NON-INTRUSIVE CHARACTERIZATION OF HEAT TRANSFER FLUID

AEROSOL FORMATION

A Thesis

by

KIRAN KRISHNA

Submitted to the Office of Graduate Studies ofTexas A&M University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

May 2001

Major Subject: Chemical Engineering

NON-INTRUSIVE CHARACTERIZATION OF HEAT TRANSFER FLUID

AEROSOL FORMATION

A Thesis

by

KIRAN KRISHNA

Submitted to the Office of Graduate Studies ofTexas A&M University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

Approved as to style and content by:

M. Sam Mannan(Co-chair of Committee)

Kenneth D. Kihm(Co-chair of Committee)

Kenneth R. Hall(Member)

Rayford G. Anthony(Head of Department)

May 2001

Major Subject: Chemical Engineering

ABSTRACT

Non-Intrusive Characterization of Heat Transfer Fluid Aerosol Formation.

(May 2001)

Kiran Krishna, B.E., Bangalore University

Co-chairs of Advisory Committee: Dr. M. Sam MannanDr. Kenneth D. Kihm

Heat transfer fluids are widely used in the chemical process industry and are

available in a wide range of properties. These fluids are flammable above their flash

points and can cause explosions. Though the possibility of aerosol explosions has been

widely documented, knowledge about the explosive potential of such aerosols is limited

and critically needed. The aerosol droplet size distributions of heat transfer fluids must

be studied to characterize their explosion hazards.

This research involves non-intrusive measurement of such aerosol sprays using a

Malvern Instrument Diffraction Particle Analyzer. The aerosol is generated by plain

orifice atomization to simulate the formation and dispersion of heat transfer fluid

aerosols through leaks in process equipment. Predictive models relating the aerosol

formation distances, aerosol droplet size, and volume concentrations to bulk liquid

pressure, temperature, fluid properties, leak size and ambient conditions are developed.

These models will be used to predict the conditions under which leaks will result in the

formation of aerosols and ultimately help in estimating the explosion hazard of heat

transfer fluid aerosols. The goal is to provide industry information that will help

improve process safety.

DEDICATION

To my parents, Christine and E.R. Krishna and my sister Radhika,

for all their love, encouragement and support.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my advisor Dr. Sam Mannan for

all his guidance and unwavering belief in me. I am truly grateful to Dr. Ken Kihm for

his indispensable advice and support. I would like to thank Dr. Ken Hall for serving on

my committee. This work would not have been completed without all the help and

encouragement I received from Dr. William Rogers. I owe a lot to my brilliant

teammates Passaporn Sukmarg and Tae-Kyun Kim, as well as Randy Marek. Finally, I

would like to thank my parents, my sister, and all my friends for their love and support.

TABLE OF CONTENTS

Page

ABSTRACT………………………………………………………………………… iii

DEDICATION……………………………………………………………………… iv

ACKNOWLEDGEMENTS………………………………………………………… v

TABLE OF CONTENTS…………………………………………………………… vi

LIST OF TABLES………………………………………………………………….. viii

LIST OF FIGURES………………………………………………………………… ix

LIST OF SYMBOLS……………………………………………………………….. xi

LIST OF ABBREVIATIONS………………………………………………………. xiii

CHAPTER

I INTRODUCTION…………………………………………………….. 1

Aerosols and Atomization..........……………………………………... 3Literature Review……………………………………………………... 6

II EXPERIMENTAL METHODOLOGY………………………………. 9

Experimental Apparatus.…………………………………………....... 9Fluid Cell and Delivery System………………………………... 9Spray Collection and Exhaust System………………………… 11The Malvern Laser Diffraction Particle Analyzer...................…. 12

Apparatus Calibration and Estimated Experimental Errors.......……… 17Malvern Laser .........................................………………. 17Pressure Transducer...................................................................... 18Thermocouples.............................................................................. 19Orifice.............………………………………………………….. 19

Measurement Procedure...…………………………………………….. 19III EXPERIMENTAL RESULTS………………………………………… 21

Method of Analysis................................................................................ 21Effect of Injection Pressure.................................................................... 30Effect of Fluid Injection Temperature.................................................... 34Effect of Orifice Size.............................................................................. 38

CHAPTER Page

IV MODELING...................................…………………………………… 41

Dimensional Analysis............................................................................. 45Properties and Data................................................................................ 50Existing Correlations.............................................................................. 52Regression Analysis............................................................................... 56Correlations and Predictions.................................................................. 58Correlation Validation............................................................................ 60

Influence of Liquid Viscosity........................................................ 60Influence of Surface Tension......................................................... 61Influence of Liquid Density............................................................ 61Influence of Liquid Velocity........................................................... 61Influence of Orifice Size............................................................... 61

V CONCLUSIONS AND RECOMMENDATIONS………………….... 63

Summary........................................................………………………… 63Implications for Process Safety..........………………………………… 64Recommendations…..………………………………………………… 65

LITERATURE CITED……………………………………………………………... 66

APPENDIX

A EXPERIMENTAL DATASHEETS………………………………….. 69

B PRESSURE TRANSDUCER CALIBRATION……………………… 86

C THERMOCOUPLE CALIBRATION………………………………… 89

D EXPERIMENTAL PROCEDURE……………………………………. 91

E HEAT TRANSFER FLUID PROPERTIES........................................... 94

F COEFFICIENT OF DISCHARGE......................................................... 97

G AEROSOL FORMATION DISTANCES.............................................. 100

VITA………………………………………………………………………………... 103

LIST OF TABLES

TABLE Page

II-1 Interpretation of Log. Diff number………………………………….…. 16

IV-1 Mean Drop Diameters..................................................……………….... 42

IV-2 Drop size correlations for plain-orifice atomizers........…………...……. 52

IV-3 Break up length correlations for plain-orifice atomizers.......................... 55

IV-4 Values of constants obtained from the regression analysis...................... 57

LIST OF FIGURES

FIGURE PageI-1 Flammability diagram at a fixed pressure…………………..………... 2

I-2 Disintegration of a cylindrical stream of liquid by (a) axisymmetricwaves; (b) asymmetric waves; (c) aerodynamic forces........................ 4

II-1 Schematic of the experimental apparatus..…………………………... 10

II-2 Diffraction particle analyzer to measure drop sizes andconcentrations…………………...........................................................

12

II-3 The Fraunhofer diffraction pattern of a single slit..………………….. 13

III-1 Light intensity plot for the undeveloped region..……………………. 22

III-2 Histogram for the undeveloped region of the spray…………………. 23

III-3 Light intensity plot for the fully atomized region……………………. 24

III-4 Histogram for the fully atomized region.............................................. 25

III-5 Light intensity plot showing the effect of beam steering……..……... 28

III-6 Histogram showing the effect of beam steering.....………………….. 29

III-7 Effect of pressure on atomization: SMD (Alkylated aromatic, 120°C, orifice diameter of 0.33 mm)……………………………….……. 31

III-8 Effect of pressure on atomization: Volume concentration (Alkylatedaromatic, 120 °C, orifice diameter of 0.33 mm)……………………... 32

III-9 Effect of pressure on atomization: SMD (Modified terphenyl, 120°C, orifice diameter of 0.33 mm)……………………………….……. 33

III-10 Effect of pressure on atomization: Volume concentration (Modifiedterphenyl, 120 °C, orifice diameter of 0.33 mm)…………………….. 33

III-11 Effect of temperature on atomization: SMD (Alkylated aromatic,300 psia, orifice diameter of 0.33 mm)................................................. 35

FIGURE Page

III-12 Effect of temperature on atomization: SMD with function kill data(Alkylated aromatic, 300 psia, orifice diameter of 0.33 mm)………... 35

III-13 Effect of temperature on atomization: Volume concentration(Alkylated aromatic, 300 psia, orifice diameter of 0.33 mm)……...… 36

III-14 Effect of temperature on atomization: SMD (Modified terphenyl,300 psia, orifice diameter of 0.33 mm)................................................ 36

III-15 Effect of temperature on atomization: Volume concentration(Modified terphenyl, 300 psia, orifice diameter of 0.33 mm).............. 37

III-16 Effect of orifice size on atomization: SMD (Alkylated aromatic, 300psia, 120 °C)......................................................................................... 39

III-17 Effect of orifice size on atomization: Volume concentration(Alkylated aromatic,300 psia, 120 °C)................................................. 39

III-18 Effect of orifice size on atomization: SMD (Modified terphenyl, 300psia, 120 °C)......................................................................................... 40

III-19 Effect of orifice size on atomization: Volume concentration(Modified terphenyl, 300 psia, 120 °C)................................................ 40

IV-1 Comparison of the predicted and measured values of SMD forexisting correlations.............................................................................. 54

IV-2 Comparison of the aerosol formation distances measured and thepredicted break up lengths.................................................................... 56

IV-3 Comparison of the experimental and predicted values of SMD........... 58

IV-4 Comparison of the experimental and predicted values of the aerosolformation distance................................................................................. 59

IV-5 Comparison of the experimental and predicted values of the volumeconcentration of the aerosol in air......................................................... 60

LIST OF SYMBOLS

CD Discharge coefficient

d Jet or stream diameter

d0 Orifice diameter

Es Potential surface energy

F The focal length of the lens L2

g Acceleration due to gravity, m/s2

I Light intensityI0 Light intensity at the center of the pattern

J1 The first-order spherical Bessel function

Jo The zero-order spherical Bessel function

l Length of a stream segment, m

L Light intensity

LB Break up length

Lf Aerosol formation distence

md Mass of a drop, kg

P Pressure, N/m2

Pa Pressure of air, N/m2

Pi Pressure inside a drop, N/m2

Q Volumetric flow rate, m3/s

q Potential growth rate of the disturbance

r Spherical droplet radius

s Radial distance in the detection plane measured from the optical axis

V Velocity of the liquid stream, m/s

Π Dimensionless group

σ Surface tension, kg/s2

ρa Density of air, kg/m3

ρG Density of gas, kg/m3

ρL Density of the liquid, kg/m3

µL Dynamic viscosity of liquid, kg/m s

µG Gas (air) viscosity, kg/m s

ν Kinematic viscosity, m2/s

LIST OF ABBREVIATIONS

cm centimeter

Lp Laplace number

m meter

mW milliwatt

nm nanometer

mL milliliter

Re Reynolds number

SMD Sauter mean diameter

We Weber number

HTF Heat transfer fluid

CHAPTER I

INTRODUCTION

Accidents in the chemical industry almost always result in the loss of

containment. Escaping fluids are released into the surrounding in the form of a liquid or

vapor or both. Liquid releases, depending on the conditions, may atomize to form an

aerosol, which is a dispersion of liquid droplets in air. These droplets have the potential

to be dispersed over a larger area than the bulk liquid. A potential problem arises when

a combustible liquid is atomized. It is a common misconception that flammable liquids

are safe below their flash points. Aerosols of flammable liquids at temperatures well

below their flash points can be as explosive as vapor-air mixtures.

