Brigham Young UniversityBYU ScholarsArchive

All Theses and Dissertations

1971-5

Transition from Laminar to Turbulent Flow for aTwo-Phase MixtureMohammed Sharief QureshiBrigham Young University - Provo

Follow this and additional works at: https://scholarsarchive.byu.edu/etd

Part of the Mechanical Engineering Commons

This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by anauthorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu, ellen_amatangelo@byu.edu.

BYU ScholarsArchive CitationQureshi, Mohammed Sharief, "Transition from Laminar to Turbulent Flow for a Two-Phase Mixture" (1971). All Theses andDissertations. 7174.https://scholarsarchive.byu.edu/etd/7174

TRANSITION FROM LAMINAR TO TURBULENT FLOW

C'l d.06~2-

•/ < h i

FORA TWO-PHASE MIXTURE

Q,

A T hesis

P resented to the

D epartm ent of M echanical Engineering Science

Brigham Young University

In P artia l Fulfillm ent

of the R equirem ents for the D egree

M aster of Science

by

Mohammed Sharief Q ureshi

May 1971

T his th e s is , by Mohammed Sharief Q ureshi, is accepted in its

p resen t form by the Departm ent of M echanical Engineering Science of

Brigham Young U niversity as satisfy ing the th esis requ irem en t for the

degree of M aster of Science.

/ 3 * Ac]. 7 o_________Date

Typed by K atherine Shepherd

To my paren ts

ACKNOWLEDGMENTS

The author w ishes to ex p ress his appreciation to D r. John N.

Cannon fo r suggesting the topic of th is study and for h is a ss is tan ce on the

many technical problem s a ris in g in th is study, and to Bill Hayes for making

the facilities of the departm ent laborato ry and shop read ily available during

the construction of the ap p ara tu s .

IV

TABLE OF CONTENTS

ACKNOWLEDGMENTS ............................................................. iv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

NOMENCLATURE . ix

C hapterI. INTRODUCTION .......................... 1

Purpose of the study Scope of the study

II. DESCRIPTION OF APPARATUS.................... 7

Pump and m otor Valving and flow control T est section Flow m easurem ent Flow visualization P re ssu re drop m easurem ent T em pera tu re m easurem ents M ixer

III. TEST PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G eneral observationsP ressu re drop m easurem ents in w aterP ressu re drop and flow m easurem ents fo r tw o-phase m ixer T em perature m easurem ent Special observation

IV. DISCUSSION OF RESULTS. . . . . . . . . . . . . . . . . . . . . . . . . . .

16

20

Method of data p resen ta tionT ransition from lam in ar to turbulent flowExperim ental re su ltsCom parison with Bingham p lastic model

v

C hapterV. CONCLUSIONS AND RECOMMENDATIONS 39

ConclusionsRecommendations

APPENDIXES . . . . . . . . . . . ........................ .. .............. ..

APPENDIX A. A nalysis of Experim ental Uncertainty APPENDIX B. A nalysis of U ncertainty in Specific Gravity

of Lucite Beads APPENDIX C . Analysis of U ncertainty in Specific Gravity

of M eriam Oil APPENDIX D. Settling-V elocity of Lucite Beads APPENDIX E . Com m ents on Pump Selection APPENDIX F . Tabulation of Data

LIST OF REFERENCES......................................................................

41

. 64

vi

LIST OF FIGURES

Figure Page

1. Representative fundam ental sh ea r d iag ram s fo r Newtonian,B ingham -plastic, p seudo-p lastic , and dilatant m a te ria lsin pipes ................... . . . . . . . . . . . . . . . . . . . . 3

2. Lucite bead size spectrum by sieve analysis . . . . . . . . . . . . . . 6

3 . Schematic d iagram of te s t a p p a r a tu s .................... 8

4 . Pump and flow control valves ....................................................... 10

5 . A general view of the te s t section ......................................... 10

6 . P ressu re drop m easurem ent, m anom eters ' s e ttin g ....................... . 12

7 . Flow m easurem ent (catch bucket, sca le s , and m ixing drum ) . . . 12

8 . Product of friction fac to r and Reynolds num ber v e rsu s Reynoldsnum ber. ....................................................................................................... 22

9. Rate of sh ear v e rsu s sh ea r ra te fo r w ater and various concen­tra tio n s of the Lucite s lu r ry . ............................................ 23

10. Lam inar velocity p ro files fo r pow er-law fluids (8, 10) . . . . . . . 25

11. P ressu re drop v e rsu s m ass flow ra te fo r 5% Lucite s lu rry . . . . 27

12. P ressu re drop v e rsu s m ass flow ra te fo r 10% Lucite s lu r ry . . . . 28

13. P ressu re drop v e rsu s m ass flow ra te fo r 15% Lucite s lu r ry . . . . 29

14. P ressu re drop v e rsu s m ass flow ra te fo r w ater . . . . . . . . . . . . 30

15. Modified Reynolds num ber v e rsu s Fanning friction fac to r . . . . . 31

16. M ass flow ra te v e rsu s p re s su re drop fo r 5% A .S .P . s lu rry . . . . 32

vii

Figure Page17 . M ass flow ra te v e rsu s p re s su re drop fo r 7 .5% A „S „P. s lu rry „ . 33

18. M ass flow ra te v e rsu s p re s su re drop fo r 9% A .S .P . s lu rry . . . . 34

viii

NOMENCLATURE

A A rea of pipe c ro ss section

ASP Aluminum silicate pigment

D Pipe d iam eter

f Darcy-Wdsbach friction fac to r (dim ensionless)

Cf Fanning friction fac to r (dim ensionless)

ft Feet

^ m ftgr G ravitation constant = 3 2 .1 7 --------- —^f sec^

gm G ram s

gpm Gallons p e r minute

hg Inches deflection on m anom eter

hf P ressu re drop, inches of w ater»

K’ Coefficient in Equation (2), (lb°force)(secn ) /(sq .f t„ )

K Fluid consistency index defined by Equation (1)

L Pipe length

li>£ Pound force

lbm Pound m ass

n" Exponent in Equation (2), dim ensionless

n Flow -behavior index (dim ensionless) defined by Equation (1)

A P P ressu re drop

Re

Re’

sec

t

u

V

W

6

A

yMe

<S~

t

w

T '

Reynolds num ber (Re = ?VD )

Modified Reynolds num ber (Re’n ’ 2 -n ’ D v g

gcK!8n - l )

Seconds

Time

Local velocity

Mean velocity

Weight

Small change

Absolute v iscosity

Effective viscosity (see Reference 4)

Density

Standard deviation

Yield s tre ss

Wall sh ear s tre s s

Shear s tre s s

Kinem atic v iscosity

CHAPTER I

INTRODUCTION

A phase is sim ply one of the s ta tes of m a tte r . M ultiphase flow is

the sim ultaneous flow of severa l p h a se s . Two-phase flow is the s im p le s t

case of m ultiphase flow.

