (x1)

and (z2) show

nds to Point

from the top

raction ⟨φ⟩y,t

e fraction fo

ent of one ph

velocity incr

d to entrain

5(x1) compare

dominated b

8 10 12 14face Level (mm)

Results

) 0.14

w the

ts x, y

of the

. It is

r very

hase in

reases

nment

ed with

by oil

16 18

160

dropl

interf

Figu

4.7

The f

inves

are an

the e

diame

proba

φin

lets below th

face from the

ure 4-26: Dim

Drople

final form o

stigated flow

nalysed. Th

ffects of inp

eters μd (def

ability histog

0.5) that ha

he interface (

e top of the c

mensionless

et Size Dis

of analysis p

ws. Both oil

he results are

put oil fracti

fined in Equa

grams for t

ave been used

00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dim

ensi

onle

ss I

nter

face

Dep

th, H

/ HT

(such as thos

channel to be

interface dep

stribution

performed on

droplets in

e shown in F

ion φin and

ations 3.8 an

the three flo

d to construc

0.1 0.2 0.In-situ

Um

= 0.07

Um

= 0.14

Um

= 0.22

Um

= 0.29

se shown in

e lower (i.e.,

pth 1 c

n

n the PLIF

glycerol solu

igures 4-27,

superficial m

nd 3.9 in Sec

ow condition

ct Figure 4-27

.3 0.4 0.5u Oil Phase F

m/s

m/s

m/s

m/s

Chapte

Figure 4-11)

a higher inte

correlated wi

images cons

ution and gl

4-28 and 4-

mixture velo

ction 3.11).

ns (with the

7(b).

0.6 0.7 0Fraction,

y,

er 4: Square S

); resulting i

erface level).

ith in-situ ph

siders the dr

ycerol soluti

-29 below. F

ocity Um on

Figures 4-28

e same inpu

0.8 0.9 1

t

Section PLIF R

in the depth

hase fraction

roplet sizes

ion droplets

Figure 4-27 s

the mean d

8 and 4-29 p

ut oil fracti

Results

of the

⟨φ⟩y,t

in the

in oil

shows

droplet

resent

ion of

161


162

(a) (b)

Figure 4-27: Mean droplet diameter μd for: (a) varying input oil fraction φin and constant

superficial mixture velocities Um 0.14 m.s-1, 0.22 m.s-1 and 0.29 m.s-1, and (b) varying

superficial mixture velocity Um and a constant input oil fraction of φin 0.5. Points a, b and c

correspond to the probability histograms in Figures 4-28 (for oil) and 4-29 (for glycerol-water).

Red symbols represent glycerol-solution droplets and blue symbols for oil droplets

At the lowest tested input oil fraction φin no glycerol solution-in-oil (w/o) droplets are observed

and the droplets are exclusively of oil-in-glycerol solution (o/w). Starting from an input oil

fraction φin 0.1 – 0.3, Figure 4-27(a) indicates that the average oil droplet diameter μd,oil

increases monotonically with an increasing input oil fraction φin. This is the case for all three

tested superficial mixture velocities, Um 0.14 m.s-1, 0.22 m.s-1 and 0.29 m.s-1. When the input

oil fraction reaches φin~ 0.5, glycerol solution droplets begin to appear in the flow together with

the oil droplets, and as the input oil fraction φin is increased further the number of oil droplets

observed in the flow decreases quickly and the flow becomes dominated by glycerol solution

droplets. Interestingly, as the input oil fraction φin is increased in the range φin 0.5 the

average oil droplet diameter μd,oil tends generally to become smaller. This trend, however, is

not as clear for the highest superficial mixture velocity of Um 0.29 m.s-1 (at least with the

investigated envelope of Um), for which the average oil droplet diameter remains in the range

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

Input oil phase fraction, in

Mea

n D

ropl

et D

iam

eter

, d (

mm

)

Um

= 0.14 m/s

Um

= 0.22 m/s

Um

= 0.29 m/s

0 0.1 0.2 0.3 0.40

0.5

1

1.5

2

2.5

3

3.5

4

Superficial Mixture Velocity Um

, (m/s)

Mea

n D

ropl

et D

iam

eter

, d (

mm

)

d,oil

d,gs

a

b c

G-SOil


163

μd,gs 2.4 – 2.9 mm (or, μd,gs ≅ 2.6 mm to within 10% that is comparable to the experimental

uncertainty in this measurements) between φin 0.5 and φin 0.87. While noting this

exception, if one considers all (both glycerol solution and oil) droplets in the flow it is possible

to conclude by considering Figure 4-27(a) that the mean droplet size in the flow increases,

reaches a maximum at around φin~ 0.5 and then decreases again as the input oil fraction φin is

increased. The peak in the mean droplet diameter μd occurs in the range 0.5 φin 0.6. This

is consistent with the finding of Pal (1993) who observed a peak in Sauter mean diameter (when

measured as a function of water concentration) around the water-in-oil to oil-in-water phase

inversion point, though it must be stated that those results were generated in a dispersed flow

regime. The peak was found at a water concentration of 30%, which is comparable with the

glycerol solution concentration at which the peak occurs in the current study.

Having considered the effect of varying the input oil fraction of φin at constant superficial

mixture velocities Um, Figure 4-27(b) shows results of mean droplet size as a function of

superficial mixture velocity Um but for a given (fixed) input oil fraction of φin 0.5. This

value was chosen as it corresponds to conditions in which both glycerol solution and oil droplets

exist concurrently in the flow. The mean oil droplet diameter μd,oil increases slightly (by about

15%) and then decreases significantly (by about 36%) as a result of the increase in the

superficial mixture velocity Um from 0.14 m.s-1 to 0.22 m.s-1, and then to 0.29 m.s-1. At the

same time, the mean glycerol solution droplet diameter μd,gs remains approximately constant at

low superficial velocities Um from 0.14 m.s-1 to 0.22 m.s-1, and then decreases by about 12% at

high velocities Um 0.29 m.s-1. From Figure 4-27(b) and if all droplets in the flow are taken

into consideration, it is found that the mean droplet size is small at both low and high superficial

mixture velocities Um and is largest at intermediate velocity values, which is in this work is

Um ≅ 0.2 m.s-1.

4.7.1

The a

dropl

dropl

Figur

m.s-1,

size d

to Po

The f

soluti

Um

dropl

oil dr

00

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty

Probabi1

above trends

lets) and 4-2

let size, one f

(a1)

(a2)

re 4-28: Flo

, (c1) 0.29 m

distribution p

oints a, b and

first observa

ion droplets

0.07 m.s-1

let diameter

roplet size hi

1 2 3 4Droplet Diam

ility Histog

can be unde

9 (for glycer

for each of th

)

)

ow images w

m.s-1, all at an

probability h

c, as labelle

ation that ca

than for oil d

the oil drop

μd,oil, while

istogram also

5 6 7 8 9meter, d

(mm)

grams

erstood with

rol solution-

he data point

with superfici

input oil fra

histograms fo

ed in Figure 4

an be made

droplets. In

let size histo

at the highe

o contains va

10 0 1 20

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty

reference to

in-oil drople

ts in Figure 4

(b1)

(b2)

ial mixture v

action φin 0

or the same c

4-27(b)

is that the s

particular, a

ogram is clo

est superficia

alues in a ver

3 4 5 6Droplet Diameter,

d(

Chapte

o Figures. 4-2

ets), which sh

4-27(b).

velocities Um

0. 5; (a2), (b2

conditions re

size distribut

t the lowest

se to a delta

al mixture ve

ry narrow ra

7 8 9 10(mm)

Pro

ba

bili

ty

er 4: Square S

28 (for oil-in

how probabi

m of: (a1) 0.0

2) and (c2) sh

espectively.

tions are bro

superficial m

a function ce

elocity of Um

nge around t

0 1 2 30

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty

Drople

Section PLIF R

n-glycerol so

ility histogra

(c1)

(c2)

07 m.s-1, (b1)

how the oil d

Data corres

oader for gly

mixture veloc

entred at the

m 0.29 m.s

the mean dia

4 5 6 7 8et Diameter, d

(mm)

Results

olution

ams of

) 0.22

droplet

ponds

ycerol

city of

mean

s-1 the

ameter

9 10

164


165

μd,oil. This reveals a strong preference for a certain size of droplet at low and high velocities in

the case of oil. At intermediate superficial mixture velocities (i.e., Um 0.22 m.s-1) some

spreading is apparent, in particular at larger diameters, which explains the slight increase in the

mean oil droplet diameter μd,oil shown directly in Figure 4-27(b).

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 4-29: Flow images with superficial mixture velocities Um of: (a1) 0.07 m.s-1, (b1)

0.22 m.s-1, (c1) 0.29 m.s-1, all at an input oil fraction φin 0. 5; (a2), (b2) and (c2) show the

glycerol solution droplet size distribution probability histograms for the same conditions

respectively. Data corresponds to Points a, b and c, as labelled in Figure 4-27(b)

On the other hand, although glycerol solution droplets are more broadly distributed as stated

previously, when the superficial mixture velocity Um is increased from 0.07 m.s-1 to 0.22 m.s-1,

the distribution broadens even further and gives rise to a higher probability of having both

smaller and larger glycerol solution droplets. Then, at the even higher superficial mixture

velocity of Um 0.29 m.s-1, the probability of finding larger droplets in the flow decreases, as

the probability of finding smaller ones continues to increase. Importantly, this latter observation

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty

Droplet Diameter, d (mm)

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty


0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty


conce

in the

cases

in Fig

4.8

This

accou

of its

4.8.1

The o

31.

Sectio

fracti

30(a)

mixtu

entrai

mixtu

super

the in

declin

4-31(

increa

erning the in

e case of oil

s to the sharp

gure 4.30(b).

Predict

section descr

unt for the en

application

Entrain1

oil phase fra

These resu

on 4.4) for a

ion combina

) it can be se

ure velocity i

ined in the

ure velocity

rficial mixtur

nput oil phas

nes at a high

(b). As the s

ases more qu

nability of the

l droplets (c

p decrease in

.

tive Tech

ribes endeav

ntrained fluid

beyond smo

ed Phase F

ction above

ults have be

a given exper

ation) with it

een that the

increases. C

glycerol solu

increase at a

re velocities

e fraction. H

her rate for h

superficial m

uickly for low

e flow to sus

ompare for

n the mean di

nique Dev

vours to deve

d droplets ab

oth stratified

Fraction

and below th

een obtained

rimental run

ts associated

oil phase fra

Conversely, fr

ution phase

a given oil in

, the oil pha

However, as

higher oil inp

mixture veloc

wer oil input

stain larger d

example Fig

iameter of b

velopmen

elop the lami

bove and bel

d flow to incl

he interface

d by couplin

(i.e., a given

d interface le

action above

from Figure 4

below the i

nput phase f

ase fraction a

the superfici

put phase fra

ity increases

t phase fracti

Chapte

droplets at hi

gures 4-29 (b

oth oil and g

nt

inar drag mo

low the inter

lude dual con

level are pre

ng the phas

n superficial

evel (from S

e the interfac

4-30(b) it is s

nterface leve

fraction. Fig

above the int

ial mixture v

actions. The

s, the oil pha

ions.

er 4: Square S

igher velocit

b) and (c)),

glycerol solu

del presented

rface so as to

ntinuous flow

esented in Fi

se distributio

mixture velo

Section 4.6).

ce decreases

seen that the

el increases

gure 4-31(a)

terface level

velocity incre

e converse is

se fraction b

Section PLIF R

ties is also ev

and leads in

ution demons

d in Section

o extend the

w.

igures 4-30 a

on profiles

ocity and oil

From Figu

as the supe

e oil phase fra

as the supe

shows that a

is independ

eases, the inte

seen from F

below the inte

Results

vident

n both

strated

4.5 to

scope

and 4-

(from

l input

ure 4-

rficial

action

rficial

at low

dent of

erface

Figure

erface

166


167

(a) (b)

Figure 4-30: Oil phase fraction as a function of input oil phase fraction φin for different

superficial mixture velocity Um: (a) above the interface level, and (b) below the interface level

(a) (b)

Figure 4-31: Oil phase fraction as a function of superficial mixture velocity Um for different

input oil phase fraction φin: (a) above the interface level, and (b) below the interface level

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Oil

Phas

e Fr

actio

n A

bove

Int

erfa

ce,

Um

=0.07 m/s

Um

=0.14 m/s

Um

=0.22 m/s

Um

=0.29 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.04

0.08

0.12

0.16

0.2


Oil

Phas

e Fr

actio

n B

elow

Int

erfa

ce,

Um

=0.07 m/s

Um

=0.14 m/s

Um

=0.22 m/s

Um

=0.29 m/s

0 0.05 0.1 0.15 0.2 0.25 0.30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


(m/s)

Oil

Phas

e Fr

actio

n A

bove

Int

erfa

ce,

in

=0.25

in

=0.50

in

=0.75

0 0.05 0.1 0.15 0.2 0.25 0.30

0.02

0.04

0.06

0.08

0.1


(m/s)

Oil

Phas

e Fr

actio

n B

elow

Int

erfa

ce,

in

=0.25

in

=0.50

in

=0.75

4.8.2

Figur

has b

the oi

Figur

that o

interf

linear

mode

Wher

Figur

three

that o

interf

(3) an

ratio)

Enhance2

re 4-32 prese

been amended

il droplets di

re 4-30 and 4

of the pure fl

face ( above

r viscosity in

el. These are

re

re 4-32 prese

φmod,1b pred

of the individ

face (and hen

nother in wh

) have been c

ed Lamina

ents a revised

d to account

ispersed belo

4-31 of Secti

luids to the v

below). Th

nterpolation

e given in Eq

and

ents the expe

dictive curve

dual fluids; (2

nce their rati

hich the visc

calculated us

ar Drag M

d version of F

for the glyce

ow the interf

ion 4.8.1. In

viscosity ratio

he revised vi

based on the

quation 4.18

.

1 2.5

.

erimental PL

s included fo

2) another in

io) have bee

osities of the

sing the Tayl

Model

Figure 4-12

erol solution

face. This ha

n Figure 4-32

o of the flow

iscosities ha

e phase fract

and Equation

1 .

0.41

IF data for c

or each; (1) o

n which the v

n calculated

e flow above

or (1932) vis

Chapte

in which the

n droplets dis

as been done

2, the viscos

w above the i

ave been cal

tions, and; (2

n 4.19, respe

constant supe

one in which

viscosities of

using a line

e and below

scosity mode

er 4: Square S

e fluid viscos

persed above

e using the re

ity ratio has

interface to th

culated via

2) the Taylo

ectively.

erficial mixtu

h the viscosity

f the flow ab

ear viscosity

the interface

el.

Section PLIF R

sity ratio ( oi

e the interfac

esults contain

been altered

he fluid belo

two means;

or (1932) vis

(4.18)

(4.19)

ure velocitie

y ratio is bas

ove and belo

interpolation

e (and hence

Results

ilaq

)

ce and

ned in

d from

ow the

(1) a

cosity

s with

sed on

ow the

n, and

e their

168


169

From inspection of Figure 4-32 it can be seen that accounting for the phase distribution (i.e., the

phase fraction of the dispersed phase above and below the interface) coupled with φmod,1b

provided excellent agreement with the experimental data and a marked improved on just using

the viscosity ratio of the individual fluids. In essence, the viscosity ratio and the superficial

mixture velocity are the fundamental parameters that have to be accounted for in order to

adequately predict the in-situ phase fraction. As oilaq→ 1 and the superficial mixture

velocities Um increases the in-situ phase fraction tends ⟨φ⟩y,t to the input phase fraction φin.

(a) (b)

(c) (d)

Figure 4-32: In-situ fraction ⟨φ⟩y,t as a function of input oil fraction φin for superficial mixture

velocities Um: (a) 0.07 m.s-1; (b) 0.14 m.s-1; (c) 0.21 m.s-1, and; (d) 0.29 m.s-1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

Um

= 0.07 m/s

mod,1b

mod,1b (Linear)

mod,1b (Taylor, 1932)

S = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

Um = 0.14 m/s

mod,1b

mod,1b (Linear)


S = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

Um

= 0.22 m/s

mod,1b

mod,1b (Linear)


S = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il P

hase

Fra

ctio

n, y,

t

Um = 0.29 m/s

mod,1b

mod,1b (Linear)


S = 1

It can

mixtu

in tha

leadin

the in

interf

the g

emul

below

the in

in the

given

input

4.9

A no

(PLIF

two i

fluids

This

spatio

chara

The i

quant

size.

n be seen th

ure velocity

at as the sup

ng to the ent

nterface and

face will low

lycerol-solut

sion viscosit

w the interfac

nterface close

e dispersed fl

n height to th

t oil phase fra

Conclu

on-intrusive

F) has been

immiscible l

s used were

experiment

otemporal in

acteristics of

images produ

titatively in

The techn

hat the in-si

increases us

perficial mix

trainment of

glycerol solu

wer the viscos

tion above th

ty) above the

ce increases

er together.

flow regime)

hat below it i

action.

usions

optical visu

developed f

iquids of ma

oil and a gly

al technique

nformation o

such flows.

uced were u

estimating th

nique has pr

itu phase fra

ing viscosity

xture velocity

one phase in

ution droplet

sity of the flo

he interface;

e interface to

the results is

The limit of

and there is

is unity. At

ualisation te

for the use o

atched refrac

ycerol-water

e is shown

of the flow

sed qualitati

he distributio

roved to be

action can b

y ratio value

y increases,

n a continuum

ts form abov

ow below th

they will re

o increase. H

s to bring the

f this is when

no interface

this point, th

echnique, na

of analysis o

ctive index;

r solution and

to be a p

w behaviour

vely for the

on and avera

e an effectiv

Chapte

be accurately

es that tend t

the flow be

m of the othe

ve it. Hence

e interface a

esults in the

Hence, as th

e viscosities

n the flow is c

and the visc

he in-situ oil

amely plana

of co-current

in this case

d the channe

powerful too

and hence,

identificatio

age of the p

ve means of

er 4: Square S

y predicted

o unit. This

ecomes incre

er, i.e., oil dr

, the presenc

and the conve

viscosity of

e degree of

of the flows

completely w

cosity ratio o

l phase fract

ar laser-indu

t liquid-liqui

discussed in

el was square

ol that can

a valuable

on of the flow

hase fraction

f capturing

Section PLIF R

as the supe

s can be expl

easingly turb

roplets form b

ce of oil belo

erse is the ca

f the flow (i.e

mixing abov

s above and b

well-mixed (

f the fluid ab

ion is equal

uced fluores

d flows invo

n this Chapte

e in cross sec

provide de

e insight int

w pattern an

ns and the d

the behavio

Results

rficial

lained

bulent,

below

ow the

ase for

e., the

ve and

below

i.e., is

bove a

to the

scence

olving

er, the

ction..

etailed

to the

d also

droplet

our of

170


171

horizontal liquid-liquid flows and has allowed a flow regime map describing this flow

behaviour to be generated in a more unequivocal way. Eight distinct flow regimes were

observed. These were approximated into four flow types: (1) stratified flow; (2) mixed flow

(i.e., a flow with two distinct continuous phase regions with droplets); (3) continuous oil-phase

dispersion; and (4) continuous aqueous-phase dispersion.

The investigated flows can be categorised generally as comprising three distinct zones, with a

continuous oil phase at the top and a continuous glycerol-water phase at the bottom, separated

by a mixed zone. The vertical space covered by the mixed zone increased at higher superficial

velocities. The interface level (vertical height from the bottom of the channel) separating the oil

and glycerol-water phases decreased when increased input oil fractions were tested, as expected,

though it was also found that the measured in-situ oil phase fraction at the measurement plane

was considerably lower than the oil phase fraction at the pipe inlet based on the supplied flow

rates of oil and glycerol-water. This was explained in terms of the different viscosities of the

two liquids and the associated viscous drag in the channel that led to a considerable difference

in bulk velocities in the measurement section. At low input oil phase fractions the interface

level was not affected by changes to the superficial mixture velocity. However, at higher input

oil fractions the interface height decreased as the superficial mixture velocity was increased.

Higher superficial mixture velocities also led to increased fluctuations of the interface level and

a smaller mean size of droplets in the flow. Glycerol solution droplets were observed

predominantly at the lower end of input oil fractions, whereas oil droplets were observed at the

higher end. For all tested mixture velocities, the mean droplet size increased initially, reached a

maximum and then decreased as the input oil fraction was increased. Further, for a fixed

(intermediate) input oil fraction, the mean droplet diameters were largest at intermediate

mixture velocities and smallest at high mixture velocities. Of these two observations the more

pronounced was the latter.


172

Having considered the phase fraction and interface information provided by the analysis of the

novel spatiotemporal measurements contained herein, the most important lesson learnt is that

simplistic modelling approaches, such as the two-fluid model, are unlikely to be capable of

representing adequately flows for such complexly mixed fluids. For example, it was reported

by Ishii and Mishima (1984) that their conventional one-dimensional two-fluid model exhibited

a number of serious shortcomings, which mainly arose due to the inadequate treatment of phase

distributions in the domain. The experimental results presented here emphasise the existence of

complex mixing patterns encountered in secondary (i.e., aqueous droplet in an oil droplet in a

continuous aqueous phase – w/o/w, or oil droplet in an aqueous droplet in a continuous oil

phase – o/w/o), and multiple (i.e., o/w/o/w and w/o/w/o, etc.) dispersions, as well as

complexities at the interface in liquid-liquid flow. Thus the current investigation underscores

the need for these particular flow behaviours to be modelled in order to achieve accurate

analytical descriptions of these important flows.

Though interesting and informative results have been obtained with a square cross section duct,

it would clearly be closer to industrial practice to use channels of circular cross section. In this

latter case, and even with matching of the refractive index of the two fluids and the use of a

transparent tube, the wall curvature can lead to significant image distortion. The work presented

in Chapter 5 attempts to overcome this disparity by use of a circular cross section visualisation

cell and a graticule method to a correct for the image distortion arising from the wall curvature

(see Section 3.10.2).

CH

La

Ho

Ci

5.1

This

sectio

descr

tube

meas

and P

descr

PLIF

pipeli

circul

the u

capab

the co

HAPT

aser-In

orizon

rcular

Introdu

chapter pre

on visualisat

ribed in Chap

was used in

urement syst

Particule Tra

ribed in this

, PIV and PT

ine systems

lar pipe sect

use of a grati

bility, and sp

o-current liqu

TER 5

nduced

ntal Liq

r Cros

uction

esents the ex

tion section

pter 4 not on

n the work

tems to inclu

acking Veloc

Chapter are

TV. The use

but is optic

tion has been

icule (printed

pecifically the

uid-liquid flo

d Fluo

quid-L

ss Sect

xperimental

detailed in

nly in the use

described in

ude (in addit

cimetry (PTV

e the first o

of a circular

cally more c

n made feasi

d target) det

e use of PIV

ow velocity p

orescen

Liquid

tion Du

results obta

Section 3.10

e of a circular

n Chapter 4

tion to PLIF)

V). To the b

obtained for

r cross sectio

challenging.

ible by using

tailed in Sec

V and PTV en

profiles.