Heat transfer fluids (HTFs) are high flash point synthetic liquids that are

omnipresent in the chemical process industry and are available in a wide range of

properties and used over a wide range of conditions. HTFs are generally considered

benign below their flash points, but they are used at high pressures and have the

potential to form aerosols upon leaking.

__________

This thesis conforms to the style and format of the AIChE Journal.

Figure I-1. Flammability diagram at a fixed pressure (Eichhorn, 1955)

Jacob Eichhorn (1955) brought out the distinction between vapor and aerosol

flammability and recognized the fact that aerosols could explode. Figure I-1 is a

conceptual diagram introduced by Eichhorn, indicating the flammability region

bounded by solid lines that represent the upper and lower vapor flammability limits.

These limits are well known and are determined by standardized testing methods. The

mist flammability region to the left of the dew point curve below the flash point, has

been depicted by fuzzy boundaries. This is because aerosol flammability limits are

unknown and have not yet been established. Data on the upper and lower flammability

limits in the vapor region are well established and are used as criteria in the design of

processes. However, due to lack of data, aerosol flammability is generally neglected,

sometimes with devastating consequences.

Factory Mutual Engineering and Research (FME&R) statistics for a recent ten

year period shows 54 fires and explosions involving HTFs, resulting in $150 million in

losses. A large number of these resulted in fires but it is the explosions that caused

larger monetary losses. One such recent incident directly attributed to a HTF aerosol

explosion resulting in a $500,000 loss (Febo and Valiulis, 1995).

Aerosols have a larger surface to volume ratio than bulk liquids. As a result, heat

and mass transfer rates are much higher. Therefore an ignition source can rapidly heat

the droplet to its flash point, initiating a fire or an explosion (Laster and Annamalai,

1989). The reason for the severity of aerosol fires or explosions is that the liquid

droplets have a larger enthalpy per unit volume that the vapor. Aerosols, upon release

can rapidly fill up an entire room, thereby creating a large flammable volume.

The main processes associated with the formation of aerosols from leaks are not

well documented and there is a lack of knowledge about the droplet sizes that result

from a leakage under various conditions, from a process safety perspective. This

information is critically needed, to study aerosol flammability and to develop

preventative measures to improve process safety in chemical industries.

Aerosols and Atomization

The process by which a liquid stream disintegrates into an aerosol is known as

atomization, which is the subject of extensive literature. Bayvel and Orzechowski

(1993), for example, provide a summary of the existing theory on the stability and

disintegration of liquid streams. However, since atomization is a random process, no

fundamentally theoretical approach is able to answer all the questions regarding

atomization (Faeth, 1987, 1990).

The velocity of the liquid stream discharged from a nozzle largely defines the

process of disintegration. Three characteristic types of disintegration have been

proposed based on the cause: axisymmetric waves, asymmetric waves, and aerodynamic

forces. Figure I-2 shows the disintegration of a liquid stream by each of these causes.

FIGURE I-2. Disintegration of a cylindrical stream of liquid by (a) axisymmetric

waves; (b) asymmetric waves; (c) aerodynamic forces

(Bayvel and Orzechowski, 1993)

These three regimes describe an increasing order of velocity. At low velocities

of the order of 1 m/s, axisymmetric waves are created by internal disturbances that

create alternating contractions and expansions of the liquid stream. Applying a force

balance:

d1lP1 = 2lσ (I-1)

d2lP2 = 2lσ (I-2)

where l is the length of the cylindrical section under consideration shown in Figure I-2

and σ is the surface tension. Hence

P1 = (d1/d2)P2 (I-3)

Thus we see that P1 > P2, since d1 > d2. The liquid therefore forces its way from

the narrower band into the wider bands, which leads to breakaway of the stream into

drops. Surface tension is the only governing force in this regime.

Now as we increase the velocity of the liquid stream, the increasing

aerodynamic forces distort the axis of the stream to form an asymmetric wave. The

differential air acceleration at the concavities and the convexities generates a negative

pressure over the convexities and an overpressure at the concavities. The jet, under the

influence of increasing differential pressure, disintegrates into relatively smaller

segments or drops.

When the velocity of the liquid drop is increased further, we see an

intensification of the atomization process, an increase in the randomness of the breakup

process, and the formation of three fairly distinguishable zones: AB represents the

compact stream zone, where the vibrations begin to develop. BC is the disintegration

zone, where the stream first breaks up into non-spherical segments known as ligaments

(Ruff et al., 1989). These ligaments undergo further breakup and reformation until

spherical droplets are formed. The fully atomized zone, CD, is where we observe only

spherical droplets.

Although descriptively the process of mechanical break-up of the liquid stream

into aerosol is known, there is scarce knowledge about the formation of aerosols from

leaking high flash point hydrocarbons such as HTFs. There is a need to develop

functional relationships between the operating conditions of the process, i.e., the

injection conditions, and the properties of the resulting atomized liquid. The important

parameters for the resulting aerosol leak are its formation distance, drop size

distribution, and volume concentration.

One goal of this research is the development of empirical models to relate the

operating conditions and liquid properties and to characterize the atomization process of

HTFs. The non-intrusive laser diffraction particle analysis (LDPA) technique using a

Malvern Laser will form the basis of the experimental data generation.

Literature Review

As mentioned earlier, Eichhorn (1955) introduced the concept of the aerosol

flammability region and stressed the importance of the droplet diameter in the analysis

of the potential hazard. Vincent and Howard (1976) and Vincent et al. (1976) studied

the use of suppression systems while discussing the hazards posed by heat transfer

media with regard to aerosol explosions. They indicated that instead of explosion

suppression, a less expensive alternative involving early detection and abatement of

leaks was critical. More information about the atomization process was needed to define

a source term for leaking streams forming aerosols. Schmidli et al. (1990) also arrived

at a similar conclusion while questioning assumptions about the drop size distributions

that were being used, namely that they were log-normally distributed.

Richer et al. (1994) attempted to arrive at a source term and studied the

atomization process with regard to water and kerosene. They demonstrated the effects

of nozzle size and geometry, spray duration, and liquid properties on the transient

behavior of aerosols in a confined space. They, however, did not try to describe the

atomization process. Watson and Tech (1985) also examined the transient aerosol

behavior.

Bowen and Shrivill (1994) studied the ignition characteristics of aerosols to

describe the combustion hazards posed by pressurized atomization. They concluded that

the combustion hazard is dominated by the effect of the aerosol droplet size, which

affects all the associated processes from the dispersion characteristics to the ignition

energies.

Some work that recognized the explosion hazards of aerosols had been done

before Febo and Valiulis (1995) gave a monetary estimate of the loss incurred.

However, most work had arrived at the same conclusion: we need to relate aerosol

formation and properties to the causative operating conditions (Johnson, 1991). This

task is an exhaustive process because atomization, being a random process, is fluid and

condition specific. Aerosol explosions have also been a problem for forensic

investigators. Sehgal et al. (1999) have discussed a case where an aerosol explosion

could have been the cause for an accident but a lack of data prevents any definite

conclusions.

To resolve this problem, lessons can be applied from the field of fuel

combustion, where the atomization process is well established for fuels. Elkotb (1982)

provided an extensive study of aerosol spray modeling for fuels. He used dimensional

analysis, to obtain an empirical correlation of the aerosol drop diameter with the

operating conditions and the fluid properties. Hiroyasu (1991) studied the drop size

distribution in diesel combustion chambers and also used dimensional analysis to

generate an empirical model.

To effectively study the process of atomization, the adopted analysis must be

non-intrusive, because of the nature of a developing spray. The use of optical

techniques has been well established in this regard. Bayvel and Orzechowski (1993)

have listed the various optical techniques used in spray characterization. One such

technique, the of Fraunhofer laser diffraction, has been discussed by Felton (1981),

Kihm and Chigier (1991), Kihm et al. (1994), Park et al. (1996), and Son and Kihm

(1998).

CHAPTER II

EXPERIMENTAL METHODOLOGY

The objective of this research is to study the atomization characteristics of heat

transfer fluids. The focus will be on the formation distances, drop size distributions and

volume concentrations of the aerosols created by plain orifice atomization to emulate a

leak in a process system. An experimental approach will depend on the Malvern Laser

Diffraction Particle Analyzer for a non-intrusive analysis technique. This chapter

includes a description of the experimental apparatus, apparatus calibration,

measurement procedure and estimated experimental errors.

Experimental Apparatus

Figure II-1 shows a schematic of the experimental arrangement, which consists

of a pressurized fluid cell and delivery system, a spray collection and exhaust system,

and the Malvern Laser Diffraction Particle Analyzer.

Fluid Cell and Delivery System

The HTF is pressurized in a 5.9 liter aluminum fluid cell capable of working at a

pressure of 2216 psia. The cell has an internal diameter of 17 cm, a height of 36 cm, and

a single port through which is connected the delivery line. The port has an annular

manifold of tubing inserted in it. The sample liquid inlet and nitrogen inlet for

MalvernReceiver

MalvernLaser

Fluid Cell

Nitrogen Tank

ExplosionProof Blower

CollectionChamber

StorageVessel

Mist Separator

Computer

Printer

Orifice

Figure II-1. Schematic of the experimental apparatus

pressurization utilizes the annular region of the manifold. The delivery line to the nozzle

is a 0.9375 cm (3/8 inch) inside diameter, flexible metal hose (model: SS-6BHT-36)

from Swagelok. It makes two right angles to align the spray in a vertically downward

direction. The nozzles were made from brass plugs (from Swagelok) because brass,

being softer than steel, is easier to drill. Various sizes of simple circular holes were

drilled into from plain orifice nozzles. The pressure transducer and thermocouple were

calibrated and installed close to the nozzle for accurate measurements of the liquid

exiting the nozzle. The pressure transducer from Sensotek (model: TJE/0713-18TJA)

has a pressure range of 3550 kPa (500 psia) with a power supply of 10.0 volt. The

transducer was supplied by a step down transformer (model: LMC-0-32) from Lambda

Electronics Corporation and read by a Keithley voltmeter (model: 181

NANOVOLTMETER).

The vent line includes a pressure relief valve from Swagelok installed in it to

prevent overpressures. The nitrogen line also included a 2000 psi Bourdon pressure

gauge to measure pressure in the fluid cell. A K-type thermocouple from Omega

records the temperature in the fluid cell. The fluid cell is heated using two strip heaters

from Omega. The nozzle and delivery line was also heated using a similar strip heater.

A K-type thermocouple is placed in contact with each heater and in a control circuit

with temperature controllers (model: CN76000) from Omega. The thermocouples to

measure nozzle temperature, cell temperature and air temperature are all connected to a

temperature indicator (model: DP80) from Omega.

The fluid cell is fixed to a positioning system composed of two optical rails

fixed at right angles to each other. The fluid cell is connected to the rails by means of an

insulating base plate and a pulley system for vertical movement.