Many common exam ples of two--phase flow occur in nature and

everyday p ra c tic e . Biological system s contain very few pure liqu ids. Body

flu ids, such as blood, m ilk, e tc . , a re a ll m ultiphase, containing a v a rie ty

of c e lls , p a r tic le s , o r d roplets in suspension. Exam ples a re equally p ro ­

fuse in the in dustria l field, and much chem ical engineering is concerned

with m ultiphase flow s. Many industria l p ro cesses such as power g e n e ra ­

tion, re frig e ra tio n , and d istilla tion depend on evaporation and condensation

cy c le s . Steel making, paper m anufacturing, and food p rocessing a ll con­

tain c ritic a l steps which depend on the p ro p er functioning of m ultiphase flow

d e v ic e s . Many problem s of a ir and w ater pollution a re due to unwanted

tw o-phase flu id s.

One exam ple of a tw o-phase system is a suspension of p a rtic le s

in a flu id . T his system is usually m ore sim ple than the equivalent g a s -

liquid o r liquid-liquid d isp ers io n . N evertheless, many com plications a r is e

in p rac tice due to fac to rs such as the wide varie ty of s izes and shapes of1

the p a rtic le s , non-uniform flow p a tte rn s , agglom eration, and in te r-p a rtic le

fo rce s . Fluidized beds fo r reduction of uranium o re , p lastic coating, soil

compaction, plasm a spraying, e tc . , a re som e engineering applications of

th is type of flow.

S olids-in-liquid suspensions and solutions are c lassified acc o rd ­

ing to the general type of functional dependence of the sh ea r s tre s s on the

ra te of shear; that is , accord ing to the general shape of the sh ear d iagram ,

o r plot of ra te of sh ea r v e rsu s sh ea r s t r e s s . T here a re two main c la s s if i­

cations; Newtonian and non-N ew tonian. The Newtonian fluids a re c h a ra c te r ­

ized by a constant v iscosity which is independent of the ra te of sh e a r . A

typical sh ear d iagram fo r such a m ate ria l is given by curve "A" in F ig ­

ure 1. The v iscosity in th is case is given by the inverse slope as follows:

A - gc r /(-d V r /d r )

Non-Newtonian fluids, on the o th er hand, exhibit a variab le v iscosity

dependent upon the ra te of sh ea r, and in some cases upon the duration of

sh e a r . These m a te ria ls a re subdivided into five general types; (a) Bingham

p lastic , (b) p seudo-p lastic , (c) d ilaten t, (d) th ixotropic, and (e) rheopectic

( 5) .

Most solutions and suspensions a re Newtonian a t low co n cen tra ­

tions, changing to one of the non-Newtonian classification when a certa in

c ritic a l concentration is reached . In the case of suspensions, this c r itic a l

concentration depends upon p artic le size and shape and upon degree of

Rat

e of

She

ar,

8V/D

3

F ig . 1 . --R epresen ta tive fundam ental sh ea r diagram s for Newton­ian, B ingham -plastic, p seudo-p lastic , and dilatant m ate ria ls in p ip es.

dispersion as well as upon concentration of the solid phase .

As in the case of true liquids, lam inar and turbulent s ta tes of

flow ex ist fo r non-Newtonian flu id s. Various c r i te r ia have been proposed

fo r defining the end of the lam inar flow regim e, depending upon the

em pirica l m odifications, specialization , and generalization of the conven­

tional Reynolds num ber.

In the case of Bingham p lastics it was found (3) that the in itiation

of turbulence in the tubes occurs a t the same Reynolds num ber as for New­

tonian fluids ( 2100) when the Reynolds num ber is defined as DV?//*-e

w h e r e i s the approxim ate effective v iscosity for Bingham p lastics at

corresponding Reynolds num ber.

Winding, Baumann, and K ranich (14) proposed that lam inar flow

of pseudoplastic fluids in tubes would end when the Reynolds num ber

defined as reaches 2100, whereyd/0 is the v iscosity at ze ro sh ear

r a te .

M etzner and Reed (8) stated that because of the close resem blance

between highly non-Newtonian fluids at low sh ear ra te and true so lids,

little eddies of the fluid in turbulent motion should behave m ore n early like

solid p a rtic le s and, for exam ple, not b reak up so readily as do the eddies

of Newtonian f lu id s . The net effect of th is difference would be to increase

the Reynolds num ber range beyond the usual (1800 to 6000) Reynolds num ­

b e r values found fo r Newtonian fluids (7, 9).

Purpose of the study

The purpose of th is study was to investigate the transition R ey­

nolds num ber region of a tw o-phase m ix tu re . Any observed difference in

the transition p rocess between these m ix tures and plain w ater would aid in

explaining the m echanism . T ransition was v isually identified and recorded

when it o ccu rred .

Scope of the study

An apparatus was built which could rec ircu la te the tw o-phase m ix­

tu re through a 40 foot length of c le a r acry lic p lastic pipe. Aluminum powder

was used to make the flow p a tte rn s v is ib le . A ttem pts were made to identify

visually the s ta r t and the end of tran s itio n . Runs w ere made with tap w ater

and at various concentrations of solid phase . The solid phase used was

Lucite beads with specific gravity of 1.1115, and an average size of 100

m esh (0.0058 in . d ia .) . In o rd e r to confirm the size of the beads, a sp ec­

trum analysis was made (see F igure 2). The specific gravity of beads was

a lso confirm ed and an analysis of uncertain ty was made (see Appendix B).

T ransition fo r w ater and tw o-phase m ixtures was visually observed along

with m easurem ents of the p re s su re drop a c ro ss the te st section fo r the

various flow ra te s .

Lucite Beads (DuPont Lot -•

Sieve A nalysis 4F-N C -99)

42 Mesh 0.2641% 0.0138" dia grain60 Mesh 0.4401% 0.0097" dia grain80 Mesh 10.3800% 0.0069" dia grain

100 Mesh 78.5211% 0.0058" dia grain115 Mesh 1.4060% 0.0049" dia grain150 Mesh 1.1444% 0.0041" dia grain170 Mesh 4.0493% 0.0035" dia grain200 Mesh 3.3451% 0.0029" dia grain250 Mesh 0.2641% 0.0024" dia grain270 Mesh 0.1761% 0.0021" dia grain400 Mesh 0.0103% 0.0015" dia grain

150 170 200 250M eshes to an Inch

F ig . 2 . —Lucite bead size spectrum by sieve analy sis

400

ON

CHAPTER II

DESCRIPTION OF APPARATUS

The apparatus was designed and built to provide the following five

functions:

1. C irculation of the sam ple fluid through the te s t sec tion .

2 . Mixing of the Lucite beads and alum inum powder with the flu id ,

3 . M easurem ent of the flow ra te through the test sec tion .

4 . M easurem ent of the p re s su re drop through the te s t sec tion .

5 . To provide a very long visual tube length.

F igure 3 is a schem atic d iagram of the apparatus showing the d irection of

the flow and the arrangem ent of the component p a r ts .

Pump and m otor

The pump was a centrifugal type of unknown m ake and model (see

F igure 4) obtained from governm ent su rp lu s . The im p e lle r d iam eter was

5 inches. Both the suction and d ischarge p o rts w ere 1 -1 /4 inches in d iam ­

e te r . The pump was capable of providing 49 .4 gpm through the te s t section

a t 1725 rpm (2). This corresponds to a Reynolds num ber of approxim ately

90,000 for c lea r w ater a t 70°F .

The m otor was a KN type made by Brown and Sharpe Company with a

7

F ig . 3 .--S ch em atic d iagram ol te s t apparatus 00

ra ted capacity of 1/2 hp.