Chapter

nce St

d Flow

uct

ained using

0.2. The w

r cross sectio

4) but also

) both Particu

best of the au

liquid-liquid

on tube is mo

The prov

g an image c

tions 3.11.1.

nabled the de

r 5: Circular S

udies

ws in a

the dedicate

work is a dev

on tube (a sq

in the exten

ular Image V

uthor’s know

d systems us

ore represent

vision of de

correction tec

. The enhan

etailed diagno

Section PLIF R

of

ed circular

velopment o

quare cross se

nsion of the

Velocimetry

wledge, the r

sing simulta

tative of indu

tailed data i

chnique invo

nced measure

ostic inspect

Results

cross-

of that

ection

laser

(PIV)

results

aneous

ustrial

in the

olving

ement

tion of

173

The

prese

4. H

wave

result

the fl

sectio

vertic

interf

wave

from

In the

of the

Figur

an or

the i

meas

5.2

The e

that

Olym

V710

circul

distor

analysis me

ented in this c

However, her

e velocity ⟨

ts, including

low regime c

ons present t

cal phase dis

face level da

e velocity res

this part of w

e work descr

e pipe and t

re 3.5). Thus

rientation wh

njection wa

urements is d

Experi

experiments

outlined in

mpus i-SPEE

0 Monochrom

lar cross-sec

rtion arising

ethodology p

chapter, are

rein the qua

⟩ and the

images of th

classification

the results f

stribution pr

ata (Section 5

sults (Section

work are pre

ribed in this

he (heavier)

s, in the expe

hich is the na

as inverted (

described in

imental O

described in

Section 4.2

D 3 high sp

matic System

ction visualis

for the refra

performed o

similar to tho

antitative ana

velocity pro

he flow regim

ns, is present

from the qua

rofiles (Secti

5.6); (4) drop

n 5.8), and; (

sented in Sec

Chapter, the

aqueous (gl

eriments des

atural one. A

(oil phase a

Chapter 6.

Operation

n this Chapte

2. However

eed camera

m used for th

sation cell inv

active index

on the exper

ose used to c

alysis is exte

ofiles in the f

mes observed

ted first in Se

antitative ana

ion 5.4); (2)

plet size dist

(6) velocity p

ction 5.10.

flow was in

lycerol solut

cribed in thi

further serie

at the botto

er were condu

r, in the ex

(see Section

he experimen

volved the u

disparities. T

Chapter

rimental dat

characterise t

ended to inc

flow ⟨U ⟩ ,

d and a flow

ection 5.3. F

alyses of the

) in-situ phas

tribution resu

profiles (Sect

nitiated by inj

tion) phase a

s Chapter, th

es of experim

m and aque

ucted by emp

xperiments d

n 3.4.1) was

nts described

use of a grati

Though the r

r 5: Circular S

ta, and the

the flows pre

clude results

. A qualitat

w regime map

Following th

e flow imag

se fractions

ults (Section

tion 5.9). Fi

njecting the o

at the bottom

he two liquid

ments was ca

eous on top

ploying a sim

described in

used rather

d in Chapter

cule to calib

refractive ind

Section PLIF R

associated r

esented in Ch

s for the inte

ive analysis

p constructed

his, the subse

es as follow

(Section 5.5

5.7); (5) inte

inally, conclu

oil phase at th

m of the tub

d phases star

arried out in w

p). This seri

milar proced

this Chapte

than the Pha

4. The use

brate for the i

dex of the flu

Results

results

hapter

erface

of the

d from

equent

ws: (1)

5); (3)

erface

usions

he top

e (see

rted in

which

ies of

dure to

er, an

antom

of the

image

uids is

174

close

boros

minim

(Pers

need

using

The i

in Ch

fracti

indep

exper

varied

Chap

The a

aim h

the a

stratif

5.3

Eight

identi

each

four

chara

ly matched,

silicate glass

mised by pla

pexTM) box

for correcti

g the graticul

investigated

hapter 4, nam

ion of oil i

pendently in

rimental con

d between 0.

pter 4.

analysis pres

has been to c

aim of enhan

fied and disp

Flow P

t distinct flo

ified using t

of the flow r

more gener

acterised by t

, there are

s circular tu

acing the bo

filled with a

on of the im

e calibration

flow conditi

mely: (1) the

in the pipe

48 runs an

nditions span

.1 and 0.9. T

sented in this

capture the f

ncing unders

persed flow.

Phenomen

ow regimes h

the same cla

regimes are p

ral flow reg

two distinct c

differences

ube visualisa

orosilicate g

a fluid of the

mage to get

n piece is det

ions are defi

superficial m

φin. Thes

nd kept cons

nned a range

The matrix o

s chapter is fo

flow regime t

standing of t

na and Re

have been ob

ssification sy

presented in

gimes, name

continuous p

between the

ation test se

lass visualis

same refrac

reliable qua

ailed in Sect

ined via the

mixture veloc

e parameter

stant for the

e of Um from

of experiment

focussed in th

transition fro

the flow cha

egime Ma

bserved in t

ystem as use

Figure 5-1.

ely: (1) stra

phase regions

Chapter

e refractive

ection. Thou

ation section

tive index (i

antitative inf

tion 3.11.1.

same two in

city Um and;

rs (defined

duration of

m 0.11 to 0.8

tal condition

he lower Um

om stratified

aracteristics i

p

he current P

ed in Chapte

Once again,

atified flow

s with drople

r 5: Circular S

index of th

ugh the dist

n inside a sq

.e., Exxsol D

formation. T

ndependent p

; (2) the inlet

in Section

f each run.

84 m.s-1. In

ns is largely t

range (0.10

d to dual cont

in the regim

PLIF study.

er 4. Instant

the flows ca

w; (2) mixed

ets in each; (

Section PLIF R

he fluids an

ortion effec

quare acrylic

D80) there is

The procedu

parameters as

t volumetric

4.2) were v

The investi

addition, φi

the same as t

to 0.42 m.s-

tinuous flow

me region be

These have

taneous imag

an be groupe

d flow, whi

3) two-layer

Results

nd the

ts are

c resin

still a

ure for

s used

phase

varied

igated

in was

that in

1); the

w, with

tween

e been

ges of

ed into

ich is

r flow,

175

Chapter 5: Circular Section PLIF Results

176

which comprised of a dispersed region and a continuous, unmixed region; and (4) dispersed

flows. These are the same as those identified in Chapter 4; the generalised grouping is

presented in Table 4-1.

A flow regime map relating the flow classifications to the input oil fraction φin and the

superficial mixture velocity Um is presented in Figure 5-2. From the flow regime map (Figure

5-2) it can be seen that the stratified flow regime is observed up to a superficial mixture velocity

of Um 0.34 m.s-1; this being 0.27 m.s-1 higher than the highest superficial mixture velocity

(i.e., Um 0.07 m.s-1) at which the stratified regime was observed for the square cross-section

visualisation section (see Figure 4-2). However, above a superficial mixture velocity of

Um 0.17 m.s-1 stratified flow is only observed at low oil input phase fractions φin 0.4.


177

(a) Stratified flow (b) Stratified flow with droplets

(c) Oil droplet layer (d) Glycerol solution droplet layer

(e) Three layer flow (f) Oil dispersion over glycerol solution

(g) Oil flow over glycerol solution dispersion (h) Glycerol solution dispersion

with glycerol solution film with glycerol solution film

Figure 5-1: Images of the 8 distinct flow regimes observed in the circular cross section

experimental campaign

1 mm


178

Above a superficial mixture velocity of Um 0.34 m.s-1 droplets are found at all oil input phase

fraction and the flow is different forms of stratified flow with droplet i.e., above Um 0.34 m.s-

1 the flow has transitioned to dual continuous flow for all oil input phase fractions. As the

superficial mixture velocity increases, the range of oil input phase fractions covered by dual

continuous flow diminishes and dispersed flows being to form at the oil input phase fraction

extremes i.e., very low (near zero) and very high (near unity) oil input phase fractions.


At a superficial mixture velocity of Um 0.84 m.s-1 the flow changes to three-layer flow at an

oil input phase fraction of φin 0.5 and to dispersed flows at higher oil input phase fractions.

Oil dispersions begin to form at an oil input phase fraction of φin 0.1 and glycerol solution

dispersions begin to form at an oil input phase fraction of φin 0.9. Compared with the flow

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Sup

erfi

cial

Mix

ture

Vel

ocity

, U

m (

m.s

-1)


Stratified FlowStratified Flow with DropletsOil Droplet LayerThree Layer FlowStratified Flow with Glycerol Solution Droplet LayerOil Dispersion over Glycerol SolutionOil Flow over Glycerol Solution Dispersion with FilmGlycerol Solution Dispersion with Film


179

regime map constructed from the results obtained for the PLIF campaign using the square cross-

section visualisation cell (see Figure 4-2), the flow regime transitions occur at higher superficial

mixture velocities for the circular tube case. For all the oil input phase fractions investigated,

dual continuous flow was not seen for superficial mixture velocity below Um 0.34 m.s-1

whereas, this transition occurred at a superficial mixture velocity of Um 0.07 m.s-1i in the case

of the square cross-section duct.

Furthermore, dispersions were observed at a superficial mixture velocity of Um 0.6 m.s-1

when using the square cross-section duct, whereas the transition to dispersions is first seen at a

superficial mixture velocity of Um 0.8 m.s-1 in the circular cross section duct. One possible

explanation for these differences might be the extra turbulent mixing caused at the transition

from the circular cross section duct to the square cross section duct in the experiments described

in Chapter 4 (though every effort had been made to make this transition a smooth one).

As was the case with the PLIF study presented in Chapter 4, the flow regimes are in good

general agreement with those from previous studies (Soleimani, 1999; Lovick and Angeli, 2003;

Hussain, 2004), yet some flow regimes identified by previous researchers were not observed in

the present study. Neither, oil-slugs-in-water (Charles et al., 1961; Hasson et al., 1970) nor

annular flows (Russell et al., 1959; Charles et al., 1961; Hasson et al., 1970 and Arirachakaran

et al., 1989) were observed in the current study. This absence of annular flows is consistent

with the observations of Angeli (1995), Nädler and Mewes (1995), Soleimani (1999) and

Hussain (2004). The absence of annular flows might be attributed to the fact that the oil phase

used in investigations where annular flow was not observed (including the present experiments)

was not dense and viscous enough to sustain an oil core.

The regime transitions observed with the circular pipe section relate much more closely to the

transitions observed by Soleimani (1999) than the experimental study presented in Chapter 4,

which

the p

veloc

at U

prese

obser

(2004

Um

wavy

m.s-1.

(1999

5.4

This

flows

Equa

super

of: (a

the fu

m.s-1;

h was perfor

present camp

cities when c

Um 0.8 m.s

ent circular

rved by Sole

4) reported

3 m.s-1; thi

y flow with d

. However,

9), which wa

Vertica

section prese

s. The metho

ation 3.3) is

rficial mixtur

a) 0.25, (b) 0

ull range oil

; (b) 0.17 m.

rmed using a

paign, howev

ompared wit

s-1 for the ci

duct data al

imani (1999

stratified-wa

s is much hi

droplets was

, the current

as a superfici

al Phase D

ents the vert

od employed

detailed in S

re velocities

0.50 and (c) 0

fractions φi

s-1; (c) 0.22 m

a square cross

ver its onset

th the flow re

ircular duct c

lign much m

), (Um 1 m

avy flow w

igher than th

only observe

t value mor

ial mixture v

Distributi

tical phase d

d to calculate

Section 3.11

Um in the ra

0.75. Figure

in and with s

m.s-1; (d) 0.2

s-section duc

t was not se

egime map p

compared to

more closely

m.s-1 ) and H

with droplets

he limit foun

ed up to supe

re closely re

elocity of Um

ion Profil

distribution p

e the vertical

.2. Figure 5

ange 0.11 to 0

e 5-4 shows

selected supe

28 m.s-1; (e) 0

Chapter

ct. Three-lay

een until mu

presented in C

o Um 0.4 m

y with the t

Hussain (2004

s at superfic

nd in the curr

erficial mixtu

elates to the

m 0.7 m.s-

es

profiles of the

oil phase fra

5-3 shows v

0.42 m.s-1 at

vertical oil p

erficial mixt

0.34 m.s-1 an

r 5: Circular S

yer flow has

uch higher su

Chapter 4 (se

m.s-1 for the

transition to

4), ( Um 0

cial mixture

rent study, in

ure velocitie

limit repor

1.

e circular se

action profile

vertical phase

selected inp

phase fractio

ture velocitie

nd; (f) 0.42 m

Section PLIF R

been identif

uperficial m

ee Figure 4-2

e square duct

three layer

.8 m.s-1). Hu

velocities

n which strat

s up to Um

rted by Sole

ction liquid-

es φ(y) (defin

e profiles φ(

put oil fractio

on profiles φ(

es Um of: (a)

m.s-1.

Results

fied in

mixture

2) i.e.,

t. The

r flow

ussain

up to

tified-

0.67

eimani

-liquid

ned in

(y) for

ons φin

(y) for

) 0.11

180


181

(a) (b)

(c)


Um at an input oil fraction φin of: (a) 0.25; (b) 0.50, and; (c) 0.75

From inspection of Figures 5-3 and 5-4 it can been seen that the flows show similar vertical

distribution characteristics to those observed in the experimental study for square cross section

ducts presented in Chapter 4. Specifically, that the flow has three distinct regimes: (1) an oil

region at the top of the pipe; (2) a glycerol solution region at the bottom of the pipe and; (3) a

mixed region separating them. This zone characterisation is illustrated in Figure 4-7 of Chapter

4.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

Um

=0.11 m/s

Um

=0.17 m/s

Um=0.22 m/s

Um=0.28 m/s

Um

=0.33 m/s

Um

=0.42 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

Um=0.11 m/s

Um=0.17 m/s

Um=0.22 m/s

Um

=0.28 m/s

Um

=0.33 m/s

Um=0.42 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

Um=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

Um=0.34 m/s

Um

=0.42 m/s


182

(a) (b)

(c) (d)

(e) (f)


superficial mixture velocity Um of: (a) 0.11 m.s-1; (b) 0.17 m.s-1; (c) 0.22 m.s-1; (d) 0.28 m.s-1;

(e) 0.34 m.s-1, and; (f) 0.42 m.s-1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.25

in

=0.50

in

=0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.17

in

=0.25

in

=0.50

in

=0.75

in

=0.83

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.12

in

=0.25

in

=0.50

in

=0.75

in

=0.87

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.10

in

=0.25

in

=0.50

in

=0.75

in

=0.90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.25

in

=0.50

in

=0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.25

in

=0.50

in

=0.75


183

For stratified flows (such as for the Um = 0.22 m.s-1 and φin = 0.12 case, presented in Figure 5-

4(c)) the mixed region covers a narrow vertical band. Figure 5-5 presents instantaneous flow

images for the flow under these conditions to demonstrate the flow is stratified. As the oil input

fraction increases for a given superficial mixture velocity, two observations are made: (1) the

height of the glycerol solution at the bottom of the pipe decreases, and; (2) the vertical range

covered by the mixed region increases i.e., the gradient of the transition from the glycerol

solution region to the oil region increases (see Section 5.4.1). From inspection of Figure 5-3 it

is seen that the gradient of the transition from the glycerol solution region to the oil region (i.e.,

the height of the mixed region) also increases as the superficial mixture velocity increases for a

given oil input fraction. The three aforementioned findings concur with the findings presented

in Chapter 4. As discussed in Chapter 4 (Section 4.3), Soleimani (1999) and Hussain (2004)

presented phase distribution profiles but for higher superficial mixture velocities (Um ≈ 2-3 m.s-

1) than analysed in the current study. Their results indicate that the gradient of the transition

from the aqueous phase (glycerol solution in the present study) region to the oil region increases

until there is a constant oil phase fraction all along the vertical profile of the pipe.

(a) (b) (c)

Figure 5-5: Instantaneous flow images for an oil input phase fraction φin 0.12 and superficial

mixture velocity Um 0.22 m.s-1 at: (a) 0 s; (b) 1 s, and; 2 s

5.4.1

Analy

increa

fracti

prese

super

Figur

for c

veloc

From

of the

zone

be se

zone

veloc

1

2

3

4

5

6

7

8

9

10

Mix

ed Z

one

Hei

ght,

Hm

z (m

m)

Mixed Z1

ysis of the re

ases with an

ion (though

ents the heig

rficial mixtur

re 5-6: Heig

onstant inpu

cities Um

m Figure 5-6(

e mixed zone

becomes sha

een that for

has a maxim

city is increa

0 0.10

10

20

30

40

50

60

70

80

90

00

Superfic

in

=0.25

in

=0.50

in

=0.75

Zone Heigh

esults shown

n increasing

this trend is

ght of the m

re velocity an

(a)

ght of Interfa

ut oil fractio

(a) it can be

e increases (

allower) for

low superfic

mum at an o

ased, it is see

0.2cial Mixture Ve

5

0

5

ht

n in Figures

g superficial

difficult to

mixed zone

nd the input

ace Zone for

on φin; (b) in

seen that as

i.e., the grad

a given oil in

cial mixture

oil input pha

en that the h

0.3 0.4locity, Um

(m/s)

5-3 and 5-4

mixture ve

discern by

as a functio

oil phase fra

r as a functio

nput oil frac

the superfic

dient of the tr

nput phase fr

velocities (U

ase fraction o

height of the

0.5)

1

2

3

4

5

6

7

8

9

10

Mix

ed Z

one

Hei

ght,

Hm

z (%

)

Chapter

reveals that

elocity and a

superficial v

on of the in

action.

on of (a) sup

ction φin for

cial mixture

ransition bet

fraction. Fur

Um = 0.11 m

of φin 0.50

mixed zone

0 0.1 0.20

0

20

0

40

50

60

70

80

90

00

Inp

Um

=0.1

Um

=0.1

Um

=0.22

Um

=0.2

Um

=0.34

Um

=0.42

r 5: Circular S

t the height o

an increasin

visual inspec

ndependent

(b)

perficial mixt

r constant su

velocity incr

tween the gly

rther, from F

m.s-1) the he

0. As the su

increases m

0.3 0.4 0.5put Oil Phase Fr

1 m/s

7 m/s

2 m/s

8 m/s

4 m/s

2 m/s

Section PLIF R

of the mixed

g oil input

ction). Figur

variables i.e

ture velocitie

uperficial m

reases, the h

ycerol zone t

igure 5-6(b)

eight of the m

uperficial m

monotonically

0.6 0.7 0.8 0raction,

in

Results

d zone

phase

re 5-6

e., the

es Um

mixture

height

the oil

it can

mixed

mixture

y with

0.9 1

184

oil in

phase

revea

prom

betwe

5.5

This

fracti

integr

image

For a

is cal

Figur

almo

Figur

mode

fracti

and φ

calcu

nput phase fr

e fraction is

al the effects

moting mixing

een the two l

In-Situ

section pres

ions have be

ration techni

e, the phase

a given run (

lculated using

re 5-7 shows

st all flow c

re 4-12). Th

el) line in Fig

ion as a func

φmod,2; their

ulated using t

raction. The

s higher at h

s of higher

g of the two

liquid phases

u Phase Fr

sents the re

een calculate

ique to acco

fraction is ca

⟨ ⟩

i.e., a fixed

g Equation 3

s that the in

conditions (a

his is indicat

gure 5-6. Tw

tion of the in

derivations

the same bas

rate of the i

higher super

turbulence l

initially sepa

s.

raction

sults for in-

ed using the

ount for the

alculated via

combination

3.5, in which

-situ oil frac

as was the ca

ted by the da

wo different

nput oil phas

are explaine

is as φmod,1b

increase in th

rficial mixtu

levels (at th

arated flows

-situ oil pha

phase distri

curvature of

a the integral;

1,

n of Um and

h, ⟨φ⟩y(t) is⟨φ

ction ⟨φ⟩y,t is

ase for the s

ata points be

approaches w

se fraction. T

ed below in

and φmod,2 a

Chapter

he height of

ure velocities

he higher sup

, thus promo

ase fraction

ibution profi

f the visuali

;

φin) the aver

⟩yi.

s lower than

square cross

eing below t

were taken to

These are pre

Sections 5.

as that used in

r 5: Circular S

the mixed z

s. Clearly, t

perficial mix

oting a diffus

⟨φ⟩y,t. The

iles coupled

sation cell w

rage in-situ o

n the input o

section duct

the 1 (h

o estimate th

esented in Fi

5.1 and 5.5.

n Figure 4-1

Section PLIF R

zone with oil

these observ

xture velocit

se ‘mixed zo

in-situ oil

with a num

wall. For a

(5.1)

oil fraction,

oil fraction φ

t – see Chap

homogeneous

he in-situ oil

igure 5-7 as

.2, and have

2.

Results

l input

ations

ties)in

one’ in

phase

merical

given

⟨ ⟩ ,

φin for

pter 4,

s flow

phase

φmod,1

e been

185

Figur

mixtu

5.5.1

The “

the fr

visco

in Fig

There

input

deriv

Reyn

re 5-7: In-si

ure velocities

Lamina1

“laminar drag

frictional pre

ous drag due

gure 5-7. It h

e is very goo

t oil fraction

vation of φmo

nolds number

itu fraction ⟨

s Um

r Drag Mo

g model” for

essure drop i

to laminar fl

has been der

od agreement

ns (typically

od,1 is outlin

r through a F

00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

In-S

itu O

il Ph

ase

Frac

tion,

y, t

φ⟩y,t as a fun

odel

r prediction o

in a two lay

low and pres

rived using th

t between φm

y, 0.1<φin

ned below.