Spray Collection and Exhaust System

The system consists of a Plexiglas collection unit, which is connected at the

bottom to a drum to collect the used HTF. The aerosol and vapor are evacuated from the

lab using a 1 HP explosion proof blower (model: PW11) from Madison Manufacturing

Company. In line with the blower is a mist separator, which removes fine liquid

droplets from the exhaust. It consists of a fine polyester felt filter that was capable of

removing droplets as small as 5 micron. The mist separator is connected to the

collection chamber using an anti-static rubber hose, to prevent static electricity from

providing an ignition source for the fine aerosol droplets.

The Malvern Laser Diffraction Particle Analyzer

Figure II-2. Diffraction particle analyzer to measure drop sizes and concentrations

(Malvern Laser Manual, 1993)

The Malvern laser system consists of a 2 mW Helium-Neon laser tube and a

detector with an array of concentric photosensitive ring diodes. The laser beam is a

collimated monochromatic beam of wavelength 780-662 mm and 1.8 mm in diameter.

When the aerosol droplets pass through the beam, they diffract the light by amounts

inversely proportional to their diameter. The diffracted light falls on 31 concentric ring

diodes in the detector with each ring detecting a certain size range of droplets. The light

intensities on each of these diodes are converted into drop size data by the computer. A

schematic of the diffracted light is shown in Figure II-2.

Figure II-3. The Fraunhofer diffraction pattern of a single slit (Airy function)

(Hecht, 1998)

The light intensity of a diffraction pattern for a spherical droplet of radius r is

described by the well-known Airy function, which is shown in Figure II-3:

21

0

)(2

=

xxJ

II (II-1)

where I0 is the intensity at the center diode, J1 is the first-order spherical Bessel

function, and x is given by

Frs

xλπ2

= (II-2)

where s is the radial distance in the detection plane measured from the optical axis and

F is the focal length of the lens.

By integrating equation (II-1) we obtain the fraction of light energy, L,

contained within a circle of radius s on the detector plane.

( ) ( )xJxJL 21

201 −−= (II-3)

where J0 is the zero-order spherical Bessel function.

For the series of detector rings in the Malvern system, the light energy incident

between the radii s1 and s2, due to a single droplet of radius r is

( ) ( )[ ] ( ) ( )[ ]2

21

201

21

20

22,1 ssss xJxJxJxJrCL +−+= π (II-4)

where C is an optical constant based on the power of the light source and the detector

sensitivity.

Therefore for N droplets of radius r, neglecting multiple diffraction, we have

( ) ( )[ ] ( ) ( )[ ] }{ 221

201

21

20

2

12,1 siisiii

M

iiss xJxJxJxJrNCL +−+= ∑

=

π (II-5)

where the size distribution consists of M size classes.

Writing equation (II-5) in terms of the mass of the droplet, W, assuming droplet

density is independent of size, we get

( ) ( )[ ] ( ) ( )[ ] }{ 221

201

21

20

12,1 siisii

M

i i

iss xJxJxJxJ

rW

KL +−+= ∑=

(II-6)

where K contains the optical constant and the density and

ρπ 343rW

N ii = (II-7)

The procedure for obtaining weight distribution uses the iterative least-square

method. The initial values of the 31 W values are estimated using a Rosen-Rammler

distribution. These initial estimates are then used to calculate 31 expected values of the

light intensity L, which then compared with the measured L values, and the least-square

error is calculated. A number of iterations are performed until the least-square error has

been minimized.

The Rosen-Rammler distribution (1933), is the simplest model and agrees well

with experimental data. It is represented by the following equation

dxXx

Xx

ndWn

n

n

−

=

−

exp1

(II-8)

where n and X are moment parameters of the Rosen-Rammler distribution function.

The accuracy of the Malvern data with the Rosen-Rammler model is provided

by the function Log. Diff., which is interpreted in Table II-1.

Table II-1. Interpretation of Log. Diff number (Malvern Laser Manual, 1993)

Log. Diff Interpretation

Log. Diff > 6 Model not appropriate or experiment incorrectly

performed.

5.5 < Log. Diff > 6 Poor fit. May be adequate for trend analysis only.

5 < Log. Diff > 5.5 Adequate fit but look for evidence of systematic

misfitting.

5 < Log. Diff > 4 Good fit. Well-presented sample.

Log. Diff < 4 Very unlikely with measured data but normal with

analytic data.

Though Fraunhofer diffraction and the Malvern system provide a useful,

versatile and non-intrusive method of droplet sizing, it is important to know the

limitations of this technique. Barth (1984) has listed the limitations and recommends

that the user know the level of compromise acceptable to his or her application.

Fraunhofer diffraction theory is applicable to droplets above 10 micron. Below

this size the errors may be unacceptably large. Multiple scattering at high spray

concentrations will cause the reported drop sizes to be biased towards the smaller drop

size ranges. Another common problem is vignetting, where the droplets are too far from

the receiving lens and the diffracted light is cut-off by the receiving lens’ finite aperture

(Wild and Swithenbank, 1986; Hamidi and Swithenbank, 1986b). This result biases the

measurements the larger sizes. When large amounts of vapor are present in the laser’s

path, significant refraction of the laser light, due to variations in the density along its

trail, causes the laser light to impinge on the rings closest to the central diode, and bias

the measurements to higher droplet sizes (Miles et al., 1989).

Apparatus Calibration and Estimated Experimental Errors

Calibration of the equipment is necessary to ensure accuracy and knowledge of

errors incurred during measurement. For this purpose, the thermocouples, pressure

transducer and the Malvern were calibrated.

Malvern Laser

The alignment of the Malvern laser is critical to the operating accuracy of the

droplet measurement system. The laser must be aligned to ensure that the maximum

intensity of light is incident upon the central diode. The receiver’s pinhole is adjusted to

ensure this. In the absence of droplets the light incident on the ring diodes nearest to the

central diode must be as low as possible: ideally zero. The remaining step of the

calibration is performed using a standardized reticle, which consists of a prepared

particle distribution on an optical plate, where the size of each particle was determined

using electron microscopy and the mean diameter then calculated. The reticle used in

this research has a reported distribution of 46.5 ± 4.7 micron and during calibration,

only values in this range were accepted. The calibration of the Malvern was repeated

every day.

Pressure Transducer

The pressure transducer readings are obtained as a ratio of the transducer output

to the input voltages, which are measured with a DC voltmeter. The pressure transducer

was calibrated against the atmospheric pressure using a dead weight pressure gauge.

The transducer was connected in parallel with the dead weight gauge and a regulated

compressed nitrogen cylinder was used as a pressure source. A variable volume also

was connected in parallel to adjust for any pressure fluctuations. The value for local

atmospheric pressure on that day was obtained from the Department of Meteorology at

Texas A&M University. The ratios of the output to input voltages were then plotted

against the absolute pressure, For both increasing and decreasing pressure tracking to

account for hysterisis. Appendix B contains the pressure calibration data for the

Sensotek pressure transducer.

The total uncertainty of the pressure transducer data is a sum of the following

1. The uncertainty of the dead-weight gauge: < 0.0100 psia

2. The Sensotek pressure transducer error: ± 0.25 psia

3. The error of fit: < 0.01 psia

4. The error in the reported local atmospheric pressure: ± 0.1 psia

Therefore the total uncertainty in the pressure data is taken as ± 0.37 psia.

Thermocouples

The thermocouples measuring the nozzle, fluid cell, and air temperatures were

all factory calibrated and reported maximum departures of + 1.5 °C and –1.11 °C over a

temperature range of 0 °C to 419 °C. The calibration data is provided in Appendix C.

Hence the total uncertainty associated with the temperature data is taken as + 1.5

°C and –1.11 °C.

Orifice

For the orifices, the total uncertainty is the sum of the following

1. Drill tolerance: ± 0.0051

2. Drill measurement: ± 0.0051

3. Hole drilling error: + 0.0051

Hence the total uncertainty of the orifice is +0.015 mm, -0.010 mm. Therefore, the

use of two decimal places in reporting orifice sizes is acceptable.

Measurement Procedure

The HTF is transferred to the aluminum fluid cell to a volume not exceeding

70% of its capacity. This is the safe limit calculated form the coefficients of thermal

expansion of the HTFs tested. The HTF is then heated to the required test temperature.

Pressurized nitrogen through a regulator was used to attain the required injection

pressure. Once the fluid cell temperature and pressure are stable at the set values, the

system is ready for testing. Before starting, the exhaust system is switched on and the

main lights turned off. During any laser measurements care is taken to ensure that the

room is devoid of any light source. The step-by-step experimental procedure is listed

in Appendix D.

CHAPTER III

EXPERIMENTAL RESULTS

The focus of this research was to emulate the fo rmation of an aerosol from a

HTF leak in an industrial process and to study the effects on the fluid atomization of the

process operating conditions and the leak size. The process conditions studied were the

HTF temperature and pressure along with the leak size. A qualitative analysis based on

similar studies was done by Sukmarg (2000) and the results in this research display

similar trends.

The study here includes two HTFs: an alkylated aromatic mixture and a

modified terphenyl mixture. A summary of the physical properties of these HTFs is

provided in Appendix E.

In this chapter the effects of pressure, temperature and orifice size on the aerosol

formation distance, the mean drop size, and the volume concentration of aerosol is

analyzed.

Method of Analysis

The Malvern Laser Diffraction Particle Analyzer system (Malvern) detects the

light intensity on the ring diodes, converts it into a histogram of the drop size

distribution, and generates a large array of statistical data. From each of these stages,

information about the atomization process is available.

As mentioned in Chapter 1, the spray can be divided into three zones: the

compact stream zone, the disintegration zone, and the fully atomized zone. The aerosol

formation region extends from the nozzle to the onset of the fully atomized region. This

undeveloped region, comprised of the compact stream zone and the disintegration zone,

represents the region where spherical droplets are in a minority.

Figure III-1. Light intensity plot for the undeveloped region

Since the Malvern analysis assumes that all diffraction is a result of spherical

droplets, the output data in this region will not be an accurate representation of the true

physical picture. The Malvern sees the liquid stream and ligaments as large spherical

drops and hence gives a very high mean droplet diameter as its output. This result can

be clearly seen on the light intensity curve, where a high intensity is observed from the

first two ring diodes, as shown in Figure III-1. This result is seen also in the drop size

distribution histogram, where an incomplete bell-shaped curve is biased towards the

higher drop sizes, as shown in Figure III-2.

Figure III-2. Histogram for the undeveloped region of the spray

The fully atomized zone is composed of a majority of spherical droplets and

hence is detected as a mono-modal distribution on the light intensity curve and a

complete bell shaped drop size distribution histogram. Figures III-3 and III-4 show the

light intensity and drop size distribution histogram, for the fully atomized region,

respectively.

Figure III-3. Light intensity plot for the fully atomized region

Figure III-4. Histogram for the fully atomized region

The aerosol formation distance is determined by analyzing the light intensity

plots and drop size distribution histograms at each measurement distance. The transition

between the stream disintegration and the fully atomized zone is not distinct, but it can

be approximated. In general, measurements were made at 5 cm intervals and the

uncertainty about the aerosol formation distance is estimated to be ± 5 cm.

The characteristic parameter used to represent the mean drop size of the spray

was the Sauter Mean Diameter (SMD). The definition of SMD and the advantage of

selecting it is discussed in Chapter IV. From the analysis of data at various conditions, it

was found that the SMD tends to remain fairly constant in the fully atomized zone. This

constancy can provide a quick estimate of the aerosol formation distance, but results

must be confirmed from the histograms and the light intensity plots.

The other parameter that was used to determine the reliability of the data with

respect to the Rosen Rammler distribution was Log. Diff. The criteria for the

interpreting the Log. Diff. values are provided in Table II-1 of Chapter II. This

differentiation between the regimes of atomization is very important in selecting which

data for modeling the atomization process.

The validity of data is affected not only by the atomization regime but also by

two other scenarios: high obscuration values and presence of significant amounts of

HTF vapor.

Obscuration is defined as the ratio of light diffracted to the light emitted and is

calculated as

laserthebyemittedLightdiodecentraltheonincidentLight

nObscuratio −=1 (III-1)

When the obscuration is very high, there are a large number of droplets

intersecting the laser. The highest accuracy of results is obtained for obscurations

between 10% and 30%. The accuracy at about 50% is acceptable but beyond 50% the

Malvern tends to yield results that are significantly biased towards the lower drop sizes.

This tendency has been explained by Hamidi and Swithenbank (1986a) as resulting

from multiple scattering. At the higher obscurations, because of an abundance of

droplets, the probability of a light ray being diffracted by more than one droplet is high.

This multiple diffraction leads to an increase in the diffraction angle and the light falling

on the outer rings. The Malvern interprets this to represent a smaller drop, thereby

biasing the results to indicate a smaller SMD. The Malvern system has utilized a

method of correction for high obscurations developed by Hamidi and Swithenbank

(1996a) to deal with this. This correction was applied to the analysis in this work by

using the correct on function, which applies the correction to all cases where the

obscuration exceeds 50%.

The other phenomenon that can compromise the reliability of the results is the

presence of significant quantities of HTF vapor. HTF vapor is generally present at all

injection temperatures and pressures. However as the temperature is raised closer to the

flash point, the increased vapor causes significant laser beam refraction, which is known

as beam steering. The refracted beam impinges on the rings close to the central diode.

The Malvern interprets this light intensity as the contribution of large drops and biases

the results towards higher drop sizes. Figures III-5 and III-6 display the effect of beam

steering on the light intensity and drop size histogram.

Figure III-5. Light intensity plot showing the effect of beam steering

Figure III-6. Histogram showing the effect of beam steering

The results, in this case, can be recalculated by omitting the first ring diode from

the calculations using the kill data function. This method is only an approximate

solution to the effect of beam steering, because the contribution of the first ring to the

true SMD is not known. Hence, SMD obtained by this method may be underestimated

and should not be considered truly representative.

The volume concentrations too, must be treated in a similar manner. Only

volume concentrations in the fully atomized zone, with no significant beam steering, are

truly representative of reality.

These were the salient features of the analysis used for the reported data. High-

speed digital photography was used also to confirm the data analysis. The effects of

pressure, temperature, and orifice size on the atomization process with respect to each

of the HTFs tested are discussed below.

Effect of Injection Pressure

The effect of pressure on atomization was studied at three pressures: 1034 kPa

(150 psia), 2067 kPa (300 psia), and 3446 kPa (500 psia). By keeping temperature

constant, the pressure was varied to determine its effect on the atomization as a function

of orifice size.

For the alkylated aromatic, the lowest pressure of 1034 kPa did not produce a

fully atomized zone up to the test limit of 41cm from the orifice. The histograms and

light intensity plots indicated that droplets were in a minority for the entire measured

extent of the spray. So the fully atomized zone, if it existed, would begin beyond 41 cm

from the orifice.

The higher pressures decreased the aerosol formation distance, i.e., the fully

atomized zone was achieved closer to the orifice. The aerosol formation distances are

provided in Appendix G. Higher pressures also resulted in smaller SMDs. This trend,

which can be seen in Figure III-7, agrees well with theory. Increasing pressure increases

the relative velocity of the liquid with respect to the stagnant air with higher shearing

which results in a greater atomization of the liquid stream. Therefore, the exiting stream

breaks up closer to the orifice and also breaks up into smaller droplets.

Volume concentration is not a strong function of the injection pressure. At lower

pressures, the reported values are not a true representation of reality, because the spray

is undeveloped. At higher pressures, increasing the pressure appears to increase slightly

the volume concentration, but the values agree within the experimental uncertainty.

Hence, pressure does not have a pronounced effect on the volume concentration, as

shown in Figure III-8.

0

20

40

60

80

100

120

140

0 15 30 45

Distance from the orifice (cm)

150 psia 300 psia 500 psia

Figure III-7. Effect of pressure on atomization: SMD

(Alkylated aromatic, 120 °C, orifice diameter of 0.33 mm)

0

0.02

0.04

0.06

0.08

0.1

0 15 30 45

Distance from the orifice (cm)

150 psia 300 psia 500 psia

Figure III-8. Effect of pressure on atomization: Volume concentration

(Alkylated aromatic, 120 °C, orifice diameter of 0.33 mm)

An important observation about the value of the volume concentrations obtained

is that values of 0.01% may seem very small, but mass concentrations, are of the order

of a thousand greater, and liquids have a much larger enthalpy concentration than

vapors.

Similarly for the modified terphenyl, the pressure has a similar effect. For higher

pressures, aerosols are produced closer to the orifice and have smaller SMDs, but have a

fairly uniform volume concentration. Figures III-9 and III-10 show the effect of

pressure on the SMD and volume concentration, respectively, for the modified

terphenyl.

0

50

100

150

200

250

0 15 30 45

Distance from the orifice (cm)

150 psia 300 psia 500 psia

Figure III-9. Effect of pressure on atomization: SMD

(Modified terphenyl, 120 °C, orifice diameter of 0.33 mm)

0

0.01

0.02

0.03

0.04

0 15 30 45

Distance from the orifice (cm)

150 psia 300 psia 500 psia

Figure III-10. Effect of pressure on atomization: Volume concentration

(Modified terphenyl, 120 °C, orifice diameter of 0.33 mm)

Effect of Fluid Injection Temperature

The effect of temperature on atomization was studied at three temperatures,

which depended upon the HTF being tested, but were always below the flash point. This

was done because the scope of the research was to study the hazard posed by a leaking

HTF below its flash point, where the fluids are often considered safe. By keeping,

pressure constant, the temperature was varied to determine its effect on the atomization

of each HTF at each orifice size.

For the alkylated aromatic, the three test temperatures were 80 °C, 120 °C, and

150 °C. The general trend observed was that aerosol formation distance is decreased as

temperature is increased. This means that at higher temperatures the fully atomized

zone will develop closer to the orifice. The values for the aerosol formation distances

are provided in Appendix G. Higher temperatures also result in smaller, SMDs. But in

many cases we see that measurements farthest from the orifice, the SMDs at the various

temperatures are similar, taking into account the Malvern measurement uncertainty. The

cooling of the droplets, which tend to approach room temperature, may cause this

asymptotic behavior. Figure III-11 shows the effect of temperature on the SMD of the

spray. At 150 °C the considerable amount of generated vapor caused beam steering.

Hence we see a drop size shifted to a larger values when compared to values at 120 °C

and 80 °C. This was then altered using the kill data function and the “corrected” results

are shown in Figure III-12. We can see that the SMDs are now lower that before,

indicating that beam steering had occurred.

020406080

100120140160

0 15 30 45Distance from the orifice (cm)

80 °C 120 °C 150 °C

Figure III-11. Effect of temperature on atomization: SMD

(Alkylated aromatic, 300 psia, orifice diameter of 0.33 mm)

020406080

100120140160

0 15 30 45Distance from the orifice (cm)

80 °C 120 °C 150 °C

Figure III-12. Effect of temperature on atomization: SMD

with function kill data

(Alkylated aromatic, 300 psia, orifice diameter of 0.33 mm)

0

0.05

0.1

0.15

0.2

0 15 30 45

Distance from the orifice (cm)

80 °C 120 °C 150 °C

Figure III-13. Effect of temperature on atomization: Volume concentration

(Alkylated aromatic, 300 psia, orifice diameter of 0.33 mm)

020406080

100120140160

0 15 30 45Distance form the orifice (cm)

95 °C 120 °C 135 °C

Figure III-14. Effect of temperature on atomization: SMD

(Modified terphenyl, 300 psia, orifice diameter of 0.33 mm)

0

0.02

0.04

0.06

0 15 30 45

Distance from the orifice (cm)

95 °C 120 °C 135 °C

Figure III-15. Effect of temperature on atomization: Volume concentration

(Modified terphenyl, 300 psia, orifice diameter of 0.33 mm)

The volume concentration, however, does not show any significant dependence

on the fluid temperature (even after omitting the first ring diode). The volume

concentrations obtained are of the order of 0.01%. Figure III-13 shows the effect of

temperature on volume concentration.

Similar trends are observed also in the study of the modified terphenyl. For

higher temperatures aerosols are produced closer to the orifice, have smaller SMDs and

temperature has an insignificant effect on the volume concentration. Figures III-14 and

III-15 show the effect of temperature on the SMD and volume concentration,

respectively, for the modified terphenyl.

The important differences between the modified terphenyl and the alkylated

aromatic are that the SMDs for the modified terphenyl are in the range of 60 to 90

micron, while for the alkylated aromatic they were between 40 and 60 micron. The

volume concentrations for the alkylated aromatic were generally around 0.01%, but the

modified terphenyls had slightly higher volume concentrations near 0.015%.

Effect of Orifice Size

The effect of orifice size on atomization was studied at three sizes: 0.20 mm

(0.008”), 0.33 mm (0.013”), and 0.58 mm (0.023”). By keeping, temperature and

pressure constant, the orifice size was varied to determine its effect on the atomization

of each HTF.

In the case of the alkylated aromatic, the 0.20 mm orifice did not develop a fully

atomized zone within the test limit of 41 cm from the orifice. For the higher orifice

diameters, however, an increasing orifice diameter reduced the aerosol formation

distance. The aerosol formation distance values are provided in Appendix G. Increasing

the orifice size decreased the SMD of the spray, as shown in Figure III-16. The 0.20

mm orifice did not produce any aerosol and hence was not depicted on the plot. Orifice

diameter also had a significant effect on the volume concentration. As shown in Figure

III-17, the highest orifice size produced the highest volume concentrations.

In the case of the modified terphenyl, we see similar trends, as shown in Figures

III-18 and III-19.

0

20

40

60

80

100

120

0 15 30 45

Distance from the orifice (cm)

0.33 mm 0.58 mm

Figure III-16. Effect of orifice size on atomization: SMD

(Alkylated aromatic, 300 psia, 120 °C)

0

0.02

0.04

0.06

0.08

0.1

0 15 30 45

Distance from the orifice (cm)

0.33 mm 0.58 mm

Figure III-17. Effect of orifice size on atomization: Volume concentration

(Alkylated aromatic, 300 psia, 120 °C)

020406080

100120140

20 25 30 35 40 45

Distance from the orifice (cm)

0.33 mm 0.58 mm

Figure III-18. Effect of orifice size on atomization: SMD

(Modified terphenyl, 300 psia, 120 °C)

0

0.02

0.04

0.06

20 25 30 35 40 45

Distance from the orifice (cm)

0.33 mm 0.58 mm

Figure III-19. Effect of orifice size on atomization: Volume concentration

(Modified terphenyl, 300 psia, 120 °C)

CHAPTER IV

MODELING

In order to effectively model a system, it is very important to define the system

boundaries. The model limits help improve the model’s accuracy of prediction and also

alerts others to the conditions of model applicability.

As mentioned earlier, the objective of this research is to emulate a leak of a HTF

in a process and to study the effects of the process operating conditions and the leak size

on the atomization process.

The three primary parameters to represent the aerosol, are the aerosol formation

distance, the SMD, and the volume concentration in air. The region where the model

will be applicable is the fully atomized zone, where the Malvern measurements are the

most reliable. Hence, the modeling process will generate source terms of leaks resulting

in aerosol and models will predict how far from the leaks the aerosols are formed, their

SMDs, and the volume concentration of the liquid droplet in air.

The mean drop diameter is the most common quantity that represents a real set

of droplets in a spray. Depending on the requirement, several different expressions of

the mean drop diameter are available. The general definition that describes all forms of

the mean diameter is:

qpm

i iqi

m

i ip

ipq

nD

nDD −

=

=

∑∑

∆

∆=

1

1 (IV-1)

by using different values of p and q, we can generate a host of mean droplet diameters,

each of which can yield different information about the spray system. Bayvel and

Orzechowski (1993) have given the commonly used mean diameters based on Equation

IV-1 and their applications, as shown in Table IV-1.

Table IV-1. Mean drop diameters (Bayvel and Orzechowski, 1993)

Mean diameter

p q Symbol Name Application

1 0 D10 Arithmetic Comparison of disperse systems

2 0 D20 Surface Surface area control, surface phenomena,e.g., absorption, vaporization

3 0 D30 Volume Volume control, volumetric phenomenon

2 1 D21 Relative surface Drop disintegration, absorption

3 1 D31 Relative volume,Probert’s

Evaporation, molecular diffusion,combustion

3 2 D32 Volume-surface, Sauter’s Drop range, mass transfer, heat transfer,combustion

4 3 D43 Mass, de Brouckere’s orHerdan’s

Drop fractionation, combustion

The ultimate aim, in this research, is for drop size data to be utilized in

determining the flammability limits of aerosols. Hence the most applicable diameter is

the Sauter Mean Diameter (SMD).

The Sauter Mean Diameter is the diameter of a uniform set of equivalent

droplets with the same total volume and the surface of all droplets as in the real set.

∑∑

∆

∆==

nD

nDSMDD

2

3

32 (IV-2)

The SMD is generally the most commonly used mean diameter statistic, because it can

be used to characterize important processes such as droplet penetration or heat and mass

transfer.

The penetration of drople ts is a measure of the ratio of the forces of inertia to the

forces of aerodynamic drag.

( )( )( )∑

∑∆

∆≈

nVDC

naDD

GD

L

2/4/

6/22

3

32ρπ

πρ(IV-3)

where ρL and ρG are the densities of the liquid and ambient air, respectively, and a is the

droplet acceleration.

The heat transfer between droplets and the ambient air can be measured as the

ratio of the heat necessary to raise the temperature of the droplet by ∆TRISE to the heat

transferred from the surrounding air at a temperature gradient of ∆TGRAD.

( )∑

∑∆∆

∆∆≈

nTD

nTDcD

GRAD

RISELL

2

3

32

6/

απ

πρ(IV-4)

where cL is the specific heat capacity of the liquid and α is the thermal conductivity.

The mass transfer between the droplets and the air can be represented as the

ratio of the mass of the droplets to the evaporation rate per unit time.

( )( )∑

∑∆−

∆≈

nCCD

nDD L

02

3

32

6/

βπ

πρ(IV-5)

where β is the mass exchange coefficient and C, C0 represents the ambient gas

concentration far away and at the droplet surface respectively.

Because of the numerous droplet sizes, it is more convenient to use statistical

distributions that approximate the drop size distribution of the spray. As mentioned in

Chapter II the distribution used in this research is the Rosen Rammler distribution. The

general Equation IV-1 can be written as

( )( )

qpq

p

pqdDdDndD

dDdDndDD −

∞

∞

∫∫

=

0

0

/

/(IV-6)

The Malvern system predicts the volume distribution, and hence Equation (IV-6)

becomes

( )( )

qpq

p

pqdDdDVdD

dDdDVdDD −

∞ −

∞ −

∫∫

=

0

3

0

3

/

/(IV-7)

Integrating Equation (IV-7) we get the relation for the SMD in terms of the two-

parameter Rosen Rammler model

( )[ ]( )[ ]

qppq nq

npXD −

+−Γ+−Γ

=1/)31/3

(IV-8)

For the Sauter Mean Diameter, where p=3 and q=2, we have

( )nX

D/1132 −Γ

= (IV-9)

where X and n are the two parameters of the Rosen Rammler model.

Dimensional Analysis

The atomization process is a very complicated phenomenon. Because of the

random nature of the stream break up, it is not conducive to analytical modeling

techniques. Many researchers have used various techniques to describe the atomization

process, but all techniques developed thus far have been very system specific.

Schweitzer (1937) discussed general trends of fluid break up and examined a number of

theories of disintegration of liquid jets and mentions that no single theory is complete.

The theories, at best, are able to explain, qualitatively, certain trends based on what

conditions could cause break up of streams.

The modeling of the atomization process is very important in fuel combustion,

where the fuel is generally sprayed before it is ignited to increase the combustion

efficiency. A vast amount of research in this regard has confirmed that drop size is the

most important parameter of combustion efficiency. To circumvent the fact that no

theory could completely and accurately describe the atomization process, various

methods were adopted to describe the atomization process quantitatively. Dimensional

analysis is the most popular quantitative method used, because the use of dimensionless

groups decrease the number of experiments required to obtain an empirical expression.

The resulting expression is based on actual experimental data and hence is readily

applicable to the system. Elkotb (1982), Park et al. (1996), Bayvel and Orzechowski

(1993), and Kihm and Chigier (1991) have provided analyses of the important

parameters required to characterize the atomization process.

The operating conditions, temperature and pressure, and the orifice diameter are

the parameters that have to be related to the aerosol formation distance, the SMD, and

the volume concentration of aerosol. The temperature mainly affects the physical

properties of the fluid, which in turn affect the atomization process. Pressure however

has a more direct influence on the atomization process. Higher pressures translate into

higher spray velocities, increasing shear at the liquid-air interface, which magnifies the

instabilities on the liquid stream, causing a faster and more effective atomization.

The parameters that are important to the atomization process are:

L The characteristic dimension of the orifice, e.g., the diameter of the orifice, d0

V Initial velocity of the exiting liquid stream

σ Surface tension of the liquid

ρL Liquid density

ρG Gas (air) density

µL Dynamic liquid viscosity

µG Dynamic gas (air) viscosity

The basis of dimensional analysis is the selection of the dimensionless

parameters by combining the above parameters. First we list all the parameters to be

included in the dimensional analysis.

SMD, d0, V, σ, ρL, ρG, µL, µG (IV-10)

All these parameters can be described by a maximum of three units: M (mass), L

(length), and T (time). From our list of eight parameters, we designate three parameters

as basic parameters. These basic parameters must contain all three units among them.

The basic parameters selected are d0, V, and ρG. The second step is to group each of the

five remaining parameters with all three basic parameters raised to unknown powers.

Each of these groups is a dimensionless parameter that is determined by determining the

powers on the basic parameters

f(Π1, Π2, Π3, Π4, Π5, Π6) = 0 (IV-11)

where

11101

cG

ba VdSMD ρ=Π (IV-12)

22202

cG

ba Vd ρσ=Π (IV-13)

33303

cG

baL Vd ρµ=Π (IV-14)

44404

cG

baG Vd ρµ=Π (IV-15)

55505

cG

baL Vd ρρ=Π (IV-16)

The condition that will make every Π dimensionless is for the right hand side of

Equations (IV-12) to (IV-16) also to be dimensionless. From this criterion, the powers

can be determined. Examining Equation (IV-12) for unit L:

0 = 1 + a1 + b1 + c1

for unit M:

0 = c1

for unit T:

0 = -b1

Therefore,

a1 = -1

b1 = 0

c1 = 0

and hence

Π1 = SMD d0-1

A similar analysis for the other dimensionless parameters yields the complete set of

criteria.

01 d

SMD=Π (IV-17)

022 dVGρ

σ=Π (IV-18)

03 VdG

L

ρµ

=Π (IV-19)

04 VdG

G

ρµ

=Π (IV-20)

G

L

ρρ

=Π 5 (IV-21)

We can replace Π3 by 3Π′ :

0

2

52

23

3 dL

L

σρµ

=ΠΠ

Π=Π′ (IV-22)

and Π4 by 4Π′ :

G

L

µµ

=ΠΠ

=Π′4

34 (IV-23)

Substituting these values, equation (IV-11) becomes

=

L

G

L

G

l

LG ddVf

dSMD

µµ

ρρ

µσρ

σρ

,,, 200

2

0

(IV-24)

or

( )NMLpWefd

SMD,,,

0

= (IV-25)

The physical significance of each of the above dimensionless groups must be

understood.

Weber number (We) represents the effect of external forces on the drop

development and stream break up and is the ratio of the dynamic forces contributed by

the ambient air to the surface tension. A higher Weber number indicates a dominance of

the dynamic forces indicating break up of the stream.

σρ 0

2 dVWe G= (IV-26)

Laplace number (Lp) is the contribution of the liquid properties to the

atomization process and it is the ratio of the surface tension forces to the viscous forces

within the liquid.

20

L

L dLp

µσρ

= (IV-27)

The density ratio (M) denotes the ratio of the air density to the liquid density.

L

GMρρ

= (IV-28)

The viscosity ratio (N) denotes the ratio of the air viscosity to the liquid

viscosity.

L

GNµµ

= (IV-29)

Also, implicit within the array of parameters mentioned here is the Reynolds

number (Re), which represents the ratio of the liquid inertial forces to the viscous

forces.

L

Vdµ

ρ0Re = (IV-30)

The following relationship holds for the Reynolds number

MLpWe

=Re (IV-31)

Therefore, we may refrain from explicitly including Re as a term in the dimensionless

equation.

Similar correlations for the aerosol formation distance (Lf) and the volume

concentration of the aerosol (XV) also are derived.

( )NMLpWefdLf

,,,0

= (IV-32)

=

0

,,,,dY

NMLpWefXV (IV-33)

Properties and Data

To ensure a reliable correlation, it is first important to ensure that the data being

applied to the correlation are reliable. The manufacturer provided the HTF property

data, which is included in a summary of the HTF properties, is given in Appendix E.

Air properties were obtained from Vasserman et al. (1966)

The experiment provided the SMD data at different injection pressures,

temperatures, and orifice sizes. The velocity of the exiting jet is a function of the

pressure gradient and the coefficient of discharge (CD) of the orifice.

From Bernoulli’s equation we derive the velocity of the exiting liquid stream.

02

2

=∆+∆

+∆

ZgVP

ρ(IV-34)

where ∆P is the difference in pressure at the orifice and the atmospheric pressure and ρ

is the HTF density. The velocity gradient is replaced by V, the exiting fluid velocity,

because the velocity in the cell may be assumed to be 0. ∆Z also is 0. With these

substitutions, the result is the ideal velocity.

ρP

Videal

∆=

2(IV-35)

But, in the real system there is a drop in the velocity at the orifice due to the constriction

of the flowing liquid. The true velocity is represented as

idealDVCV = (IV-36)

where CD is the coefficient of discharge of the orifice and is a function of the orifice

geometry and the Reynolds number. For Reynolds numbers less than around 2000, the

coefficient of discharge is found to increase linearly with the square root of the

Reynolds number.

Re∝DC (IV-37)

In the turbulent region the coefficient of discharge remains constant. The values for the

coefficient of discharge of each nozzle were determined as a function of the Reynolds

number at the orifice, and the results are tabulated in Appendix F.

Existing Correlations

The existing drop size correlations available are mainly for diesel injection

systems. Table IV-2 provides us the different correlations that may be applicable to the

system under consideration.

Table IV-2. Drop size correlations for plain-orifice atomizers (Lefebvre, 1989)

Investigators Correlations

Merrington and

Richardson L

L

U

dSMD

2.02.1500 υ=

Harmon052.078.015.015.0648.007.03.03330 −−−−= GGLLL UdSMD ρµσρµ

Tanasawa and Toyoda ( )

×+

= −

5.0

25.01 331147

ddUSMD

L

L

GL

σρµ

ρσ

Hiroyasu and Katoda 135.0131.0121.02330 −∆= LA PQSMD ρ

Elkobt ( ) 54.006.0737.0385.008.3 −∆= LALL PSMD ρσρυ

UL velocity of the liquid, m/s

d discharge orifice diameter, m

µ dynamic viscosity, kg/m s

ν kinematic viscosity, m2/s

ρA, ρG air/gas density, kg/m3

ρL liquid density, kg/m3

σ surface tension, kg/s2

∆ PL injection pressure differential across nozzle, Pa

Q volumetric flow rate, m3/s

None of the above correlations are able to accurately predict the measured

values. They are not capable of predicting the change in SMD with distance. This may

be because of the specific nature of such correlations with respect to fluids for which

they were developed and the atomization apparatus. The comparison of predicted and

measured values is shown in Figure IV-1. The uncertainty range for the Malvern’s

measurements is indicated on the plot.

Lefebvre (1989) and Bayvel and Orzechowski (1993) have provided a few

correlations for the jet break up length for flow in the turbulent region, which are listed

in Table IV-3.

Though he break up length refers to the length up to which the stream exiting

the nozzle will remain compact before breaking up into ligaments, it may be beneficial

to compare this to the aerosol formation distances determined from the experiment.

Figure IV-2 shows the comparison of the measured aerosol formation distances and the

predicted break-up distances. It is unclear, from this diagram if we can deduce any

relation ship between the two.

0

50

100

150

200

250

300

0 50 100 150 200 250 300Measured SMD (micron)

Merrington andRichardson

Harmon

Tanasawa andToyoda

Elkotb

limit ofuncertainty

limit ofuncertainty

Figure IV-1. Comparison of the predicted and measured values of SMD for

existing correlation

Table IV-3. Break up length correlations for plain-orifice atomizers (Lefebvre,

1989; Bayvel and Orzechowski, 1993)

Investigators Correlations

Grant and Middleman 32.0051.8 WedLB =

Iciek 31.005.11 WedLB =

Lyshevskii

21.1

308.071.00442

−

−−

=

L

GB LpWedL

ρρ

LB Jet break up length, cm

We Weber number

Lp Laplace number

d0 Orifice diameter, cm

ρG air/gas density, kg/m3

ρL liquid density, kg/m3

0

5

10

15

20

25

30

35

40

0 10 20 30 40

Measured Lf (cm)

Grant and Middleman

Iciek

Lyshevskii

ideal

Figure IV-2. Comparison of the aerosol formation distances measured and the

predicted break up lengths

Regression Analysis

The dimensionless parametric equations for which solutions were desired were

of the forms:

( ) ( ) ( ) ( ) 11110

1 EDCB NMLpWeAd

SMD= (IV-38)

( ) ( ) ( ) ( ) 2222

02 EDCB NMLpWeA

dLf

= (IV-39)

( ) ( ) ( ) ( )3

0

33333F

EDCBV d

YNMLpWeAX

= (IV-40)

The constants A1…F1, A2…E2 and A3…F3, were determined for each fluid. This was

done using multiple linear regression by converting the above equations into their

logarithmic forms. The statistical correlation was based on 95% confidence intervals

and the constants obtained are shown in Table IV-4.

Table IV-4. Values of the constants obtained from the regression analysis

Constants Alkylated Aromatic Modified Terphenyl

A1 4.49*1054 2.07*105

B1 -0.5426 -0.465

C1 -0.2308 -0.212

D1 19.1936 2.535

E1 -0.2952 0.5925

A2 1.75*1022 4.1E+261

B2 -0.827 -0.505C2 -1.059 0.126D2 4.122 92.496

E2 -0.744 -4.140

A3 2.34*10213 1.4*10242

B3 -0.394 -0.307

C3 0.688 0.370

D3 89.373 78.859

E3 -5.099 -3.767

F3 -0.799 -1.38

Correlations and Predictions

The correlations for both fluids showed a good agreement with the data. The

coefficient of multiple regression in both cases was above 70% for the volume

concentrations, above 80% for the SMDs and above 90% for the aerosol formation

distances and most of the values predicted from the correlation are within the ±5 micron

measurement uncertainty of the Malvern system. Figures IV-3, IV-4, and IV-5 show the

agreement of predicted values from the correlation with the measured data.

0

20

40

60

80

100

0 20 40 60 80 100

Measured SMD (micron)

Alkylated aromatic Modified terphenyl

Upper Lower

Figure IV-3. Comparison of the experimental and predicted values of SMD

0

10

20

30

40

0 10 20 30 40

Measured Lf (cm)

Alkylated aromatic Ideal Modified terphenyl

Figure IV-4. Comparison of the experimental and predicted values of the aerosol

formation distance

0

0.01

0.02

0.03

0.04

0.05

0 0.01 0.02 0.03 0.04 0.05

Measured Volume Concentration (%)

Alkylated aromatic Modified terphenyl ideal

Figure IV-5. Comparison of the experimental and predicted values of the volume

concentration of the aerosol in air

Correlation Validation

The correlation validation is performed on the basis of the basic parameters that

are described by the dimensionless groups. All the obtained equations are expanded in

terms of the basic parameters and the exponent on each parameter is examined for its

significance.

Influence of Liquid Viscosity

All the exponents for viscosity are positive, which means that higher viscosities

result in larger SMDs and also larger aerosol formation distances. Therefore, while a

higher viscosity hinders atomization, under conditions where atomization does occur,

the SMD will be larger.

Influence of Surface Tension

All exponents for surface tension were positive, which indicates that, while

higher surface tension is capable of producing larger droplets, it also hinders aerosol

formation (Tabata et al., 1985).

Influence of Liquid Density

All exponents of liquid density are negative, which means that more dense fluids

will produce smaller droplets while atomizing much closer to the orifice. This can be

rationalized by the fact that denser liquids have a higher kinetic energy and

consequently smaller droplets develop.

Influence of Liquid Velocity

Liquid velocity always has a negative exponent. Higher velocities are caused by

higher injection pressures and result in smaller droplets as well as shorter aerosol

formation distances (Tabata et al., 1985).

Influence of Orifice Size

The orifice size had the greatest effect of the volume concentration as shown by

its positive exponent. Higher orifice sizes resulted in higher volume concentrations.

The correlations have a good agreement with experiment and their implications

can be rationalized by theory. This is very important for the validity of any correlation.

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

This research has demonstrated that there is a dependence of aerosol drop size

distributions on the operating conditions and the leak size. The most important

conclusion for process safety is that significant quantities of aerosol are formed from

HTFs at conditions well below their flash points. However, there are threshold

conditions below which significant amounts of aerosols were not formed in the tested

ranges. Operating conditions and leak size also had a significant effect on the drop size,

atomization distance, and the amount of aerosol generated.

Summary

A study of the validity of the model provided a good corroboration for

observations made with respect to the experimental data. The influence of liquid

properties on the atomization was rationalized for three properties, namely, liquid

density, viscosity and surface tension. Higher liquid densities produced smaller

droplets, whereas higher viscosity and surface tension produced larger droplets.

However viscosity also had a significant impact on the aerosol formation distance.

Higher viscosities increase the aerosol formation distances, because the viscous forces

tend to hold the liquid stream together. Temperature indirectly affected the atomization

through the liquid properties. At higher temperatures, liquids have lower densities,

lower viscosities, and lower surface tensions.

Pressure had a more direct influence on the atomization. Higher injection

pressures increased the liquid velocity, which hastened the atomization and also made it

more severe, i.e., it resulted in smaller droplet sizes and shorter aerosol formation

distances.

The orifice size had the most prominent effect on the volume concentration of

aerosol in air. Higher orifice size produced larger volume concentrations.

Implications for Process Safety

Development of the model will help define a source term for leaking fluids

forming aerosols. The other lessons that industry can learn from this research are based

on the above summary.

During the design process the engineer must consider the following in addition

to the design criteria:

• The HTF with the higher density will form smaller droplets on leaking.

• The HTF with the higher viscosity is less likely to form aerosol.

• The HTF with the higher surface tension will form larger droplets on leaking.

• Higher operating pressures will produce aerosols closer to the leak and smaller drop

sizes.

The model for the aerosol formation distances will help the designer arrive at

locations for obstacles and guard surfaces around potential leak zones, to prevent the

formation and dispersion of aerosols. HTF selection can be based on which liquids are

less likely to form aerosols. Design criteria also can incorporate the data to arrive at

operating conditions that are less likely to produce aerosols.

Recommendations

The aim of this research was to understand the mechanisms of HTF aerosol

formation through leaks in process equipment. Atomization is a random process and

hence offers a complicated and seemingly unsolvable system to model. However, as

demonstrated in this research, useful information has resulted from studying the effects

of the injection conditions on the atomization process. The effect of altering certain

properties of the HTF such as surface tension, by adding small quantities of impurities

should be studied.

Using the model described here to define source terms for leaks forming

aerosols will help optimize existing dispersion models by relating the dispersion back to

the operating conditions of the process.

Finally, the study of aerosol combustion as a function of drop-size distributions,

concentrations, and fluid properties will be help estimate the upper and lower explosive

limits of HTF aerosol/air mixtures. This information will help industry better

understand the phenomenon of aerosol explosions and thereby improve process safety.

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APPENDIX A

EXPERIMENTAL DATASHEETS

Date: 10/11/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.33 mm

Pressure: 500 psia (3446 kPa)

Temperature: 80 °C

Average room temperature: 19.2 °C

Table A-1. Data for the alkylated aromatic at 80 °C, 500 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %6 80.9 492.6305 74.88 0.116411 81.4 494.0521 59.16 0.054016 81.4 498.3168 49.27 0.009821 81.4 498.3168 33.03 0.015426 81.0 501.1600 51.29 0.031431 81.6 494.0569 49.47 0.026836 80.3 495.4785 53.00 0.022241 80.3 499.7434 54.91 0.0227

Date: 10/06/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.33 mm

Pressure: 300 psia (2067 kPa)

Temperature: 80 °C

Average room temperature: 19.0 °C

Table A-2. Data for the alkylated aromatic at 80 °C, 300 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %11 80.8 302.3605 150.56 0.172216 82 312.3037 118.23 0.084721 81.8 299.4975 59.83 0.014426 80.3 306.6013 54.74 0.014331 80.3 302.3308 63.98 0.015336 82.0 292.2513 49.49 0.009341 81.8 305.1758 44.97 0.0083

Date: 10/11/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.33 mm

Pressure: 150 psia (1034 kPa)

Temperature: 120 °C

Average room temperature: 18.7 °C

Table A-3. Data for the alkylated aromatic at 120 °C, 150 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %11 121.9 158.5157 124.86 0.033516 122.8 159.9354 112.93 0.023721 123.4 159.9385 64.55 0.007126 123.1 158.5172 113.71 0.014431 122.1 158.5219 95.75 0.010136 122.1 158.5219 77.85 0.006441 121.8 159.9431 118.21 0.0154

Date: 10/11/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.33 mm

Pressure: 300 psia (2067 kPa)

Temperature: 120 °C

Average room temperature: 18.9 °C

Table A-4. Data for the alkylated aromatic at 120 °C, 300 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %21 120.3 302.0338 106.34 0.042526 120.0 303.4549 47.65 0.011131 119.2 302.0427 46.73 0.008336 119.3 303.4639 56.19 0.011041 119.8 302.0457 53.71 0.0078

Date: 10/12/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.58 mm

Pressure: 300 psia (2067 kPa)

Temperature: 120 °C

Average room temperature: 17.6 °C

Table A-5. Data for the alkylated aromatic at 120 °C, 300 psia and orifice diameter

of 0.58 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %16 119.2 315.0435 78.71 0.094621 119.2 305.1668 69.95 0.063626 119.1 302.6432 65.89 0.051531 117.8 311.0922 63.50 0.039936 119.6 290.7621 58.95 0.030041 120.3 299.1887 48.41 0.0148

Date: 10/12/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.33 mm

Pressure: 500 psia (3446 kPa)

Temperature: 120 °C

Average room temperature: 18.2 °C

Table A-6. Data for the alkylated aromatic at 120 °C, 500 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %6 120.6 502.8646 55.94 0.076811 120.4 502.5965 37.23 0.032216 120.2 496.7710 33.04 0.02221 120.3 499.3985 32.85 0.016626 120.2 498.1556 35.84 0.015031 120.1 497.0517 38.55 0.012336 120.2 496.9536 40.40 0.012241 121.5 494.1601 41.02 0.0086

Date: 10/12/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.33 mm

Pressure: 300 psia (2067 kPa)

Temperature: 150 °C

Average room temperature: 18.0 °C

Table A-7. Data for the alkylated aromatic at 150 °C, 300 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %11 149.3 317.4866 120.98 0.127816 149.8 317.1861 87.75 0.068521 149.9 317.2018 70.53 0.033426 150.1 316.9268 64.97 0.021431 150.3 305.6296 65.27 0.016436 147.2 315.5679 58.79 0.012341 148.3 312.7651 59.29 0.0094

Date: 10/13/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.20 mm

Pressure: 300 psia (2067 kPa)

Temperature: 120 °C

Average room temperature: 18.4 °C

Table A-8. Data for the alkylated aromatic at 120 °C, 300 psia and orifice diameter

of 0.20 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %41 123.1 307.263 251.51 0.0099

Date: 10/13/2000

Fluid: Alkylated aromatic

Orifice diameter: 0.20 mm

Pressure: 500 psia (3446 kPa)

Temperature: 120 °C

Average room temperature: 18.4 °C

Table A-9. Data for the alkylated aromatic at 120 °C, 500 psia and orifice diameter

of 0.20 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %36 120.8 513.9995 240.69 0.009131 119.7 513.9791 146.44 0.002441 121.1 513.9791 134.21 0.0447

Date: 10/31/2000

Fluid: Modified terphenyl

Orifice diameter: 0.33 mm

Pressure: 300 psia (2067 kPa)

Temperature: 95 °C

Average room temperature: 16.2 °C

Table A-10. Data for the modified terphenyl at 95 °C, 300 psia and orifice diameter

of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %21 95.2 314.7773 144.66 0.053126 96.2 314.7649 126.50 0.038331 96.5 314.7649 101.14 0.020736 97.2 314.7618 74.26 0.012141 96.0 309.0482 98.34 0.0184

Date: 10/31/2000

Fluid: Modified terphenyl

Orifice diameter: 0.33 mm

Pressure: 300 psia (2067 kPa)

Temperature: 130 °C

Average room temperature: 16.3 °C

Table A-11. Data for the modified terphenyl at 130 °C, 300 psia and orifice

diameter of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %26 130.7 300.6186 115.69 0.036031 131.1 302.0338 104.36 0.030636 132.7 300.6127 109.50 0.029541 128.6 300.6157 66.41 0.0109

Date: 10/31/2000

Fluid: Modified terphenyl

Orifice diameter: 0.33 mm

Pressure: 500 psia (3446 kPa)

Temperature: 120 °C

Average room temperature: 16.8 °C

Table A-12. Data for the modified terphenyl at 120 °C, 500 psia and orifice

diameter of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %16 118.9 498.6811 62.99 0.026821 118.4 508.6195 56.60 0.020626 118.9 502.954 84.74 0.037831 119.1 508.6295 60.23 0.019736 118.6 505.7843 63.66 0.019941 118.3 505.7993 51.75 0.0120

Date: 11/01/2000

Fluid: Modified terphenyl

Orifice diameter: 0.33 mm

Pressure: 150 psia (1034 kPa)

Temperature: 120 °C

Average room temperature: 16.8 °C

Table A-13. Data for the modified trephenyl at 120 °C, 150 psia and orifice

diameter of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %36 116.3 162.9361 201.21 0.018141 117.8 161.5135 149.01 0.0075

Date: 11/01/2000

Fluid: Modified terphenyl

Orifice diameter: 0.20 mm

Pressure: 300 psia (2067 kPa)

Temperature: 120 °C

Average room temperature: 16.8 °C

Table A-14. Data for the modified terphenyl at 120 °C, 300 psia and orifice

diameter of 0.20 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %11 122.7 305.2028 87.66 0.030816 121.4 305.2028 121.92 0.030621 122.5 305.2028 78.35 0.019026 119.4 305.2058 74.14 0.013431 122.2 305.2058 64.44 0.007736 123.2 305.2088 63.58 0.008141 117.3 305.2058 65.45 0.0076

Date: 11/01/2000

Fluid: Modified terphenyl

Orifice diameter: 0.58 mm

Pressure: 300 psia (2067 kPa)

Temperature: 120 °C

Average room temperature: 16.8 °C

Table A-15. Data for the modified terphenyl at 120 °C, 300 psia and orifice

diameter of 0.58 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %26 121.4 308.0481 114.2 0.050431 122.4 312.3160 98.03 0.035236 120.4 313.7293 95.22 0.031041 120.2 308.0511 75.64 0.0207

Date: 11/01/2000

Fluid: Modified terphenyl

Orifice diameter: 0.33 mm

Pressure: 300 psia (2067 kPa)

Temperature: 120 °C

Average room temperature: 16.8 °C

Table A-16. Data for the modified terphenyl at 120 °C, 300 psia and orifice

diameter of 0.33 mm

Distance fromthe orifice (x)

Temperatureat the nozzle

Pressure atthe nozzle SMD Volume

concentrationcm °C psia micron %26 117.1 300.929 121.05 0.037331 118.2 302.3456 114.63 0.029736 116.6 302.3605 119.63 0.025841 116.8 302.3575 85.53 0.0131

APPENDIX B

PRESSURE TRANSDUCER CALIBRATION

Table C-1. Calibration data for the Sensotek pressure transducer

Vout Vin Vout/Vin Pressure(psig)

AtmosphericPressure (psia)

Pressure(psia)

0.005 10.103 0.000 60.000 14.149 74.1490.009 10.109 0.001 110.000 14.149 124.1490.012 10.159 0.001 160.000 14.149 174.1490.016 10.300 0.002 210.000 14.149 224.1490.019 10.256 0.002 260.000 14.149 274.1490.023 10.296 0.002 310.000 14.149 324.1490.027 10.295 0.003 360.000 14.149 374.1490.030 10.294 0.003 410.000 14.149 424.1490.034 10.294 0.003 460.000 14.149 474.1490.038 10.293 0.004 510.000 14.149 524.1490.041 10.292 0.004 560.000 14.149 574.1490.038 10.293 0.004 520.000 14.149 534.1490.035 10.292 0.003 470.000 14.149 484.1490.031 10.292 0.003 420.000 14.149 434.1490.024 10.293 0.002 320.000 14.149 334.1490.020 10.293 0.002 270.000 14.149 284.1490.017 10.293 0.002 220.000 14.149 234.1490.013 10.293 0.001 170.000 14.149 184.1490.009 10.295 0.001 120.000 14.149 134.1490.006 10.296 0.001 70.000 14.149 84.1490.003 10.296 0.000 30.000 14.149 44.1490.005 10.296 0.000 60.000 14.149 74.1490.009 10.297 0.001 110.000 14.149 124.1490.012 10.297 0.001 160.000 14.149 174.1490.016 10.298 0.002 210.000 14.149 224.1490.020 10.299 0.002 260.000 14.149 274.1490.023 10.300 0.002 310.000 14.149 324.1490.027 10.299 0.003 360.000 14.149 374.1490.030 10.299 0.003 410.000 14.149 424.1490.034 10.299 0.003 460.000 14.149 474.1490.038 10.296 0.004 510.000 14.149 524.1490.041 10.297 0.004 560.000 14.149 574.149

The atmospheric pressure at College Station, Texas on September 03, 2000 was 28.8

inches of mercury.

y = 142962x + 3.6042R2 = 1

0

100

200

300

400

500

600

700

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045

Vout/Vin

Pre

ssur

e (p

sia)

Figure C-1. Calibration of the Sensotek pressure transducer (TJE/0713-18TJA:

#595564)

APPENDIX C

THERMOCOUPLE CALIBRATION

Table C-1. Temperature calibration of thermocouples

Thermocouplelocation

Temperaturereading

(°C)

Departure (°C)

Actualtemperature

(°C)0 0.06 -0.06

100 0.17 99.83232 1.11 230.89

Nozzle

419 1.44 417.560 0.06 -0.06

100 0.17 99.83232 1.11 230.89

Fluid cell

419 1.44 417.560 0.11 -0.11

100 1.11 98.89232 -1.11 233.11

Air

419 1.50 417.50

The thermocouples were all factory calibrated by Omega and reported maximum

departures of + 1.5 °C and –1.11 °C over a temperature range of 0 °C to 419 °C. Hence

the total uncertainty associated with the temperature data is taken as + 1.5 °C and –1.11

°C.

APPENDIX D

EXPERIMENTAL PROCEDURE

1. Depressurize the Fluid Cell by opening the valve at the vent line.

2. Check the spring in the pressure relief valve for the correct range of working

pressure.

3. Fill HTF into the glass storage with the desired amount.

4. Open the valve at the fill line and wait until all HTF is transferred into the Fluid

Cell, then close the valve.

5. Attach the test nozzle. Adjust the nozzle so that the spray is straight and the center

of the spray passes through the laser beam.

6. Replace the insulation, both on the Fluid Cell and the spray line.

7. Turn on the temperature control box connected to the heater strip to heat the system.

Initially, the set temperature can be adjusted to a much higher level than the

required temperature to accelerate the heating process. Decrease the set temperature

when the temperature of HTF is close to the required test temperature.

8. Ensure that room ventilation is working at all times.

9. Pressurize the Fluid Cell to the test pressure and wait until the pressure gauge on

fluid cell comes to equilibrium.

10. Check the focal length of lens L2. In this case 300 mm is selected (refer to

instructions in Malvern Laser manual).

11. The Malvern Laser must be aligned on a daily basis. The reticle will be placed at the

focal lens, L2. Move the reticle until the laser beam just passes through the glass

part and not the particle part. Measure the particle size distribution by using the set

zero mode (F3). Then move the reticle again so the laser beam will pass through to

the particle part. By setting the independent model, measure the particle size

distribution using the measured sample and analyze (F5). The exact particle size

distribution for D(v,0.5) should be 46.5 micron. If the error is greater than 5%, the

alignment of the detector must be adjusted.

12. If the error is greater than 5%, clean the reticle and lens using lens cleaning fluid

and lens tissues.

13. Turn the knobs (both x and y direction) in the Malvern’s detector box until the

synchronizer reaches the maximum value, to ensure that the lasers alignment is

good.

14. Repeat (11) again. If the error is still greater than 5%, keep adjusting.

15. Ensure that the printer is online. All data must be backed up by a hard copy of the

results.

16. Turn on the exhaust system. The exhaust system must be turned on during the

measurements to ensure that aerosol does not accumulate in the laboratory.

17. Now the system is ready to make measurements. Turn off all the lights in the room

and measure the background (F3).

18. Open the spray valve to a certain position (this position needs to be fixed throughout

every measurement). Wait until the spray is steady for about 10 seconds. Ensure that

the temperature and pressure are at the required setting. Measure the droplet size

distribution with the F5 mode. The measurement is set to 500 sweeps per one time

measurement. This step will take about 5 seconds.

19. Write down the temperature and pressure data on the data sheet.

20. Close the spray valve and turn on the light.

21. During this time Malvern software will calculate the size distribution.

22. Write down the value of Sauter mean diameter, volume concentration, obscuration,

and Log Diff.

23. Save data on disk.

24. For the next measurement, go back to (17).

25. Ensure that the nitrogen cylinder valve is closed, the residual nitrogen in the system

is vented, and all power supplies switched off during shut down.

26. Drain the Mist Separator every day after all the measurements, but not after more

than 10 measurements.

27. Change the filter in the Mist Separator on a monthly basis.

28. Clean all equipment before testing another fluid.

APPENDIX E

HEAT TRANSFER FLUID PROPERTIES

Summary of the properties of the alkylated aromatic heat transfer fluid

Appearance Clear yellow liquidComposition Synthetic hydrocarbon mixtureOperating Range -25 °C to 290 °C (-15 °F to 550 °F)Moisture Content, Maximum 250 ppmFlash Point (ASTM D-92) 177 °C (350 °F)Fire Point (ASTM D-92) 218 °C (425 °F)Autoignition Temperature (ASTM E-659) 343 °C (650 °F)Kinematic Viscosity, at 40 °C 19.0 cStKinematic Viscosity, at 100 °C 3.5 cStDensity at 25 °C 868 kg/m3 (7.25 lb/gal)Specific Gravity (60 °F/60 °F) 0.876Coefficient of Thermal Expansion at 200 °C 0.000961/°C (0.000534/°F)Average Molecular Weight 320Pour Point -54 °C (-65 °F)Pumpability, at 2000 mm2/s (cSt) -28 °C (-19 °F)Pumpability, at 300 mm2/s (cSt) -8 °C (17 °F)Minimum Temperatures for

Fully Developed Turbulent Flow (Re = 10000)

10 ft/sec, 1-in tube 67 °C (152 °F)

20 ft/sec, 1-in tube 45 °C (114 °F)

Transition Region Flow (Re = 2000)

10 ft/sec, 1-in tube 24 °C (75 °F)

20 ft/sec, 1-in tube 11 °C (52 °F)

Boiling Range, 10% 340 °C (644 °F)Boiling Range, 90% 390 °C (734 °F)Normal Boiling Point 351 °C (664 °F)Heat of Vaporization at Maximum Use Temp290°C

228 kJ/kg (98.1 Btu/lb)

Optimum Use Range -25°C to 290°C (-15°F to 550°F)Extended Maximum Use Temperature 315 °C (600 °F)Maximum Film Temperature 335 °C (635 °F)Pseudocritical Temperature 512 °C (953 °F)Pseudocritical Pressure 13.2 bar (191 psia)Pseudocritical Density 258 kg/m3 (16.1 lb/ft3)

Summary of the properties of the modified terphenyl heat transfer fluid

Appearance Clear, pale yellow liquidComposition Modified terphenylOperating Range 0 °C to 345 °C (30 °F to 650 °F)Moisture Content 150 ppmFlash Point (ASTM D-92) 184 °C (363 °F)Fire Point (ASTM D-92) 2212 °C (414 °F)Autoignition Temperature (ASTM D-2155) 374 °C (705 °F)Kinematic Viscosity, at 40 °C 29.6 cStKinematic Viscosity, at 100 °C 3.8 cStDensity at 25 °C 1005 kg/m3 (8.39 lb/gal)Specific Gravity (60 °F/60 °F) 1.012Coefficient of Thermal Expansion at 200 °C 0.000819/°C (0.000455/°F)Average Molecular Weight 252Pour Point -32 °C (-25 °F)Pumpability, at 2000 mm2/s (cSt) -3 °C (27 °F)Pumpability, at 300 mm2/s (cSt) 11 °C (52 °F)Minimum Temperatures for

Fully Developed Turbulent Flow (Re = 10000)

10 ft/sec, 1-in tube 72 °C (162 °F)

20 ft/sec, 1-in tube 53 °C (128 °F)

Transition Region Flow (Re = 2000)

10 ft/sec, 1-in tube 35 °C (96 °F)

20 ft/sec, 1-in tube 26 °C (78 °F)

Boiling Range, 10% 348 °C (658 °F)Boiling Range, 90% 392 °C (738 °F)Normal Boiling Point 359 °C (678 °F)Heat of Vaporization at Maximum Use Temp345°C

272 kJ/kg (117 Btu/lb)

Optimum Use Range 0-345 °C (30-650 °F)Maximum Film Temperature 375 °C (705 °F)Pseudocritical Temperature 569 °C (1056 °F)Pseudocritical Pressure 24.3 bar (353 psia)Pseudocritical Density 317 kg/m3 (19.8 lb/ft3)

APPENDIX F

COEFFICIENT OF DISCHARGE

The coefficient of discharge (CD) of the orifices used was very important in

determining the true velocity of the liquid stream being ejected from the orifice. The CD

had to be determined at a wide range of velocities ranging from the laminar to the

turbulent region. Estimation of the CD was done using a combination of measurements

and empirical correlations.

Asihmin et al. (1961) have a correlation for CD values over a wide range of

Reynolds numbers: 100 to 1.5*105; and for l0/d0 in the range 2 to 5 and claim an

accuracy of 1.5%.

( ) 100

Re/58

23.1−

+=

dlCD (F-1)

Figure F-1. Characteristic dimensions of a plain orifice

For the 0.33 mm and the 0.58 mm orifices, the CD values are calculated using

this formula. The results are plotted in Figure F-2.

For l0/d0 in the range 1.5 to 17 and Reynolds nombers in the range 550 to 7000,

Nakayama (1961) provides the following correlation with an accuracy within 2.8%:

8.000

6/5

Re65.1/11.17Re

+=

dlCD (F-2)

This correlation was used to estimate the CD value for the 0.20 mm orifice which is

plotted in Figure F-2.

0.00

0.20

0.40

0.60

0.80

1.00

100 1000 10000 100000Re

d-0.20 mm

d-0.33 mm

d-0.58 mm

Figure F-2. Variation of CD with Reynolds Number

APPENDIX G

AEROSOL FORMATION DISTANCES

Table G-1. Aerosol formation distances for the alkylated aromatic mixture

Effect of temperature

Alkylated aromatic, 300 psia, 0.33 mm 80 °C 35 cm

120 °C 25 cm

150 °C 20 cm

Effect of pressure

Alkylated aromatic, 120 °C, 0.33 mm 150 psia >40 cm

300 psia 25 cm

500 psia 15 cm

Effect of Orifice

diameter

Alkylated aromatic, 300 psia, 120 °C 0.20 mm >40 cm

0.33 mm 25 cm

0.58 mm 15 cm

Table G-2. Aerosol formation distances for the modified terphenyl mixture

Effect of temperatureModified terphenyl, 300 psia, 0.33 mm 95 °C 30 cm

120 °C 25 cm

135 °C 20 cm

Effect of pressure

Modified terphenyl, 120 °C, 0.33 mm 150 psia >40 cm

300 psia 25 cm

500 psia 15 cm

Effect of Orifice

diameter

Modified terphenyl, 300 psia, 120 °C 0.20 mm 15 cm

0.33 mm 25 cm

0.58 mm 25 cm

VITA

Kiran Krishna was born in Bombay, India, on August 1, 1976, to Christine and

E.R. Krishna. After completing his schooling in St. Joseph’s Boys’ High School,

Bangalore, he pursued his bachelor’s degree in Chemical Engineering from the

Rashtreeya Vidhyalaya College of Engineering, Bangalore University between 1994

and 1998. In January 1999, he entered Texas A&M University to pursue his master’s

degree in Chemical Engineering. During his study he was also employed as a graduate

research assistant. He will remain with the Department of Chemical Engineering to

pursue his doctoral studies.

Permanent address: “Ashraya”, 411, 9th Cross,

2nd Block, R.T. Nagar,

Bangalore – 560032,

India.