Valving and flow control

T hree gate valves of d ifferent sizes (1-1/4 in ., 1/2 in ., and 1/4

in .) and one needle valve w ere provided fo r the flow co n tro l. The needle

valve was used for fine control during lam in ar flow and tran sitio n , w hereas

the two o thers w ere meant for fully developed turbulent flow. The 1-1 /4 in .

d iam eter valve was used fo r flushing the system to re lieve the se ttling p ro b ­

lem with the beads. Between the two taps, which w ere provided fo r flow

m easurem ent, a fifth valve was in sta lled . The purpose of th is valve was to

iso late the system from the mixing d ru m . W henever th is valve was open

and the two taps w ere closed , the fluid was trapped into the loop. This was

used as a m eans of preventing w ater m arks from form ing in the c le a r p lastic

pipe during overnight periods and other tim es between runs when the pump

was shut off, and a lso fo r rec ircu la tin g the sam e fluid through the te st s e c ­

tion fo r v isual study of flow.

One m ore gate valve was provided in the rec ircu la tion loop which

was always kept wide open. In the fa r end of the te s t section a 1/4 in . gate

valve was a lso used to contro l the a ir t ra p .

T est section

The te s t section was a 40 foot length of c lea r cast acry lic p lastic

pipe (see Figure 5). The inside d iam eter was 1.25 inches and the wall

thickness was 0.25 inches. Since the pipe was not available as a single

10

F ig . 4 . --Pump and flow control valves

F ig . 5 .--A general view of the te s t section

11

40 foot length, the te s t section had to be constructed by joining nine se p ­

a ra te sections of pipe, each about 4 feet 2 inches long. Each two sections

w ere joined by p lastic flanges. P lastic flanges w ere made separately and

then glued with the round ends of the pipe by m eans of a p lastic cem en t. No

problem was faced in joining the m etal pipe with the plastic pipe as two such

sections w ere a lready available (2).

Flow m easu rem ent

A ven turi m eter was insta lled in the flow loop, but p re ssu re d iffe r­

en tials were so sm all fo r the low flow ra te s involved that it was v e ry d iffi­

cult to get good read in g s .

The weigh bucket method was used to determ ine die flow' r a t e .

The rubber hose at the d ischarge end was able to move m anually from the

m ixing drum to the catch bucket so that a ll the fluid leaving the te s t section

in a given tim e period could be caught and weighed. Toledo sca les, model

2081, w ere used fo r all w'eight m easu rem en t. The resolution fo r these

sca les was 1/2 o z . (See F igures 6 and 7 .)

Flow v isualiza ti on

In o rd e r to identify the point w here the tu rbs s ta rted and where

the flow becam e fully turbulent, it was n ecessa ry to make the flow p a tte rn s

v isible . Very fine aluminum powder was added to the w ater and to the two-

phase m ixture fo r th is p u rp o se . During lam inar flow the p a rtic le s w ere

d istribu ted evenly through the flow, while during the turbulent flow the

12

Fig. 6 . --P re ssu re drop m easurem ent, m anom eters' setting

F ig . 7 . --F low m easurem ent (catch bucket, sca les, and m xing drum).

p a rtic le s swept along by the tu rbs produced dark and light a re a s c o r re s -

13

ponding to the m ovement of the flu id .

T his flow v isualization system was sa tisfac to ry , allowing a ll flow

p a tte rn s to be determ ined v isually , and also showing flow p ro files a c ro ss

the tube except with the aluminum silicate te s t s . During lam inar flow with

w ater and alum inum flakes the fa s te r flow at the core as well as the slow er

flow n ear the wall was c lea rly v is ib le .

P ressu re drop m easurem ent

P ressu re taps w ere placed in the te s t section wall 26 feet, 4 -1 /2

inches a p a r t. The upstream tap was 10 feet from the beginning of the te s t

sec tio n . Thus the flow was well developed in the te s t sec tion . Also, the

turbulence c rea ted by the 90° elbow hastened the flow developm ent. T ests

with plain w a ter showed that the data fo r lam inar, tran s itio n , and turbulent

flow com pared very favorably with Moody's curve for smooth pipes (see

Figure 8).

The p re s su re drop a c ro ss the te s t section was v e ry sm all during

lam inar flow. In o rd er to reduce the high percentage of uncertain ty fo r

the calculation of the friction fac to r and the Reynolds num ber, it was felt

that the b i-flu id m anom eter m ust give sufficient deflection a t a low flow

r a te . Many fluids wre re tr ied , but Meriam. oil of specific gravity 1.04 was

found to be b est suited fo r th is pu rpose . T his reduced the experim ental

uncertain ty to a very large ex ten t. (See Appendix A fo r the calculated value

of uncerta in ty .)

14

Two M eriam bi-flu id m anom eters w ere used together fo r p re s su re

drop m easu rem en t. The lower fluid was M eriam oil w ith a specific gravity

of 1.20 in one and was M eriam oil with a specific g rav ity of 1„04 in the

o th e r. The p re ssu re taps w ere connected to them by m eans of tee joints

which divided the flow into two d irections and each w as connected to each

m anom eter. Polyflow 1/4 in , p lastic tubing was used fo r making a ll the con­

nections (see Figure 6). At low flow ra te s , and even a t high flow ra te s ,

M eriam bi-flu id m anom eter with specific gravity 1.04 was a fine indication

of p re ssu re drop, w hereas the o ther one was a co arse indication of the sam e.

At a very high flow ra te it was found to be n ecessa ry to shut the low specific

gravity fluid m anom eter because of the very high p re s s u re d iffe ren tia ls .

Readings w ere taken in inches and tenths of inches. The following form ula

was used fo r conversion of gauge reading to inches of w ater:

Inches of w ater = ( Q0il - £w ater) hg

- (1.2 - 1.0) hg

= (0.2) hg for 1.2 m anom eter o il

(0.04) hg for 1.04 m anom eter oil

T em peratu re m easurem ents

An iron-Constantine therm ocouple together with a Brown portable

potentiom eter, model 126 \V3, was used fo r the tem p era tu re m easurem ent.

An ice bath was provided fo r keeping the re ference junction at 32°F . The

15

one end of the therm ocouple was pinned with the pipe th read s a t the fa r end

of the te s t section w hereas the o ther end was held a t a constant tem p era tu re .

M ixer

The m ixer used was a Lightning m ix er, of which the purpose was to

keep the flow turbulent in the m ixing d ru m . T his was n e ce ssa ry to avoid

any settling problem in the drum that would a lte r the concentration ra tio in

the te s t sec tion . The m ixer consisted of an e lec tric m o to r with a long shaft

33 inches in length. Two p ro p e lle rs w ere provided in the end. The m otor

was made by Mixing Equipment Company with Model NC4, 1725 rpm , 1/4 hp.

CHAPTER III

TEST PROCEDURE

Five d ifferen t te s t p rogram s w ere made with this a p p ara tu s . The

purpose of each te s t p rogram will be explained in the following descrip tion

of the te s t procedure .

G eneral observations

The purpose of this te st p rogram was to learn how the apparatus

would behave and how to control the flow. A secondary objective was to

look fo r any unusual phenomena which would w arran t special investigation.