Fanning fricti

Δ12

4

0.1 0.2 0Inpu

Um

=0.11 m

Um

=0.17 m

Um

=0.22 m

Um

=0.28 m

Um

=0.34 m

Um

=0.42 m

mod,1

mod,2

S = 1

nction of inp

of the in-situ

yer flow, i.e.

ssure drop in

he same basi

mod,1 and the

0.5) and lo

Firstly, the

ion factor f:

416

.3 0.4 0.5ut Oil Phase F

m/s

m/s

m/s

m/s

m/s

m/s

Chapter

put oil fractio

u phase fracti

., by conside

the pipe. Th

s as φmod,1b i

experimenta

ower superfic

dimensionl

0.6 0.7 0Fraction,

in

r 5: Circular S

on φin for di

ion was deve

ering an equ

his model is

in Chapter 4

al results, pa

cial mixture

ess pressure

0.8 0.9 1

Section PLIF R

ifferent supe

eloped by equ

uilibrium be

denoted by

.

articularly at

e velocities.

e is related t

(5.2)

Results

rficial

uating

tween

φmod,1

lower

The

to the

186

Once

where

and;

Here,

param

Final

e written for e

e:

1

, is defin

meters used t

ly, the mode

each phase ‘

≡

;

ned as the pe

to construct E

Figure 5-8

elled in-situ o

i’ and after e

.1

2

eriphery of

Equations 5.2

: Stratified li

oil phase frac

equating pres

. 1

.2

;

each layer i

2 to 5.5 are d

iquid-liquid f

ction ⟨φ⟩y,t pr

Chapter

ssure drops Δ

in contact w

defined in Fi

flow model c

resented in F

r 5: Circular S

Δp/L, Equatio

4

with the wall

igure 5-8 bel

construction

Figure 5-7 is

Section PLIF R

on 5.2 reduc

(5.3)

(5.4)

(5.5)

l; a summar

ow.

defined as:

Results

es to:

ry, the

187

In Eq

fluids

5.5.2

The s

exact

mom

oil fr

Yoil

with

the st

that t

highe

5.5.3

This

liquid

homo

existe

line l

quations 5.2

s has not bee

Differen2

second mean

t same meth

mentum balan

raction ⟨φ⟩y,t

Ygs H

the experime

tudy using a

the interface

er viscosity o

Homoge3

section asses

d flows, i.e.

ogeneous flo

ence of slip b

abelled S = 1

, ⟨φ⟩y

to 5.6 θ is

en included in

ntial Mom

ns of compar

hodology as

nce (Bird et a

t 0.5 and

HT/2 in Fig

ental results.

a square cros

level is adju

of the glycero

eneous Flo

sses the suita

the velocit

ow model is

between the

1 in Figure 5

y,t

in radians.

n the calcula

entum Ba

ison, denoted

φmod,2 prese

al., 2001) an

when the in

gure 5-8. T

. Therefore,

ss-section vi

usting in ord

ol solution.

ow Model

ability of usi

ty ratio of t

compared w

phases. Th

-7.

1

It should be

ation of

lance Mod

d by φmod,2 i

ented in Figu

nd is applicab

nterface leve

This form of

, the same co

sualisation c

der to satisfy

and Slip R

ing the homo

the fluids (d

with the sepa

he homogeno

Chapter

2

e noted that

, .

del

in Figure 5-7

ure 4-12; it

ble to the sp

el H is at th

f prediction i

onclusions ca

cell, presente

y the increase

Ratio

ogenous flow

defined in E

arated flow m

ous flow mod

r 5: Circular S

the contact

7 has been ca

is derived fr

ecial case in

he midpoint

is also in ex

an be drawn

ed in Chapte

ed viscous d

w model to c

Equation 4.1

model which

del is denote

Section PLIF R

(5.6)

area betwee

alculated usin

from a differ

n which the i

t of the pipe

xcellent agree

as were ma

er 4. Specifi

drag caused b

haracterise l

1) is unity.

h accounts f

ed by the thin

Results

en the

ng the

rential

in-situ

e, i.e.,

ement

de for

fically,

by the

iquid-

The

for the

n sold

188


189

As was the case with the results presented in Chapter 4 (see Figure 4-12), it is seen from

Figure 5-7 that the homogenous flow model over-predicts the in-situ phase fraction. Again, the

extent of the over-prediction increases with an increasing oil input fraction. In a bid to address

the predictive shortcoming of adopting a homogenous flow model, Figure 5-9 investigates

whether a single S value or expression, can be used to characterise these flows.

From Figure 5-9(a) it is evident that the use of the homogenous flow model (i.e., S = 1) gives a

very poor characterisation of the flows of the current experimental campaign, albeit except at

the lowest input oil phase fractions investigated. The findings are the same as those of

Chapter 4 (see Figure 4-14) and hence give further validation of the inadequacy of the

homogeneous flow model to characterise the result for the flow matrix investigated (which are

roughly the same for Chapters 4 and 5).

(a) (b)

Figure 5-9: Experimental results and correlations for: (a) slip ratio S as a function of input oil

fraction φin, and: (b) in-situ oil phase fraction ⟨φ⟩y,t as a function of input oil fraction φin

From Figure 5-9(a) a “best fit” correlation for the slip ratio is shown, the equation for which is:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8


Slip

Rat

io, S

S = 1

S = 5.7177in

+0.3626

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

y, t

= 0.5404in

+0.0104

y, t

= in

/[(5.7177in

+0.3626)(1-in

)+in

]


190

5.7177 0.3626 (5.7)

This is rather similar to the “best fit” correlation for the slip ratio for the experimental results of

Chapter 4. To highlight the similarity, the in-situ phase fraction that can be calculated from the

slip ratio correlations (Equations 5.7 and 4.15) i.e., Equations 4.16 and 5.8, are shown together

in Figure 5-10. The correlation for in-situ phase fraction derived from Equation 5.7 and

Equation 4.14 (Equation 5.8 below) is seen to have excellent agreement with the experimental

data and is (again) an improvement on using a linear expression to relate the input oil phase

fraction to the in-situ phase fraction.

⟨φ⟩y,t 5.7177 0.3626 1 (5.8)

Figure 5-10: Comparison of the correlations for in-situ oil phase fraction ⟨φ⟩y,t as a function of

input oil fraction φin for the square cross-section visualisation cell PLIF results (Equation 4.16)

shown in blue and the circular cross-section visualisation cell PLIF results (Equation 5.8) shown

in red

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu O

il Ph

ase

Frac

tion,

y,

t

y, t

= in

/[(5.7177in

+0.3626)(1-in

)+in

]

y, t

= in

/[(5.8251in

-0.1448)(1-in

)+in

]


191

Due to the fact that the superficial mixture velocity is not accounted for in Figure 5-9, Figure 5-

11 examines the effect of the input oil phase fraction φin on the slip ratio S at constant

superficial mixture velocities Um and includes a comparison with experimental data acquired by

Lovick and Angeli (2004) for an oil-water system.

Figure 5-11: Slip ratio S as a function of input oil fraction φin for different superficial mixture

velocities Um PLIF data is presented in blue and the results from Lovick and Angeli (2004) are

presented in red)

The same conclusions can be drawn from Figure 5-11 as from Figure 4-15 in Chapter 4.

Specifically, that for a given oil input phase fraction, as the superficial mixture velocity

increases the slip ratio decreases. For the reasons outlined in Section 4.5.3, it can again be

deduced that as the superficial mixture velocity increases beyond a critical point, the flow is

sufficiently well mixed (i.e., dispersed) that it can be can be adequately described via the

homogenous flow model. In Section 5.9 the slip ratio is linked to the velocity profile (and the

associated flow regime) as a means to verify the conditions under which a homogenous flow

model suitably describes the flows.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8


Slip

Rat

io, S

S = 1U

m = 0.80 m/s (Lovick and Angeli, 2004)

Um

= 3.00 m/s (Lovick and Angeli, 2004)

Um

= 0.11 m/s

Um

= 0.17 m/s

Um

= 0.22 m/s

Um

= 0.28 m/s

Um

= 0.34 m/s

Um

= 0.42 m/s

5.5.4

Figur

Lovic

drag

Figur

lamin

the s

entrai

the la

Howe

data f

flow

hence

Model A4

re 5-12 comp

ck and Ange

model φmod,1

res 4-16 and

nar drag mod

superficial m

inment of on

aminar drag m

ever, for suf

for Um 3.

regime) that

e ⟨φ⟩y,t φin

Application

pares the PL

eli (2004) an

1 (Equation 5

d 4-17 in C

del provides

mixture velo

ne liquid as d

model break

fficiently hig

00 m.s-1) the

t it can be ad

n.

n and Com

LIF in-situ p

nd Russell et

5.6). The sam

Chapter 4, n

excellent ag

ocity increa

drops into a c

s down.

gh superficia

e flow becom

dequately cha

mparison

phase fractio

t al. (1959) a

me conclusio

amely that

greement wi

ases, mixing

continuum o

l mixture ve

mes sufficien

aracterised b

Chapter

n results wi

and with the

ons can be dr

at low supe

ith the exper

g in the flo

f the other; w

elocities (see

ntly well mix

y the homog

r 5: Circular S

th the exper

e predictions

rawn from Fi

erficial mixtu

rimental resu

ow increase

when such en

e the Lovick

xed (i.e., it i

geneous flow

Section PLIF R

rimental resu

from the la

igure 5-12 as

ure velocitie

ults. Howev

s leading t

ntrainment o

and Angeli,

is in the disp

w model, i.e.,

Results

ults of

aminar

s from

es the

ver, as

to the

occurs,

, 2004

persed

, S = 1

192


193


mixture velocities Um compared with data from Lovick and Angeli (2004) and Russell et al.

(1959)

As mentioned in Section 4.5, the difficulty arises when trying to predict the in-situ phase

fraction between these two boundaries (stratified and dispersed flows), i.e., for dual continuous

flows. However, as was demonstrated in Chapter 4, good agreement with the laminar drag

model can be obtained for dual continuous flow when effective viscosities are calculated for the

fluid mixtures below and above the interface. It will be demonstrated in Section 5.8 that very

good agreement is yielded when using an amended form of the laminar drag model in which the

entrainment of one fluid in a continuum of the other is accounted for to enable the viscosities of

the flow above and below the interface to be deduced from the values for the single fluids. As

this has been demonstrated to work in Chapter 4, the undertaking has not been repeated herein,

however, the principle is demonstrated pictorially by means of an envelope plot in Figure 5-13.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-s

itu

Oil

Pha

se F

ract

ion,

y,

t

mod,1(LIF Data)


mod,1(Russell et al. 1959)

Um=0.17 m/s

Um=0.34 m/s





S = 1

5.6

This

analy

altern

funct

0.28 m

Interfa

Section pres

ysis of the

native predic

tion of input

m.s-1.

In-s

itu

Oil

Phas

eFr

acti

on,

Fig

ace Level

sents the exp

PLIF image

ction approac

t oil fraction

00

1

Insi

tu O

il P

hase

Fra

ctio

n, y,

t

InU

μ

μw

μoil

ure 5-13: In

perimental da

es, and also

ches. Figure

n φin for fix

Input O

ncreasing Um

Dua

Flo

Stratified

oil

water

→ 1

μwater

-situ phase f

ata for interf

o presents c

e 5-14 presen

xed superfici

Oil Phase

Dual Co

Flow Re

al Continuous

w Region

d Flow

Stratifie

No Sl

Chapter

fraction enve

face level in

comparisons

nts the result

ial mixture v

Fraction,

ontinuous

egion

s

ed Flow

μw

μ

μ

lip (S 1)

r 5: Circular S

lope

stratified flo

s between th

ts of the inte

velocities fro

in

Increasing Um

water

μoil

→ 1

μoil μwater

Section PLIF R

ows obtained

he data and

erface level H

om Um 0

1

Results

d from

d two

H as a

.11 to

194


195

(b) (b)

(c) (d)

Figure 5-14: The mean (μ) and upper (μ + 2σ) and lower (μ a2σ) limits for the interface level H

as a function of input oil fraction φin for superficial mixture velocities Um of: (a) 0.11 m.s-1; (b)

0.17 m.s-1; (c) 0.22 m.s-1, and (d) 0.28 m.s-1

The results reveal that, for a given superficial mixture velocity Um, the interface level decreases

as the oil input fraction increases. This trend is seen to be more prominent for higher superficial

mixture velocities. Figure 5-14 shows the interface level H as a function of superficial mixture

velocity Um for a given oil input fraction ranging from φin 0.25 to 0.75.

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

a

b c

x y

z

1 2

3


196

(b) (b)

(c)

Figure 5-15: The mean (μ) and upper (μ + 2σ) and lower (μ a2σ) limits for the interface level H



probability histograms in Figures 5-16, 5-17 and 5-18 respectively

Inspection of Figure 5-15 reveals that as the superficial mixture velocity Um increases, the mean

interface level decreases for a given oil input fraction φin. From comparison of Figures 5-15(a)

to 5-15(c) it is seen that as the oil input oil fraction φin increases, the rate at which the interface

level decreases for an increasing superficial mixture velocity Um increases. These trends are

seen more clearly in Figures 5-21 and 5-22.

0 0.1 0.2 0.30

4

8

12

16

20

24

28

Superficial Mixture Velocity, Um (m.s-1)

Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.1 0.2 0.30

4

8

12

16

20

24

28


(m.s-1)

Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.1 0.2 0.30

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

a b c

x

k l

z

y

m

5.6.1

Figur

for th

14(a)

x1 →

level

veloc

in int

show

the 9

which

confi

Probabi1

res 5-16 and

he points that

) and 5-14(d

z1) and the

μH decrease

city Um. Fro

terface level

wn in Figure

95% confiden

h have been

dence interv

ility Histog

d 5-17 presen

t have been u

d), respective

histograms (

es with an in

om compariso

l increases a

5-14 indicat

nce interval

n numbered

val is approxi

grams

nt instantane

used to const

ely. From i

(a2 → c2 and

ncreasing oil

on of Figure

as the super

e no discern

(μ - 2σ→ μ

1 → 3 an

imately cons

eous images

truct the mea

inspection o

d x2 → z2), o

l input oil fra

es 5-14(a) →

rficial mixtu

nable trend in

+ 2σ). How

nd shown in

tant for a giv

Chapter

and interfac

an interface l

of the instant

one can easi

actions φin f

→ 5-14(d) it is

ure velocity

n the extent o

wever, with

n Figures 5-

ven superfici

r 5: Circular S

e level prob

level plots sh

taneous ima

ily see that t

for a given s

s seen that th

Um is incre

of the distrib

the exceptio

-14(b) and

ial mixture v

Section PLIF R

ability histog

hown in Figu

ages (a1 → c

the mean int

uperficial m

he rate of dec

eased. The r

bution spread

on of three p

5-14(c), the

velocity Um.

Results

grams

ures 5-

c1 and

erface

mixture

crease

results

d, i.e.,

points

e 95%

197


198

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 5-16: Flow images with input oil fraction φin of (a1) 0.25, (b1) 0.50, (c1) 0.75, all at a

superficial mixture velocities Um = 0.11 m.s-1; (a2), (b2) and (c2) show the probability

histograms for the same conditions respectively. Data corresponds to Points a, b and c, as

labelled in Figure 5-14(a)

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty

Interface Level, H (mm)0 4 8 12 16 20 24 28

0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty

Interface Level, H (mm)


199

(x1) (y1) (z1)

(x2) (y2) (z2)

Figure 5-17: Flow images with input oil fraction φin of (x1) 0.25 m.s-1, (y1) 0.50, (z1) 0.75, all at

a superficial mixture velocities Um = 0.28 m.s-1; (x2), (y2) and (z2) show the probability

histograms for the same conditions respectively. Data corresponds to Points a, b and c, as

labelled in Figure 5-14(d)

Figures 5-16 to 5-18 present frames and the probability histograms for the points that have been

used to construct the mean interface level plots shown in Figures 5-15(a) to 5-15(c),

respectively. From inspection of the images (a1 → c1, k1 → m1 and x1 → z1) and the histograms

(a2 → c2, k2 → m2 and x2 → z2), one can conclude that the mean interface level μH decreases for

an increasing superficial mixture velocity Um while at the same time the interface level

fluctuation range widens. We would expect that at a low superficial mixture velocity Um, when

the flow is stratified, that the interface level would be flat and stable H (Shaha, 1999).

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty



200

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 5-18: Flow images with superficial mixture velocities Um of: (a1) 0.11 m.s-1, (b1) 0.17

m.s-1, (c1) 0.28 m.s-1, all at an input oil fraction φin 0.25; (a2), (b2) and (c2) show the

probability histograms for the same conditions respectively. Data corresponds to Points a, b and

c, as labelled in Figure 5-14(a)

From inspection of Figures 5-16 to 5-20 it can be seen that at lower superficial mixture

velocities the interface level is found to cover only a narrow range of vertical heights (see

Figures 5-16(a2) and 5-18(a2)) consistent with a smooth stratified flow. The height of the mixed

zone is seen to increase at the transition to dual continuous flow; see Figures 5-17(z2) and 5-

20(z2).

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty



201

(k1) (l1) (m1)

(k2) (l2) (m2)

Figure 5-19: Flow images with superficial mixture velocities Um of: (k1) 0.11 m.s-1, (l1) 0.17

m.s-1, (m1) 0.28 m.s-1, all at an input oil fraction φin 0.50; (k2), (l2) and (m2) show the


m, as labelled in Figure 5-14(b)

The widening of the interface height range with increasing superficial mixture velocity is a

manifestation of the corresponding increase of the amplitude of the waves on the interface and

is probably linked to the onset and increase of turbulence in the flow as the superficial mixture

velocity increases. Increased turbulence can lead to droplet formation and the entrainment of

one phase in a continuum of another which can further widen the range of interface level

heights.

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


Figur

m.s-1,

proba

and z

5.6.2

Figur

Hmod

in ve

flows

Chap

and d

input

00

0.2

0.4

0.6

0.8

1

Prob

abili

ty

(x1)

(x2)

re 5-20: Flo

, (x1) 0.28

ability histog

z, as labelled

Lamina2

re 5-21 show

,1 predicts th

ery good agr

s (Um 0.11

pter 4 that du

droplet forma

t phase fracti

4 8 12Interface Le

)

)

ow images w

m.s-1, all at

grams for th

in Figure 5-

r Drag Mo

ws that the m

he lowering o

reement with

1 to 0.17 m.

ue to the fact

ation the mo

on as the sup

16 20 24evel, H (mm)

with superfici

t an input o

he same cond

14(c)

odel

odified form

of the interfa

h the experi

s-1) in which

t that the lam

del fails to c

perficial mix

28 0 40

0.2

0.4

0.6

0.8

1

Prob

abili

ty

(y1)

(y2)

ial mixture v

oil fraction φ

ditions respe

m of the lamin

ace level H a

imental data

h the flow c

minar drag m

capture that t

xture velocity

8 12 16Interface Level, H (m

Chapter

velocities Um

φin 0.75;

ectively. Da

nar drag mod

as the oil inpu

a points relat

contains no

model does n

the interface

y increases.

20 24 28mm)

Prob

abili

ty

r 5: Circular S

m of: (x1) 0.1

(x2), (y2) a

ata correspon

del (Equation

ut fraction φ

ting to low-

droplets. It

not account f

level decrea

0 4 80

0.2

0.4

0.6

0.8

1

Interfa

Section PLIF R

(z1)

(z2)

11 m.s-1, (x1)

and (z2) show

nds to Point

n 5.6), denot

φin increases

-velocity stra

was discuss

for phase bre

ases for a giv

12 16 20face Level, H (mm)

Results

) 0.17

w the

ts x, y

ted by

and is

atified

sed in

eak-up

ven oil

24 28

202

Figur

mixtu

5.6.3

Figur

stratif

liquid

are su

simila

with t

re 5-21: Inte

ure velocities

Predicti3

re 5-22 com

fied flow m

d-liquid flow

uch that the

ar to the cas

the present d

erface Level

s Um

ive Techni

mpares the ex

odels presen

ws generally

oil phase is

e of a gas-liq

data in Figure

00

4

8

12

16

20

24

28

Inte

rfac

e L

evel

, H

(m

m)

l H as a fun

ique of Ha

xperimental

nted by Hall

over-predict

less dense t

quid flow an

e 5-22(a).

0.2O

Um

=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

Hmod,1

ction of inpu

all and Hew

results for

and Hewitt

ts the data. H

than the aqu

nd the Hall an

0.4Oil Input Fract

Chapter

ut oil fractio

witt (1993)

interface lev

t (1993). Th

However, th

eous phase,

nd Hewitt m

0.6 0.tion,

in

r 5: Circular S

on φin for di

)

vel with pre

he Hall and

he liquids in

but also less

model for this

.8 1

Section PLIF R

ifferent supe

edictions from

Hewitt mod

the present

s viscous. T

s case is com

Results

rficial

m the

del for

study

This is

mpared

203


204

(a) (b)

Figure 5-22: Interface Level H as a function of input oil fraction φin for different superficial

mixture velocities Um featuring interface level models presented by Hall and Hewitt (1993) for:

(a) stratified liquid-liquid flow, and (b) stratified gas-liquid flow

It is seen that both predictive techniques capture the lowering of the interface level with an

increasing oil input phase fraction. However, the liquid-liquid model over-predicts the interface

level for all flowing conditions investigated; the difference increases with an increasing oil input

phase fraction for a given superficial mixture velocity. The model for gas-liquid systems shows

excellent agreement with the present experimental data.

The breakdown in the ability of the Hall and Hewitt (1993) liquid-liquid model to accurately

predict the interface level as the superficial mixture velocity increases can be attributed to the

model assuming a flat interface between the two liquids. However, and particularly at higher

mixture velocities, the interface is not flat and is covered with waves. The Hall and Hewitt gas

liquid flow model takes account of such waves by assigning an enhanced interfacial friction.

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

Hall & Hewitt (1993)gas-liquid

Um

=0.11 m/s

Um

=0.17 m/s

Um=0.22 m/s

Um=0.28 m/s

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

Hall & Hewitt (1993)liquid-liquid

Um

=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

5.7

This

the P

were

wall.

of, ei

these

chara

glyce

show

mean

3.11.

proba

5-23.

Drople

section prese

PLIF images

first correcte

Here, the re

ither: the ab

experiment

acteristics of

erol solution

ws the effects

n glycerol so

5). Figures

ability histog

et Size Dis

ents the resu

for the circu

ed (using the

esults presen

sence, or; th

ts, it was n

f oil droplets

droplets – i

s of: (a) oil i

olution drop

s 5-24 and

grams (a2 →

stribution

ults for dropl

ular tube cas

e graticule m

nted are for g

he lack of ab

not possible

s entrained i

n – oil are p

input fractio

let diameter

5-25 presen

c2 and x2 →

n

let size whic

e. As explai

method) for th

glycerol solu

bundance of

e to obtain

in the aqueo

presented in

n φin, and; (

rs μd,gs (defi

t instantaneo

→ z2) for the p

Chapter

h have been

ned in Chap

he distortion

ution droplets

f oil – drople

a sufficien

ous (glycero

Figures 5-23

(b) superficia

ined in Equa

ous images

points labell

r 5: Circular S

n obtained fro

pter 3 and ab

caused by th

s –in – oil.

ets – in – gl

nt sample s

l solution) p

3 to 5-25 be

al mixture v

ations 3.8 an

(a1 → c1 a

led a → c an

Section PLIF R

om the analy

bove, these im

he circular ch

As a conseq

lycerol solut

size to stud

phase. The r

elow. Figure

elocity Um o

nd 3.9 in Se

nd x1 → z1

nd x → z in F

Results

ysis of

mages

hannel

quence

ion in

dy the

results

e 5-23

on the

ection

1) and

Figure

205


206

(a) (b)

Figure 5-23: Mean glycerol solution droplet diameter μd,gs for: (a) varying input oil fraction φin

and constant superficial mixture velocities Um 0.22 m.s-1, and; (b) varying superficial mixture

velocity Um and a constant input oil fraction of φin 0.25. Points a, b and c correspond to the

instantaneous images a1 → c1 and probability histograms a2 → c2 in Figure 5-24. Points x, y

and z correspond to the instantaneous images x1 → z1 and probability histograms x2 → z2 in

Figure 5-25

Figure 5-23(a) indicates that for a fixed superficial mixture velocity Um, the average glycerol

solution droplet diameter μd,gs increases at a constant rate with an increasing oil input fraction

up to φin 0.5. However, as the oil input fraction φin is increased further, the average glycerol

solution droplet diameter decreases monotonically, i.e., the mean droplet diameter is shown to

peak at an oil input fraction of φin 0.5 with a value of μd,gs 4.1 mm, at a superficial mixture

velocity of Um 0.22 m.s-1. As was seen with the PLIF study presented in Chapter 4, this

result is consistent with the fining of Pal (1993) who observed a peak in the droplet size at the

phase inversion point, φin,water 0.3. This is also consistent with the findings of Liu (2005)

who also observed a maximum in the droplet size at the phase inversion point.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


Mea

n D

ropl

et D

iam

eter

, d (

mm

)

0 0.1 0.2 0.3 0.4 0.5 0.60

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


(m.s-1)

Mea

n D

ropl

et D

iam

eter

, d (

mm

)

x y

z a

b

c

Figur

mixtu

soluti

14%)

m.s-1,

5.7.1

Figur

instan

From

mixtu

diame

Figur

clear

super

Um

mixtu

re 5-23(b) sh

ure velocity

ion droplet d

) as a result

, and then to

Probabi1

res 5-24 and

ntaneous ima

m Figure 5-24

ure velocity

eter range th

re 5-25(x2) s

preference f

rficial mixtu

0.42 m.s-1)

ure velocity i

hows results

Um for a gi

diameter μd,g

of the increa

0.42 m.s-1.

ility Histog

d 5-25 show

ages for the p

4 it can be se

(in this case

hough the dis

hows that, a

for droplets o

ure velocity

, however, t

is increased.

for mean gly

iven (fixed)

gs increases

ase in the su

grams

w probabilit

points a → c

een that as th

e, Um 0.22

stribution bec

at a low supe

of a certain

y is increa

the probabil

ycerol soluti

input oil fra

slightly (by

uperficial mix

ty histogram

c and x → z in

he oil input f

2 m.s-1) the g

comes more

erficial mixtu

size. The pr

ased (firstly

lity for sma

Chapter

on droplet si

action of φin

about 6%)

xture velocit

ms of glycer

n Figure 5-2

fraction is in

glycerol solut

uniform wit

ure velocity

reference for

to Um

aller droplets

r 5: Circular S

ize as a func

n 0.25. T

and then de

ty Um from

rol solution

3(a) and 5-2

creased for a

tion droplets

th increasing

of Um 0.2

r this size is

0.28 m.s-1

s decreases

Section PLIF R

ction of supe

The mean gly

ecreases (by

0.22 m.s-1 to

droplet siz

3(b), respect

a given supe

s occupy the

oil input fra

22 m.s-1, ther

maintained

and then o

as the supe

Results

rficial

ycerol

about

o 0.28

e and

tively.

rficial

e same

action.

re is a

as the

on to

rficial

207


208

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 5-24: Flow images with a superficial mixture velocity Um = 0.22 m.s-1 at oil input

fractions φin of: (a1) 0.25, (b1) 0.50 and, (c1) 0.87; (a2), (b2) and (c2) show the glycerol solution

droplet size distribution probability histograms for the same conditions respectively. Data

corresponds to Points a, b and c, as labelled in Figure 5-23(a)

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Pro

babi

lity


0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Prob

abili

ty


Figur

veloc

dropl

corre

5.8

The i

adopt

inves

veloc

fracti

endea

veloc

veloc

mixtu

00

0.2

0.4

0.6

0.8

1

Prob

abili

ty

(x1)

(x2)

re 5-25: Flo

cities Um of (

let size distr

sponds to Po

Interfa

interfacial w

ted is detai

stigating the

city Um; (2)

ion φin; (3)

avour has no

city. Here, th

city is within

ure velocities

1 2 3 4Droplet Diam

)

)

w images w

(x1) 0.22, (y

ribution prob

oints x, y and

acial Wav

ave velocity

iled in Sec

relationship

the superfic

the velocit

ot provided a

he results are

n the range

s in the back

5 6 7 8 9meter,

d (mm)

with an oil inp

1) 0.28 and,

bability hist

d z, as labelle

ve Velocity

⟨ ⟩ has

ction 3.11.6

p of the in

cial velocity

ty at the in

a clear quanti

e presented i

0-0.5 m.s-1,

kground flow

10 0 1 20

0.2

0.4

0.6

0.8

1

Prob

abili

ty

(y1)

(y2)

put fraction

(z1) 0.42; (x2

tograms for

ed in Figure

y

been determ

. Though

nterface wav

y of the indi

terface, and

itative insigh

in Table 5-1

and is typic

w.

2 3 4 5 6Droplet Diameter,

d

Chapter

fractions φin

2), (y2) and (

the same c

5-23(b)

mined from th

an extensi

ve velocity w

ividual phase

d; (4) the in

ht into the fa

for referenc

cally of the

7 8 9 10

d (mm)

Prob

abili

ty

r 5: Circular S

n = 0.25 at s

(z2) show the

onditions re

he PLIF imag

ve analysis

with: (1) su

es Uoil and

nterface leve

actors which

ce. We can

same order

0 1 2 30

0.2

0.4

0.6

0.8

1

Droplet

Section PLIF R

(z1)

(z2)

uperficial m

e glycerol so

espectively.

ges; the proc

was perfo

uperficial m

Ugs; (3) oil

el, However

govern inter

see that the

as the supe

4 5 6 7 8t Diameter,

d (mm)

Results

mixture

olution

Data

cedure

ormed,

mixture

input

r, this

rfacial

wave

rficial

9 10

209


210

Table 5-1: Interface wave velocity ⟨ ⟩ results

Superficial Mixture

Velocity, Um (m.s-1)

Oil Input

Fraction, φin

Interface Wave Velocity ⟨ ⟩

Mean (m.s-1) Standard Deviation (m.s-1)

0.11

0.25 0.00 0.00

0.50 0.01 0.00

0.75 0.22 0.09

0.17

0.25 0.14 0.08

0.33 0.39 0.13

0.50 0.40 0.18

0.66 0.14 0.09

0.75 0.39 0.17

0.22

0.12 0.00 0.00

0.25 0.37 0.12

0.50 0.41 0.13

0.63 0.40 0.11

0.75 0.24 0.07

0.87 0.28 0.06

0.28

0.10 0.47 0.26

0.20 0.44 0.17

0.25 0.41 0.14

0.40 0.48 0.16

0.50 0.52 0.13

0.60 0.53 0.10

0.70 0.53 0.10

0.75 0.49 0.11

0.80 0.45 0.09

0.90 0.38 0.08

5.9

This

techn

funct

as a f

the in

Figur

0.42

fixed

been

inspe

oil in

mixtu

depen

as th

transi

veloc

Thou

may

veloc

chang

chang

veloc

partic

Velocit

section pres

niques detail

tion of superf

function of f

nterface level

re 5-26 show

m.s-1 at oil i

d superficial

divided by t

ection of Fig

nput fraction

ure velocity

ndence to th

he mixed zo

ition through

city is increas

ugh the veloc

be thin bou

city may chan

ge in velocit

ge” at the i

cities investi

cular, Figure

ty Profiles

ents velocity

led in Sectio

ficial mixtur

flow regime.

l is exami

ws velocity p

input fraction

mixture velo

the superfici

ure 5-26 it c

φin collapse

(though wi

he superficial

ne in Figur

h the differe

sed.

city of the tw

undary layer

nge significa

ty from one

interface is

gated, Um =

e 5-11), the

s

y profile resu

on 3.11.7.

re velocity fo

Finally, the

ined.

rofiles for su

ns φin of (a)

ocity Um an

ial mixture v

can be seen t

to a ‘generi

ith some ex

l mixture ve

e 4-7 of Ch

ent flow reg

wo phases m

rs in the int

antly. These

phase to the

seen to be

= 0.11 to 0.2

Slip Ratio S

ults that hav

The velocit

or a constant

e relationship

uperficial mi

0.25; (b) 0.

d fixed oil i

velocity of th

that once no

ic’ profile th

xceptions).

locity, name

hapter 4). T

gimes that ar

must be close

erface regio

changes ma

e other as th

most prom

22 m.s-1. A

S between th

Chapter

ve been gene

ty profile re

oil input fra

p between ve

ixture velocit

50, and; (c)

input fraction

hat run, i.e.,

ormalised, th

at is largely

However, t

ely the interf

This depende

re encounter

e to being th

on in either

ay manifest t

e interface r

minent for th

s first discu

he two liqui

r 5: Circular S

erated using

sults are pr

actions and th

elocity at

ties in the ra

0.75. For a

n φin) the ve

it has been

e velocity pr

independent

there is a re

face region,

ence can be

red as the su

he same at th

or both pha

themselves a

region is trav

he lowest su

ussed in Sec

id phases is

Section PLIF R

the PTV and

esented first

hen, subsequ

t the interfac

ange Um 0

a given run (

elocity profi

normalised.

rofiles for a

t of the supe

egion that r

(which is lab

attributed t

uperficial m

he interface,

ases in whic

as an apparen

versed. The

uperficial m

tion 5.5.3 (s

highest for

Results

d PIV

t as a

uently,

ce and

0.11 to

(i.e., a

le has

From

given

rficial

retains

belled

to the

mixture

, there

ch the

nt step

“step-

mixture

see in

these

211


212

conditions. From Figure 5-11 it is also seen that the Slip Ratio increases with input oil phase

fraction. Comparing Figures 5-26(a) and 5-26(b), the “step-change” at the interface is seen to

increase with oil input phase fraction. Ultimately, if there is sufficient shear (i.e., a sufficient

velocity difference) across the interface, this will give rise to the Kelvin-Helmhotlz instability

which can cause waves at the common interface and the onset of a transition to other flow

regimes, first dual continuous flow and ultimately dispersed flow which have their own

characteristic velocity profiles, as discussed in Section 5.9.1.

(a) (b)

(c)

Figure 5-26: Normalised velocity profiles ⟨ m⟩⁄ for different superficial mixture velocities


0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28

Normalised Streamwise Velocity, Ux / Um

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Um

=0.56 m/s

Um

=0.50 m/s

Um

=0.33 m/s

Um

=0.22 m/s

Um

=0.11 m/s

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28


Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Um

=0.56 m/s

Um

=0.50 m/s

Um

=0.33 m/s

Um

=0.22 m/s

Um

=0.11 m/s

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28


Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Um

=0.67 m/s

Um

=0.50 m/s

Um

=0.33 m/s

Um

=0.22 m/s

Um

=0.11 m/s

5.9.1

In the

aqueo

rise to

chang

rise t

the v

simpl

Figur

(2008

Figur

image

Um =

veloc

of th

Flow Re1

e present exp

ous phases, w

o laminar flo

ge in the nat

to characteris

velocity distr

ler case of si

re 5-27: Vel

8)

re 5-28 pres

es (b1 → b

= 0.17 m.s-1 a

city profiles (

he test sect

egime Ana

periments, th

with the (low

ow in the aqu

ture of the fl

stic changes

ribution betw

ingle phase f

locity profile

ents normali

b3) for two

and φin = 0.

(a1 → a2) in

ion, the ve

alysis

here was a co

wer) aqueous

ueous phase

low from the

in the natur

ween lamina

flows in a tub

es for: (a) lam

ised velocity

stratified fl

17, and; (2)

relation to th

elocity profi

onsiderable d

s phase havin

co-existing w

e lower to th

re of the velo

r and turbul

be as shown

(a)

(b)

minar flow, a

y profiles (a

low cases, w

) Um = 0.28

he flow imag

le follows

Chapter

difference in

ng a much h

with turbulen

he upper regi

ocity profile

lent flow is

in Figure 5-2

and; (b) turbu

a1 → a3) and

with the fol

m.s-1 and φ

ges (b1 → b2

a parabolic

r 5: Circular S

n viscosity be

higher viscos

nt flow in the

ion would be

. This chang

illustrated b

27.

ulent flow, t

d correspond

llowing inpu

φin = 0.38.

2) shows that

curve up

Section PLIF R

etween the o

sity. This can

e oil phase. S

e expected to

ge in the natu

by considerin

taken from S

ding instanta

ut condition

Inspection o

t, from the b

to the inte

Results

oil and

n give

Such a

o give

ure of

ng the

Sellens

aneous

ns: (1)

of the

bottom

erface,

213


214

characteristic of a velocity profile for laminar flow (see Figure 5-27(a)). For Um =0.28 m.s-1

(Figure 5-28 (2)) the velocity profile in the upper region is clearly of a turbulent type. For

Um = 0.17m.s-1 there is a step change in velocity in the interface region and, above this region,

the velocity profile in the oil phase seems to be more characteristic of a laminar than a turbulent

flow.

(a1) (b1)

(a2) (b2)

Figure 5-28: Velocity profiles (a1 → a2) and instantaneous images (b1 → b2) for: (1) Um = 0.17

m.s-1 and φin = 0.17, and; (2) Um = 0.28 m.s-1 and φin = 0.38

The results shown in Figure 5-28 are consistent with the Reynolds numbers of the individual

phases which can be calculated using a combination of the volumetric flow-rates ( of the

individual phases coupled with the respective in-situ phase fractions, such that,

0 1 2 3 40

4

8

12

16

20

24

28

Normalised Streamwise Velocity, Ux/<Um

>

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

a

b


215

Re. .

, (5.7)

where,

⟨ ⟩ , . . 4

, (5.8)

and,

⟨ ⟩ , . .2

, (5.9)

where is the total cross-sectional area of the pipe and is the cross-sectional area occupied

by phase i.

It is found that for the results shown in Figure 5-28 (1) both liquids have a Reynolds number in

the laminar range (Re < 2000), Reoil = 943 and Regs = 60, i.e., the flow is dominated by viscous

forces rather than inertial forces and hence both the Reynolds number and velocity profile for

each of the phases indicates that away from the interface both liquids are travelling as laminar

flow. Performing the same analysis for the case shown in Figure 5-28(2) indicates that the

glycerol solution is still travelling as laminar flow (Regs = 55); this is supported by the shape of

the velocity profile for the glycerol solution in Figure 5-28(a2). However, the Reynolds number

for the oil phase is no longer in the laminar region (Reoil = 3414). This is in line with the shape

of the velocity profile of the oil phase in Figure 5-28(a2), which is steeper closer to the pipe wall

and so more characteristic of a turbulent flow. It should be emphasised that the results

presented in Figure 5-28 and the associated calculations of the Reynolds numbers of the

individual phases were for runs in which the two phases remain separated and there are no

droplets present, i.e., for stratified flow only.


216

Figure 5-29 presents a velocity profile and an instantaneous flow image for the case of a

stratified flow with droplets; the stratified flow regime changes into the stratified flow with

droplets as the superficial velocity is increased. On comparison with the velocity profiles

presented for stratified flow (see Figure 5-28), the step-change (arising due to a shear layer) is

no longer observed and the profile follows a much smoother transition due to the mixing at the

interface of the two fluids.

(a) (b)

Figure 5-29: Velocity profile (a) and instantaneous flow image (b) for stratified flow with

droplets at Um = 0.42 m.s-1 and φin = 0.50

It can be seen that the flow profile within the glycerol solution phase (i.e., up to ≈ 8 mm) is

parabolic, which, on comparison with Figure 5-28(a) indicates that the glycerol solution is

travelling as laminar flow. Above the mixing zone the same observation is made with respect to

the oil phase, indicating it is also laminar flow.

Figure 5-30 presents a velocity profile and an instantaneous flow image for at Um = 0.84 m.s-1

and φin = 0.50. Here the flow regime is three-layer flow. Three distinct regions to the profile are

identifiable, these being: (1) a single phase glycerol-solution region (i.e., up to ≈ 16 mm), (2)

a highly dispersed region (i.e., from ≈ 8 mm up to ≈ 24 mm), and (3) a single phase oil

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)


217

region up to the top of the channel. From the shape of the velocity profile it is deduced that all

three regions are turbulent.

(a) (b)

Figure 5-30: Velocity profile (a) and instantaneous flow image (b) for three-layer flow with

droplets at Um = 0.84 m.s-1 and φin = 0.50

Figure 5-31 presents velocity profiles and instantaneous flow images for (1) Um = 0.67 m.s-1

and φin = 0.75, and; (2) Um = 0.56 m.s-1 and φin = 0.75, respectively. In both cases, there is a

thin layer (up to ≈ 2 mm) of glycerol-solution on the pipe wall. Above ≈ 2 mm there is a

second layer arising from the flow of a glycerol-solution droplet region above the glycerol-

solution film, travelling at a different velocity to that of the film.

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

uali

satio

n Se

ctio

n H

eigh

t, H

T (m

m)

1

2

3


218

(a1) (b1)

(a2) (b2)

Figure 5-31: Velocity profiles (a1 → a2) and instantaneous images (b1 → b2) for: (1)

Um = 0.67 m.s-1 and φin = 0.75, and; (2) Um = 0.56 m.s-1 and φin = 0.75

Figure 5-32 presents normalised velocity profiles (a1 → a2) and instantaneous images (b1 → b2)

for dispersed flows. Figure 5-32 (1) (Um = 0.84 m.s-1 and φin = 0.25) shows results for a

dispersion of oil droplets in glycerol solution and Figure 5-32 (2) (Um = 0.83 m.s-1 and

φin = 0.90) shows results for a dispersion of glycerol solution droplets in oil. Inspection of the

velocity profile in Figure 5-32(a1) in relation to the instantaneous flow image shown in Figure

5-32(b1) shows that the step changes in the velocity profile observed at ≈ 24 mm and ≈ 20

mm are due to discrete layers of oil droplets flowing at different velocities.

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

uali

satio

n Se

ctio

n H

eigh

t, H

T (m

m)


219

(a1) (b1)

(a2) (b2)

Figure 5-32: Velocity profiles (a1 → a2) and instantaneous images (b1 → b2) for dispersed flows,

at: (1) Um = 0.84 m.s-1 and φin = 0.25, and; (2) Um = 0.83 m.s-1 and φin = 0.90

Finally, Figure 5-33 presents interface level values as a function normalised interface level

velocity ( ⟨ m⟩⁄ ). From inspection of the figure it is evident that once normalised, the

velocity at the interface increases with an increase in the interface level.

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

uali

satio

n Se

ctio

n H

eigh

t, H

T (m

m)

0 1 2 3 40

4

8

12

16

20

24

28


>

Vis

uali

satio

n Se

ctio

n H

eigh

t, H

T (m

m)

Fi

A mo

This

analy

reduc

profil

togeth

5.10

A no

incor

partic

liquid

the s

repre

achie

arisin

wall

igure 5-33: I

ore sophistica

analysis tak

ysis can be u

ction process

les in such f

her with an a

Conclu0

ovel, non-in

rporating las

cle tracking v

d flows in a

tudy present

sentative of

eved through

ng from the c

material and

Interface leve

ated analysis

es account o

used to exam

s described a

flows. A det

assessment o

usions

ntrusive, spa

ser-induced

velocimetry

circular pipe

ted in Chap

industrial pi

h the use of a

curvature ref

d into the in

00

4

8

12

16

20

24

28

Inte

rfac

e L

evel

, H

(m

m)

el as a fun

s of stratified

of interfacial

mine critically

above and al

tailed descrip

of its implica

atiotemporall

fluorescence

(PTV), was

e section. Th

pter 4 but it

ipeline syste

an optical ca

fraction thro

nspected flow

0 0.5Normalised In

nction norma

d laminar liq

l tension and

y the assump

lso gives inf

ption of the

ations in the p

ly resolved

e with both

developed a

he current ex

makes use

ms (i.e., wit

alibration tec

ough the ima

ws. As was

1 1nterface Level V

Chapter

lised interfac

quid-liquid flo

d contact ang

ption of a fla

formation on

Ng (2002) a

present work

optical (las

h particle im

nd then used

xperimental

of a test se

th a circular

chnique to co

aging line-of

s the case in

.5 2Velocity, U

H/<

r 5: Circular S

ce level velo

ow is presen

gle at the tri

at interface im

n the two-dim

analysis is g

k.

ser) measur

mage veloci

d to measure

campaign is

ection with

cross-section

orrect for the

f-sight throug

n Chapter 4,

2.5<U

m>

Section PLIF R

city ( ⟨ m⁄

nted by Ng (2

iple interface

mplicit in th

mensional ve

given in Chap

rement techn

imetry (PIV

co-current l

a developm

a geometry

n). This has

e image dist

gh the test se

, the experim

Results

m⟩)

2002).

e. The

e data

elocity

pter 6

nique,

V) and

iquid-

ment of

more

s been

tortion

ection

mental

220


221

technique is again shown to be a powerful tool that can provide detailed spatiotemporal

information of the flowing behaviour. Characterisation of the flows has been developed herein

to include both phase information and velocity profiles.

The findings of the current study in terms of flow regimes are comparable to those of Chapter 4.

Eight distinct flow regimes have again been observed. These have been grouped into the

following four flow types: (1) stratified flow; (2) mixed flow (i.e., a flow with two distinct

continuous phase regions with droplets); (3) continuous oil-phase dispersion; and (4) continuous

aqueous-phase dispersion.

As was the case in Chapter 4, the flow is again seen to be comprised of three distinct zones,

with a continuous oil phase at the top and a continuous glycerol-water phase at the bottom,

separated by a mixed zone. The vertical space covered by the mixed zone increased at higher

superficial velocities.