To s ta r t , the mixing drum was filled with 30 gallons of c le a r w a te r .

The w ater tem p era tu re was m easured using an iron-Constantine th e rm o ­

couple and was reco rd ed . The pump was s ta rted and the w ater was allowed

to c irc u la te . W ater and 50 gms of aluminum powder w ere mixed with th ree

drops of a Jet Dry detergent in a flask and w ell shaken . It was then allowed

to stand for about five m inu tes. A fter th is length of tim e, the aluminum

powder would a ll be settled to the bottom of the fla sk . The w ater from the

top was poured off and the washed alum inum powder was poured into the

mixing d rum . D ifferent flow ra te s w ere then tr ie d , and the flow p a tte rn s

w ere observed . No flow ra te m easurem ents, o r p re s su re drop m easurem ents,

16

w ere m ade.

17

T hese te s ts showed that the turbulent flow p a tte rn s w ere c lea rly

v is ib le . It was learned that with approxim ately 50 gins of alum inum powder

in the system , the flow p a tte rn s w ere c lea rly seen . The lam inar, tran sitio n ,

and turbulent flow regions could all be distinguished v isu a lly . The turbulent

slugs w ere defined very c lea rly in the transition reg io n .

P re ssu re drop m easurem ents in w ater

The m ixing drum was filled with 30 gallons of w a te r . The a lu m i­

num powder was added as described above, and the w a te r tem p era tu re was

noted and re c o rd e d . With the flow control valves set fo r no flow through

the te s t section , the b i-flu id m anom eters w ere checked fo r a ir bubbles to

make su re the p re ssu re d ifferen tia ls m easured would be as nearly c o rre c t

as p o ssib le .

D ifferent flow ra te s w ere sent through the te s t sec tion . F o r each

valve setting the p re ssu re drop a c ro ss the te s t section w as m easured and

reco rd ed . T h is procedure was repeated until lam inar, tran sitio n , and fully

developed turbulent flow had been observed .

P ressu re drop and flow m easurem ents fo r tw o-phase m ixture

A fter testing with the w ater, te s t runs w ere m ade with 5 p e r cent,

10 p e r cent, and 15 p e r cent load ra tio s of Lucite beads added . To s ta r t

w ith, the m ixing drum was filled with 83500 cc of pure w a te r . A carefu lly

18

weighed quantity of Lucite beads was added. A few drops of Jet Dry d e te r ­

gent w ere a lso poured in the m ixing d ru m . The m ixer was then s ta rted to

m ake the 5 p e r cent concentration s lu r ry . The pump was now s ta rted and

the s lu rry was allowed to c irc u la te . D ifferent flow ra tes w ere then sent

through the te st section and fo r each valve setting , p re ssu re drops and flow

ra te s w ere m easured in the sam e w as as in the case of w a te r . The sam e

procedure was repeated fo r 10 p e r cent and 15 p e r cent concentration

s lu r r i e s .

S im ilar te s ts w ere made with aluminum silicate solids a t 5 p e r

cent, 7 -1 /2 p e r cent, and 9 p e r cent loading ra tio s . Aluminum flakes were

added a t 5 p e r cent loading but the flow patterns were not v is ib le . No a lum ­

inum flakes w ere added at 7 -1 /2 p e r cent and 9 p e r cent loadings.

T em peratu re m easure ment

An iron-Constantine therm ocouple was used for tem pera tu re m ea­

su rem en t. During the experim ental p rocedure a very careful observation

was made to note any significant change in tem p era tu re during the experim ental

p ro c e ss . No change was observed , and the tem peratu re was a lm ost constant

during the experim ental runs for both w ater and Lucite s lu r r ie s .

Special observation

The purpose of th is te s t was to detect any roughness in the te s t

section and a lso to find the effects of s tre s s c racks on flow p a tte rn s which

w ere observed in the te s t section due to unknown rea so n s .

19

To te s t fo r roughness, the flow was adjusted so that it was well

below the transition reg ion . The tap on the d ischarge end of the flow would

then be suddenly opened so that the flow would jump well up into the turbulent

reg ion . Any roughness along the te s t section would then cause the flow to

tra n s is t at the cite of roughness to turbulent flow.

The te s t section was a lm ost com pletely smooth as no appearance

of the above phenomenon w as observed .

CHAPTER IV

DISCUSSION OF RESULTS

Method of data p resen ta tion

It has been found experim entally (8, 10, 13) that the rela tionsh ip

between sh ea r s tre s s and ra te of sh ea r for a g rea t many non-Newtonian

fluids, possibly the m ajo rity , may be rep resen ted closely over wide ranges

of sh ea r ra te by a tw o-constant pow er function of the form

(1)

The ( ------ ) is the sh ea r ra te w ritten fo r flow within a c irc u la r duct. And r

equation of th is type, though em p irica l, appears to rep resen t the rheological

p ro p ertie s fo r a wide v arie ty of non-Newtonian fluids b e tte r than m ost other

proposed equations and certa in ly b e tte r than any o ther available two “constant

equation. F o r th is reason the pow er-law rheological model w ill be adopted

in this p resen t analysis .

When the flow is in a c irc u la r tube, it can be shown (8) that

where

“C w =DAP

4L= K ' ( ^ ) n ’

v D

, d In (DAP/4L)n =--------------------------- = n

d In (8V/D)

20

(2)

( 3 )

K’ = K (3n' - 1

/,

21

and ) (4)4n'

The valves of n ' and K' can be determ ined experim en tally by m easuring the

p re ssu re d ro p and the flow ra te s in a tube. The va lv es of DAP/4L can then

be plotted ve rsu s valves of 8V/D on log-log co o rd in a tes . The slop of the

line in the lam inar region is n ' and the in tercep t fo r 8V/D = 1 is the valve

of K' (see Figure 9).

The coefficient n ' is generally known as the physical property of

the fluid which ch arac te rizes its degree of non-Newtonian behav io r. If it

is a constant with the valve of unity, Equation (2) becom es

T w * K’ ( ------ ) - .................... (5)d r

which is the linear relationship between sh ea r ra te of Newtonian flu id s.

On the other hand, if n ’ is le ss than unity, one will obltain the Ostwald

equation for pseudoplastic fluids, v i s . ,

“ K ( — ) . . e . o o o . (6)d r

Sim ilarly , if n ' is g re a te r tiian unity, the fluid is dilattant in c h a ra c te r .

The g re a te r the divergence of n ' from unity (in e ith e r d irection), the m ore

non-Newtonian the fluid is .

It is noted that n' defines the degree of non-Newtonian behavior

of the fluid and K' defines its consistency . The large;r the valve of K ',

the th icker o r "m ore viscous" the flu id .

(Fri

ctio

n F

acto

r) (

Rey

nold

s N

umbe

r),

f . R

e22

F ig . 8 . --Product of friction fac to r and Reynolds num ber ve rsu s Reynolds num ber.

Shea

r S

tres

s (D

£>P/

4L),

lbf/

ft23

Rate of Shear (8V/D, Sec-1)F ig . 9. --R ate of shear v e rsu s sh ea r ra te fo r w ater and various co n cen tra ­

tions of the Lucite s lu rry .

24

In R eference 8 i t was found that the p re s su re drop v e rsu s flow ra te

data can be re la ted by the modified Newtonian re la tionsh ip

Cf = 16/R e' . . . . . . . . . . . . . . . . .(7 )

w here the modified Reynolds num ber is defined as

Dn ' y 2 ~n 'g

ScK' ^• ( 8)

F or Newtonian fluids in lam inar flow the velocity is p a rab o lic .

As n ’ d ec rea se s tow ards ze ro , the lam inar-velocity p rofile becom es p ro ­

g ressive ly f la tte r , and in the lim iting case of n ' =0 it i.s perfectly f la t. On

passing from the lam inar to the turbulent flow region th e lam inar-velocity

profile is flattened by a net turbulent momentum tra n s fe r from the high to

the low velocity a r e a s . Hence turbulence leads to the sam e general effect

on the velocity profile as does a decreasing valve of n '„ F u rth e rm o re , when

n ' is c lose to z e ro , the velocity p rofile is so nearly flail that it can be a lte red

only very little on passing from lam inar to turbulent flow . In the lim iting

case of n ' = 0 w here the lam inar-velocity p rofile is p e rfec tly fla t, th e re can

be no distinction between lam inar - and turbulent-m ean velocity p ro files (see

F igure 10 fo r various velocity p ro file s).

T ransition fro m lam inar to turbulent flow

The tran s itio n from lam inar to tu rbulent flow o c cu rs fo r a certa in

range of the Reynolds num ber, depending upon the in le t conditions and

25

n=0

Local velocity , U f t/se c

n=0»l

0 ¥ 10 Local velocity, U ft/sec

Local velocity , U f t/se c Local velocity, U f t/se c

Newtonian fluid

Local velocity , U f t/se c Local velocity, U f t/se c

F ig . 1 0 .--L am in a r velocity p ro files fo r power-law fluids (8, 10)

26

roughness conditions inside the p ipe . In th is flow loop, the transition range

was observed to begin a t about a Reynolds num ber of 1746 and end a t about

5136 fo r plain w a te r . While the flow is in the transition range it consists of

regions of turbulent spots called turbulent slugs or spots, and regions of

lam inar flow. The size of the turbulent spots in the pipe v a rie s depending

on how high the Reynolds num ber is , and how fa r along the pipe the flow has

trav e led .

Experim ental re su lts

S tre s s -sh e a r d iagram s of the tw o-phase m ixture and w ater a re

given in F igures 11, 12, 13, and 14. F igure 9 shows the data of the lam inar

flow on logarithm ic co o rd ina tes . The pow er law constant (n'), and the con­

sistency index (K') a re determ ined from the curves in F igure 9 . These

cu rves a re stra igh t lines fo r a ll th ree concentration ra tio s . This indicates

that the power law rheological model will fit the data reasonably w ell.

The m ost fam ilia r method of p resen ting data of fluid flow is the

graph re la ting the Fanning friction fac to r to the Reynolds num ber. In the

case of non-Newtonian fluids, a modified Reynolds num ber a s defined p r e ­

viously is u sed . A plot of the Fanning friction fac to r versus the modified

Reynolds num ber is shown in F igure 15, which contains a ll the lam inar

data points obtained in th is study.

F o r the non-Newtonian system s studied by Dodge and M itzner (5),

with n ' less than unity, the onset of turbulence always occurred at Rey­

nolds num ber slightly g re a te r than those fo r Newtonian sy s tem s . F u rth e r-

Pre

ssur

e D

rop,

Inc

hes

of W

ater

27

0 .5

0 .4

0 .3

0 . 2

0 .1

0 .00 .0 0.1 0.2 0.3

M ass Flow Rate, (lbm /se c )F ig . 1 1 .--P re ssu re drop v e rsu s m ass flow ra te fo r 5% Lucite s lu rry

Pre

ssur

e D

rop,

In

ches

of

Wat

er28

O.E

0.4

0.3

0.2

0.1

0 .00 .0 0.1 0 .2 0 .3

Mass Flow Rate, (lbm/s e c )F ig . 1 2 .--P re ssu re drop versus m ass flow r a te for 13% Lucite s lu rry

Pre

ssur

e D

rop,

Inc

hes

of W

ater29

M ass Flow Rate, (lbm /se c )F ig . 1 3 .--P re ssu re drop versu s m ass flow ra te for 15% Lucite s lu rry

Pre

ssur

e D

rop,

Inc

hes

of W

ater

30

M ass Flow Rate, (lbm/s e c )F ig . 1 4 .- -P re ssu re drop v e rsu s m ass flow ra te fo r w ater

Fann

ing

Fri

ctio

n F

acto

r, C

f31

5 6 7 8 ? # 2Modified Reynolds Number, Re'

F ig . 1 5 .--M odified Reynolds num ber v e rsu s Fanning friction factor

ress

ure

Dro

p, I

nche

s of

Wat

er

s l u r r y .F ig . 1 6 . --M ass flow ra te ve rsus p re s su re drop for 5% A .S .P .

Pre

ssur

e D

rop,

In

ches

of

Wat

er

.33

F ig . 1 7 .--M ass flow ra te v e rsu s p re ssu re drop fo r 7.5% A .S .P . s lu rry .

Pre

ssur

e D

rop,

Inc

hes

of W

ater

s l u r r y .F ig . 1 8 . --M ass flow ra te versus p re s su re d rop for 9% A .S .P .

35

m o re , th e ir data showed some evidence that the Reynolds num ber c o r r e ­

sponding to the onset of turbulence in c rease s slowly with decreasing values

of n ' . F or exam ple, with n ’ of 0 .726, they observed the s ta r t of the t r a n s i ­

tion region a t a Reynolds num ber of about 2700, w hereas for an n' of 0.38

the onset of turbulence was observed a t a Reynolds num ber of about 3100.

The values of n ' obtained, from F igure 9 show the pseudoplastic

behavior of the m ix tu re . Values of n ' increase slightly with the in c rease of

concentration ra tio s , but th is in c rease is not la rg e . Increase of co n cen tra ­

tion from 5 to 10 p e r cent changes the value of n ' from 0 .6 to 0 .605 and a

fu r th e r increase up to 15 p e r cent changes to 0.62 only. However, these

d ifferences a re within the experim ental e r r o r and may therefo re not r e p r e ­

sent d ifferent values; i . e . , the above a sc rib ed influence due to concen tra ­

tions may not ex ist at a l l .

F igure 14, which is a plot of Cf-Re' shows the delay in transition

p ro cess due to the non-Newtonian behavior of the m ix tu re . The c ritic a l

Reynolds num ber in all th ree cases lie s very close to each o th e r. They

actually show a slight delay due to the in c rease of concentration. The con­

clusion which apparently can be drawn front th is is that an in c rease in the

concentration re su lts in an increase of flow behavior index, which in turn

re su lts in an in c rease of c ritic a l Reynolds num ber. This is inconsistant

with the re su lts of Dodge and M etzner (5) described in the last parag rap h .

The s ta r t of the transition region is generally identified by the

deviation of the flow data from the lam inar Cf = 16/R e' line . Dodge and

and M etzner in th e ir study w ere not su re about the effect of change of n '

36

on c ritic a l Reynolds num ber, because the experim en tal data close to die

onset of turbulence exhibited sufficient sc a tte r to p roh ib it a p re c ise defin i­

tion of the tran sitio n reg ion . The tran sitio n -reg io n portion of the friction

fac to r curves was located somewhat a rb i tra r i ly .