The laminar drag model (tailored for a circular cross-section pipeline) is again shown to give

excellent agreement with experimental in-situ phase fraction and interface level results. The

gas-liquid interface level predictive technique presented by Hall and Hewitt (1993) is shown to

have excellent agreement with the current experimental results.

The velocity profile results give insights into the nature of the flow (laminar or turbulent) in

various regions of the cross section and at various flow conditions.

Though the current Chapter presents a detailed account of the behaviour of co-current liquid-

liquid flows, there is little discussion is made about the instability mechanisms that are driving

flow regime transition and development of the flow. The work described in Chapter 6 develops


222

the current study by using a different inlet orientation to investigate the effects different

instability mechanisms (particularly, the Rayleigh-Taylor instability) have on the flow.

CH

Inv

Co

Str

6.1

In Ch

PLIF

visua

25.4 m

glyce

D80)

prese

chann

would

(

HAPT

vestiga

onfigu

ratifie

Introdu

hapter 5, stud

and the ve

alisation cell

mm internal

erol solution)

phase was

ent Chapter, t

nel and the

d naturally s

1) To determ

If the re

reasonabl

TER 6

ation o

ration

ed Liqu

uction

dies of liquid

elocity profi

was placed L

diameter tes

) phase was

injected at t

the experime

oil phase at

eparate. The

mine whethe

sults for the

ly be argued

of the

n on H

uid-Li

d-liquid flow

les measure

LE = 6.20 m

st section. In

injected at

the top of th

ents were rep

the bottom,

e objectives i

er the flow h

ese two extr

d that fully-de

Effect

Horizon

iquid F

ws are report

ed using PTV

(such that L

n the work de

the bottom o

he channel. I

peated with t

, i.e. in the o

n this further

had become f

reme injecti

eveloped flow

Chapter 6: P

ts of th

ntal In

Flows

ted in which

V and PIV.

LE/D = 244) f

escribed in C

of the chann

In the experi

the aqueous p

opposite orie

r study were

fully develop

on scenarios

w had been a

PLIF Results:

he Inle

nitially

the flow wa

. In those m

from the inle

Chapter 5, the

nel and the l

imental work

phase injecte

entation to t

as follows:

ped at the m

s were simi

achieved.

Instability An

et

y

as visualised

measurement

et of the horiz

e heavier (aq

lighter oil (E

k described

ed at the top

that in which

measurement

ilar, then it

nalysis

using

ts, the

zontal

queous

Exxsol

in the

of the

h they

point.

could

223

Chapter 6: PLIF Results: Instability Analysis

224

(2) To investigate whether the additional instabilities might arise as a result of the change

in injection strategy giving rise to different flow structures (flow patterns). Specifically,

in the case of the aqueous phase being injected above the oil phase, Rayleigh-Taylor

instability may occur, giving rise to a phase breakup mechanism whose effects may

persist from the inlet to the measurement section.

Though the main focus of this Chapter is on the presentation of this new set of experimental

results, several additional features have also been addressed which include:

(1) Considering the effects of interfacial instabilities on flow patterns. A background

discussion on this topic is given in what follows below in Section 6.1.

(2) The effects of contact angle and interfacial tension have been evaluated on the basis of

the analysis of Ng (2002). This work is presented in Section 6.8.2.

The development of the flow from (initially) stratified flow to the more complex flow regimes

(i.e., dual continuous and dispersed flows) can arise due to increased flow complexity and

enhanced mixing that is associated with turbulence.

Turbulence arises at higher flow velocities (i.e. higher liquid flow rates), from nonlinear inertial

effects (described by the Reynolds number) that cannot get damped out (or, dissipated) by

viscous (momentum) diffusion. It is no surprise that the regimes maps presented in Chapters 4

and 5 showed stratified flows at lower superficial mixture velocities, and increasing

phenomenological flow complexity at higher velocities.

However, the flow complexity can also be augmented by the following instability mechanisms:

1. Kelvin–Helmholtz (KH) instability

If small amplitude waves are present at the interface in a stratified flow, the pressure

above the waves changes in a manner which is out of phase with wave height. This

causes a suction force on the wave peaks. If this suction force is sufficient to overcome


225

the influences of gravity and surface tension, then the waves can grow leading to the

Kelvin-Helmholtz instability.

2. Rayleigh–Taylor (RT) instability

This instability mechanism is relevant to flows where a dense fluid is situated above a

lighter fluid with gravity acting, and again, involves the instability of the interface

between two liquid layers. In this case the heavier liquid will sinks under gravity into

the lighter liquid which is displaced, and the lighter liquid flows upwards and has a

fingering nature with bubbles of the lighter liquid rising into the denser liquid above,

and spikes of the heavier liquid descending into the lighter liquid below.

Either of these mechanisms can give rise to mixing of the stratified layers.

The onset of the aforementioned instabilities can be predicted by means of several

dimensionless numbers that can characterise liquid-liquid flows. Those pertinent to the current

analysis are detailed below.

The Richardson number (Ri) expresses the ratio of potential to kinetic energy:

Ri , (6.1)

where is a representative vertical lengthscale and a representative velocity.

For a flow with a varying distribution of density and velocity (though with the lighter fluid

layers over the heavier ones), the onset of the Kelvin-Helmholtz (KH) instability is given by a

suitably-defined Ri number. Typically the layer is unstable for Ri 0.25. The Ri number values


226

for the matrix of experimental conditions for the high-speed PLIF-PTIV campaigns of Chapter 5

and in the present chapter are:

Ri ⁄ 0.05 0.3⁄ – 0.05 0.07⁄ 0.5 10 with ~0.005m and Um 0.07 – 0.3 m.s-1

Ri ⁄ 0.1 0.3⁄ – 0.1 0.07⁄ 1 20 with ~0.01m and Um 0.07 – 0.3 m.s-1

Ri ⁄ 0.05 0.5⁄ 0.3 with ~0.005 m and Um 0.4 m.s-1

Ri ⁄ 0.1 0.6⁄ 0.3 with ~0.01 m and Um 0.6 m.s-1

We can see that for the range of superficial velocities used, the Richardson number is typically

greater than 0.25, and we would not expect the KH instability mode to occur, though at the

higher velocity ratios between the two phases (i.e., highest and lowest inlet phase fractions) it

would begin to play a role.

The Atwood number (A) is a ratio of buoyancy to gravity and is employed in the study of

hydrodynamic instabilities in density stratified flows. It is written as a ratio of the density

difference between the two liquids to the sum of the same densities,

A ⁄ , (6.2)

where the subscript "1" denotes the heavier and "2" the lighter fluid.

In Rayleigh-Taylor (RT) instability, the vertical penetration distance y (this is actually denoted

as z in Figure 6-1(a)) of the fluid interface into the two phases (or equivalently, the outer edges

of the “mixing zone”) is a function of the timescale τ Ag , where is the time, such that an

asymptotic scaling law y ατ is obeyed.

Figur

Glim

Dimo

of de

mixin

(Dim

with

0.05×

Assum

inves

exper

re 6-1: (a) D

mm et al., (200

onte and Sch

ensity ratios

1 1⁄

ng layer in th

monte and Sch

a2 ~ 0.05 ± 0

×1.50.33 = 0.0

ming the bu

stigation, the

riments is [ca

(a)

Definitions f

00)

hneider (2000

s (R, where

] using a lin

he flow. For

hneider, 2000

0.005 and a1

057 and a2 ~

ubbles and s

e time for t

alculated fro

from Dimon

0) investigate

e R ⁄

near electric

r a constant a

0) amplitude

1 ~ a2 RDa wi

0.05.

spikes are fr

the bubbles

om Equation

nte and Schn

ed the turbul

) 1.3 R

motor, back

acceleration,

es were found

,

ith Da ~ 0.33

om a RT in

to move to

6.3]

Chapter 6: P

neider (2000

lent RT insta

R 50 [0.1

klit photogra

the bubble (

d to increase

3 ± 0.05. He

nstability in

o the bottom

/ /

PLIF Results:

(b

0), and; (b)

ability over a

15 A 0

aphy and LI

(Glimm et al

e as:

ere: R = 1.5

the liquid–li

m of the pip

0.45 s; an

Instability An

b)

Simulations

an extensive

0.96, where

IF to diagno

l., 2001) and

(6.3)

and A = 0.2

iquid flows

pe in the p

nd the time n

nalysis

from

range

e A

se the

d spike

2, a1 ~

under

resent

needed

227


228

for the spikes to reach to the top of the pipe is / / 0.42 s. The distance

travelled by the bulk flow during this advection time is 0.07 to 0.3 m.s-1 × 0.45 s = 0.03 to 0.14

m. This is at least 44 times less the 6.20 m distance from the inlet to the visualisation section.

Certainly it is expected that there is enough time for the bubbles and spikes to extend all the

way across the liquid height and the fluid to mix in the vertical direction due to the RT

instability. Even at the highest investigated velocity of Um 1.46 m.s-1, the distance travelled is

1.46 m.s-1 × 0.45 s = 0.66 m, an order of magnitude shorter than the 6.2 m development length.

As mentioned previously, the Reynolds number measures the ratio of inertial to viscous forces:

. (6.4)

When the viscous forces dominate, the flow is characterised by smooth laminar flow (i.e.,

stratified flow). On the other hand, when the inertial forces dominate the viscous forces, the

flow becomes turbulent leading to instabilities such as eddies, vortices and waves (at the

interface). The values of Re for the current experimental conditions are given in Table 6-1.

Table 6-1: Reynolds numbers for the current experimental matrix

Um (m/s) Re (Oil) Re (G-S)

0.07 240 20

0.3 1,040 80

1 3,480 260

1.46 5,080 370

N.B.: Typically Re < 2,000 – 3,000 should be a laminar flow, with little “mixing”, such that a

flow should remain mainly stratified in the absence of the RT instability.


229

Considering the above, there are two main mechanisms for “mixing” in the liquid-liquid flows

studied in the work described in this thesis:

1. High Reynolds numbers (hence inertial forces dominated flow) leading to turbulence.

This is observed in the velocity profiles shown in Figure 5-28(a2) in which it is seen that

the oil layer is turbulent (detected from the oil profile shape and the Reynolds number

of the oil phase, 3414) whereas the glycerol solution layer is laminar

( 55) and has a and parabolic velocity profile for the phase. For these

independent variable conditions (Um = 0.28 m.s-1 and φin = 0.38) the onset of waves at

the interface are observed and the transition from stratified flow to stratified wavy flow

is triggered by the transition of the oil phase to the turbulent Reynolds number region.

2. RT instability in the inverted flow (the inverted inlet orientation is explained in Section

6.2), which is the motivation behind the experiments presented in the present chapter.

Recall also that, from the above calculated Ri values and considering the KH instability onset

threshold (Ri 0.25), we can say that this instability is not usually an issue at the flows

discussed here, but could begin to play a role at the extreme inlet phase fractions and at higher

superficial mixture velocities, where the shear between the two liquid-liquid flow layer is at its

greatest.

Considering the independent variable matrix and the inlet configuration, there are, between

Chapter 5 and the experimental results presented herein, four different flow instability scenarios,

these are listed in Table 6-2 below.

N.B.:

curre

So, in

is dom

the w

mech

introd

top o

6.2

The

outlin

and a

orien

flow,

introd

sectio

Scenario N

1

2

3

4

: Scenario 1

nt (Chapter 6

n synopsis, f

minated by

work presen

hanisms have

ducing the te

f the less den

Experi

experimenta

ned in Sectio

an Olympus

ntation is “in

i.e., the glyc

duced to the

on is shown i

Number

and 2 relate

6) PLIF cam

for the PLIF

high Reynol

nted in Cha

e on flow r

est fluids into

nse fluid (Ex

imental O

al campaign

on 5.2 i.e., w

s i-SPEED

nverted” with

cerol-solutio

e test section

in Figure 3.5

Table 6-2: F

Reyno

to the PLIF

mpaign.

and PIV/PTV

lds numbers

apter 5 by

regime transi

o the test sec

xxsol D80 oil

Operation

was carried

with a circul

3 high spee

h respect to

on is introduc

n above the

5 and the two

Flow instabil

olds number

Laminar

Turbulent

Laminar

Turbulent

campaign in

V study pres

leading to t

investigating

ition from i

ction such tha

l) with the ai

d out using

ar cross-sect

ed camera (

that in Chap

ced to the tes

less dense l

o inlet config

Chapter 6: P

lity scenarios

r (Re)

n Chapter 5,

sented in Cha

turbulence.

g the influe

initially strat

at the denser

im on imposi

the same o

tion visualisa

(see Section

pter 5 as to

st section abo

liquid. A p

gurations are

PLIF Results:

s

RT i

S

S

U

U

scenarios 3

apter 5, flow

The current

ence that di

tified flow.

r fluid (glyce

ing a RT inst

operational p

ation cell (se

n 3.4.1). H

induce a RT

ove the oil; th

photograph o

illustrated in

Instability An

instability

Stable

Stable

Unstable

Unstable

and 4 relate

w regime tran

t chapter dev

ifferent insta

This is do

erol solution)

tability mode

procedure a

ee Section 3

However, the

T instability

he denser liq

of inlet to th

n Figure 6-1.

nalysis

to the

nsition

velops

ability

ne by

) is on

e.

s that

.10.2)

e inlet

in the

quid is

he test

.

230

The e

Chap

variab

veloc

spann

varied

range

flow

Figur

the “i

6.3

Apply

regim

camp

flow,

instan

obser

Chap

experimenta

pter 5. A cam

bles used to

city and

ned a range

d from 0.1 t

e Um = 0.11

to enhance th

re 6-2: Inlet

inverted” inl

Flow P

ying the flo

mes observed

paign. The tw

and; (2) gly

ntaneous flow

rved. This

pters 4 and 5

l matrix is s

mpaign 48 ru

o classify th

the inlet vo

of superfici

to 0.9. The

to 0.42 m.s-

he understan

(a)

orientation f

et configurat

Phenomen

ow regime c

d in the PLIF

wo regimes a

ycerol soluti

w images ar

is because

there was a

similar to th

uns was perfo

he runs in C

olumetric ph

ial mixture v

quantitative

-1 to capture

nding of the m

for (a) the “n

tion as used

nology and

lassification

F campaigns

absent from

ion dispersio

re presented

within the

relatively br

hat used for

ormed that w

Chapter 4 an

hase fraction

velocity from

e analysis fo

the develop

mechanism d

normal” conf

in the curren

d Regime

system def

of Chapters

the current e

on with a gly

in Figure 6-

scope of th

road range in

Chapter 6: P

PLIF and P

were each def

nd Chapter 5

n of the oil

m 0.

ocused on th

pment of stra

driving this f

figuration as

nt (Chapter 6

e Map

fined in Cha

4 and 5 hav

experimental

ycerol soluti

-3 to convey

he classificat

n the number

PLIF Results:

PIV/PTV stu

fined by the

5 i.e., the su

. The e

11 to 0.84 m

he superficial

atified flow t

flow regime t

(b)

used in Chap

6) PLIF study

apter 4, only

e been obser

l campaign a

ion film. H

y the 6 diffe

tion method

r of droplets

Instability An

udies present

same indepe

uperficial m

experimental

m.s-1 and

l mixture ve

to dual conti

transition.

pter 5, and; (

y.

y 6 of the 8

rved in the c

are: (1) three

However, 8 (n

rent flow re

dology adopt

presented in

nalysis

ted in

endent

mixture

l runs

was

elocity

nuous

(b)

8 flow

urrent

e layer

not 6)

gimes

ted in

n both:

231


232

(1) the oil droplet layer flow regime, see Figure 6-3(c) and 6-3(e), and; (2) the glycerol solution

droplet layer regime, see Figures 6-3(d) and 6-3(f).

A flow regime map relating the flow regime classifications to the independent variables, the

superficial mixture velocity and the inlet volumetric phase fraction of oil in the pipe is

presented in Figure 6-4. The flow regime map is again in good agreement with those presented

by previous researchers (Soleimani, 1999; Lovick and Angeli, 2003; Hussain, 2004). However,

on comparison with the flow regime map presented in Chapter 5 (see Figure 5-2) it can be seen

that the stratified flow with droplets flow regime is seen at both lower superficial mixture

velocities ( 0.17 m.s-1 opposed to 0.22 m.s-1) and lower oil input fractions in the

current campaign (see Figure 6-2). It is found that the onset of the flow regime characterised

stratified flow with a glycerol solution droplet layer occurs at the same superficial mixture

velocity (i.e., 0.42 m.s-1 ) in both the results described in Chapter 5 (aqueous phase

injected at bottom of tube) and in the study reported in the current chapter (aqueous phase

injected at the top of the tube).


233

(a) Stratified flow (b) Stratified flow with droplets



(e) Oil dispersion over glycerol solution (f) Oil flow over glycerol solution dispersion

with glycerol solution film

Figure 6-3: Images of the 8 distinct flow regimes observed in the circular cross experimental

campaign with an “inverted” inlet configuration


234

On visual inspection of Figure 6-4, in comparison with Figure 5-2 in Chapter 5, it can be seen

that the flow regime maps are largely comparable. The major difference between the flow

regime maps presented in Chapters 5 and 6 is that oil droplets are a considerably more prevalent

in Figure 6-4 (in Chapter 6) than they are in Figure 5-2 (in Chapter 5). In particular, the oil

droplet layer flow regime is seen across a much broader range of conditions ( 0.28 -

0.55 m.s-1) in Figure 6-4 as opposed to just at 0.55 m.s-1 in Figure 5-2.


From the RT instability preliminary analysis in Section 6-1, based on Equation 6.3, and

considering the time that should elapse from the flow entering the test section to reach the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Sup

erfi

cial

Mix

ture

Vel

ocity

, U

m (

m.s

-1)


Stratified FlowStratified Flow with DropletsOil Droplet LayerStratified Flow with Glycerol Solution Droplet LayerOil Dispersion over Glycerol SolutionOil Flow over Glycerol Solution Dispersion with Film

visua

be af

concl

descr

(see F

When

contin

Howe

2(a))

fracti

2(b))

super

is als

are “i

flow

indep

result

input

below

differ

6.4

This

(see F

alisation cell,

ffected by t

luded that th

ribed in Chap

Figure 6-3(b)

n the flow re

nuous flow r

ever, the tran

is seen to o

ions 0

inlet config

rficial mixtur

so seen that t

inverted” at t

for the “n

pendent varia

ting from the

t phase fracti

w the interfa

rences are di

Vertica

section prese

Figure 6-2(b

, it was calcu

the inlet con

he flow is stil

pter 5, and t

) compared t

egime maps p

regime classi

nisition to du

occur at a su

0.4 and

guration the

re velocity o

there is a hig

the inlet. Th

normal” and

able values.

e inlet config

ion ( 0

ace and, to a

scussed later

al Phase D

ents the verti

b)). Figure

ulated that s

nfiguration.

ll displaying

these differen

to Figure 5-1

presented in

ification the

ual continuou

uperficial m

0.40 m.s-1

e transition

of 0.17

gher occurren

his is evident

d the “inver

Hence it i

guration. Th

0.4) in Figur

a lesser degr

r in this chap

Distributi

ical phase di

6-5 shows v

sufficient tim

However,

characterist

nces must be

1(b)).

Figures 5-2

flow regime

us flow for t

mixture veloc

for 0

to dual con

7 m.s-1 for al

nce of oil dr

t from Figure

rted” inlet c

s clear that

he predomina

re 5-2 and 6

ee, a lack of

pter.

ion Profil

istribution re

vertical phas

Chapter 6: P

me should ha

from the ex

ics different

e due to the

and 6-4 are c

maps becom

the “normal”

city of

0.4, whereas

ntinuous flow

ll oil input p

roplets below

e 6-7 in whic

configuration

the flow is

ant differenc

6-4 is the exi

f glycerol-w

es

esults for the

e distributio

PLIF Results:

ave elapsed f

xperimental

to those obs

“inverted” i

compared in

me much mor

” inlet config

0.22 m.s-1

for the “inv

w occurs at

hase fraction

w the interfac

ch instantane

ns are show

still exhibiti

e between th

istence of an

water droplets

“inverted” i

on profiles φ

Instability An

for the flow

results it c

served in the

inlet configu

terms of the

re closely ali

guration (Fig

at oil inlet

verted” (Figu

t the much

ns investigat

ce when the

eous images

wn for the

ing characte

he flows at lo

n oil droplet

s above it.

inlet configu

(y) for supe

nalysis

not to

an be

e work

uration

e dual

igned.

ure 6-

phase

ure 6-

lower

ed. It

flows

of the

same

ristics

ow oil

t layer

These

uration

rficial

235


236

mixture velocities in the range Um 0.11 to 0.42 m.s-1 at selected input oil fractions φin of: (a)

0.25; (b) 0.50, and; (c) 0.75. It corresponds to Figure 5-3 of Chapter 5 albeit with the different

inlet configuration to the test section and, has been calculated using the same technique i.e., that

given in Section 3.11.2. Figure 6-6 shows vertical phase distribution profiles φ(y) for a range of

input oil fractions φin for superficial mixture velocities Um of: (a) 0.11 m.s-1; (b) 0.17 m.s-1; (c) 0.22

m.s-1; (d) 0.28 m.s-1; (e) 0.34 m.s-1 and; (f) 0.42 m.s-1; This relates to Figure 5-4 of Chapter 5.

(a) (b)

(c)


Um at an input oil fraction φin of: (a) 0.25, (b) 0.50, and (c) 0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

Um=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

Um=0.33 m/s

Um

=0.42 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

Um=0.11 m/s

Um=0.17 m/s

Um

=0.22 m/s

Um=0.28 m/s

Um

=0.33 m/s

Um

=0.42 m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (%

)

Um

=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

Um=0.34 m/s

Um

=0.42 m/s


237

(a) (b)

(c) (d)

(e) (f)


superficial mixture velocity Um of: (a) 0.11 m.s-1, (b) 0.17 m.s-1, (c) 0.22 m.s-1, (d) 0.28 m.s-1,

(c) 0.33 m.s-1, (d) 0.42 m.s-1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n S

ectio

n H

eigh

t, H

T (%

)

in

=0.25

in

=0.50

in

=0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.17

in

=0.25

in

=0.50

in

=0.75

in

=0.83

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.12

in

=0.25

in

=0.50

in

=0.75

in

=0.87

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (%

)

in

=0.10

in

=0.25

in

=0.50

in

=0.75

in

=0.90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

uali

satio

n S

ecti

on H

eigh

t, H

T (%

)

in

=0.25

in

=0.50

in

=0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

90

100

Oil Fraction,

Vis

uali

satio

n S

ecti

on H

eigh

t, H

T (%

)

in

=0.25

in

=0.50

in

=0.75

a

b c

d e

1


238

Figure 6-6 shows vertical phase distribution profiles φ(y) for a range of input oil fractions φin for

superficial mixture velocities Um of: (a) 0.11 m.s-1; (b) 0.17 m.s-1; (c) 0.22 m.s-1; (d) 0.28 m.s-1;

(e) 0.34 m.s-1 and; (f) 0.42 m.s-1. This relates to Figure 5-4 of Chapter 5.