This study, although lim ited , was different from a ll the previous

w ork. During experim ental procedure a ll the atten tion was paid in observing

visually the s ta r t of the transition reg ion . Several runs w ere made to v isu ­

ally identify the end of the lam in ar flow and the end of the transition reg ion .

It has a lready been stated above that an in c re a se of concentration

ra tio in c reases the value of n* and th is re su lts in an in c re a se of the c ritic a l

Reynolds num ber. This is only a p re lim inary conclusion . The values of

n ’ obtained from the data in th is study lie very close to each o ther and a

slight change of the slope of curves in F igure 9 can m ake them alm ost equal.

The slope of die lines can be changed slightly by jo in ing the data points in a

slightly d ifferent way. The sam e is tru e fo r the values of K '. Although

every effort was made while plotting these lines the p o ss ib ilitie s s till

e x is t. The values of the c ritic a l Reynolds num ber fo r each concentration

ra tio shows a slight delay in the tran sitio n p ro c e ss , but the values lie so

close to each other that it looks like that transition begins a lm ost a t the

sam e c ritic a l Reynolds num ber fo r each concentration r a t io .

The deviation from purely lam in ar o r s tream line motion has been

observed to occur a t Reynolds num ber as low as about 1000 for lam inar

37

flow (8). The form ation of tru ly p e rs is te n t eddies and substan tia l deviation

of the velocity profile from the parabola of the lam in a r region occurs ra th e r

suddenly over a narrow range of Reynolds num ber n e a r 2100. M etzner and

Reed in th e ir paper (8) show that the non-Newtonian d a ta should begin to

deviate appreciably from the lam inar f=64/Nre line a t approxim ately the

sam e ra tio of viscous sh ea r to in e rtia fo rces as do Newtonian data fo r

smooth pipes; nam ely a t C f=0.008. T here should be a n in c rease in the

transition Reynolds num ber ran g e . The breadth of the tran s itio n region

in c reases as n ’ d e c re a se s . It has been proposed a f te r co rre la tin g a ll l i t e r ­

a tu re data on non-Newtonian fluids that both Newtonian and non-Ne wtonian

fluids leave the region of stable s tream line flow when ff f i r s t drops to a

value of about 0 .008 o r less (8).

The data obtained from this study w ere a lm ost in agreem ent with

the above sta tem en t. The deviation from lam inar flow s ta r te d with the value

of Cf dropped below 0.00526 in the case of the two-phasie m ixture and 0.008

in the case of w a te r . In the case of w ater fo r which n*--l, the transition

region was from Reynolds num ber 1746 to 5136. When th e value of n' had

dropped to 0 .6 (in the case of the tw o-phase m ixture) th e transition region

was extended to 8400.

Com parison with Bingham p lastic model

The power law rheological model was adopted In a ll the above

analy sis , which was fa irly sa tisfac to ry as the curves off the ra te of sh ea r

38

and shear s tre s s w ere s tra ig h t lines (F igure 9). The s tra ig h t line (F igures

11, 12, and 13) extrapolated to non-zero values of sh e a r s tre s s a t ze ro

shear ra te like the yield s tre s s in a Bingham p lastic m a te r ia l . The

extrapolated data suggest that the value of yield s tre s s in c re a se s slightly

a s the concentration ra tio in c re a se s . At 5 p e r cent load fraction the ex trap o ­

lated value is 1.01225 x 10~4 psf, w hereas a t 10 p e r cen t and 15 p e r cent

-4load fraction the extrapolation in c reases to 1.1565 x 10 psf and 1.9275

-4x 10 p sf, fo r the Lucite beads.

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

The purpose of th is study was to observe how a tw o-phase m ixture

tran s is ted from lam inar to turbulent flow. This was done sa tisfac to rily

and the s ta r t and end of the transition region w ere v isu ally observed for

w ater and the Lucite tw o-phase m ix tu res .

Conclusions

The following conclusions can be drawn from the p re sen t study:

1. T ransition from lam inar to turbulent flow with tw o-phase m ix ­

tu re s was found to take place within a Reynolds num ber range h igher than

the Newtonian transition reg ion .

2 . The low er c ritic a l Reynolds num ber co rresponding to the onset

of turbulence appeared to in c rease with decreasing valuses of the flow

behavior index. At rd equal to 0 .6 the onset of turbulence was observed

at a Reynolds num ber of about 3040.

3 . The tran sitio n region was found to be extended with the d e c re a s ­

ing values of flow behavior index .

4 . No significant evidence of any difference betw een the transition

p rocess fo r the d ifferent concentrations of Lucite beads could be seen . This

39

40

was an indication that the transition p rocess was independent of the concen­

tra tion ra tio up to 15 p e r cent concentration of Lucite beads.

The above conclusions a re based on data taken with plain tap w ater

and Lucite s lu r r ie s .

Recom m endations

1 . Since the low er c ritic a l Reynolds num ber and the broadness

of the tran sitio n region in c reases with the decreasing values of n ', te s ts

should be run at d ifferent values of n ' than w ere covered by th is study to

fu r th e r investigate th is effect.

2 . A serious problem of plugging the flow control valves was

observed during experim ental runs of the tw o-phase m ixture . L a is was a

ve ry se rio u s p rob lem . Instrum entation should be built to avoid th is p ro b ­

lem . A p re ssu rized system with the flow con tro l by the regulation of p r e s ­

su re would be the one best suited for this purpose .

3 . In the end of th is study it was observed that an ordinary w ater

pump was not suited fo r pumping of the s lu r ry . Pump selection m ust be

m ade accord ing to the nature of the fluid to be pumped (see Appendix E

fo r com m ents on pump selection).

4 . A homogeneous solid phase m ust be used for fu rth er studies of

so lid -liqu id suspensions of non-Newtonian s lu r r ie s .

5 . Work in th is a rea needs to be extended into the high Reynolds

4number (> 1 0 ) turbulent reg ion .

APPENDIXES

APPENDIX A

ANALYSIS OF EXPERIMENTAL UNCERTAINTY

43

The table below shows the quantities m easured during the runs for

plain w ater, along with the estim ated uncertainty in the m easu rem en t. The

data for points 1 and 17, F igure 8, w ere selected fo r analysis to dem on­

s tra te how the uncertain ty fo r the plotted values of the friction fac to r varied

with increasing flow ra te s .

The v iscosity and density w ere taken from tables in S tree te r (12)

w here they a re given as functions of tem p era tu re . Since the undertainty in

the tem peratu re m easurem ent was - 0 .2 5 °F , the estim ated uncertain ties

for v iscosity and density a re based on the change in these quantities for a

- 0 .025°F change in tem p e ra tu re .

Quantity Magnitude U ncerta in tyPercentage of

U ncertainty

a p 0.6485 in . ± 0 .0 1 in . ± 1.54200

w 4.2500 lbm ± 0 .0 5 lbm ± 1.17647

t 62.7500 se c . ± 0 .1 0 s e c . ± 0 .15936

D 1.2500 in . ± 0 .0 1 in . ± 0.80000

L 26.4000 f t. ± 0 .0 4 f t. ±0.15152

e 62.2965 lbm/ f t 3 ±0.00156 lbm/ f t 3 ±0.002512

1.06775xl0~5 fth r

±0 .00344x l0"5 ft h r

±0.32217

Co 1.0402 gm /cc — 0.0001547 gm /cc ±0.01472

Point 1

Point 17

44

Quantity Magnitude U ncertaintyPercentage o Uncertainty

AP 12 „ 15 in . 0 .02 in . 0.16461

W 18.80 lbm 0.15 lbm 0.79787

t 62.00 s e c . 0 .10 s e c „ 0.16129

D 1.25 in . 0.01 in . 0.80000

L 26.40 f t . 0 .04 f t . 0.1515

Q 62.29465 iiA L ft?

0.00156 ^ ft3

0.00251

1.0402 gm /cc 0.0001547 gm /cc 0.01472

1.06775 ft2/h r 0.00344 ft2/h r 0.32217

The percentage of uncertain ty in the calculated values for the

friction facto r and fo r the Reynolds num ber can be estim ated as the sum

and the difference of the u ncerta in ties in the m easured data used to make

the ca lcu la tio n s .

Since Re = VD/^

it can a lso be stated as

Re = 4W/ -rc 9 i. t D

As m = w/t and V = riV £ A = 4 m / ^ D 2

then

S Re 6 W 2 _w ; ; ( f )2 -(Ai)2 (“ )2D 11/2

Re. - (I)

AP

W

t

D

L

Q

The percentage of uncertain ty in the friction fa c to r can be e s t i ­

mated in the sam e fashion.

t -- Ilf / (L /D ) ( V2/2g)

h ( = < ^ > < g o )

12

Finally ,

2 AP Co D g

L V2

2 AP eo D g T\?D2-------------------- ( - )

L 4m z

2 AP D g ( a ?D 2 t 2

L 4 W2

TTg Q nD3 Z t 22 W2

Then,

b f=v

6AP 2 — > 4

S?o ^^o

- / 2 $W .21 w ' ) i

U ncertainty in f.R e is given by

& (f .Re) f.R e

( 2 )

\.<t >2 4 <t t >2 ] 1 / 2 .......... <3>

Plugging in values in Equations (1), (2), and (3) re su lted in the estim ated

uncertain ties shown below .

45

46

Point Percentage of Percentage of Percentage ofNo. U ncertainty in f U ncertainty in Re Uncertainty in (f.Re)

1 ± 1.6485588 ± 0.784148 ± 1.825504

17 ± 1.8328830 ±0.230726 ±1.8328830

APPENDIX B

ANALYSIS OF UNCERTAINTY IN SPECIFIC

GRAVITY OF LUCITE BEADS

The table below shows the density of Lucite beads m easured in

the lab o ra to ry .

Reading D ensity gm /cc

1 1.12

2 1 .10

3 1.106

4 1.120

^L M = 4 .446 /4 = 1 .1115 g m s/c c

Reading ^ L " ?LM "di

1 0.0085 72 .20

2 -0.0115 132.20

3 -0.0055 30 .25

4 0.0085 72 .20

^ - k \ t ( ? lLi = l

- ?M)2] V 2

z]~ x 306.85 x 10"6J 1 /2

= (76.71 x 1 0 '6 ; 1/2

= 0.876 x 10~2

= 0.00876 gm s/cc

48

(1.1115 - 0.00876) g m /c c

1.1115 ! 0.79%

Percentage of uncertain ty = - 0.79%

^ M

or

49

APPENDIX C

ANALYSIS OF UNCERTAINTY IN SPECIFIC GRAVITY

OF MERIAM OIL

The table below shows the density of M eriam oil m easured in the

laboratory :

Reading z D ensity g m s /c

1 1.041660

2 1.043940

3 1.041660

4 1.038666

5 1.041660

?om = 5.20147/5 = 1.040294 g m /cc

Reading i = ^o ?om ( *o" ^om) x

1 0.00127 1 . 6 0

2 -0.00204 4.1610

3 0.00127 1.612

4 0.001728 2.98(0

5 -0.001270 1 .612

- [ - i t < i - m>T/2>- 1=1

= 0.0001547 gm /cc

0 ; 1.040294 - 0.0001547 gm /cc

o r 0 = 1.040294 - 0.01472 % gm /cc

Percentage of uncertain ty «= - 0.01472 %

51

APPENDIX D

SETTLING-VELOCITY OF LUCITE BEADS

53

The free settling velocity of a sm all p a rtic le can be obtained by a

force balance (3).

Dg * B - mg = 0

Ds ■* B = mg

G"^Ut r Q ■» 4/3 r Q3 ^ g = 4/3 r Q3 € sg

Ut = ^ r o ( ^ s" &

At 70°F

Qs = 1.1115 gm s/cc

eL = i .0000 g m s/cc

g = 980.0000 c m s/se c

yU= 1.0100 x 10~3 g m -se c /c m 3

o r 9 .9 x 10 3 d y n es-sec /cm 3

( 1 )

The average d iam eter of the p a rtic le = 0.006 inches

r Q = 3 x 10~3 inch

or r 0 = 7 .62 x 1 0 '3 cm

Plugging a ll these values in Equation (1), the settling velocity is

given by

ut = 0.1424 cm /sec

With th is value of te rm ina l velocity , the tim e requ ired fo r the

beads to settle down com pletely in the p lastic te st section is 22.3 s e c s .

54

Actual settling was m ore rapid than 22.3 se c . as a ll beads do not begin

a t the top of the tube . Thus those beads n ear the bottom of the pipe as

they en ter the te s t section settle out f i r s t .

APPENDIX E

COMMENTS ON PUMP SELECTION

56

Almost no inform ation is available in the l i te ra tu re on the s e le c ­

tion of pumps fo r non-Newtonian m a te r ia ls . The following inform ation

was obtained from R eference 1.

In pumping Bingham -plastic pseudoplastic , and thixotropic m a te ria ls ,

a centrifugal pump can be used . The head and efficiency as given for w ater

can be co rrec ted for m a te ria ls to be pumped by m eans of the head and

efficiency fa c to rs . T hese fac to rs a re given (11) as a fuinction of a pump

Reynolds num ber. This Reynolds num ber can be b ased on the density of the

m ixture and the turbulent v isco s ity . If the turbulent v isco sity has not been

determ ined, the coefficient of rig id ity fo r B ingham -plastics o r the lim iting

v iscosity , for pseudoplastics can be used . Open Im p e lle rs should be

employed where the p a rtic le size is large o r w here the p a r tic le s would tend

to plug the sm all passages in a closed im p e lle r. A cem trifugal pump p ro ­

duces high ra te s of sh ea r and thus reduces the v isco s ity of the m a te ria l, a

d esirab le resu lt from the pumping standpoint; how ever, degradation and

d ispersion of the p a rtic le s may take place and in some teases be u n d e s ir­

a b le . F o r these applications it may be p referab le to u se diaphragm pumps

vOi;, in some ca se s , piston pum ps. R o ta ry -g ear pumps cannot be used with

suspensions because of the rapid w e a r.