Once again, the flow is seen to adhere to the zone characterisation first presented in Chapter 4

and illustrated in Figure 4-7, i.e., there are three distinct regions to the flow: (1) an oil region;

(2) a glycerol solution region, and; (3) a mixed region separating them. The dynamics of the

mixed region parallel the findings of Chapters 4 and 5. Specifically, the mixed region covers a

very narrow vertical band for stratified flows and increases for a given superficial mixture

velocity; as oil input fraction is increased the height of the mixed band increases. In addition,

the height of the glycerol solution layer at the bottom of the pipe decreases under the

aforementioned conditions. The vertical height covered by the mixed region is also seen to

increase as the superficial mixture velocity (for a given oil input fraction) increases.

However, on further inspection it is seen that the phase distribution profiles for several of the

runs (i.e., independent variable combinations) feature “kinks” in the mixed zone (labelled a → e

in Figure 6-6). These are found exclusively at low oil input phase fractions, predominantly at

φin 0.1 to 0.25. On visual inspection of these instantaneous flow images (see Figure 6-7) it is

observed that the kinks can be attributed to an oil droplet layer below the interface.

Figure 6-7 also features instantaneous images of the flow for the same independent variables but

for the “normal” inlet configuration from Chapter 5 (left hand side, i.e., those denoted by an

“a”). From comparing the “inverted” inlet condition results (right-hand side, i.e., those denoted

by a “b”) with the “normal” inlet condition results (left hand side), it is concluded that the inlet

configuration does have an effect on the flow regime at the distance far downstream of the inlet

(L/D = 244) at which the PLIF-PTIV measurements were taken.


239

1a 1b

2a 2b

3a 3b

4a 4b

Figure 6-7: Instantaneous flow images for: (1) 0.17 m.s-1 for 0.17; (2);

0.22 m.s-1 for 0.12; (3) 0.28 m.s-1 for 0.25, and; (4) 0.33 m.s-1

for 0.25; “a” refers to the “normal” inlet configuration and “b” to the “inverted” inlet

configuration.


240

A more complex mixed-zone profile is seen for the conditions 0.28 m.s-1 for 0.1

(labelled “1” in Figure 6-6(d)). An instantaneous image of the flow for these conditions is

presented in Figure 6-8(b); this is presented alongside an instantaneous image of the flow for the

same independent variable values but taken for the “normal” inlet configuration (see Figure 6-

8(a)). Analysis of the profile labelled “1” from Figure 6-6(d) in relation to Figure 6-8(b) (in

actual fact, the following remark is based upon observation of the video of the aforementioned

flowing conditions) reveals that there are three distinct regions to the oil dispersion in the flow.

These are: (i) a layer of small oil droplets at the top of the pipe, below which there is (ii) a layer

of fast moving long oil droplets, and below which (iii) is another layer of oil droplets albeit the

same size as those at the top of the channel. On comparison with Figure 6-8(a) it is seen that the

flow is significantly different. This can be attributed to the inlet configuration inducing a RT

instability hence more mixing in the flow. As calculated in Section 6.1, enough time has

elapsed for the droplets to reach the top of the channel, which is what is observed in Figure 6-

8(b). However, these risen oil droplets have not coalesced to form a continuous oil region at the

top of the channel. The reasons for this result are discussed below.

(a) (b)

Figure 6-8: Instantaneous flow images for a superficial mixture velocity 0.28 m.s-1 and an

oil input phase fraction 0.1 for: (a) the “normal” inlet configuration, and; (b) the

“inverted” inlet configuration


241

The coalescence of two droplets of one phase (in this case, oil) in a continuum of another phase

(in this case, glycerol solution) is governed by the dynamics of the intervening film.

Essentially, for coalescence to occur, the film has to drain away under the pressure created by

the two droplets coming together until the film is sufficiently thin locally for intermolecular

effects to come into operation to rupture it. However, this drainage, and ultimately coalescence,

is retarded by the viscosity of the film (and also any surfactants present that can rigidify the

interface). In this case, the glycerol solution film has a significantly higher viscosity than the oil

phase and hence results in the drainage process being slower, retarding the coalescence process.

It is possible to estimate the time take for the film to drain based on the viscosity of the

continuous phase. This offers one possible explanation why oil droplets are more readily seen

than glycerol solution droplets; should glycerol solution droplets form, the oil film drainage

time necessary for their coalescence may be much lower than the glycerol solution film drainage

time for the coalescence of two oil droplets. Furthermore, one would expect the “inverted” inlet

configuration to results in smaller oil droplets than the “normal” inlet configuration (whether

this is in fact the case will be examined in Section 6.7) and droplet size will also have a role to

play in the coalescence of the two oil droplets.

This reasoning presents a possible explanation of the difference in flow regimes arising from the

two different inlet orientations and that if a “fully developed” flow regime does exist for a given

set of independent variables (superficial mixture velocity and input oil phase fraction) the time

necessary for its formation (for the “inverted” inlet case in particular) cannot be solely based on

the droplet and spike settling times but must also account for the conditions necessary for the

droplets to coalesce. In other words, the droplet coalescence dynamics may persist far

downstream of the inlet, giving rise to (possibly) very different flow regimes. It also

emphasises the need to consider the inlet conditions when comparing results from modelling

predictions to actual liquid-liquid flows.

6.4.1

Figur

veloc

result

veloc

fracti

phase

comp

Figur

for c

veloc

6.5

This

confi

0

20

40

60

80

100

Mix

ed Z

one

Hei

ght,

Hm

z (m

m)

Mixed Z1

re 6-9 prese

city, and; (b)

ts for the “n

city, the mix

ion for the “i

e fraction as

parison, it is

re 6-9: Heig

onstant inpu

cities Um

In-Situ

section pres

guration to t

0 0.10

0

0

0

0

0

Superfi

in

=0.25

in

=0.50

in

=0.75

Zone Heigh

ents the heig

) input oil ph

normal” inle

xed zone he

inverted” inle

s was observ

seen that the

(a)

ght of Interfa

ut oil fractio

u Phase Fr

sents the res

the test secti

0.2 0ficial Mixture Velo

ht

ght of the m

hase fraction

et configura

eight remain

et, as oppose

ved with the

e mixed zone

ace Zone for

on φin; (b) in

raction

sults for in-

ion inlet (Fig

0.3 0.4ocity, U

m (m/s)

mixed zone

n. On compa

ation) it is s

ns relatively

ed to exhibiti

e “normal” i

e height is lar

r as a functio

nput oil frac

-situ oil pha

gure 6-2(b))

0.5

0

10

20

30

40

50

60

70

80

90

100M

ixed

Zon

e H

eigh

t, H

mz (

%)

Chapter 6: P

as a functio

arison with F

seen that for

stable for a

ing an increa

inlet configu

rger for the “

on of (a) sup

ction φin for

ase fraction

. To recap,

0 0.1 0.20

0

0

0

0

0

0

0

0

0

0

In

Um=0.11 m

Um

=0.17 m

Um

=0.22 m

Um

=0.28 m

Um

=0.34 m

Um=0.42 m

PLIF Results:

on of: (a) su

Figure 5-6 (i

r a given su

an increasin

ase with an in

uration. Sec

“inverted” in

(b)

perficial mixt

r constant su

⟨φ⟩y,t for th

the in-situ o

0.3 0.4 0.5nput Oil Phase Fr

m/s

m/s

m/s

m/s

m/s

m/s

Instability An

uperficial m

i.e., the equiv

uperficial m

g oil input

ncreasing oil

condly, on f

let configura

ture velocitie

uperficial m

e “inverted”

oil phase fra

0.6 0.7 0.8action,

in

nalysis

mixture

valent

mixture

phase

l input

further

ation.

es Um

mixture

” inlet

actions

0.9 1

242


243

were calculated by using the phase distribution profiles coupled with a numerical integration

technique to account for the curvature of the visualisation cell wall; see Equations 5.1 and 3.5.


mixture velocities Um

The results concur with the findings in Chapters 4 and 5 (see Figure 4-12 and 5-7, respectively);

specifically, from Figure 6-10 it can be seen that the in-situ oil fraction ⟨φ⟩y,t is lower than the

input oil fraction φin for almost all flow conditions; indicated by the data points being below the

1 (homogeneous flow model) line in Figure 6-10.

Two different, but in both cases simple, approaches have been taken to estimate (i.e., model) the

in-situ oil phase fraction as a function of the input oil phase fraction. These are presented in

Figure 6-10 as φmod,1 and φmod,2; their derivations are explained below and have been calculated

using the same basis as φmod,1b and φmod,2 in Figure 4-12.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


In-S

itu O

il Ph

ase

Frac

tion,

y, t

Um

=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

Um

=0.34 m/s

Um

=0.42 m/s

mod,1

mod,2

S = 1

6.5.1

This

lamin

owing

The l

with

seen

veloc

can b

gives

Figur

is de

predi

and b

6.5.2

This

balan

exper

adjus

glyce

Lamina1

form of ana

nar flow and

g to the circu

laminar drag

the low sup

at like-for-l

city velocitie

be attributed

s rise to incr

re 6-7) which

erived) and t

ctive ability

below the int

Differen2

predictive t

nce, see Sect

rimental resu

sting in orde

erol solution.

r Drag Mo

alysis is base

d pressure dr

ular geometr

g model, as w

perficial mixt

like flowing

es Um values

to the impo

reased turbul

h moves the

towards dua

of the mode

erface are am

ntial Mom

technique is

tion 4.5.2 fo

ults. Hence,

er to satisfy

odel

ed on consid

rop in the p

ry, features th

with the resu

ture velocity

g conditions

s) for the “no

osed RT inst

lence and in

flow away f

al continuou

el deteriorate

mended to ac

entum Ba

denoted by

or the deriva

, the same c

the increase

dering an equ

pipe. The d

he revisions p

ults in Chap

y experiment

(i.e., input

ormal” inlet

tability (due

n turn more m

from stratifie

us flow for

es; unless the

ccount for the

lance Mod

y φmod,2 and

ation. This

conclusion ca

ed viscous dr

Chapter 6: P

uilibrium bet

derivation is

presented in

ters 4 and 5

tal results. A

oil fraction

configuratio

to the “inve

mixing (e.g.

ed flow (for

which, it is

e viscosities

e entrained f

del

is based up

is again in

an be made

rag caused b

PLIF Results:

tween the vi

presented in

Section 5.5.

5, shows very

Although, be

n φin and su

on, shown in

erted” inlet c

, the oil dro

which the la

s seen in Ch

of the flowi

flow.

pon a differ

excellent ag

i.e., that the

by the highe

Instability An

iscous drag d

n Appendix

1.

y good agree

etter agreem

uperficial m

n Figure 5-7.

configuration

oplet layer se

aminar drag m

hapter 4, th

ing material

rential mome

greement wit

e interface le

er viscosity o

nalysis

due to

2 but

ement

ment is

mixture

This

n) that

een in

model

at the

above

entum

th the

evel is

of the

244

6.5.3

This

homo

single

Figur

fracti

The f

flow

accou

data b

flow

suffic

vortic

00

1

2

3

4

5

6

Slip

Rat

io, S

Homoge3

section inve

ogeneous flo

e value or ex

re 6-11: Exp

ion φin, and:

findings are

model gives

unted for in t

by Lovick a

well when

ciently high t

ces) acting to

0.1 0.2 0.Inpu

S = 1S = 5.6228

eneous Flo

estigates the

w model (

xpression for

(a)

perimental re

(b) in-situ oi

synonymous

s a very poo

terms of the

nd Angeli (2

n the superf

to lead to tur

o mix the flo

3 0.4 0.5 0ut Oil Phase Fra

8in+0.0828

ow Model

e slip ratio

1) to char

r the slip ratio

esults and co

il phase fract

s with those

or characteri

flow regime

2004), a hom

ficial mixtur

rbulence, wit

ow to the exte

0.6 0.7 0.8 0action,

in

and Slip R

of the flow

racterise the

o can be used

orrelations fo

tion ⟨φ⟩y,t as

of Chapters

sation of the

e. As establ

mogeneous fl

re velocity

th its associa

ent that the f

0.9 10

0.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

In-s

itu O

il Ph

ase

Frac

tion,

y,

t

Chapter 6: P

Ratio

ws and in tu

flows. Figu

d to characte

or: (a) slip ra

a function o

s 4 and 5, sp

e current flo

lished upon c

flow model o

(and hence

ated broadba

flow changes

0 0.1 0.2 00

1

2

3

4

5

6

7

8

9

1

Inp

y, t

= 0

y, t

=

PLIF Results:

urn the suit

ure 6-11 inve

erise the flow

(b)

atio S as a fun

of input oil fr

pecifically, th

ow matrix. T

comparison w

only beings t

e also Reyn

and flow stru

s to dispersed

0.3 0.4 0.5 0put Oil Phase Fr

0.5111in

+0.456

in

/[(5.6228in

+0.0

Instability An

ability of us

estigates whe

ws.

nction of inp

raction φin

hat a homog

This can aga

with experim

to characteri

nolds numb

uctures (eddie

d flow.

0.6 0.7 0.8 0raction,

in

0828)(1-in

)+in

]

nalysis

sing a

ether a

put oil

genous

ain be

mental

se the

er) is

es and

0.9 1

245


246

The slip ratio results are extremely similar to the correlations for the in-situ phase fraction

results in Chapters 4 and 5. The correlation for the current results is given in Equation 6.5.

5.6228 0.0828 (6.5)

A correlation for the in-situ phase fraction based on Equations 6.5 and 4.14 is given in Equation

6.6 below:

⟨φ⟩y,t 5.6228 0.0828 1 (6.6)

This is plotted along with the correlations for the results in Chapters 4 and 5 (Equations 4.16

and 5.8, respectively) in Figure 6-13; more below.

Figure 6-12 compares the experimental results slip ratio from all three experimental campaigns.

Figure 6-12(a) indicates that the results are broadly similar. This leads to the conclusion that the

flows, at least with regards to the slip ratio, are dominated by the same flow and mixing

processes, e.g., turbulent transport.


247

(a) (b)

Figure 6-12: (a) Slip ratio S as a function of input oil fraction φin for all three PLIF

experimental campaigns, and; (b) Slip ratio S as a function of input oil fraction φin for different

superficial mixture velocities Um, where “a” denotes the “normal” inlet configuration and “b”

the “inverted” inlet configuration

Figure 6-12(b) explores the relative trends between the two circular cross-section campaigns for

constant superficial mixture velocities Um , from which two observations are made: (1) that as

the superficial mixture velocity increases, the slip ratio tends towards unity, and; (2) the results

are largely independent of the inlet orientation. Figure 6-12(b) also shows that there is an

exception to the earlier conclusion concerning the similarity of the slip ratio across the flow

campaigns; the “normal” inlet flows at medium inlet fractions (φin ~ 0.3-0.7) and velocities

(Um = 0.14 - 0.28 m.s-1) typically experience lower slip ratios than their “inverted” counterparts.

Clearly a secondary mechanism must be responsible for this, not accounted for by Um (or Re).

Figure 6-13 indicates that there is a characteristic in-situ phase fraction curve for the current

system, based upon the test fluids and the independent variables (superficial mixture velocity

and input oil phase fraction). Hence, it can be deduced that after the entrance length

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8


Slip

Rat

io, S

Square Cell PLIF ResultsCicular Cell PLIF ResultsCircular Cell PLIF Results - "Inverted" Inlet

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8


Slip

Rat

io, S

Um = 0.07 m/s

Um = 0.14 m/s

Um = 0.22 m/s

Um = 0.28 m/s

a b

(L/D

orien

Figur

corre

sectio

confi

6.6

The r

PTIV

two s

Figur

fixed

same

veloc

0

0.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

In-s

itu O

il Ph

ase

Frac

tion,

y,

t

= 244) to th

ntation and th

re 6-13: (a)

lations for t

on visualisat

guration (blu

Interfa

results of the

V images are

simple estima

re 6-14 prese

d superficial

results of th

city Um.

0 0.1 0.20

1

2

3

4

5

6

7

8

9

1

Inp

Square CCircular Circular

he visualisat

he test section

(a)

) In-situ pha

the square c

tion section

ue)

ace Level

e interface le

presented in

ation approa

ents the resul

mixture vel

he interface l

0.3 0.4 0.5put Oil Phase Fr

Cell PLIF ResultsCell PLIF ResultsCell PLIF Results

tion cells, th

n geometry.

ase fraction

cross-section

with the “n

evel analysis

n this section

ches in predi

lts of the inte

ocities from

level H, but

0.6 0.7 0.8raction,

in

- Alternate Inlet

he in-situ ph

experimenta

n visualisatio

normal” inlet

that has bee

n. The sectio

icting the int

erface level H

m Um 0.11

as a function

0.9 1

0.

0.

0.

0.

0.

0.

0.

0.

0.

In-s

itu O

il Ph

ase

Frac

tion,

y,

t

Chapter 6: P

hase fraction

al results, an

on section (

t configurati

en performed

on is also co

terface level

H as a functi

1 to 0.28 m.

n of the corr

0 0.1 0.20

1

2

3

4

5

6

7

8

9

1

Inp

y, t

=

y, t

=

y, t

=

PLIF Results:

n is indepen

(b)

nd; (b) In-si

black) and

ion (red) an

d on the “inv

ncerned with

in stratified

ion of input

s-1. Figure

responding s

0.3 0.4 0.5put Oil Phase F

= in

/[(5.8251in

-0.

= in

/[(5.7177in

+0

= in

/[(5.6228in

+0

Instability An

ndent of the

itu phase fra

the circular

d “inverted”

verted” inlet

h the suitabil

flows.

oil fraction φ

6-15 presen

superficial m

0.6 0.7 0.8raction,

in

.1448)(1-in

)+in

]

0.3626)(1-in

)+in

]

0.0828)(1-in

)+in

]

nalysis

e inlet

action

cross

” inlet

PLIF-

lity of

φin for

nts the

mixture

0.9 1

]

]

248


249

(a) (b)

(c) (d)

Figure 6-14: The mean (μ) and upper (μ+2σ) and lower (μ–2σ) limits for the interface level H

as a function of input oil fraction φin for superficial mixture velocities Um of: (a) 0.11 m.s-1, (b)

0.17 m.s-1, (c) 0.22 m.s-1, and (d) 0.28 m.s-1

Two trends are observed from Figures 6-14 and 6-15. Firstly, that for a given superficial

mixture velocity, as the oil input phase fraction increases, the interface level reduces. The

second observation is that as the superficial mixture velocity increases, the fluctuation of the

interface level heights also increases; this is seen most prominently in Figure 6-15(b) and is

pursued in Section 6.6.1.

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.2 0.4 0.6 0.8 10

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

a b

c

x

y

z


250

(a) (b)

(c)

Figure 6-15: The mean (μ) and upper (μ+2σ) and lower (μ–2σ) limits for the interface level H



probability histograms in Figures 4.12, 4.13 and 4.14 respectively.

The widening of the upper (μ - 2σ) and lower (μ + 2σ) interface level limits (for the 95%

confidence interval) with an increasing superficial mixture velocity can be attributed to

turbulence. As the superficial mixture velocity increases, the Reynolds number increases,

which, when sufficiently high will lead to turbulence which can present as waves at the

common interface which can grow in amplitude with superficial mixture velocity. This trend

0 0.1 0.2 0.30

4

8

12

16

20

24

28


(m.s-1)

Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.1 0.2 0.30

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

0 0.1 0.2 0.30

4

8

12

16

20

24

28


Inte

rfac

e L

evel

, H

(m

m)

-2+2

a b c

x

k l

z y

m

can in

rise a

thus w

6.6.1

Figur

proba

plots

Figur

super

histog

labell

00

0.2

0.4

0.6

0.8

1

Prob

abili

ty

ntensify whe

a KH instabi

widening the

Interfac1

res 6-16 an

ability histog

shown in Fi

(a1)

(a2)

re 6-16: Flo

rficial mixtu

grams for th

led in Figure

4 8 12Interface Le

en the super

ility at the c

e 95% confid

ce Level Pr

nd 6-17 pre

grams for the

gures 6-14(a

)

)

ow images w

ure velocitie

he same con

e 6-14(a)

16 20 24evel, H (mm)

rficial mixtur

common inte

dence interva

robability

esent instan

e points that

a) and 6-14(c

with input oil

es Um = 0.

nditions resp

28 0 40

0.2

0.4

0.6

0.8

1

Prob

abili

ty

re velocity p

erface, which

al for the inte

Distributi

ntaneous im

t have been u

c), respective

(b1)

(b2)

l fraction φin

.11 m.s-1; (

pectively. D

8 12 16Interface Level, H (m

Chapter 6: P

passes anothe

h will manif

erface level h

ions

ages and c

used to cons

ely.

n of (a1) 0.25

a2), (b2) an

Data correspo

20 24 28mm)

Prob

abili

ty

PLIF Results:

er threshold,

fest as waves

height further

correspondin

struct the me

5, (b1) 0.50,

nd (c2) show

onds to Poin

0 4 80

0.2

0.4

0.6

0.8

1

Interfa

Instability An

, Ri 0.25, g

s at this inte

r.

g interface

ean interface

(c1)

(c2)

(c1) 0.75, a

w the proba

nts a, b and

12 16 20ace Level, H (mm)

nalysis

giving

erface,

level

e level

ll at a

ability

d c, as

24 28

251


252

From inspection of the instantaneous images (a1 → c1 and x1 → z1) and the histograms (a2 → c2

and x2 → z2), one can readily see that the mean interface level μH decreases gradually with an

increasing oil input oil fraction φin for a given superficial mixture velocity Um. For the

histograms presented in Figure 6-16, the superficial mixture velocity is Um 0.11 m.s-1. From

Table 6-1 it is seen that for a superficial mixture velocity of this order, both phases have a

Reynolds number that corresponds to laminar flow. As a result, the influence of the transport

(mixing) associated with turbulent fluctuations at the common interface will be absent, and only

very low amplitude waves are to be expected and in turn, for the interface level to cover only a

very narrow range of heights. This is what is seen in the results in Figure 6-16.

(x1) (y1) (z1)

(x2) (y2) (z2)

Figure 6-17: Flow images with input oil fraction φin of (x1) 0.25, (y1) 0.50, (z1) 0.75, all at a

superficial mixture velocities Um = 0.17 m.s-1; (x2), (y2) and (z2) show the probability

histograms for the same conditions respectively. Data corresponds to Points x, y and z, as

labelled in Figure 6-14(c)

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty



253

For the histograms presented in Figure 6-17, the superficial mixture velocity is Um 0.22 m.s-1,

thus, the flow cases in Figure 6-17 have higher Reynolds numbers than those in Figure 6-16. As

a result, the influence of turbulent disturbances at the interface will be greater and, in turn,

waves of greater amplitude are expected in Figure 6-17; albeit still relatively low amplitude

waves owing to the Reynolds numbers still being low. On comparison with Figure 6-16, it is

observed that the interface level probability distributions presented in Figure 6-17 are associated

with a larger spread (higher standard deviation), as expected.

Proceeding further, Figures 6-18 to 6-20 present instantaneous images and interface level

probability histograms for the points that have been used to construct the mean interface level

plots shown in Figures 6-15(a) to 6-15(c), respectively.

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 6-18: Flow images with superficial mixture velocities Um of: (a1) 0.11 m.s-1, (b1)

0.17 m.s-1, (c1) 0.28 m.s-1, all at an input oil fraction φin 0.25; (a2), (b2) and (c2) show the

probability histograms for the same conditions respectively. Data corresponds to Points a, b and

c, as labelled in Figure 6-15(a)

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty



254

From the instantaneous images (a1 → c1 and x1 → z1) and the histograms (a2 → c2 and x2 → z2),

two key observations are made. Firstly, that as the superficial mixture velocity increases for a

constant oil input phase fraction, the mean interface level remains roughly constant; this is more

obviously noticeable in Figure 6-15. The second key observation is aligned with the findings of

Figures 6-16 and 6-17; that as the superficial mixture velocity increases the probability

distribution for the interface level heights widens. Further to this, these trends are seen to be

most prominent for intermediate input oil phase fractions (φin 0.5).

(k1) (l1) (m1)

(k2) (l2) (m2)

Figure 6-19: Flow images with superficial mixture velocities Um of: (k1) 0.11 m.s-1, (l1)

0.17 m.s-1, (m1) 0.28 m.s-1, all at an input oil fraction φin 0.50; (k2), (l2) and (m2) show the


m, as labelled in Figure 6-15(b)

The interface level probability distribution results for low superficial mixture velocities and low

input oil phase fractions are found to be highly comparable for both inlet configurations

investigated; compare Figures 5-18 and 6-18. However, a disparity between the results for the

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1Pr

obab

ility



255

two different inlet orientations develops as the superficial mixture velocity increases for

intermediate input oil phase fraction (φin 0.5). This can be attributed to the fact that under

these conditions, oil droplets below in the interface are more readily found when using the

“inverted” inlet orientation which gives rise to further fluctuations in the interface level.

(x1) (y1) (z1)

(x2) (y2) (z2)

Figure 6-20: Flow images with superficial mixture velocities Um of: (x1) 0.11 m.s-1, (x1) 0.17

m.s-1, (x1) 0.29 m.s-1, all at an input oil fraction φin 0.75; (x2), (y2) and (z2) show the

probability histograms for the same conditions respectively. Data corresponds to Points x, y

and z, as labelled in Figure 6-15(c)

On further comparison of Figures 5-18 to 5-20 with Figures 6-18 to 6-20 it is seen that the mean

interface level height is largely the same, regardless of the inlet configuration which just widens

the probability distribution when it is set to impose a RT instability (i.e., is “inverted).

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


0

0.2

0.4

0.6

0.8

1

Prob

abili

ty


6.6.2

Figur

(Equa

“inve

Figur

mixtu

The l

the U

inlet

to ris

Howe

given

prese

the “

Lamina2

re 6-21 prese

ation 5.6), d

erted” inlet co

re 6-21: Inte

ure velocities

laminar drag

Um 0.17 m

orientation.

se with the

ever, the inte

n oil input ph

ent below the

“inverted” in

r Drag Mo

ents predicte

denoted by

onfiguration

erface Level

s Um

g model give

m.s-1 flow cas

It should be

increased su

erface level t

hase fraction

e interface fo

nlet orientati

00

4

8

12

16

20

24

28

Inte

rfac

e L

evel

, H

(m

m)

odel

ed values of

Hmod,1, alon

n PLIF-PTIV

l H as a fun

s excellent a

se; more so t

e noted that f

uperficial m

then lowers p

n. This obser

or the superf

ion), which

0.2O

Um

=0.11 m

Um

=0.17 m

Um

=0.22 m

Um

=0.28 m

Hmod,1

interface lev

ng with inte

runs.

ction of inpu

agreement w

than for the

from Um 0

mixture veloc

progressively

rvation can b

ficial mixture

results in t

0.4Oil Input Frac

m/s

m/s

m/s

m/s

Chapter 6: P

vel obtained

erface level

ut oil fractio

with the exper

same condit

0.11 to 0.17 m

city for a gi

y from Um

be attributed

e velocities U

the raising

0.6 0tion,

in

PLIF Results:

from the la

experiment

on φin for di

rimental resu

tions when u

m.s-1 the inte

iven input o

0.17 to 0.28

d to the oil dr

Um 0.17 m

of the inter

.8 1

Instability An

minar drag m

tal results fo

ifferent supe

ults, especial

using the “no

erface level i

oil phase fra

8 m.s-1, again

roplet layer t

m.s-1 (arising

rface level i

nalysis

model

or the

rficial

lly for

ormal”

s seen

action.

n for a

that is

g from

in the

256

exper

appea

of thi

curre

of the

with

agree

6.6.3

The e

6-22

(Figu

Figur

mixtu

(a) str

00

4

8

12

16

20

24

28

Inte

rfac

e L

evel

, H

(m

m)

riments with

ars to captur

is oil droplet

nt results co

e experiment

the predictio

ement with th

Hall and3

experimental

along with in

ure 6-22(a)) a

re 6-22: Inte

ure velocities

ratified gas-l

0.2

Hall & Hewit

Um

=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

h Um 0.11

e the interfac

t layer that g

mpared with

tal results for

ons of Hmod,1

he experimen

d Hewitt (1

l results gene

nterface leve

and, liquid-li

(a)

erface Level

s Um featurin

liquid flow, a


tt (1993)gas-liquid

s

s

s

s

1 and 0.17 m

ce level well

gives the ind

h those in Ch

r stratified fl

1, it can be c

ntal results, i

1993) Pred

erated with th

el predictive

iquid flow (in

l H as a fun

ng interface

and; (b) strat

0.6 0.8on,

in

m.s-1. Henc

l at Um 0

dication that

hapter 5 (see

low (Um 0

concluded tha

irrespective o

dictive Tec

he “inverted”

models by H

n Figure 6-22

ction of inpu

level models

tified liquid-

1

00

4

8

12

16

20

24

28

Inte

rfac

e L

evel

, H

(m

m)

Chapter 6: P

ce, the fact

.17 m.s-1 is c

the laminar

Figure 5-21

0.11 m.s-1) fo

at that lamin

of the inlet o

chnique

” inlet arrang

Hall and Hew

2(b)).

ut oil fractio

s presented b

liquid flow

0.2

Hall & Hewit

Um

=0.11 m/s

Um

=0.17 m/s

Um

=0.22 m/s

Um

=0.28 m/s

PLIF Results:

that the lam

coincidental.

drag model

). Neverthel

or each of the

nar drag mod

rientation.

gement are p

witt (1993) fo

(b)

on φin for di

by Hall and H


tt (1993)liquid-liquid

s

s

s

s

Instability An

minar drag m

It is the pre

better predic

less, on inspe

e inlet orient

del is in very

presented in F

or gas-liquid

ifferent supe

Hewitt (1993

.6 0.8on,

in

nalysis

model

esence

cts the

ection

tations

y good

Figure

flows

rficial

3) for:

1

257

Both

input

the in

phase

mode

super

the w

veloc

case o

6.7

This

from

μd,gs f

of Um

Resul

const

create

from

dropl

size i

of the

predictive t

t phase fracti

nterface leve

e fraction inc

els assume a

rficial mixtur

widening of th

city that was

on which the

Drople

section pres

the “inverte

for both pha

m 0.28 m.s

lts at other s

tant input oil

e these plots

data in the

let size is m

is in the rang

e pipe).

techniques c

ion, althoug

el, with the e

creases. On

a flat interfac

re velocity in

he interface

reported in

e model is ba

et Size Dis

sents the dro

d” runs. The

ses as a func

s-1. The resu

uperficial m

l phase fract

s. On comp

normal inle

uch more er

ge from abou

capture the l

gh, as seen in

xtent of the

ne possible e

ce between t

ncreases the

level probab

Section 6.6

ased.

stribution

oplet size an

e results con

ction of input

ults are shown

mixture veloci

tions are not

paring Figure

et configurat

rratic for the

ut 1.5 mm to

owering of

n Figure 6-22

over-predict

explanation f

the two flow

interface m

bility histogra

.1). Thus, t

n

nalysis that h

tained herein

t oil phase fr

n in Figure 6

ities or, as a

t presented s

e 6-23 with

tion, it can b

e “inverted”

a maximum

Chapter 6: P

the interface

2(b), the liqu

tion being m

for this is tha

wing fluids,

moves away f

ams with an

he flow is n

has been per

n are limited

raction φin at

6-23.

function of

ince there w

the correspo

be stated tha

inlet conditi

of about 4.5

PLIF Results:

e level with

uid-liquid m

more significa

at the Hall a

whereas we

from being f

increasing s

no longer rep

rformed on

to the mean

t a superficia

superficial m

were insuffici

onding Figu

at the behav

ion. The typ

mm (this is

Instability An

an increasin

odel over-pr

ant as the inp

and Hewitt (

know that

flat (this is se

superficial m

presentative

the PLIF- im

n droplet diam

al mixture ve

mixture veloc

ient data poi

ure 5-23 gene

viour of the

pical mean d

25% of the h

nalysis

ng oil

redicts

put oil

(1993)

as the

een in

mixture

of the

mages

meters

elocity

city at

ints to

erated

mean

droplet

height

258

Figur

const

circle

6.8

This

detail

orien

(i.e.,

range

Refer

the v

three

profil

re 6-23: Me

tant superfic

es) and oil dr

Velocit

section pres

led in Secti

ntation. Figu

the velocity

e Um 0.11

rring to Figu

elocity profi

selected inp

le is the case

ean droplet

ial mixture

roplets (red s

ty Profiles

sents velocit

ion 3.11.7 o

ure 6-24 sho

profile has b

to 0.84 m.s-1

ure 6-24, and

iles for a fixe

put oil fract

e with the low

0 00

1

2

3

4

5

6

7

8

Mea

n D

ropl

et D

iam

eter

, d (

mm

)

diameter μd

velocity of

squares)

s

ty profile re

on the PLIF

ows velocity

been divided

1 at oil input

d in line with

ed oil input

tions φin, the

west φin (= 0

0.1 0.2 0.3Input

as a functi

Um 0.28 m

esults that h

F images ac

profiles for

d by the supe

fractions φin

h what was o

fraction φin

e case with

.25).

3 0.4 0.5t Oil Phase F

Chapter 6: P

ion of input

m.s-1, for gl

have been g

cquired whe

normalised

erficial mixtu

n of (a) 0.25;

observed in

collapse to a

the greatest

0.6 0.7 0Fraction,

in

PLIF Results:

oil phase f

ycerol soluti

generated usi

en using the

superficial m

ure velocity

(b) 0.50, and

Section 5.9,

a ‘generic’ p

t deviations

.8 0.9 1

d G-S

d Oil

Instability An

fraction φin

ion droplets

ing the tech

e “inverted”

mixture velo

of that run)

d; (c) 0.75.

, once norma

profile. Out

from this ge

nalysis

and a

(blue

hnique

” inlet

ocities

in the

alised,

of the

eneric

259


260

(a) (b)

(c)

Figure 6-24: Normalised velocity profiles ⟨ ⟩⁄ for different superficial mixture velocities


In more detail, the interface region is seen to retain a dependence on the superficial mixture

velocity, with the “step change” observed in Figure 5.9 also present in the results for the

inverted inlet configuration. In the “normal” inlet orientation flows in Chapter 5 this step

change was attributed to a velocity difference between the two liquids either side of the

interface – there is slippage (i.e., a non-unity slip ratio) across the interface – with the trends

aligning with those found for the slip ratio. The shear layer is seen to increase with input oil

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28

Normalised Streamwise Velocity, Ux / U

m

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Um

=0.67 m/s

Um

=0.50 m/s

Um

=0.33 m/s

Um

=0.22 m/s

Um

=0.11 m/s

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28


Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Um

=0.67 m/s

Um

=0.50 m/s

Um

=0.33 m/s

Um

=0.22 m/s

Um

=0.11 m/s

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28

Normalised Streamwise Velocity, Ux / U

m

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Um

=0.67 m/s

Um

=0.50 m/s

Um

=0.33 m/s

Um

=0.22 m/s

Um

=0.11 m/s

phase

limite

The “

veloc

(Reyn

interf

added

additi

profil

illustr

interf

variab

6.8.1

This

flow

intera

concu

Figur

althou

in com

Table

e fraction; th

ed ability to

“normal” inl

city profiles)

nolds numbe

face (typical

d effect of

ional instabi

les, namely,

rated in Figu

face for som

ble combinat

Flow Re1

section pres

from the sam

actions betw

urrence with

re 6-25 pres

ugh the velo

mplete agree

e 6-1 it is se

he absence of

capture the v

let orientatio

that were w

er and trans

lly expected

a Kelvin-He

lity mechani

the Rayleig

ures 6-7 and

me flow case

tions are hig

egime Ana

sents pairs o

me run. The

ween the two

those establ

sents a veloc

ocity profile

ement with t

een that both

f the shear la

velocity prof

on flows in

well accounte

ition to turb

at the extre

elmholtz ins

ism at play th

gh-Taylor ins

d 6-8, this ca

es. Howeve

ghly compara

alysis

of velocity p

intention is

o phases, i.e

lished in Sect

city profile

only extends

those seen in

h phases hav

ayer from the

file above the

Chapter 5 e

ed for by the

bulence) and

eme inlet ph

stability. Ho

hat can influ

stability. A

an results in

er, the veloc

able for the tw

profiles along

explain the e

e., the flow

tion 5.9.1.

and an inst

s up to the in

n Figure 5-28

ve Reynolds

Chapter 6: P

e φin 0.75

e interface le

exhibited flo

change in th

d, if there w

hase fraction

owever, in t

uence the flow

s discussed

the entrainm

city profiles

wo inlet orie

g with insta

emerging vel

w regime. T

tantaneous im

nterface, it c

8 for the “no

s numbers in

PLIF Results:

cases can b

evel for these

ow transition

he superficia

was sufficient

ns close to z

the current

w regime and

previously i

ment of oil d

for like-for

entations.

antaneous PL

locity profile

The findings

mage for str

can be seen t

ormal” inlet o

n the laminar

Instability An

e attributed

e runs.

ns (and asso

al mixture ve

t shear acro

zero or unity

study there

d thus the ve

in the chapte

droplets belo

r-like indepe

LIF images o

es by means

s are in com

ratified flow

that the resul

orientation.

r flow regio

nalysis

to our

ciated

elocity

ss the

y), the

is an

elocity

er and

ow the

endent

of the

of the

mplete

w, and

lts are

From

on and

261


262

thus, the parabolic velocity profile [which is a characteristic of laminar flow, see Figure 5-27(a)]

of the glycerol solution flow is expected.

A “step” is seen in the velocity profile at a height of approximately 20 mm, which is a shear

layer arising from the bulk velocity difference of the two phases. Based on the run conditions,

namely the input oil phase fraction (φin = 0.50) and the in-situ oil phase fraction (⟨φ⟩y,t 0.21)

and Equation 4.14, it can be calculated that the flow has a non-unity slip ratio (in this case,

S 3.8), and thus (from Equation 4.11) it is seen that the oil velocity is larger than the glycerol

solution velocity. Owing to this, a shear layer and thus a shift to the right in the velocity profile

above the interface is expected.

(a) (b)

Figure 6-25: Velocity profiles (a) and instantaneous images (b) for a superficial mixture

velocity of Um = 0.11 m.s-1 and an input oil phase fraction φin = 0.50

For the flow regimes that can collectively be termed dual continuous flow, the “step” (shear

layer) at the interface is absent and the profile over the mixed region becomes flatter, i.e., the

flow regime develops from a parabolic velocity profile that is characteristic of laminar flows to

a flatter one indicative of turbulent flows. This would be expected since for the flow to develop

a mixed region, flow mixing arising from some form of instability or fluctuations will need to

occur. As previously discussed (and although a Rayleigh-Taylor instability has been imposed

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28


Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)


263

on the flow in the current study) the main driver for mixing in the experimental conditions

covered in the work done with both inlet configurations is related to the broadband turbulent

fluctuations (and enhanced transport) which can cause mixing of the flow and thus the

formation of droplets in one phase in a continuum of the other. These fluctuations are produced

from nonlinear inertial forces in the flow and can be described by the Reynolds number (owing

to increased superficial mixture velocities), which passes a transitional threshold value. Here a

flow with a turbulent velocity profile (see, Figure 5-27(b)) is expected.

Figure 6-26 presents a velocity profile and an instantaneous image for the glycerol solution

droplet layer flow regime (i.e., dual continuous flow). From Table 6-1 it can be seen that the

Reynolds number of the oil phase for the experimental run presented in Figure 6-28 is in the

turbulent region.

(a) (b)

Figure 6-26: Velocity profiles (a) and instantaneous images (b) for a superficial mixture

velocity of Um = 0.84 m.s-1 and an input oil phase fraction φin = 0.50

At even higher superficial mixture velocities (relative to the flow case presented in Figure 6-26)

the turbulence intensity (magnitude of the fluctuations in the flow) increases leading to further

mixing of the phases. In addition, high levels of shear at the interface, at high or low inlet phase

fractions, can lead to the onset of the Kelvin-Helmholtz instability mechanism and in turn,

0 0.5 1 1.5 2 2.5 3 3.5 40

4

8

12

16

20

24

28


Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

furthe

transi

dispe

Figur

Um =

6.8.2

It is

taken

diagn

partic

Vi

liti

Sti

Hi

htH

()

Vi

liti

Sti

Hi

htH

()

er mixing.

ition to disp

ersed region;

re 6-27: V

= 0.84 m.s-1 a

Contact2

important to

n at the cent

nostic techni

cularly for th

0 0.50

4

8

12

16

20

24

28

Normalis

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

0 0.50

4

8

12

16

20

24

28

Normalis

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

Ultimately,

persed flow

see Figure 6

(a1)

(a2)

Velocity pro

and φin = 0.10

t Angle An

o note that th

treline of the

iques that h

he in-situ ph

1 1.5 2sed Streamwise V

1 1.5 2sed Streamwise V

these differe

which are

6-27.

)

)

files (a1 →

0, and; (2) U

nalysis

he presented

e visualisatio

has been app

hase fraction

2.5 3 3.5Velocity, Ux

/ Um

2.5 3 3.5Velocity, Ux

/ Um

ent mechani

characterised

a2) and in

Um = 0. 83 m

d in-situ oil

on section, o

plied. A k

estimations

4

4

Chapter 6: P

sms for mix

d by turbule

nstantaneous

.s-1 and φin =

phase fracti

owing to the

key assumpti

from the re

PLIF Results:

xing the flow

ent velocity

(b1)

(b2)

images (b

= 0.90

on and velo

e planar nat

ion that has

esulting data

Instability An

w will lead

profiles ove

b1 → b2) for

city profiles

ture of the o

s been empl

, is that the

nalysis

to the

er the

r: (1)

s were

optical

loyed,

flows

264


265

have a flat interface; this ignores the effects of surface tension and the contact angle at the pipe

wall (see Figure 6-28) which is a reasonable assumption when the density difference between

the two fluids is large, Ng (2002). Curvature at the interface can become significant for systems

with a density ratio near unity, small diameter pipelines and large interfacial tension. Hence the

appropriateness of this assumption to the current PLIF studies needs to be investigated.

The interface between two fluids can be characterised by some key parameters, one of which is

the Bond number (Bo) which is a ratio of the gravitational forces to the inertial forces; as the

Bond number increases the common interface tends towards a flat surface. The expression for

the Bond number is given in Equation 6.7 below,

Bo∆ . . . cos

, (6.7)

where ∆ is the density difference between the phases; is the acceleration due to gravity; is

the radius of the pipe; is the inclination of the pipeline, for the current system 0° (see

Figure 6-28(b)), and; is the interfacial tension.

Prior to evaluating the Bond number for the current system it should be noted that the interface

will be a flat surface if Equation 6.8 is satisfied:

1 ⟨φ⟩y,t,cos sin

, (6.8)

where is the contact angle, see Figure 6-28(a).

Figur

side v

The c

filling

dropl

three

dropl

meas

angle

re 6-28: The

views, Ng (2

contact angle

g a box cons

let of the gly

hours was

let, as shown

ured using i

e was found t

(a)

e geometry

2002)

e for the two

structed of th

ycerol-solutio

allowed for

n in Figure 6

imageJ. Thi

to be 51

Figure

θ

and coordina

o test fluids h

he same mate

on into the oi

this. Then

6-29, and the

is was then

.3° with a sta

6-29: Conta

ates of the f

has been me

erial as the te

il. Then allo

n a camera w

e contact ang

repeated 10

andard devia

act angle mea

Chapter 6: P

flow systems

easured using

est section wi

owing enough

was used to

gles at either

times. Usin

ation of σ 3

asurement te

PLIF Results:

(b)

s, showing:

g the followi

ith Exxsol D

h time for th

take an im

r side of the

ng this techn

3.3°.

chnique

θ

Instability An

(a) axial, an

ing technique

D80 and inser

he droplet to

age of the s

droplet were

nique, the co

nalysis

nd; (b)

e. By

rting a

settle;

settled

e then

ontact

266


267

Now, applying this value to Equation 6.6, it is found that 0.28. This implies that when the

glycerol solution hold-up is 0.28 (i.e., the in-situ oil phase fraction ⟨φ⟩y,t, 0.72) the

interface will be a flat surface. However, for holdup values less than this, 0.28 (i.e., in-situ

oil phase fraction ⟨φ⟩y,t, 0.72) the interface is expected to be concave and conversely, for

holdup values less than this, 0.28 (i.e., in-situ oil phase fraction ⟨φ⟩y,t, 0.72) the interface

is expected to be convex. From reviewing the in-situ phase fraction results (see Figures 5-7 and

6-10) it is seen that a glycerol solution hold-up value of 0.28 (i.e., the in-situ oil phase

fraction ⟨φ⟩y,t, 0.72) was not encounter in either of the PLIF campaigns involving the circular

cross section visualisation cell (all recorded hold-up values were higher). However, based upon

the prediction from φmod,1 for stratified flow, a glycerol solution hold-up value of 0.28 is

obtained for an input oil phase fraction of φin 0.95. Now, considering that all measured

glycerol solution hold-up value are lower than the value yielded from Equation 6.6, it is

expected that the liquid-liquid interface for stratified flow will be convex. Therefore, it is

necessary to calculate the Bond number to assistance in the evaluation of the interface

curvature; from Equation it is found to be Bo 250.

Ng (2002) presented predictions for the shape of the interface which can be compared with the

current liquid-liquid system using the calculated Bond number (Bo 250) and the contact angle

( 51.3°). Figure 6-30 presents the predictions from Ng (2002) for the shape of the interface

based upon a Bond number of Bo 250 and different contact angles (note that the results

pretaining to a contact angle of 0.9 radians (51.6°) are shown in Figure 6-33(b)).

Figur

(b)

by Ng

From

imme

system

the fl

phase

nume

One

centre

that w

re 6-30: Inte

0.3 ; (c)

g (2002)

m Figure 6-3

ediate vicinit

m, the interf

luid boundar

e fraction re

erical integra

limitation o

eline of the

we have use

erface shapes

0.5 , an

0 it is seen

ty of the pip

face shape is

ry with the p

esults which

ation techniqu

of the curren

pipeline, aga

ed. Althoug

(a)

(c)

s for a Bond

nd; (d) 0

that the inte

pe wall and

s flat irrespe

pipe wall. T

h were calcu

ue assumed a

nt work is

ain owing to

gh modelled

d number Bo

0.7 , all for

erface shape

that for the

ective of the

This is an im

ulated from

a flat surface

that the vel

o the planar n

for differen

Chapter 6: P

(b)

(d)

250 and

0.1, 0.2,

e for stratifie

Bond numb

contact ang

mportant find

m the phase

e at the interf

locity profil

nature of the

nt system pa

PLIF Results:

contact angl

, … , 0.9 com

ed flow is fl

ber (Bo 25

gle, apart from

ding, as it va

distribution

rface.

es are meas

e optical diag

arameters tha

Instability An

les: (a)

mputational r

flat apart fro

50) of the c

m the region

alidates the i

profiles us

sured only a

gnostic techn

an for the c

nalysis

0.1 ;

results

m the

urrent

n near

in-situ

sing a

at the

niques

urrent

268


269

system, the three-dimensional results generated by Ng (2002) can give an insight into the

overall shape of the velocity profile of the flow.

Figure 6-31 presents interface level values as a function normalised interface level velocity

⟨ ⟩⁄ . The trend observed is the same as that seen in Chapter 5 (see Figure 5-33).

Specifically, that once normalised, the velocity at the interface increases with an increase in the

interface level.

Figure 6-31: Interface level as a function normalised interface level velocity ( ⟨ ⟩⁄ ).

Ng (2002) presented dimensionless flowrate values as a function of hold-up (i.e., the

dimensionless interface level). The modelled results Ng (2002) obtained are based on a contact

angle of 3⁄ (≈ 51.6°) are shown in Figure 6-32. From Figure 6-32 it is seen that the

dimensionless flowrate increases with interface level. Furthermore, when the Bond number is

sufficiently high (Bo 25), the dimensionless flowrate (as a function of hold-up) results tend

towards the same profile; for the current system, the value is Bo 250. Now, although this is

higher than the Bond number Ng (2002) used to generate the velocity profile results in Figure 6-

33, one can infer that because the Bond number Ng (2002) used to generate the results was

sufficiently high (Bo 50), the results are applicable to the current system. From Figure 6-33 it

0 0.5 1 1.5 2 2.50

4

8

12

16

20

24

28

Normalised Streamwise Velocity, UH / Um

Vis

ualis

atio

n Se

ctio

n H

eigh

t, H

T (m

m)

is see

increa

exper

on co

interf

Figur

Bo

Figur

0

en that dime

ases with int

rimental find

omparison w

facial velocit

re 6-32: Va

0.1, 1, 10, 2

re 6-33: Va

0.25, 0.5 and

ensionless in

terface level)

dings. As the

with results

ty covers a b

ariation of

25, 50 and 10

ariation of t

d 0.75 (Bo

nterfacial vel

). Thus the s

e Bond numb

presented b

road range, e

the dimensi

00 with a con

he dimensio

50 and

locity (at the

simulated res

ber of the cu

by Ng (2002

extending ac

ionless flow

ntact angle

onless interf

3⁄ ), taken

Chapter 6: P

e centreline)

sults by Ng (

urrent system

2) – that at

cross most of

w rate with

3⁄ , tak

facial velocit

from Ng (20

PLIF Results:

) increases w

(2002) concu

m is large it c

the interfac

f the width of

hold-up an

ken from Ng

ty profile fo

002)

Instability An

with hold-up

ur with the c

an be conclu

ce, the max

f the pipeline

nd Bond nu

(2002)

or hold-up v

nalysis

p (i.e.,

urrent

uded –

ximum

e.

umber,

values

270

Ng (2

show

profil

less d

Figur

angle

m

Firstl

the cu

have

angle

Figur

shear

One m

in the

2002) presen

wn in Figure 6

le with Bond

dense phase)

re 6-34: Ve

e of 3⁄

⁄ wher

ly, for the pro

urrent system

a flatter inte

e is very sim

res 6-34(a) a

r layer at the

major differe

e current sys

nted directly

6-34 below;

d number, co

a feel for the

(a)

locity profil

3 and a Bon

re A is the le

ofiles shown

m is significa

erface that th

milar is less im

and 6-34(b) o

interface inc

ence between

stem the les

images of t

considering

ontact angle

e three-dime

e across the

nd number o

ess dense pha

n in Figure 6-

antly higher

he convex on

mportant tha

on the basis

creases as the

n the current

s dense pha

three-dimens

these profile

and viscosity

ensional prof

e pipe cross

of Bo 10 f

ase, Ng (2002

-34 the Bond

( 250).

ne featured in

an the Bond

of their diffe

e m moves a

t system and

se (Exxsol D

Chapter 6: P

sional veloci

es coupled w

y ratio (wher

file type can

section for

for: (a) m

2)

d number is B

So, based o

n Figure 6-34

number, as

erent m valu

away from un

d the results g

D80) is also

PLIF Results:

ity profiles.

with the shap

re m ⁄

start to be m

(b)

a hold-up of

1.6, and; (

Bo 10 whe

on Figure 6-3

4(b). The fa

seen Figure

ues it is seen

nity.

generated by

the less vis

Instability An

Two of the

e behaviour

where A

made.

f 0.3, co

b) m 45 w

ereas the val

30 the system

act that the co

6-30. Comp

that extend

y Ng (2002) i

scose phase

nalysis

se are

of the

is the

ontact

where

lue for

m will

ontact

paring

of the

is that

hence

271

m

interf

flow

34(b)

acros

6.9

An

meas

been

the p

study

phase

descr

by th

the tu

The

comp

below

Chap

pipe.

dispe

curre

then t

1; the value

face (as seen

of the two l

) yet rotated

ss a great wid

Conclu

advanced o

urement of l

applied to a

present chapt

y presented i

e at the top

ribed in Chap

he Rayleigh-T

ube and influ

findings of

parable thoug

w the interfa

pter 5 were o

The regimes

ersion with a

nt chapter a

the two flow

e is m 0.0

n in Figure 6-

iquids used

180° with a

dth of the cha

usions

optical diag

iquid phase

acquire meas

ter results ar

n Chapter 5

of the tube

pter 5). This

Taylor instab

uence the obs

the current

gh not identi

ace has been

observed in t

s not observe

glycerol solu

re evaluated

w regime map

03. Therefor

-25). In esse

in the curren

flat interfac

annel.

gnostic tech

(with PLIF)

surements of

re provided f

, by investig

e rather than

s change intr

bility. The ef

served flow b

study, in t

ical to those

n observed,

the study wi

ed in this ca

ution film. H

d on the mor

ps are very si

re, the “step”

ence, the thre

nt experimen

ce with a ma

hnique capa

and flow vel

f horizontal,

from an exp

gating the in

n at the bott

roduces the p

ffects of this

behaviour.

terms of flo

of Chapter 5

and only six

ith the aqueo

se were (1) t

However, if t

re general ba

imilar.

Chapter 6: P

” in the velo

ee-dimension

ntal study wi

aximum velo

able of the

locity distrib

initially stra

perimental ca

fluence of in

tom (as was

possibility o

instability n

ow regimes

5. An increa

x of the eig

ous phase be

three-layer fl

the flow regi

asis of transi

PLIF Results:

ocity profile

nal velocity p

ill be compa

city at the in

e high-spee

bution (with P

atified liquid

ampaign that

njecting the

s the case in

f phase brea

near the inlet

and their c

ased propensi

ght flow regi

eing injected

flow, and; (2)

ime maps of

ition to dual

Instability An

will be abov

profile for la

arable to Figu

nterface exte

d spatiotem

PTV and PIV

d-liquid flow

t goes beyon

heavier (aqu

n the experi

akup near the

may persist

haracteristic

ity for oil dr

imes identifi

d at the top

) glycerol so

f Chapter 5 an

l continuous

nalysis

ve the

aminar

ure 6-

ending

mporal

V) has

ws. In

nd the

ueous)

ments

e inlet

along

s, are

roplets

fied in

of the

olution

nd the

flow,

272


273

From the flow regime map it is seen that for flows in which roughly equal volumetric flowrates

(i.e., 0.5) of the two-liquids are injected into the pipeline, the velocity for transition from

stratified flow to other flow regimes (i.e., dual continuous and in turn, dispersed flow) is higher

than for input oil phase fractions that approach the limits (i.e., 0 and 1). This is expected

because at 0.5 flow regime transition is governed by turbulence (i.e., related to Reynolds

number).

The same velocity profile behaviour has been found in the current study as were found in

Chapter 5. In addition, in the current Chapter the work has been extended to analyse the

horizontal interface shape that separates the two phases, which has been found to be relatively

flat. This validates the methodology for calculating the in-situ phase fraction, the central tenet

of which was that the assumption that the interface was flat across the pipe cross-section.

CH

Co

W

7.1

The f

(1)

(2)

HAPT

onclus

ork

Conclus

following ma

For what

Fluoresce

Velocime

experime

liquid-liq

combinat

the two fl

The initia

the image

used. In t

found po

TER 7

ions a

ions

ain conclusio

t is believed

ence (PLIF)

etry (PIV) h

nts have bee

quid flow fac

tion (aqueous

luids have be

al experimen

e distortion c

the later expe

ossible to co

nd Su

ons have been

d to be the

), Particle

has been use

en facilitated

cility (TOW

s glycerol so

een precisely

nts were cond

caused by th

eriments, wh

rrect the rec

uggesti

n drawn from

first time,

Tracking V

d in the stu

d by the refu

WER) and the

olution and E

y matched.

ducted using

he (transparen

here circular

ceived image

Chapter 7

ions fo

m the work d

a combinat

Velocimetry

udy of horizo

urbishment of

e developme

ExxolTM) in w

a square cro

nt) walls if a

cross section

es for this d

: Conclusion

or Futu

described in t

tion of Plan

(PTV) and

ontal liquid-

f an existing

ent and use

which the re

oss section du

a circular cro

n pipes were

distortion by

n and Future

ure

this thesis:

nar Laser In

d Particle I

-liquid flows

g Imperial Co

of a liquid/

fractive indi

uct which av

oss section d

e employed,

y photograph

Work

nduced

Image

s. The

ollege

/liquid

ces of

voided

duct is

it was

hing a

274

Chapter 7: Conclusion and Future Work

275

graticule placed at the centre of the channel and using a computer image processing

system to generate undistorted images.

(3) The PLIF images gave a clear indication of the distribution of the phases at the channel

centre line and the images (and particularly the movie sequences of images) could be

used qualitatively in obtaining information about the flow patterns occurring. New

insights were obtained about the nature of the flow patterns as a result of this process.

The PLIF images could also be used quantitatively in generating data on phase

distribution, in-situ phase fraction, interface level and drop size distribution. Extensive

information on all these quantities (and comparison of the measurements with previous

information and models) is presented in this thesis.

(4) In the circular tube experiments, two methods of injection of the phases were used. In

the first (see Chapter 5), the heavier (glycerol solution) phase was injected in its natural

location at the bottom of the channel. In the second case (see Chapter 6), the heavier

phase was injected at the top of the channel. In this case, breakup of the liquid at the

injector would be expected to occur as a result of Raleigh-Taylor instability. Even with

the considerable distance between the injection point and the measurement location

(6.20 m, such that ⁄ = 244) some differences are still observed between the flows

resulting from the two injection strategies.

(5) Extensive data on velocity profiles were obtained using PTV and PIV. Examination of

these profiles indicated major differences between the two phases. In the lower

(aqueous glycerol solution) phase, the profile usually showed the curved shape

characteristic of laminar flow. In the upper (ExxolTM D80) phase, the velocity profile

often showed the flattened form characteristic of turbulent flow.

(6)

7.2

The t

inves

(1)

Extensive

with a sim

were also

that the g

6). The

assumptio

Chapter 6

of wettin

investigat

assumptio

tests.

Sugges

technology d

stigations. Sp

In the ex

phase to

was Eosi

negligible

surface ac

“shadows

therefore,

e work was c

mple lamina

o made with

gas-liquid for

laminar-lam

on of a flat

6) by conside

ng angle at

tion, measur

on of a flat i

stions for

developed in

pecific sugge

xperiments d

allow clear i

in Y. Thou

e effect on i

ctive), the dy

s” on the im

, that a searc

carried out on

ar-laminar st

the stratified

rm of their m

minar and H

interface. T

ering the mod

t the triple

rements were

interface was

Future W

the work des

estions for th

described he

identification

ugh separate

interfacial te

yestuff did s

mages reflect

h for a more

n modelling

tratified flow

d flow mode

model fitted

Hall and He

The validity

del of Ng (20

interface a

e made of the

s a reasonab

Work

scribed here

e extension o

re, a fluores

n of that pha

e measurem

ension (and w

significantly

ting this par

e optimal dye

Chapter 7

of the flows

w model (see

els of Hall an

the present

ewitt (1993

of this assu

002). In this

and of inte

e wetting an

le approxim

can clearly b

of the work a

scent dyestu

ase in the PL

ents indicat

was therefor

absorb the l

rtial absorpt

estuff be und

: Conclusion

s. Much of t

e Appendix

nd Hewitt (1

data well (se

) models a

umption was

s latter mode

erfacial tens

gle. It was c

ation in mod

be a basis for

are as follow

uff was adde

LIF studies.

ted that this

re unlikely t

laser light sh

ion process.

dertaken.

n and Future

the data fitted

2). Compa

993) and rev

ee Chapters

are based o

s investigated

el, account is

ion. To aid

concluded th

delling the p

r extensive f

ws:

ed to the aq

The dyestuff

s dyestuff h

to be signific

heet and pro

It is sugg

Work

d well

risons

vealed

5 and

n the

d (see

taken

d this

hat the

resent

further

queous

ff used

had a

cantly

duced

gested,

276


277

(2) It is strongly suggested that an investigation should be performed to identify a series of

refractive index matched test fluid pairs that can be employed in the TOWER facility,

so that the influence of the physical properties of the test fluids on flow development

can be investigated. Further to this, PLIF campaigns in which surfactants are added to

the flow should be performed to enhance understanding of how their presence effects

the flowing behaviour, particular the flow regimes and velocity profiles.

(3) The refractive indices of the test fluids are functions of temperature. If a heat exchanger

were inserted into the TOWER facility prior to the test section inlet it would allow the

flow inlet temperature to be maintained at a value for which the refractive indices of the

two test fluids are most closely matched, hence minimising the distortion to the PLIF

images arising due to the disparity in the refractive indices of the test fluids caused by

the temperature fluctuations.

(4) Fitting the TOWER facility with pressure transducers would allow the simultaneous

recording of pressure drop with PLIF and PTV/PIV measurements. The availability of

pressure gradient measurements would allow a much broader scope of analysis to be

undertaken.

(5) There is a need for better prediction methods for flow regime transitions in liquid-liquid

flows. The development of such methods might lean on what has been done in gas-

liquid flow. A detailed investigation of the phase inversion phenomenon (which is

accompanied with a characteristic spike in pressure drop) could be carried out with the

aid of PLIF and PIV/PTV images and measurements.

(6) In light of the differences in the flow regimes arising from the different inlet

orientations, the current work could be progressed by investigating the flow at different


278

axial positions downstream of the test section inlet to develop the understanding of the

progression to fully developed flow. This could be further developed by investigating

the influence of mixing elements at the inlet to the test section upon reaching fully

developed flow.

(7) For the PLIF studies presented in Chapters 4 to 6, the test section was horizontal; the

influence of different inclinations on the flow is an area of significant practical

importance and this area could be pursued with the methods developed in the present

study.

(8) The channel wall material can have a significant influence on liquid-liquid flows (as

was shown in the work of Angeli and Hewitt, 2000a). In the present work, the test

section upstream of the measurement section was made of stainless steel. It would be

instructive to study any changes which might occur with different pipe materials, such

as acrylic resin.

(9) Though the focus in the present work has been on pipeline flows (and there is scope for

much further work in this area as discussed above) the PLIF and PTV/PIV system

developed in the current work could be utilised to investigate other forms of liquid-

liquid systems, such as stirred vessels.

(10) In the present work, the PTV and PIV methods have been used primarily to measure

mean velocity fields. However, there is no reason why this technology could not be

extended to the investigation of fluctuating velocities including fluctuations arising

from interfacial wave action and turbulence and such an extension is strongly

recommended.

References

279

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Appendix 1: Start-Up and Shut-Down Procedure

291

APPENDIX 1:

Start-Up and Shut-Down Procedure

The TOWER rig is a complex facility. It is important to operate it in an efficient and safe

manner. Thus, for the benefit of future users, it has been considered useful to place on record

here a summary of the start-up and shut-down procedures.

Start-Up Procedure

1. Check all valves are closed

2. Ensure that the aqueous phase (water or, in the present work aqueous glycerol solution) and

oil tanks are at least ¾ full. If not, open valve CV5 and/or CV6 respectively and add water

and/or oil until tanks reach desired level, then fully close both valves

3. Fully open the valves before (BV5 & BV2) and the valves after (BV6 & BV7) the pumps

4. Fully open control valves CV1 and CV3, and partially open CV2 and CV4

5. If running the aqueous phase at low flow, fully open valve BV10. If running the aqueous

phase at high flow, fully open valve BV11

6. If running oil at low flow, fully open valve BV12. If running oil at high flow, fully open

valve BV13

7. To introduce water flow to the top of the inlet, open valves BV15 and BV19. To introduce

water flow to the bottom of the inlet, open valves BV14 and BV18

8. To introduce oil flow to the top of the inlet, open valves BV17 and BV19. To introduce oil

flow to the bottom of the inlet, open valve BV16 and BV18. Ensure that the phases are always

introduced at opposing orientations.

Appendix 1: Start-Up and Shut-Down Procedure

292

9. Open valve BV21

10. Open CV5 and CV6

11. Switch on pumps M1 and M2

12. Bleed pressure transducer tappings upstream and downstream to remove any trapped air.

13. Increase aqueous phase flowrate by opening CV2 whilst simultaneously closing valve CV1.

Increase oil flowrate by opening CV4 whilst simultaneously closing valve CV3. Adjust each to

desired levels

Shut-Down Procedure:

1. Turn off pumps M1 and M2

2. Close valves CV5 and CV6

3. Close valve BV21

4. Shut all valves in the mixing section (BV15-BV19)

5. Close all valves flow meter valves (BV10-BV13)

6. Fully close valves CV4, CV3, CV2 and CV1

7. Close BV5 and BV6, BV2 and BV7

Appendix 2: Derivation of Laminar Drag Model

293

APPENDIX 2

Derivation of Laminar Drag Model

Equation 4.2 has been derived by first considering the frictional pressure drop Δp experienced

by each of the two test fluids over a pipe length L:

Δ , (A1)

Δ , (A2)

Δ , (A3)

where the subscript ‘oil’ denotes the oil flow and the subscript ‘gs’ that of the glycerol solution.

The hydraulic diameter D is,

, (A4)

with Ai and Pi the cross-sectional area and the wetted perimeter of fluid ‘ ’ respectively. Also, fi

denotes the Fanning friction factor of fluid ‘ ’ that for laminar flow is given as,

, (A5)


294

and, Rei is the Reynolds number associated with the flow of fluid ‘ ’, which in turn is defined

as,

. (A6)

Equating the pressure drops for each liquid flow in our arrangement gives,

Δ Δ Δ . (A7)

Now, substituting the laminar relation for the Fanning friction factor from Eq. A5 into the

frictional pressure drop equation for each liquid, i.e., Eq. A2 for oil and Eq. A3 for the glycerol

solution, and dividing the oil pressure drop by that of the glycerol solution, i.e., Eq. A2/Eq. A3,

gives,

1 . (A8)

After substituting the Reynolds number definition (Eq. A6) for each liquid flow into Eq. A8 we

obtain,

1 . (A9)

Returning to the hydraulic diameters of the two fluid flows from Eq. A4, we can also write,

2 , (A10)


295

2 . (A11)

where Yi is the (absolute) time-averaged depth of liquid ‘i’ and W is the width of the square

channel, such that,

. (A12)

Note that, in Equation A11, the wetted perimeter for each phase is taken as the sum of the

perimeter of the phase in contact with the wall of the channel plus the interfacial perimeter.

Dividing through the expressions for the two hydraulic diameters (Eqs. A10 and 11), we have,

. (A13)

Now we define a dimensionless liquid flow depth,

, (A14)

and substitute this into Eq. A13 to obtain,

. (A15)

The substitution of the hydraulic diameter ratio Dgs Doil⁄ from Eq. A15 into the expression for

the pressure drop ratio Δpoil Δpgs, Eq. A9, gives,


296

1 . (A16)

Finally, performing a mass balance gives:

⇒ . (A17)

Substituting the superficial velocity ratio Uoil Ugs⁄ from Eq. A17 into the pressure drop ratio

Δpoil Δpgs, Eq. A16 gives:

1 , (A18)

⇒ , (A19)

in which, parameter X has been defined as being equal to the multiple of the ratios of the

volumetric flow rates and dynamic viscosities of the glycerol solution to the oil flows.

Therefore, we obtain Eq. 4.2 as,

4 4 4 4 1 0 . (A20)

297

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