In pumping dilatan t m a te ria ls , it is n ecessa ry to use a slow-m oving

pump in o rd e r to keep the v iscosity as low as p o ss ib le . Pumps of this type

a re diaphragm , squeegee types, piston, and screw .

Blow cases can be used fo r any type of m a te r ia l . Agitation may

57

be requ ired for cases of rapidly settling so lid s . C are should be exercised

not to perm it a i r to en te r the line, a s it is very difficult to separa te the a ir

from p lastic and viscous m a te r ia ls .

APPENDIX F

TABULATION OF DATA

W ater (F igures 8 and 14)

55!

No. m

I o

'I l+

h f_ f.R e

1 0.04460 0.0260 0.07819 63.95909

2 0.05698 0.0336 0.06190 64.68873

3 0.06750 0.0400 0.05217 64.79361

4 0.09524 0.0560 0.03694 64.49027

5 0.09760 0.0570 0.03580 64.04620

6 0.11002 0.0700 0.03460 69.78820

7 0.14554 0.1060 0.02994 79.87014

8 0.15220 0.1160 0.02996 83.58840

9 0.15532 0.1200 0.02914 84.78854

10 0.16282 0.1380 0.03114 92.95290

11 0.17312 0.1460 0.03001 94.98730

12 0.18467 0.1760 0.03087 104.54095

13 0.18581 0.1800 0.03119 106.26542

14 0.19292 0.2220 0.03568 126.20016

15 0.24684 0.3400 0.03388 151.06269

16 0.29541 0.4800 0.03296 169.29202

17 0.30323 0.5100 0.03318 184.46614

60

5 Per cent Lucite S lurry by Weight (F igure 11)

No. m bf

1 0.0834 0.050

2 0.1030 0.056

3 0.1430 0.070

4 0.1600 0.072

5 0.1540 0.090

6 0.1632 0.110

7 0.1585 0.120

8 0.1630 0.130

9 0.1725 0.160

10 0.1915 0.200

11 0.1980 0.280

12 0.2970 0.480

13 0.300 0.540

10 Per Cent Lucite S lurry by Weight (F igure 12)

1 0.085 0.055

2 0.1025 0.0625

3 0.115 0.0670

4 0.1450 0.0800

5 0.1520 0.0900

6 0.1650 0.1015

61

No. m hfX

7 0.1675 0.1250

8 0.2075 0.2075

9 0.2325 0.2725

10 0.2575 0.3500

11 0.2887 0.4325

12 0.3050 0.4900

13 0.3250 0.5650

15 Per Cent Lucite S lurry by Weight (F igure 13)

1 0.0875 0.060

2 0.1175 0.070

3 0.1500 0.075

4 0.1675 0.100

5 0.2150 0.200

6 0.4525 0.530

5 Per Cent A .S .P . S lurry by Weight (F igure 16)

1 0.0233 0.03

2 0.0433 0.04

3 0.0733 0.05

4 0.1050 0.06

5 0.1300 0.12

6 0.1683 0.27

15 Per Cent Lucite S lurry by Weight (F igure 13)

5 Per Cent A .S .P . S lu rry by Weight (F igure 16)

62

No. m hf

7 0.2333 0.52

8 0.3067 0.76

7 .5 Per Cent A .S .P . S lurry by Weight (F igure 17)

1 0.0034 0.018

2 0.0082 0.021

3 0.0833 0.075

4 0.0902 0.080

5 0.1300 0.1080

6 0.1716 0.218

7 0.1883 0.32

8 0.1900 0.34

9 0.1983 0.37

10 0.2400 0.82

11 0.3233 1.5

12 0.400 1.885

9 Per Cent A .S .P . S lurry by Weight (F igure 18)

1 0.01166 0.022

2 0.0833 0.092

3 0.1266 0.130

4 0.1433 0.175

5 0.1766 0.520

7 .5 Per Cent A .S .P . S lurry by Weight (F igure 17)

9 Per Cent A .S .P . S lurry by Weight (F igure 18)

63

6 0.2400 1.04

7 0.246 1.10

8 0.366 1.81

No. m hf_

LIST OF REFERENCES

LIST OF REFERENCES

1. A lves, G. E . , and Boucher, D. E . "Pipeline Design fo r Non-NewtonianSolutions and Suspensions," Chem ical Engineering P ro g re ss , Vol.48 (1942), 385.

2 . Bates, L . D. "V isual Flow Loop Design fo r Particle-L aden F lu id s ."Unpublished M aste r 's p ro jec t, Brigham Young U niversity , 1970.

3 . Binder, R. C ., and Busher, J . E . "Turbulent Flow of Non-NewtonianS y s tem s," Journal of Applied M echanics, Vol. 13A (1946), 101.

4 . Brodkey, R . S . The Phenomena of Fluid M otions. Los A ngeles, C a li­fo rn ia; Addison-W elly Publishing Company, 1970.

5 . Dodge, D. W ., and M etzner, A . B. "Turbulent Flow of NonHMewtonianSystem s , " Journal A m erican institu te of Chem ical Engin e e r s , V o l.5 (1959), 189. “

6 . K rieg er, I . M ., and M ar on, S. H. Journal of Applied Phy sics , Vol. 23(1952), 147.

7 . McAdams, W. H. Heat T ra n sm iss io n . New York: McGraw Hill, 1964.

8. M etzner, A . B ., and Reed, J . C . "Flow of Non-Newtonian FluidsC orre la tion of the L am inar, T ransition , and Turbulent Flow R egion ,” Journal Am erican Institute of Chem ical Engineers, Vol. 5 (1955),434. ~~ —

9. Senecal, V . E ., and Rothfus, R . R. Chem ical Engineering P ro g ress ,V ol. 44 (1953), 537.

10. Skelland, A . H. P . Non-Newtonian Flow and Heat T ra n s fe r . New York:John Wiley and Sons, 1967.

11. Stepanoff, A . J. C entrifugal and Axial Flow Pum ps. New York: JohnWiley and Sons, 1948.

12. S tre e te r , V. L . Handbook of Fluid D ynam ics. New York: M cGraw-HillBook Company, 1961,

65

66

13. W eltmann, R . N . Industria l Engineering C h em istry , V ol. 48 (1956),386.

14. Winding. C . C .; Baumann, G. P .; and K ranich, W. L . Chem icalEngineering P ro g ress , Vol. 43 (1947), 527, 613.

TRANSITION FROM LAMINAR TO TURBULENT FLOW

FOR A TWO-PHASE MIXTURE

Mohammed Sharief Q ureshi

D epartm ent of M echanical Engineering Science

M . S. D egree, May 1971

ABSTRACT

T ransition from lam inar to turbulent flow fo r a tw o-phase m ixture was observed in a c lea r p lastic p ipe . Aluminum powder was used to make the flow p a tte rn s v is ib le .

The transition p ro cess fo r the tw o-phase m ixture was delayed over that of plain w ater and occurred over a w ider range of flow.

The low er c ritic a l Reynolds num ber as well as the length of die tran sitio n Reynolds num bers region appeared to increase with the decreasing value of the non-Newtonian flow behavior index. No significant difference in the c ritic a l Reynolds num ber for transition w as observed due to the increase of loading ra tio for the Lucite b ead s . T here was some change, however, with the aluminum silicate s lu rry loading.

COMMITTEE APPROVAL: