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NASA Contractor Report 174760

NASA-CR-174760

19840024320

A Theoret%cal and Experimental Study

of Turbulent Evaporating Sprays

A.S.P. Solomon, J-S. Shuen, Q-F. lhang and G. M. Faeth

The PennsylvaniaState University

UniversityPark, Pennsylvania

{,I."i :;=,_D .R

I.A_GLEYRESEARCHCENTER

LIBRARY,NASA

flAMI_.TO_VIRGINIA

Prepared for

NATIONALAERONAUTICSAND SPACE ADMINISTRATION

Lewis ResearchCenter

; Under Grant NAG 3-190

https://ntrs.nasa.gov/search.jsp?R=19840024320 2018-05-11T19:31:19+00:00Z

i

A Theoretical and Experimental Study

of Turbulent Evaporating Sprays

SUMMARY

A study of the structure of sprays, limited to the properties of

evaporating sprays, is described. Several models of these processes

were evaluated by comparison of predictions with new measurements in

evaporating sprays completed during this investigation. Analysis and

measurements were limited to the dilute portions of the flows, where

the volume fraction of the continuous phase was greater than 99.1%.

Three models of the process were evaluated: (I) a locally

homogeneous flow (LHF) model, where slip between the phases was

neglected and the flow was assumed to be in local thermodynamic

equilibrium; (2) a deterministic separated flow (DSF) model, where sllp

was considered but effects of turbulent fluctuations on interphase

transport rates and drop dispersion by the turbulence were Ignored; and

(3) a stochastic separated flow (SSF) model, where effects of

interphase slip, turbulent fluctuations and turbulent dispersion were

considered using random sampling for turbulence properties in

conjunction with random-walk computations for drop motion. All three

models used a k-E model which was extensively evaluated for constant

and variable density single-phase jets during earlier work in this

laboratory.

The new experiments employed Freon 11 sprays, produced by an

air-atomlzing injector in a still environment. Mean and fluctuating

velocities and Reynolds stress were measured in the continuous phase

using laser Doppler anemometry. Liquid mass fluxes were measured by

slide impactlon. Drop sizes were measured by slide impactlon and

photography. Simultaneous measurements of drop size and velocity were

obtained using a multiflash photographic technique. Mean concentration

of injected fluid was measured by isokinetic sampling and analysis with

a gas chromatograph. Mean gas-phase temperatures were measured using

shielded fine-wlre thermocouples.

The LHF and DSF models did not provide very satisfactory

predictions over the present measurements. The DSF model generally

underestimated the rate of spread of the dispersed phase as a result of

ignoring effects of turbulent dispersion. The LHF model provided

reasonably good predictions for flows containing small drops, but was

unsatisfactory for most practical flows. In earlier evaluations, LHF

models generally overestimate the rate of spread of dispersed phases

due to neglect of sllp. However, the LHF model underestimated spread

rates for the present evaporating sprays. This indicates that LHF

models do not always provide an upper bound on the rate of development

of dilute drop-laden flows--as suggested in the past. Differences

between measurements and predictions of the DSF and LHF models were

smaller than observed for nonevaporatlng sprays, however, since

decreasing mass of the dispersed phase by evaporation causes the flow

to approach a single-phase flow.
ii

In contrast to the other models, the SSF model provided reasonably

good predictions of the present measurements. While this result is

encouraging, uncertainties in initial conditions for some of the data

limits the thoroughness of the evaluation of the SSF model. Some

effects of drops on turbulence properties were observed in dense

regions of the sprays. Treatment of such dense flow effects will

require extension of the present SSF model. The SSF approach, however,

appears to provide an attractive formulation for treating nonlinear

interphase transport processes in drop-laden turbulent flows. Current

work in this laboratory is considering extension of the method to

combusting sprays as well as consideration of effects of turbulence

modulation.
iii

TABLE OF CONTENTS

Page

SUMMARY ............................ i

NOMENCLATURE ......................... v

I. INTRODUCTION ....................... I

2. THEORY .......................... 4

2.1 Introduction ..................... 4

2.2 Locally Homogeneous Flow Model ............ 4

2.2.1 Governing Equations ............. j 4

2.2.2 State Relationships .............. 5

2.2.3 Computations ................. 8

2.3 Deterministic Separated Flow Model .......... 8

2.3.1 Discrete Phase ................ 8

2.3.2 Continuous Phase ............... 11

2.3.2.1 Description of Model ......... 11

2.3.2.2 State Relationships ......... 14

2.3.2.3 Probability Density Function Model. 15

2.4 Stochastic Separated Flow Model ........... 17

3. EXPERIMENTAL METHODS ................... 19

3.1 Introduction ..................... 19

3.2 Test Apparatus .................... 19

3.3 Measurement Techniques and Instrumentation ...... 23

3.3.1 Gas-Phase Properties ............. 23

3.3.1.1 Velocity Measurement ......... 23

3.3.1.2 Temperature Measurement ....... 26

3.3.2 Liquid-Phase Properties ............ 26

3.3.2.1 Drop Size Measurements ........ 26

3.3.2.2 Drop Size and Velocity Correlation

Measurement ............ 29

3.3.2.3 Liquid Flux Measurement ....... 32

3.3.3 Other Measurements .............. 33

3.3.3.1 Concentration Measurement ...... 33

3.3.3.2 Jet Momentum Measurement ....... 33

3.4 Experimental Conditions ............... 33

4. RESULTS AND DISCUSSION .................. 36

4.1 Introduction ..................... 36

4.2 Initial Conditions .................. 36

4.2.1 Jet Momentum, Spray Angle and Gas-Phase

Properties ................. 36

4.2.2 Liquid'Phase Properties ............ 37

4.3 Axial Variation of Spray Properties ......... 47

4.4 Radial Variation of Mean Spray Properties ...... 53

4.5 Radial Variation of Gas-Phase Turbulence Properties 59

. 4.6 Sensitivity Study .................. 66
iv

5. SUMMARY AND CONCLUSIONS .................. 73

5.1 Summary ....................... 73

5.2 Conclusions ..................... 74

REFERENCES .......................... 77

APPENDIX A: SUMMARY OF PROPERTIES OF SPRAY FLUIDS ...... 80

A.I Freon-11 ......... 80

A.2 Air -,ooo,ooo.oolo,o.o..e,,., 80

A.3 Evaluation of Mixing Rules for Gaseous Mixture .... 80

A.3.1 Thermal Conductivity ............. 80

A.3.2 Viscosity ................... 81

APPENDIX B: STATE RELATIONSHIPS FOR LHF PREDICTIONS OF

EVAPORATING SPRAYS ................ 82

APPENDIX C: DROPLET LIFE HISTORY CALIBRATION TESTS ...... 86

C.I Calibration Apparatus ................ 86

C.2 Theoretical Model of Droplet Life History Calibration

Tests ....................... 88

C.3 Calibration Test Results ............... 88

APPENDIX D: INITIAL CONDITIONS OF MEAN GAS-PHASE FREON-11

MASS FRACTION (YFg) AND SQUARE OF MASS FRACTION

FLUCTUATIONS (gFg) AT x/d = 50 FOR THE SF MODEL

PREDICTIONS OF THE EVAPORATING SPRAYS ...... 91

APPENDIX E: DATA FOR THE EVAPORATING SPRAY (CASE I) ..... 95

E.I Gas-Phase Properties ................. 95

E.2 Liquid-Phase Properties ............... 103

APPENDIX F: DATA FOR THE EVAPORATING SPRAY (CASE 2) ..... 112

F.I Gas-Phase Properties ................. 112

F.2 Liquid-Phase Properties ............... 120
v

NOMENCLATURE

" Symbol Description

a acceleration of gravity

B mass transfer driving potential, Equation (2.20)

Cf drop concentration

CD drag coefficient

C i parameters in turbulence model

Cp specific heat at constant pressure

d injector diameter

dp drop diameter

D mass diffusivity

f mixture fraction

g square of mixture fraction or gas-phase mass

fraction fluctuations

G llquid mass flux

h heat transfer coefficient

h i enthalpy of species i

k turbulence kinetic energy

Le dissipation length scale

m drop mass

mass flow rate

m" mass flux at drop surface

Mi molecular weight of species i

n number of drop groups

ni number of drops per unit time in group i

Np,Ns convection correction, Equation (2.21)

P pressure
vi

P probability density function (PDF)

Pr Prandtl number

r radial _istance

R ideal gas constant

Re Reynolds number

Sc Schmidt number

S_ source term

Sp_ drop source term

SMD Sauter mean diameter

t time

te eddy lifetime

T temperature

u axial velocity

Up drop velocity vector

v radial velocity

v i specific volume of species i

Vj volume of computational cell j

w tangential velocity

x axial distance

Xp drop position vector

AXp path length of drops in an eddy

Yi mass fraction of species i

At time of drop residence in an eddy

average property factor, Equation (2.24)

€ rate of dissipation of turbulence kinetic energy

value of maximum probability

_t turbulent viscosity
vii

P density

drop relaxation time

oi turbulent Prandtl/Schmidt number

generic property

o standard deviation of PDF

Subscripts

a air

avg average value

c centerline quantity

f liquid-phase property

F Freon-11

g gas-phase property

i drop group or coordinate direction

o injector exit condition

P drop property

s drop surface condition

ambient condition

Superscripts _ ,

(-) time-averaged quantity

( )' time-averaged fluctuating quantity

( ) Favre-averaged quantity

( )" Favre-averaged fluctuating quantity

. ( ) vector quantity

I. INTRODUCTION

The objective of this investigation was to complete measurements

of spray structure, useful for evaluation of models of the process.

The work was motivated by the need for additional experimental

information on sprays, as expressed in several recent reviews

[1,2] I The tests considered evaporating sprays, generated by an

air-atomizing injector, in a still environment. This arrangement has

simple geometry and well-defined boundary conditions, which facilitates

model evaluation. Furthermore, evaporating sprays highlight effects of

turbulence on drop dispersion and drop heat and mass transfer

phenomena, as well as effects of drops on the properties of the

continuous phase, while minimizing complications due to combustion.

Data obtained in the present investigation was also used to begin model

evaluation considering methods typical of recent spray models. The

present report is part of a systematic investigation undertaken in this

laboratory, to aid in spray model development and evaluation [3-11].

During the first phase of this investigation [3-6], models of

particle-laden jets were developed and evaluated, using existing

measurements in particle-laden jets available in the literature. While

predictions for some models were encouraging, the evaluation was

inhibited throughout by insufficient information concerning initial

conditions. Moreover, the flow structure data available in the

existing measurements were not complete in some cases, which further

hindered model evaluation.

Subsequently, complete measurements of the structure of

particle-laden jets were undertaken _n this laboratory to supplement

the data base of existing measurements in the literature [7,8]. The

experiments considered dilute solid-particle-laden jets in a still

environment, considering three particle-size groups and two loading

ratios. Measurements included mean and fluctuating velocities of both

phases, partlcle-mass fluxes, particle-size distributions, and

calibration of particle drag properties. Particular attention was

given to defining initial conditions of the flows, to obtain definitive

evaluation of spray models. Simplified models ignoring either

interphase sllp or turbulent dispersion yielded poor agreement with the

measurements [7,8]. In contrast, a stochastic separated flow model of

the process, which treated effects of interphase slip and turbulent

dispersion performed reasonably well over the new data base,

encouraging its extension to liquid sprays.

The next phase of the study considered nonevaporating sprays

injecting into a stagnant environment [6,9]. Mean and fluctuating

velocities of the contlnuous phase were measured, using laser Doppler

anemometry (LDA) techniques. Drop sizes were measured using the

Fraunhofer diffraction and slide impaction methods. Liquid fluxes in

the sprays were obtained using an isokinetic sampling probe. Model

INumber in brackets denote references.
evaluation was limited, however, due to lack of measurements of drop

properties and incomplete initial conditions.

Subsequently, the nonevaporating spray work was extended by

completing measurements of drop properties and initial conditions

[I0,11]. A multlflash photographic technique was employed to obtain

simultaneous measurements of drop size and velocity in the entire spray.

New predictions using typical recent spray models were then compared

with the completed structure measurements to obtain a more convincing

evaluation of the models. As in the case of the particle-laden jets

[7,8], simplified models ignoring either turbulent dispersion of drops

or sllp between the phases performed poorly. On the other hand, the

stochastic separated flow model, which included effects of slip and

turbulent dispersion, predicted the structure of the nonevaporating

sprays reasonably well [I0,11]. A notable feature of the results was

that the stochastic model performed quite well in spite of significant

effects of turbulent dispersion exhibited by the sprays. There was no

modification of the model from its original calibration for

partlcle-laden jets (where effects of turbulent dispersion were not

significant). These and other results [I0,11] encouraged further

extension of the stochastic model to evaporating sprays.

Existing data on the mean and turbulent structure of evaporating

sprays is limited. A recent review discusses early work in the field

[I]. Yule et al. [12] have since reported measurements in evaporating

kerosene sprays from a twin-fluld injector in a coflowing stream which

could be preheated. Measurements of particle size were undertaken

using a laser tomographic llght-scattering technique while mean drop

and continuous-phase Velocities were measured using LDA.

Tishkoff et al. [13,14] have also reported measurements for

evaporating sprays. The system studied was an n-heptane spray from a

solid cone atomizer which was injected into a low velocity, coaxial

flow of air. The spray plume shape was studied using photographic,

shadowgraph and light-scattering techniques. In addition, droplet-size

distributions, liquid-phase volume fractions, and vapor-concentratlon

measurements were made at two axial locations. Drop size and velocity

measurements were obtained using an imaging technique.

The existing measurements in evaporating sprays are generally

inadequate for evaluating spray models due to lack of complete

information on flow structure, awkward flow configurations or

incomplete characterization of injector properties. The present

investigation seeks to provide data on evaporating sprays useful for

evaluating spray models, by consldering a simple spray configuration

with well-deflned initial and boundary conditions and relatively

complete structure measurements. Predictions using typical recent

spray models are also compared with the completed structure

measurements, to gain further understanding of two-phase/turbulence

interactions in evaporating situations.

The structure of sprays is generally influenced by turbulent

dispersion of the discrete phase. Turbulent dispersion of drops is

examined during this investigation by comparing predictions of several
theoretical models with the present measurements in evaporating sprays.

Past models of turbulent particle-laden jets and sprays often consider

two limiting cases instead of treating turbulent drop dispersion [1,2].

At one limit the drops and the continuous phase are assumed to have

equal rates of turbulent diffusion. The locally homogeneous flow (LHF)

approximation provides a consistent formulation of this limit. This

• implies that interphase transport rates are infinitely fast, so that

both phases have the same velocity at each point in the flow. The LHF

approximation provides best results for flows containing small drops,

where characteristic response times of drops are small in comparison to

characteristic times of turbulent fluctuations. LHF models have been

extensively evaluated during earlier work in this laboratory, but only

yielded accurate predictions for drop sizes smaller than most practical applications [15-17].

Turbulent drop dispersion is neglected entirely at the other limit.

This implies that drops follow deterministic trajectories since they

only interact with mean properties of the continuous phase, yielding a

deterministic separated flow (DSF) model. Such an approximation is

appropriate for flows containing large drops, where characteristic drop

response times to flow disturbances are large in comparison to

characteristic turbulent fluctuation times. Several spray models have

been proposed along these lines, e.g., E1 Banhawy and Whitelaw [18],

Mongia and Smith [19], Boyson and Swithenbank [20] , and Faeth and

coworkers [I-11], among others [I]. Due to the complexities of sprays

and uncertainties in initial conditions, however, the value of DSF

models has not been clearly established as yet.

Most practical particle-laden flows exhibit properties between

these limits and require consideration of turbulent particle dispersion.

Early dispersion models, discussed by Yuu et al. [21] apply a gradient

diffusion approximation with empirical correlations of turbulent

particle exchange coefficients. This approach is not practical,

however, since such exchange coefficients are influenced by both

particle and turbulence properties--requiring excessive effort to

accumulate a data base sufficient for general application of the method.

Several recent studies of turbulent drop dispersion use stochastic

separated flow (SSF) methods to circumvent the limitations of the

gradient diffusion approach. Stochastic analysis requires an estimate

of the mean and turbulent properties of the continuous phase. Drop

trajectories are then computed by random sampling to find instantaneous

continuous phase properties. Mean and fluctuating drop properties are

found by Monte Carlo methods--where a statistically significant number

of drop trajectories are averaged to obtain system properties.

r

SSF models have been applied to particle-laden jets. Yuu et al.

[21] use empirical correlations of mean and turbulent properties for

SSF analysis of their particle dispersion measurements. Gosman and

Ioannides [223 propose a more comprehensive approach, where flow

properties for the stochastic calculations are computed with a k-E

turbulence model. This approach has been adopted by the present
authors in their study of partlcle-laden jets and sprays, after only

minor modification [I-11].

In the following, the models are described first of all.

Experimental methods used for measurements in evaporating sprays are

then discussed. The report concludes with an evaluation of the models

using the new spray measurements.

2. THEORY

2.1 Introduction

Three theoretical models of spray processes were considered:

(I) a locally homogeneous flow (LHF) model, where sllp between the

phases is neglected and the flow is assumed to be in local

thermodynamic equilibrium; (2) a deterministic separated flow (DSF)

model, where sllp and finite interphase transport rates are considered

but effects of drop dispersion by turbulence and effects of turbulence

on interphase transport rates are ignored; and (3) a stochastic

separated flow (SSF) model, where effects of interphase sllp, turbulent

dispersion and turbulent fluctuations are considered using random

sampling for turbulence properties in conjunction with random-walk

computations for drop motion.

All models employ the widely adopted procedures of k-£-g

turbulence models for the gas phase, since this approach has been

thoroughly calibrated during earlier work [I-11,15-17]. Major

assumptions for the gas phase are: exchange coefficients of all

species and heat are the same, buoyancy only affects the mean flow, and

kinetic energy is negligible. Effects of buoyancy are generally small

in practical sprays, and neglecting kinetic energy limits the model to

low Mach number flows, which is appropriate for the test conditions to

be examined as well as for most practical combustion chambers. The

assumption of equal exchange coefficients is widely recognized as being

acceptable for high Reynolds number turbulent flows typical of spray

processes. Other assumptions will be described when introduced since

they differ for each model.

In order to ensure adequate numerical closure with reasonable

computation costs, the models are limited to boundary-layer flows with

no reclrculation. The present test flows are axisymmetric with no

swirl; therefore, the analysis is posed accordingly. The advantage of

these conditions is that they correspond to cases where the turbulence

models were developed [23] and have high reliability.

2.2 Locally Homogeneous Flow Model

2.2.1 Governing Equations

The basic premise of the LHF model is that the rates

of interphase transport are fast in comparison to the rate of

development of the flow as a whole. This implies that all phases have

the same velocity and temperature at each point in the flow.
Past formulations of the LHF model 115-17] use the

Reynolds-averaged form of the governing equations. However, the

Favre-averaged form of the equations has been proposed as a more

formally correct treatment of the physical processes occurring in

turbulent variable density and combusting flows 124]. Furthermore, the

Favre-averaged form of the governing equations reduces to the

Reynolds-averaged form for constant density flows. Jeng and Faeth 125]

_ used the Favre-averaged equations and established a single set of

turbulence model constants which satisfactorily predict both constant

and variable density jets. Following Jeng and Faeth 125], the

Favre-averaged governing equations for the LHF model based on the

assumptions discussed in Section 2.1 are written as follows:

-~~ I _ -~~ ! _ - 3¢)

ax +-r Dr (rpv ) :- r Dr (r_eff, ¢ _-_ + (2.1)

where

(2.2)

P

is a Favre-averaged quantity and~¢ is a generic quantity. The

conservation equations of mass (¢ = I), momentum, mixture

fraction, turbulent kinetic energy, rate of dissipation of turbulent

kinetic energy and the square of the mixture fraction fluctuations are

obtained using Equation (2.1) and the expressions for _, Ueff,. and

S_ shown in Table I along with the appropriate empirical constants.

T_e empirical constants were established for noncombusting and

combusting single-phase flows and are not changed when sprays are

considered [1,15-17,25].

The turbulent viscosity is calculated from the turbulent kinetic

energy and the rate of dissipation as follows:

_ k2

Ut = C p--_ (2.3)

2.2.2 State Relationships

Under the LHF approximation, the flow is equivalent to

a single-phase flow and effects of the dispersed phase only appear in

the representation of thermodynamic properties (temperature, density,

enthalpy, etc.) and molecular transport properties (viscosity, thermal

conductivity, etc.). The representation of these properties is

generally called the state relationships for the flow. Finding state

relationships for thermodynamic properties involves conventional

adiabatic mixing calculations, with the local state of the mixture

specified by the mixture fraction, f, (the fraction of

material at a point which originated at the injector). State

relationships used for the present LHF predictions for the case I and

case 2 evaporating sprays followed past practice [I] and are summarized

in Appendix B.
Table I. Source Terms in Equation (2.1)

Peff,€ S_

I ---- 0

P + Pt a (p= - _)

(u/Sc) + (Ut/of) 0

-2

E p + (pt/Oc) (C_:IPt( _} - Cc2P_:){_:/k)

2

g (p/SC) + (Pt/Og) CglPtL__ j N Cg2pgc/k

C C_I Cgl C_2=Cg2 ok oE of=og Sc

0.09 I.44 2.8 I.87 I.0 I.3 0.7 0.7

!
\

7

With equal exchange coefficients, instantaneous properties are

only a function of mixture fraction. This allows determination of all

scalar properties (temperature, composition and density), as a function

of mixture fraction--once and for all 11,23]. The mass-averaged mean

and variance of the flow properties are then found from the

_ass-averaged probability density function for mixture fraction,

P(f) as follows 124,25]

:_ flo_(f)_(f)df (2.4) P

_,,2:____;°i(_(f)__)2_(f)df (2.5)

p

where p is obtained from

= (flop(- I 7P(f) ) df)-I (2.6)

Similarly, time-averaged means and variances are expressed as follows:

= P f_ (¢(f)/p(f)) P(f) df (2.7)

€,2 = f_ P(f) I (¢(f) _ _(f))2 _(f) df (2.8)

In Equations (2.4) and (2.5), ¢(f) is known from the state

[elatlonshlps, cf., Appendix B. A functional form must be assumed for

P(f), although the specific form used has little effect on

predictions. A clipped Gausslan fun_tlon [24,25] was employed for the

Favre probability density function, P(f). P(f) depends on the most

probable value _ and the standard devi_tlon c of the distribution which

can be found from the local values of f and g as follows:

g = fol(f _ _)2 _(f) df (2.10)

Both f and g are known from the solution of the equations.

Therefore, Equations (2.9) and (2.10) provide two implicit equations

to solve for the most probable value p and standard deviation c of

P(f). This completes the specification of the probability density

function. Mass and tlme-averaged values of the density, temperature
°_

8

and composition can then be obtained from Equations (2.4) and (2.7),

respectively, where ¢(f) is specified by the equation of state.

2.2.3 Computations

Initial conditions for the calculations are prescribed

at the injector exit similar to past work [15-17]. In the absence of

other information, all properties are assumed to be constant at the

injector exit, aside from a shear layer having a thickness equal to I%

of the injector radius at the passage wall. The constant property

portion of the flow is specified as follows:

x : O, r < 0.99d/2; Uo : _o/_o, fo = I, k° : (O.02u o)2,

_o = 2.84 x 10-5 -Uo3/d , go

0 (2.11)

The initial variation of u and f in the shear layer was assumed to be

linear. Equation (2.11) provides the inner boundary condition until the

shear layer reaches the spray axis after which all gradients at the

axis are zero. In the shear layer, initial values of k and € were

found by solving their transport equations while neglecting convection

and diffusion terms; while g was assumed to be p[op£rtlonal to the

local kinetic energy, k. The ambient values of u, f, k,

and g are all zero for the flows considered here.

The calculations were performed uslng a modified version of GENMIX

[26]. The computational grid was similar to past work [15-17]: 33

cross-stream grid nodes; streamwlse step sizes limited to 6% of the

current flow width or an entrainment increase of 5%--whlchever was

smaller.

2.3 Deterministic Separated Flow Model

2.3.1 Discrete Phase

The deterministic separated flow model adopts the main

features of the LHF model, but only for the gas phase. The liquid

phase is treated by solving the Lagrangian equations of motion of the

drops and then computing the source terms in the governing equations

for the gas phase, resulting from interphase transport processes. This

general procedure corresponds to the particle tracking or particlesource-in-cell methods used in most recent two-phase models and is

often called a discrete droplet model (DDM) [1,2].

The main assumptions related to momentum coupling between the two

phases, of the drop trajectory calculations, are as follows: dilute

spray with a drag coefficient equivalent to a single solid sphere in an

infinite environment; ambient conditions given by mean-flow properties;

quasisteady gas phase; negligible drop shattering; and negligible

collisions.
Drops leaving the injector are divided into n groups, defined by

the initial position, size, velocity and direction. The subsequent

motion of each group is given by

. . t _ dt i : 1 2,3 (2.12) Xpi = Xpoi + Io pi ' '

The mean drop velocity is determined by integrating the equation for

conservation of momentum

dUpi d2 P CD lUp-Ul (Upl-Ui) + ai i = 1,2,3 (2.13) m d'---'t-: - (_/8) P

The standard drag coefficlent_for solid spheres is employed in the

calculations, approximated as follows [I]:

Re2/3

CD = 2._4_4 Re (I + --) 6 ' Re < 1000

= 0.44 , Re > 1000 (2.14)

d lu -ul

where, Re = P P

(2.15)

The following additional assumptions, related to heat and mass

transfer coupling between the two phases, are made for the drop

trajectory and life history calculations: the radial velocity of the

liquid surface due to evaporation of liquid is neglected; the

solubility of ambient gases in the liquid is negligible; the vapor

pressure of the liquid at the drop surface temperature is used to

determine the vapor mass fraction at the liquid surface; effects of

curvature (surface tension) on vapor pressure is ignored since it is

generally found that this effect is small for pressures greater than

I atm and drop diameters greater than I micron [I]; the gas-phase Lewis

number is unity; Dufour and Soret effects are neglected; effects of

forced convection are represented by empirical correlations; transport

processes within the drop are represented by the limiting case of the

thin skin model; and drop transport characteristics are computed from

mean gas-phase properties in the vicinity of the drop neglecting

effects due to turbulent fluctuations. The last assumption is

characteristic of the DSF model and will be relaxed for the SSF model.

All the above assumptions are common for dilute spray models and their

justification is discussed by Faeth [I].

It is generally necessary to treat transient effects of drop

heating throughout the lifetime of a drop, since transport processes

" within a drop have characteristic times which are comparable to drop

lifetimes [I]. Exact analysis of internal drop transport processes is

not feasible, therefore, two limiting cases have usually been examined

by past investigators [I]. In the first case, or thin skin model for
I0

the llquid-phase transport, heat and mass diffusivities in the liquid

phase are assumed to be zero so that the bulk-liquid properties remain

at the injected condition• However, an infinitely thin surface layer

is assumed to be heated and has composition changes required by phase .I

equilibrium. The second case, or uniform temperature model, involves

the assumption of infinite thermal diffuslvlty. In this case, the drop

temperature is spatially uniform, but time varying. Both models have

been shown to predict quite similar evaporation rates (which is the

most important variable of interest) for evaporating and combusting

sprays at atmospheric pressure [I]. The thin skin model was chosen in

the present study since it affords other major simplifications for the

contlnuous-phase analysis, as will be seen later.

With the above assumptions, the following drop conservation

equations are solved, in addition to Equations (2.12)-(2.15), for each

drop group i:

dd

pi = _ 2_,!/(Upi Pf) (2.16)

dXpi 1

h(T - Tpsi) = _ hfg (2.17)

where,

• TT

m i dpi

p D = 2 NS in (I + B) (2.18)

h dpl

k = 2 Np In (I + B)/B (2.19)

B = (YFgs - YFg )/(I - Y_gs (2.20)

0.276 ReI/2 (Pr or Sc) I/3

Np or NS = I + (2.21)

(I + 1.232/(Re (Pr or Sc)4/3)) I/2

In Equation (2.19), h is a heat transfer coefficient that has been

corrected for convection and mass transfer effects. Equation (2.21) is

a multlpllcatlve correction for heat and mass transfer with convection

proposed by Faeth [I], and provides a reasonable correlation of

existing data for Re < 2000.

In Equation (2.20)' YF_6S is determined, knowing the liquid

surface temperature and the pressure, from the vapor pressure

characteristic of the liquid

Y _ f (T , P) (2.22)

Fgs Ps
ii

The particular vapor pressure relationship, along with other properties

of Freon-11, and the mixing rules used in the present calculations are

presented in Appendix A.

In Equation (2.13), the size and mass of the drop are related as

follows:

= d3

m i (_/6) Pbf pi (2.23)

where Pbf is the bulk liquid density which remains constant at the

injected condition under the assumptions of the thin skin model. All

other properties in Equations (2.12)-(2.21) are either at the surface

state or an average condition for the flow field around the drop.

Average properties were computed at a mean state defined as follows:

Cavg = e Cgs + (I - e) Cg_ (2.24)

where ¢ is a generic quantity representing either mass fraction or

temperature, and 0 _ _ _ I.

Uncertainties in proper average transport properties to be used in

the drop trajectory calculations are a potential source of error. This

error was minimized by calibrating the drop life history calculations

with single drop experiments. A description of the calibration

experiments and the results are described in Appendix C. Based on the

present tests, a value of e = 0.75 was used in Equation (2.24).

2.3.2 Continuous Phase

2.3.2.1 Description of Model

This portion of the analysis also utilizes

the dilute spray approximation. This implies that the void fraction is

unity and that the presence of drops does not contribute directly to

the generation or dissipation of turbulence (the latter effect is

frequently called turbulence modulation).

The interaction between the liquid and gas phases yields an

additional source terms Sp on the RHS of Equation (2.1). For

conservation of momentum, this term is found by computing the net

change of momentum of each drop class i as it passes across a

computational cell j.2 The momentum source term per unit cell

volume is as follows:

2Only one index is needed to define a cell since the calculation is

parabolic and each computational cell is defined by its radial

position.
12

n

Momentum: S . = ( [ _i((mi_ ) - (mi_po) )j)/Vj (2.25)

puj i=I pi in out

where nl is the number of drops per unit time in each class and in and

out denote drop conditions entering and leaving the computational cell.

This procedure allows for complete momentum coupling between the two

phases.

The following assumptions are used to treat heat and mass transfer

effects: the gas-phase Lewis number is unity; the mixing process in

the gas-phase is adiabatic, and the transport processes in the

llquld-phase is represented by the thin skin model. The last

assumption precludes the need to solve the energy equation, since all

the heat reaching the drops is used to gasify the liquid. Furthermore,

the conserved scalar approach (for mixture fraction) is no longer used.

Instead, the conservation equation for Freon-11 yapor mass fraction,

YFg, is solved. All other scalar properties of the gas-phase, e.g.,

temperature, density and composition, can then be determined, provided

state relationships relating these scalar properties as a function of

Freon-11 vapor mass fraction can be constructed. The state

relationships used in the present study are described in the next

section.

The conservation equation for YFg has a source term S.... wJF on the

RHS of Equation (3.1). This term is found by computing the n_t change

of mass of each drop group i as it passes across a computational cell

j, and is given as follows:

SpYFg3_.= I i=I ni ((ml)in - (mi)out) 1/V'j 3 (2.26)

The conservation equation for mass also has a source term Spm on

the RHS of Equation (2.1), which is identical to Equation (2.26).

Inclusion of this source term requires a fundamental restructuring of

the GENMIX computational code, since the governing equations are solved

in the dimensionless stream function domain [26]. For dilute sprays

considered in the present study, this distributed source term Spm has a

negligible contribution to the total mass flow rate at any

cross-section of the flow, since entrainment rates are much higher.

For instance, it was found that the contribution of Spm to the total

mass flow rate of the continuous phase between x/d = 50 and 250 was

approximately 1.5-3% of the entrained flow in the case I and case 2

evaporating sprays, respectively. Therefore, Spm was not included in

the conservation equation for mass, since the relatively significant

effort required for program modification was not warranted in the

present study.
(D

h

fo ' fo

rh h

QO I 00

r_g, hg

ril h Q _ Q

h

°oo Q

Figure i. Schematic representation of the mixing process.
14

Finally, the conservation equation for Freon-11 vapor mass

fraction fluctuations, gw_ equivalent to tile8-equation in Equation

(2.1), is solved as requl_ed by the second-order turbulence model• The

remainder of the continuous-phase analysis is similar to the LHF model

except for the state relationships and the probability density function

model, which is described in the following sections•

2.3•2.2 State Relationships

For the separated flow models, the variations of

of enthalpy, composition, temperature and density of the gaseous

mixture with Freon-11 vapor mass fraction are provided by the state

relationships. All gases are assumed to be ideal gases, since the

experimental results were all obtained at relatively low pressures.

Combustion is not treated, therefore, chemical reaction is ignored.

Furthermore, under the assumptions of the present analysis, the mixing

process is adiabatic and occurs at constant pressure.

With the above assumptions, the adiabatic mixing process at any

point in the flow can be shown schematically as in Figure I. Stream I

originates from upstream of the injector exit, and consists of Freon-11

liquid and air since an air-atomizing injector was used• Stream 2

represents ambient air, which does not contain any Freon-11.

Conservation of species yields

mg = mfo (2.27)

= _ + _ (2.28)

a ao a_

Conservation of energy yields

• + _ h = _ h + _ h (2•29) mfo hfo + mac hao a_ a_ g g a a

It is assumed that the ambient air and injector air are at the same

state, which closely approximates experimental conditions; therefore,

= h

ha° a (2.30)

Using the ideal gas assumption, and combining Equations (2.27)-(2.30),

we have, in terms of gas-phase mass fractions,

YFg (hfgo + Cpg (To - T)) + Ya Cpa (To - T) = 0 (2.31)

where,

Ya = I - YFg (2.32)

Therefore, the properties at each point in the flow correspond to the

thermodynamic state reached when an amount YFg of injected Freon-11 at

its initial state and (I - YFg) of air at ambient conditions, are

adiabatically mixed at the ambient pressure of the jet. Given the

Freon-11 vapor mass fraction, the composition and temperature of the
15

gaseous mixture is obtained from Equations (2.31) and (2.32). The

mixture specific volume is obtained from

v = IYFg/Pg + Ya/Pa I (2.33)

where the air and vapor densities are obtained from the ideal gas

" expression at the temperature and total pressure of the mixture.

At a Freon-11 vapor mass fraction of YFg : 0.292, the Freon-11

vapor-alr mixture becomes completely saturated. For present

conditions, the saturation temperature at this state is 240.3 K. Any

further increase in the Freon-11 vapor mass fraction YFg is assumed to

result in the condensation of the excess vapor which then remains

suspended as fogllke droplets in the gas-phase. The total mixture is

very likely to follow the locally homogeneous approximation, so that

the temperature of the mixture is assumed to remain constant at the

saturation value. At such conditions, however, the specific volume of

the gaseous mixture is recalculated to account for the condensed

portion of the Freon-11 vapor, as follows:

v = I(YFg - 0.292)/pf + 0.292/pg + ya/Pa I (2.34)

In Equation (2.34), the densities are evaluated at the saturation

temperature, 240.3 K. Figure 2 shows the state relationship obtained

from the analysis described above. The properties of the spray fluids

used to construct the state relationship are presented in Appendix A.

2.3.2.3 Probability Density Function Model

The mean value of any scalar quantity ¢ (other

than k, e and gFg) can be determined from its variation with YFg if

the probability density function of YFg, P(YFg), is known as a

function of position in the flow. Given P(YFg), the mass-averaged

means and variances of any scalar ¢ is given by Equations (2.4) and

(2.5), respectively, with f replaced by YFg As before, a clipped

Gaussian function was assumed for P(YFg) _(YFg) is characterized by

the most probable value U, and the standard deviation o of the

distribution which can be found from the local values of YFg and gFg as follows:

YFg = _ YFg P(YFg ) dYFg (2.35)

gFg = f_ (YFg _ YFg )2 _(YFg ) dYFg (2.36)

Both YFg and gFg are known from the solution of their respective

conservation equations. Therefore, Equations (2.35) and (2.36) provide

. two implicit equations to solve for _ and o. This completes the

specification of the probability density function.
16

Z

o Ya F-- 0.6

U

,,::1[

n,,

I.I.

0.4 REON- II

VAPOR

0.0 I I I

0.0 02 0.4 0.6 0.8 _.0

GAS- PHASE FREON- I I MASS FRACTION, YFa

Figure 2. State relationship for the Freon-ll

vapor-air mixture (SF Model).
17

Time-averaged scalar properties of the continuous phase are needed

in the drop trajectory and life history computations, Equations

(2.13)-(2.21). These were found, as before, from Equations

(2.6)-(2.8), with f replaced by YFgTime-averaged velocity of the continuous phase surrounding the

drops is also needed in the discrete phase computations. However, to

obtain the time-averaged velocity from the Favre-averaged velocity, the

correlation be known, since involving fluctuating density and fluctuating velocity must

(2.37)

In the present study, this correlation was assumed to be zero, so that

the Favre- and time-averaged velocities are equal.

The gas-phase equations are solved in the same manner as the LHF

model. The only change in this portion of he program involves addition

of the new source terms given in Equations (2.25) and (2.26). The drop

motion equatlons, Equations (2.12)-(2.21), are solved at the same time,

algorithm. in a stepwise fashion, using a second-order finite difference

Computations with the separated flow models were initiated at

x/d = 50 for all the test sprays, which was the position nearest the

injector where adequate spatial resolution was obtained so that profile

measurements could provide initial conditions for the calculations.

These initial conditions included measurements of mean and fluctuating

gas-phase properties, liquid flux, drop size and axial components of

the mean and fluctuating drop velocities for both evaporating sprays.

Initial conditions for _ were computed using Equation (2.3) and the

measured values of O, k and the Reynolds stress.

Downstream of x/d = 50 the void fraction was always greater than

99.1%; therefore, the dilute spray approximation was justified with

1800 littledroperror. groups.The computations for the DSF model employed no less than

2.4 Stochastic Separated Flow Mode]

The DSF model considers only deterministic trajectories for

drop groups. The stochastic separated flow model, however, includes

effects of turbulent fluctuations on drop dispersion and interphase

moment Ioannides um transport [22]. rates by using a technique proposed by Gosman and

- The stochastic model involves computing the trajectories of a

statistically significant sample of individual drops as they move away

from the injector and encounter a random distribution of turbulent

. eddies--utilizlng Monte Carlo methods. The key elements of this

approach are the methods for specifying the properties of each eddy and

the time of interaction of a drop with a particular eddy.
18

Properties within a particular eddy are assumed to be uniform, but

properties change in a random fashion from eddy to eddy. The

trajectory calculation is the same as the DSF model, involving solution

of Equations (2.12)-(2.21); however, mean-gas properties in these

equations are replaced by the instantaneous properties of each eddy.

The properties of each eddy were found at the start of drop.eddy

interaction by making a random selection from the probability density

function (PDF) of velocity. Velocity fluctuations were assumed to be

isotropic with a Gausslan PDF having a standard deviation of (2k/3) I/2

and mean components 0, 7, O. This ignores the distinction between

Favre- and time-averaged velocities (the latter being the quantity that

should be sampled), since, as mentioned earlier, the correlation

involving fluctuating density and fluctuating velocity was assumed to

be zero. The cumulative distribution function for each velocity

component was constructed and sampled. This involved randomly

selecting three numbers in the range 0-I and computing the velocity

components for these three values of the cumulative distribution

function.

The instantaneous scalar properties of each eddy were found in a

similar manner. Scalar properties of the continuous phase are only a

function of Freon-11 vapor mass fraction YFg" The instantaneous scalar

properties of each eddy are also only a function of the instantaneous

value of YFg- At any point in the flow, the Favre clipped Gaussian

distribution function of YFg was constructed knowing the values of YFg

and gFg- This Favre PDF can be used to calculate the conventional

time-averaged probability density function, P(YFg), as follows [25]:

p(YFg) P(YFg) = p P(YFg) (2.38)

The cumulative distribution function for YFg can be constructed from

the time-averaged PDF. This distribution was randomly sampled by

selecting a random number in the range 0-I to find the instantaneous

value of YFg" The instantaneous temperature, composition and density

of the eddy was found by using the instantaneous value of YFg in

conjunction with the state relationships, Figure 2.

A drop was assumed to interact with an eddy for a time which was

decided from either the eddy lifetime or the characteristic size of an

eddy [I-5]. The characteristic size of an eddy was taken to be the

dissipation length scale.

L _ C 3/4 K3/2/E (2.39)

e U

The eddy lifetime was computed from the following:

I/2

t = L /(2k/3) (2.40)

e e

Drops were assumed to interact with an eddy as.long as the time of

interaction, At, and the distance of interaction IAXp I, satisfied the

following criteria:
19

At < te , IA p] - e (2.41)

Drop capture by an eddy corresponds to ending the interaction with the

first criterion while a drop traverses an eddy when the interaction is

ended with the second criterion.

The remaining computations are similar to the DSF model, except

that the source terms of Equations (2.16) and (2.26) are computed for

the random-walk trajectories of the drops--as opposed to the

deterministic solution. Also, more drop trajectories must be

considered to obtain statistically significant drop properties

(generally 5000-6000 trajectories were used). A by-product of the

additional calculations, however, is that the SSF model yields both

mean and fluctuating drop properties. This provides an additional test of model performance.

3. EXPERIMENTAL METHODS

3.1 Introduction

The experimental apparatus provided convenient optical and

probe access to the flow. The injector and the fluid delivery system

allowed selection of fine and coarse sprays and assured long-term

repeatability of the test spray conditions.

The following flows were examined during the present study:

I. An isothermal air jet--to check experimental techniques.

2. Two evaporating sprays (with Sauter mean diameters of 30 and

58 _m).

Nonintrusive instrumentation included the laser-Doppler

anemometer and multiflash photography. Other measurements involved

probes such as isokinetic sampling probes, shielded thermocouples and slide impactors.

3.2 Test Apparatus

The requirement for a flow configuration having no zones of

reclrculation, a simple geometry and well-deflned boundary conditions

is met with the apparatus illustrated in Figure 3. The injector was

mounted on a two-dimensional traversing mechanism at the center of a

cage assembly (I m square by 2.5 m high). For all the test flows,

injection was vertically downward into stagnant room air. The flow was

protected from room disturbances using 16-mesh screens all around the

cage. Major traversing, to obtain radial profiles of flow quantities,

. involved moving the entire cage assembly, which was mounted on a

bearing track. This approach keeps the flow nearly concentric with the

vertical axis of the cage, which minimizes disturbance of the

axlsymmetric flow due to off-center screen positions, and also allows
MovableScreenedEnclosure MalvernReceiver _

ReceivingOptics

°

Injectorwith2-D

Traverse Minicomputer

Printer

Malvern Tmnsmitfer /\ I

..LDA Sending / \

/ \ Counter

50mW He-N e Laser_._ /Spray\ RMS Voltmeter

/ \

Oscilloscope L Integrating

Digitel

/ Voltmeter

LinearPositioner EnclosureTrack (Radial Traverse)

Figure 3. Sketch of the experimental apparatus.
21

optical instrumentation to be mounted on a rigid base. Unisllde

arrangements were used to position the injector relative to the

measurement location.

A plenum chamber with an exhaust system was included at the bottom

of the cage. The inlet to the plenum chamber is screened and is I m

below the plane of instrumentation. The screened inlet provides

uniform suction thus keeping the flow axisymmetric. The only purpose

of the exhaust system was to prevent the smallest drops from

recirculating and its operation did not introduce a coflow of any

significance. Testing showed that the disturbance levels were less

than I% at the measurement location.

Measurements from this arrangement should be attractive for those

wishing to evaluate models. The flow is analogous to a jet in

stagnant surroundings, yielding a parabolic (boundary layer) flow. The

turbulence characteristics of such a flow can be modeled more reliably

than flows with recirculation. Naturally, boundary layer flows greatly

simplify problems of obtaining accurate numerical solutions, releasing

computer time for use in the two-phase portion of the problem. The

absence of coflow eliminates problems of flow separation on bulky

injector elements. Boundary conditions are well-defined, since there

are no uncertainties regarding wall friction and heat losses and inlet

flow properties which are encountered in enclosed chambers.

The flow system of the injector is illustrated in Figure 4. A

Spraying Systems Company air atomizing injector (model I/4 J2050 fluid

nozzle and 67147 air nozzle with outlet diameter of 1.194 mm) was used

for all the spray tests. The injector delivers a full-cone spray with

no swirl. This injector is identical to that used by Faeth and

coworkers [15-17].

The air flow to the injector is controlled with a pressure

regulator and metered with a critical flow orifice to ensure long-term

stable operation. The pressure regulator was a Matheson model 4

regulator with a 0-21MPa output capacity. The pressure upstream of

the critical-flow orifice was measured with a Heise absolute pressure

gauge with a 0-2.1MPa capacity. The pressure gauge was calibrated

with a dead-weight tester and the orifice was calibrated with a

Precision Scientific Company wet-test meter (0.283 liters/rev.).

The liquid was stored in a tank under pressure. Since the tank

was not agitated and pressure levels were mod@rate (0.3-0.8 MPa), the

dissolved air content of the spray liquids was negligible. The liquid

flow is controlled with a valve and metered with rotameters. A

Matheson model 604 rotameter, used to meter the evaporating spray

liquid, was calibrated with a sight-gauge apparatus.

The spray liquid must be well-defined material in order to

. facilitate use of the measurements by others. Freon 11 supplied by

Pennwalt Corporation was used for tests with the evaporating sprays.

The properties of Freon 11 are summarized in Appendix A. In order to

maintain repeatable flow and atomization conditions the entire test

cell was heated to above-normal temperatures--to 27 ± I°C.
m

_CRITICAL FLOW

ORIFICE

20 MPa _ /t"

AIR SUPPLY _" "_ 1 1

_ "'''''". • •

VENT _._

ROTAMETER

LIQUID SUPPLY

TANK @ GAGE

REGULATOR

LIQUID PRESSURE GAGE

FEED TANK _ FILTER

VALVE

Figure 4. Sketch of the injector flow system.
23

3.3 Measurement Techniques and Instrumentation

3.3.1 Gas-Phase Properties

3.3.1.1 Velocity Measurement

Table 2 is a summary of the flow structure

measurements made and the techniques employed for each measurement.

Mean and fluctuating gas velocities were measured using a

dual-beam, single-channel, frequency-shlfted laser-Doppler anemometer

(LDA). An equipment llst for the LDA system appears in Table 3. The

sending and receiving optics had a focal length of 242 mm with a 11.61°

angle between beams. A 200 mm focal length lens was used to focus the

scattered light onto a photomultiplier. The aperture diameter of the

photomultipller was 0.25 mm. The receiving lens was masked with a

beam-stop which provided a collection aperture having a diameter of 25

mm. The above optical configuration produced a measuring volume 0.470

mm in length and 0.098 mm in diameter, with a fringe spacing of 3.128

_m.

Seeding particles for operation of the LDA were provided in two

ways. In the two-phase region, the smallest drops provided adequate

seeding, while erroneous signals from large drops were eliminated by

setting a low signal amplitude limit on the counter data processor,

since large drops yield large pedestal signals. This natural source

was supplemented by seeding the surroundings of the spray using oil

particles which are present suspended in the exhaust of a vacuum pump.

The average diameter of the particles was 0.6 um at a concentration of

2.8 x I0lu particles/m3. Photographic measurements showed that the

maximum concentration of spray drops was about 3.0 x 109 drops/m3 at

x/d = 40 in the 30 _m SMD evaporating spray. The concentration of

spray drops was over two orders of magnitude less than the

concentration of the seeding particles in other downstream positions of

the test sprays. Therefore, gas velocities were primarily measured,

with a small bias due to spray drops. The seeding techniques provided

a relatively high signal rate so that concentration biasing was

eliminated by using time averages. This procedure involved adjusting

external seeding until intermlttency was no longer observed on the

oscilloscope trace of the LDA detector output.

Mean and fluctuating velocity components of the gas phase were

measured at various axial and radial locations in al! the four test

sprays. An integration period of one minute or more was used to

determine the mean quantities. Radial profiles were obtained in a

single traverse across the spray and components of mean and fluctuating

velocities were recorded by employing different beam orientations at

each radial location. _Measurements of the tangential component of the

fluctuating velocity (w'2) I/2 were made with a separate traverse in

the third direction. The use of several beam orientations allowed

,- measurement of Reynolds stress. Reynolds stress measurements are

valuable for checking model predictions and for locating the flow

centerllne (since Reynolds stress is zero at the centerllne and doesn't
Table 2. Summary of Instrumentation for Spray Structure Measurements

Measurement Technique Equipment

Mean and fluctuating gas Dual-beam, forward scatter laser-Doppler Spectra Physics Model 125A

velocities, anemometer, frequency shifted with (50 mW) He Ne laser, rest

tracker and burst counter data processing. TSI, Inc.

Drop size and velocity. Double-flash shadow photography. In-house design.

Drop size distributions, a)Slide impactlon. In-house design.

b)Photography. In-house design.

Liquid flux. Slide impaction. In-house design.

Mean gas-phase temperature. Fine-wlre thermocouple shielded from In-House design, 25 um

drop impacts, diameter wires.

Mean composition of major Isokinetic sampling and analysis Varian model 920 gas

species, with gas chromatograph, chromatograph with hot-wire

detector.
25

Table 3. LDA Equipment List

Component Manufacturer Model

Helium-Neon Laser Spectra Physics 125A

Integrated Optics Thermo-Systems 900

Frequency Shifter Thermo-Systems 9180

Photodetector Thermo-Systems 960

Frequency Tracker Thermo-Systems 1090

Burst Counter Thermo-Systems 1980

RMS Voltmeter Thermo-Systems 1060

Dual-Beam Oscilloscope Thermo-Systems 561A

Integrating Digital Voltmeter Hewlett-Packard 240IC
26

exhibit the broad maxima encountered for other variables). The above

measurements were found to be repeatable within 5%.

3.3.1.2 Temperature Measurement

Mean-gas temperatures in the evaporating

spray were measured using a fine-wire thermocouple. It is difficult to

obtain accurate mean temperature measurements in sprays due to effects

of drop impaction. For this reason a shielded temperature probe which

circumvented most of the difficulties was used [16]. A sketch of the

thermocouple probe is shown in Figure 5. A 25 _m diameter

chromel-alumel butt-welded thermocouple was located along the

centerline of a 1.6 mm OD hemispherical shield. The shield was

positioned upstream of the probe so that all but the smallest drops

(diameter less than 10 _m generally) impinged on it.

The thermocouple was spot welded onto 0.75 mm diameter lead wires

of the same material. The reference junction was placed in a reference

cell, manufactured by Thermo-Electric Company, maintained at O°C. A

Hewlett-Packard integrating digital voltmeter, model 240 IC, was used

to integrate the signal over one minute periods to determine the mean

temperature. The measurements were repeatable to within 15%.

Temperature measurements in the evaporating spray were restricted

to distances greater than x/d = 250 and x/d = 500 in the case I (30 _m

SMD) and case 2 (58 um SMD) evaporating sprays, respectively.

Measurement at closer distances were unobtainable due to the formation

of ice on the thermocouple shield.

3.3.2 Liquid-Phase Properties _

3.3.2.1 Drop Size Measurement

Two methods were used to determine the drop

size distributions and Sauter mean diameters (SMD) at various locations

in the test sprays. The first method used for drop size measurements

involved inertial impaction [15]. A sketch of the slide impactor is

shown in Figure 6. Small glass slides coated with a layer of magnesium

oxide are momentarily exposed to the flow using a pneumatically driven

shutter. Drops leave a crater in the coating, which can be related to

the initial drop size [15]. The slides are then viewed under a

microscope and each drop impression is sized and counted. Typically ,

2000 drops were counted at each measurement location to obtain

statistically reliable results. The collection efficiency of the

shutter mechanism was calculated for a range of droplet sizes for a

given gas velocity [15]. This was then used to correct the number of

droplets actually collected. The SMD at each location was calculated

directly from the drop size distributions. A measurement of liquid

mass-flux is also possible by the slide impaction method and will be

described in a subsequent section.

The second method used to determine drop-size distributions

involved an imaging technique, viz., double-flash photography, which

was primarily used for simultaneous measurements of drop size and
27

/

//

/

THERMOCOUPLEWIRE

0.0 25 mm DIA.,

CHROMEL-ALUMEL

CERAMIC INSULATOR

HALF WIDTH,STAINLESS

STEEL HYPODERMICNEEDLE

O.D. 1.6mm

I.D. 1.2 mm

Figure 5. Sketch of the thermocouple probe.
I,O

oo

°LS SSL'DI\ SUPPORT ROD 6.35 DIA.

DIRECTION _ '_'--'TO AIR

']1' OF TRAVEL SUPPLY

101.6 :-! GUIDE ROD

6. :35 O.D. TUBE

Figure 6. Sketch of the droplet impactor.
29

velocity. A description of the imaging technique is given in the next section.

3.3.2.2 Drop Size and Velocity Correlation Measurement

The optical system used for the double-flash

shadow photograph technique for drop size and velocity measurements is

shown in Figure 7. The arrangement consists of two submicrosecond

flash sources, a lens system to focus the light and a camera, all

arranged on the same optical axis [27]. The flashes are fired

consecutively, at electronically controlled times, so that two images

of each of the moving droplets are obtained on the same photographic

negative. Subsequent magnification of the negative, measurement of the

size and distance traveled by the droplet, as well as knowledge of the

time interval between the flashes yields the size and velocity of the

droplets. A typical double-flash shadow photograph is shown in

Figure 8.

A General Radio type 1538-A Strobotac and type 1539-A Stroboslave

were used as the first and second flash sources, respectively, cf.,

Figure 7. They produced flashes having durations of 0.5 Us and 0.8 us,

respectively, and effectively stopped the motion of the droplets. The

first flash was located at the focal point of lens I so that a parallel

beam illuminated the field of view, yielding the sharpest shadow image.

The second flash was arranged so that the light was focused onto the

point of origin of the first flash. Since the second flash was of

longer duration, it produced a darker image than the first--providing a

means for identifying flow reversals.

The strobe units were triggered consecutively by means of a

speclally-designed pulse generator. The generator delivered pulses

that met the input specifications of the strobe units and was also

equipped with a variable time delay circuit so that the time interval

between the pulses could be selected in the range 0.1-1000 us. These

pulses were recorded, as well, with a two-channel Nicolet Explorer III

digital oscilloscope, model 204-A, so that the'time interval could be

measured within 0.05 us. Typical intervals used for the present test

conditions ranged from 2-80 Us_

Various configurations of camera lenses, film and data reduction

methods were used in different regions of the sprays. Obtaining

initial conditions of drop size and velocity required good spatial

resolution in relatively dense regions of the sprays. In these regions

a Graphlex Optar, f/4.7, 135 mm focal length lens, in conjunction with

a rectangular magnifier lens (27 mm x 40 mm, 60 mm focal length), was

used as the imaging lens system. A Graphlex 4 x 5 still camera was

_ located at the end of an extension tunnel to give a primary

magnification of 38:1. The resulting rectangular area of the spray

viewed (2.34 mm x 2.29 mm) provided satisfactory spatial resolution at

x/d = 50. Polaroid type 57 film (3000 ASA) was used wlth this setup

and measurements of drop diameter and interimage distances were made by

further magnlficatlon under a calibrated microscope.
V L_

o

SPRAY CAMERA LENS

FLASH 2 FLASH I 11\/

LENS 3 LENS 2 / LENS I /

/ ,

I \

- 7

- T _--

I \

i \

i \

PHOTOGRAPH IC

PLATE

= 2-CHANNEL NICOLET

STROBE DIGITAL OSCILLOSCOPE

UNITS

PULSE GENERATOR WITH

VARIABLE TIME DELAY

Figure 7. Sketch of the double-flash photography system.

• • t i
31

Figure 8. A typical double-flash photograph.
32

In the dilute regions of the sprays (x/d _ 100) the primary

magnification was reduced to 6:1 and Agfa pan Vario-XL Professional 35

mm film (50-1600 ASA) was used. The negatives were projected on a

screen at greatly increased magnifications to make measurements of size

and distance between images. The spray area viewed with this

arrangement was 5.7 mm x 8.0 mm.

^

The depth-of-field in which droplets appear to be in focus in the

optical sampling volume increases with increasing drop size. This

behavior results in an underestimation of the relative number of small

drops. Depth-of-field bias corrections were applied to all

photographic measurements of drop size distributions in the present

study using a procedure similar to Reference [11]. Also, only the

axial component of the drop velocities was recorded.

The overall accuracy of the present method for velocity

measurements was estimated to be ± 10%. The uncertainty associated

with size was on the order of ± 10% for drops having diameters greater

than 25 um. This uncertainty increased to ± 25% for drops whose

diameters were smaller than 25 _m. The minimum drop size measurable

within the above limits of error was 10 _m. Approximately 600 to 800

drops were counted at each measurement location to obtain drop size and

velocity distributions, which were processed to find mean and

fluctuating axial velocities and the SMD. Since the number frequency

of the large drops (> 60 um) at any given measurement location was

relatively low, measurements of fluctuating velocities for the large

drops are only qualitative. The SMD data obtained by this imaging

method and the slide impaction method agreed within 15%.

3.3.2.3 Liquid Flux Measurement

Liquid flux measurements for the evaporating

sprays employed slide impactlon. As described earlier, the slide

impaction method provides a measurement of drop size distributions. In

addition, a measurement of liquid mass-flux was also obtained by

measuring the time of exposure of the magnesium oxide coated glass

slide and the area over which the drop impressions are sized and

counted.

The slide impactor, shown in Figure 6, is equipped with a

pneumatically driven shutter mechanism designed to expose the slide to

the spray for a given time period. Perforations in the body of the

shutter allow determination of the shutter speed by means of a laser

beam-photodlode combination, the output of the photodiode being fed

into a Nicolet digital oscilloscope. The liquid mass-flux was

determined by dividing the total liquid mass (after correction of the

number of droplets collected, as described previously) by the

collection area and the exposure time. The overall uncertainty

associated with the technique was estimated to be ± 20 percent for

liquid mass-flux, based on measurements of this quantity in

nonevaporating sprays [11].
33

3.3.3 Other Measurements

3.3.3.1 Concentration Measurement

The mean composition of injected fluid for

the evaporating sprays was determined by isoklnetic sampling and

subsequent analysis with a gas chromatograph. The technique provided a

direct measurement of the local mixture fraction of the flow.

A sketch of the sampling probe, which was similar to the one used

by Shearer et al. [15], is shown in Figure 9. The tip of the sampling

probe is heated to prevent moisture in the air from condensing and

freezing at the probe inlet during the evaporating spray tests.

Suction was applied to the sampling probe by a vacuum pump. The

suction flow rate was measured by a Precision Scientific wet-test meter

and the flow rate was adjusted to match the local gas velocity

determined earlier from the velocity measurements.

The samples were analyzed by a Varian, model 920, gas

chromatograph using a hot-wire detector. A 5 ml gas-tlght syringe was

used to transfer the sample from the sampling port to the gas

chromatograph. The separating column was stainless steel, 3.175 mm OD

by 183 cm in length packed with PORAPAK Q (80-100 mesh). The oven and

detector temperatures of the gas chromatograph were maintained at 160Oc

and 200Oc, respectively. Helium was used as the carrier gas at a flow

rate of 20.0 cc/min. Various mixtures of 99.9% purity Freon-11

(purchased from Matheson Gas Products) and air were used to calibrate

the chromatograph. The calibration procedure indicated that the peaks

were symmetrical and that the concentration was a linear function of

peak height for the concentration range of interest.

The mean injected-fluid concentration data was integrated over the

cross-section of the sprays at far downstream locations (e.g., x/d =

x/d = 250 and 500 for the case I spray and x/d = 500 for the case 2

spray), by assuming locally homogeneous conditions. This was checked

against injector liquid mass flow rates to determine the collection

efficiency of the technique.

3.3.3.2 Jet Momentum Measurement

The momentum of each of the test sprays was

determined by measuring the axial force on an impingement plate held

near the exit of the nozzle (95 mm diameter plate, 25 mm from the

nozzle). A Unimeasure 80 force transducer was used to measure the

force. The transducer was calibrated by placing known weights on the

plate. The exit velocity of the two-phase spray was then calculated

from the Jet momentum and the mass flow rate. This calculation assumes

locally homogeneous flow, and serves as initial conditions for the LHF

spray model.

3.4 Experimental Conditions

Table 4 shows the experimental conditions for the case I and

case 2 evaporating sprays. Case I is a finer spray than case 2.
34

,,---Smm _

o o CERAMIC

E __INSULATION

ou / I HEATER

: / I I

/ /

- /

/

/ /

/

/

/

i = GLASS TUBE

/

/

/

/

Figure 9. Sketch Of the sampling probe for concentration measurements.
35

Table 4. Summary of Test Conditions for Evaporating Spraysa

Flow Air Jet Sprays

Case -- I 2

Injected fluids air air and air and

Freon-11b Freon-11b

Injector flow rates, mg/s

Gas 338 138 120

Liquid 0 1450 1894

Loading ratioc 0 7.71 15.78

Jet momentum, mN 120.1 105.7 59.7

Initial velocity, m/sd 175 64.5 29.64

Reynolds numberd 2.6 x 104 4.1 x 104 3.6 x 104

SMD, ume 0 30.6 58.1

Spray anglef -- 27 29

aAll flows employ Spraying Systems air-atomizing injector (model

I/4J2050 nozzle, No. 67147 air nozzle, 1.194 mm injector exit

diameter). Ambient and injector inlet temperature 300 ± I K, ambient

pressure, 97 kPa.

bManufactured by Pennwalt Corporation, refrigerant grade, 99.8 purity.

CRatio of injected liquid to gas flow rates.

dAssuming LHF. The viscosity of air was employed for the Reynolds

number.

eArea-weighted average SMD measured by slide impaction at x/d = 50.

fDetermined from concentration measurements at x/d = 50.
36

Selection of the SMD of these sprays was done with the aid of slide

impaction measurements at x/d = 50. Also shown in Table 4 are the

experimental conditions for an air jet test which was used to check

experimental techniques [11].

The loading ratio of the sprays was selected to be within the

range of most practical liquid-fuel injection systems. Axial and

radial profiles of various flow quantities in the sprays were measured

using the techniques discussed earlier to obtain a detailed knowledge

of the spray structure. In addition, initial conditions of flow

quantities were measured so that predictions of the various spray

models could be compared with the present measurements.

4. RESULTS AND DISCUSSION

4.1 Introduction

In the following sections the experimental findings

concerning the structure of the two evaporating sprays, ef., Table 4

for operating conditions, will be presented. In addition, the

comparison of measurements and the predictions of the three theoretical

models of spray processes (LHF, DSF and SSF, cf., Section II) will be

discussed.

Time-averaged mean and fluctuating velocities were measured but

are compared here with predicted Favre averages (the former since

Favre- and time-averaged velocities are usually nearly the same [25],

the latter due to reasons mentioned in Chapter II). Since

concentration measurements by isokinetic sampling are Favre averages

and time- and Favre-averaged drop properties are identical, predicted

Favre averages apply directly for these properties. Since temperatures

were measured with a relatively small thermocouple and are, therefore,

closer to tlme-averaged values, predicted Favre-averaged temperatures

were first converted to time averages, using Equation (2.7), before

comparing with measurements.

The measurements of mean and fluctuating velocities in the air jet

were in good agreement with earlier measurements by Shearer et al. [15]

using a similar twln-fluid injector. The comparison between

measurements and predictions were also satisfactory. This established

an acceptable baseline for measurements in the sprays and these results

will not be considered any further here.

4_2 Initial Conditions

4.2.1 Jet Momentum, Spray Angle and Gas-Phase Properties

Due to its small size, measurements at the exit of the

injector were limited to mass flow rate and momentum of the two-phase

Jet. The latter measurement was completed using an impact plate,

similar to Reference [15].
37

Spray angles for the evaporating sprays were determined from

concentration measurements, at x/d = 50, to determine the presence of

Freon-11 at the edges of the sprays. The values for the case I and

case 2 sprays are 27° and 29° , respectively.

Due to limitations of spatial resolution, profiles of spray

properties were only measured at x/d _ 50. For the continuous phase,

detailed measurements of mean and fluctuating gas velocities, Reynolds

stress and kinetic energy of the gas phase were undertaken at x/d = 50,

in order to define initial conditions for the SF computations. These

measurements will be illustrated later, when all gas-phase properties

are discussed. Also, for the SF computations, initial conditions of

mean Freon-11 vapor mass fractions were deduced from liquid flux, drop

velocity and total Freon-11 concentration measurements at x/d = 50,

while Freon-11 vapor mass fraction fluctuations were estimated from LHF

predictions of the fluctuation intensity of the square of mixture

fraction fluctuations at x/d = 50. The analysis and procedure for the

last two initial conditions for the continuous phase are presented in

Appendix D.

4.2.2 Liquid-Phase Properties

Detailedmeasurementsof liquid flux, drop-size

distributionsand mean and fluctuatingdrop velocitieswere also

undertakenat x/d = 50 for both the evaporatingsprays. Liquid flux

measurementswere completedby the slide impactlontechniqueas

described in Section 3.3.2.3. The results for the case I and case 2

sprays are illustratedin Figure 10.

As in the case of the nonevaporating sprays, two techniques were

used to measure drop-size distributions at x/d = 50. Drop-slze

distributions for various radial positions at x/d = 50 for the case I

and case 2 sprays using the slide impactlon technique are illustrated

in Figure 11. The same measurements using the double-flash

photographic technique are shown in Figure 12. Figure 13 illustrates

the radial distribution of SMD across the sprays as calculated from the

drop-slze distribution data using both techniques. The double-flash

photographic technique also yields measurements of drop velocity as a

function of size, and these data, at x/d = 50, are illustrated in

Figures 14 and 15 for the case I and case2 sprays, respectively.

From Figures 11 and 12, the gross properties of the size

distributions for both the case I and case 2 sprays do not change with

radial location except in small detail, e.g., the increase in the

number fraction of the smallest drops. It is difficult to compare the

drop-slze distributions obtained by the slide impaction and

. photographic techniques, since: (I) the slide impactlon technique

yields a temporal average while the photographic technique yields a

spatial average; (2) drops with diameters less than 15 um were not

measured by the photographic technique, while the slide impaction data

indicates a large number fraction in these sizes; and (3) the size

ranges used with each of the techniques are dissimilar. For the case I

spray, if drops with diameters < 15 um are disregarded in the slide

impactlon results, then the peaks of the size distributions obtained by
38

1.0

Io I I I I

A

.8 m _

O

06--

x/d " 50 :

|_ 0 O.4--

CASE DATA A

0.2-- I O

2 z_ 0

o.o I I I I I

0.00 0.04 0.08 0.12 0.16 0.20 0.24

r/x

Figure i0. Initial conditions of liquid flux for

the evaporating sprays at x/d = 50.
25.0 _-., I I I I I I I I I I I I I

I l CASE I

--LJ --Ix/d =50 CASE 2:

12.5-- L...3 r/x =0.00 ,_.,_r_---_ x---/d =r/x50=0.00

o.o .--'_'_"m

_ -'1 r"_. 0.05 0.05

>o.. 12.5-L.-J L 30.2 pm 62.6 pm

z L_ _ -

" L,

_ 0.0 ['J _'

1"- 0. I0 0. I0

28.7 pm 58.8 pm

u.. 12._- "1__ _ -

"=' --] I

_ 0.0 --1

:::) 0.15 0.15

z i 31.5 pm _ 60.2 pm 12.5- I_ I _

_ 0.0 - ,

L.p%_ 0.20 _n- 12.5 pm 54.8pm

0.0 I I I ,---._ I . i0.0 12.7 25.4 38.1 50.8 63.5 0.0 12.7 25.4 38.1 50.8 63.5 762 88.9 101.6

DROPLET DIAMETER (pm)

Figure II. Drop-size distributions for the evaporating sprays at x/d = 50 (slide impaction results).
4O

37.5 I I I I I I I I I I I

'l__CASE x/d = 50I CASE x/d = 502

250 -

r/x =0.00 r/x =0.00

SMD =31.3 pm SMD=59.7 pm

12.5--

"1 r- t__.

"_ OO = I

o_ ., 0.05 -1.- 0.05 Zu.i 12.5- 31.2pm --

1 60.6pm -

'-'_o".o '_ , r- _ ,

" -- o.51.Tpm,o _1LL o57.6.pm,o

m iP_5- "_ -

z o.o I"-I r-7_ --

0.15 I 0.15 •_ 29.4 pm "-! 57.5 pm

12.5- m -

<_j I -L_

"' J-k _ 0.0 F-.

0.20 __, 0.20

30.4 pm 59.1 pm

125

L,--

0.0 I I I I I F-" I , , ,

I0 20 30 40 50 60 I0 30 50 70 90 I10 130

DROPLET DIAMETER (pro)

Figure 12. Drop-size distributions for the evaporating

sprays at x/d = 50 (photographic results).
41

70 I I I I I

A

6( ,- _ • • _

50-

E 40-

a

30- B • o Q

o_ o • -

x/d = 50

20-

DATA CASE TECHN IQUE

O I SLIDE IMPACTION

• I PHOTOGRAPHIC I0-- ._ .

A 2 SLIDE IMPACTION

• 2 PHOTOGRAPHIC

o I I I I I

0.00 0.04 0.08 O.I 2 O.16 0.20 0.24

r/x

Figure 13. Radial variation of SMD in the

evaporating sprays at x/d = 50.
42

30.0 I I I I

A

o o 9, 9, o

o A A "_

O O

O O O O

20.0-- 0

A []

f_

[]

- 0 [] []

v

V v

1o.o -

V v

V %7 DATA r/x

o 0.00

- A 0,05 -

CASE I o 010

x/d = 50 0 015

V 0.20

o.o I I I I

I0 20 30 40 50 60

DIAMETER (pm)

Figure 14. Initial conditions of mean axial drop velocity versus

drop size at x/d = 50 for the case 1 evaporating spray.
' 43

32.0 I I I I I

CASE 2 DATA r/x

_ x/d = 50 o 0.00

A 0.05

O 0.10

o 0.15 24.0 -

v 0.20 --

Z_

Z_ Z_

- 0 A

o @ -

0 8 0

0 0 0 0

•--,IE 16.0 - o o o o

0 0 0 0

8.0- o v

0 [] V

V

V

-- V

V

V V

o.o I I I I I

0 20 40 60 80 _00 _20

DIAMETER (pm)

Figure 15. Initial conditions of mean axial drop velocity versus

drop size at x/d = 50 for the case 2 evaporating spray.
44

the two techniques coincide approximately, cf., Figures 11 and 12.

This behavior is expected, since the variation of drop velocity with

size is moderate at this location, cf., Figure 14. The same general

observation can be made for the case 2 spray, however, with increasing

r/x positions the peaks in the size distributions obtained using the

slide Impactlon technique occur at diameters larger than in the case of

the photographic technique since the drop velocity varies significantly

with drop size at larger r/x positions, cf., Figure 15.

Except for the details noted above, differences between the slide

impactlon and photographic techniques are small, since the SMD obtained

using both techniques compare well, cf., Figure 13. This is due to the

relatively insignificant contribution to the S_D of the smallest size

drops, and also suggests only moderate influence of velocity bias.

Finally, the SMD is nearly invarlant over the cross-section of the

spray, similar to the behavior observed with the nonevaporatlng sprays

for the same location and injector [I0,11].

The variation of mean drop velocity as a function of drop size and

radial position at x/d _ 50 is illustrated in Figures 14 and 15 for the

two sprays. Drop velocities are relatively independent of size near

the axis, but tend to increase with size near the edge of the flow.

With the exception of drops having diameters _ 25 _m at the edges of

the case 2 spray, drops of all sizes and at all radial positions in

both sprays were found to possess axial velocities 5-400% above the

local gas-phase velocities (to be shown later).

Initial conditions of fluctuating axial drop velocities as a

function of drop size and radial location at x/d _ 50 are illustrated

in Figures 16 and 17 for the two sprays. The measurements exhibit a

great deal of scatter, similar to the data for the nonevaporating

sprays for the same location and injector [I0,11]. This behavior is

expected at this location due to the relative proximity of the injector

exit. The relative fluctuation levels (relative to the mean axial drop

velocities at the centerllne) were between 6-17%, which is lower than

the nonevaporating spray data at the same location.

As mentioned earlier, the photographic method did not provide

sufficient resolution to measure mean and fluctuating radial drop

velocities. Hence, for SF model computations, the initial mean radial

drop velocity was assumed to increase linearly from the spray axis to

the edge of the flow, matching the spray angle at the latter condition,

viz,, _p : 0.7 _p r/x. Initial conditions of fluctuating radial drop

velocities were specified to be a constant ratio of the corresponding

measured fluctuating axial drop veloclty, viz., (_p,,2)I/2 : (_p,,2)I/2/3.0"

These specifications were made with the help of limited photographic

observations and are exactly the same as that used for the

nonevaporatlng sprays [10,1]],°since the injector and the location are

the same for both types of sprays. The sensitivity of the predictions

of these estimates and other initial conditions will be considered

later.
45

60 I I I I

CASE I

x/d = 50

5.0-

V V

_.0_

v

A

._ _ o

3.0- V _ A -

-- 0 I-I O

-" o ,?,

v 2.0- o A o _

DATA r/x 0

o 0.00

1.0-- z_ 0.05

O 0.10

[3 0.15

v 0.20

o.o 1 1 1 1

I0 20 30 40 50 60

DIAMETER (pro)

Figure 16. Initial conditions of fluctuating axial drop velocity versus

drop size at x/d = 50 for the case I evaporating spray.
46

4.O I I I I I

[]

[]

_7

3.0-- _ v _

[] V

V []

V

20-

N

-_ 0 O A A [] O []

_'_ 0

,,, 0 A _Q.

---(= _ o o 8 ,'-, oo o

V CASE 2 o

V x/d = 50 1.0--

DATA r/x A

o 0.00

A 0.05

o 0.I0

[] 0.15

v 0.20

o.o l I i I l

0 20 40 60 80 100 120

DIAMETER (_m)

Figure 17. Initial conditions' of fluctuating axial drop velocity versus

drop size at x/d = 50 for the case 2 evaporating spray. _
47

4.3 Axial Variation of Spray Properties

Having established initial conditions, the remaining

measurements were used to evaluate model predictions; beginning at the

injector exit for the LHF model and at x/d = 50 for both the SF models.

Predicted (LHF and SSF models) and measured mean gas-phase

velocities along the axis of the two sprays are illustrated in Figure

18. The LHF model overestimates the rate of development of the sprays,

with performance deteriorating as the SMD of the spray increases. This

behavior is similar to the recent nonevaporatlng spray results in this

laboratory [I0-11], as well as past findings for evaporating sprays

[1,15]. In contrast, the SSF model provides satisfactory predictions

for both sprays.

Similar results for mean total mass fraction of Freon-11 (both

liquid and gas phases) are shown in Figure 19. In this case, predicted

mean mixture fraction is illustrated for the LHF model, since the two

quantities are proportional under the LHF approximation. The data of

Shearer et al. [15] for a Freon-11 spray with SMD and loading ratio

very similar to the case I spray of the present study is also shown for

comparison. The performance of the LHF model is again poor, due to

neglect of slip and loss of thermodynamic equilibrium. In general,

the SSF model provides reasonably good predictions over the range where

it was used.

Predicted (DSF and SSF models) and measured mean axial drop

velocities for the two sprays are illustrated in Figures 20 and 21.

The SSF model predicts a somewhat more rapid deceleration than the DSF

model for each drop size, due to the nonlinearity of the drop drag law

interacting with turbulent fluctuations. Both models provide fair

agreement with measurements particularly at large x/d. Larger errors

at x/d near 100 probably result from errors in the specification of

initial conditions, since initial rates of dispersion are sensitive to

estimates of initial velocity fluctuations.

SSF model predictions of fluctuating axial drop velocities

generally underestimated the measurements, just as in the case of the

nonevaporating spray study [I0,11]. As described in Section 3.3.2.2,

measurements of fluctuating axial drop velocities were of limited

accuracy and were generally inconclusive for SSF model evaluation due

to the added uncertainties in the initial conditions for these

properties; therefore, these results will not be considered here.

Figure 22 is an illustration of the variation of SMD along the

axis of the two sprays. For nonevaporating sprays, turbulent drop

dispersion causes the SMD to increase with increasing x/d due to drop

dispersion, [I0,11]. For the evaporating sprays, however, this effect

is counteracted by drop evaporation; therefore, the SMD remains

relatively constant until the largest drops finally evaporate.

Predictions of both the DSF and SSF models are comparable and are in

fair agreement with measurements, suggesting that effects of dispersion

are less significant for evaporating sprays than for nonevaporating

sprays.
48

I I I I I I II I I I I I I I II

0.0_ I I I I l llll I I I I i Ill

_0 20 40 60 80_00 200 4006O0 _000

xld

Figure 18. Predicted and measured mean gas-phase velocities

along the axis of the evaporating sprays.
49

i I *I) I i I I lJ I I l I I I I I

1.0 ----- _'-X

__ \ \ \ \

_ \ \

0.5- \ \

\ \

- \ \q

\

_. _ \ CASE 2

I>- \ -

j>.

CASE I

rv" \

0 \

O.I -- \\\

I_-° DATAW CASE \ \0 -

- \ \ -

I_--" - O0 I \ \ -

0.05 - \ \ _

_ A,k 2 xxx\lrr_ _

0 SHEARERET AL \ \

- w. \ \ -

THEORY DATA SHOWN BY \ \

__ LHF CLOSED SYMBOLS ARE

SSF CORRECTED BY MASS FLOWRATE CONSERVATION

CONSIDERATIONS

0.01 I J I I I I _l I I I J, lJ

I0 50 I00 500 I000

x/d

Figure 19. Predicted and measured mean mixture fraction

(LHF) or total Freon-ll mass fraction (SSF)

along the axis of the evaporating sprays.
5O

sao I I I I '

O 0 0 0

o o o x/__d

- __ -

20.0 / 150

_ o o o

_I 250

Io.0- _ a -

DATA x/d

THEORY o 50

DSF ---.------ A I00

SSF , 0 150

El 250

o.( ] I I ]

0 2O 50 40 50 60

DIAMETER (pm)

Figure 20. Predicted and measured mean axial drop velocities

along the axis of the case 1 evaporating spray.
o.o I I I I I

0 20 40 60 ao Joo a20

DI AME TE R ( IJm )

Figure 21. Predicted and measured mean axial drop velocities

along the axis of the case 2 evaporating spray.
I00 I I I I I I I I I I I I I I

DATA CASE T HEORY

o I DSF ------

80 z_ 2 ., SSF

--- CASE 2 ,

-

60 _ - -

oo 40-

O - 0

-- CASE I

0 I I I I I I I I I I I I I I

20 40 60 80 I00 200 400 600 800

x/d o

Figure 22. Predicted and measured SMD along the axis of the evaporating sprays.
53

Measurements of drop-size distributions along the axis of the two

sprays are illustrated in Figure 23. Drop evaporation and drop

dispersion counteract one another, so that the overall character of the

size distributions remain approximately the same, until the largest

drops finally begin to disappear.

Figure 24 is an illustration of the comparison between the

predictions (LHF and SSF models) of the axial variation of the mean

gas-phase temperature with some limited experimental results.

Predictions of the LHF and SSF models shown are time-averaged values.

The poor performance of the EHF model is similar to the results of

Shearer et al [15], and shows the effect of the loss of kinematic and

thermodynamic equilibrium. The SSF model, on the other hand, better

predicts the measurements and tends to approach the data at large

values of x/d for the case I spray. The discrepancies between the

measurements and the predictions of the SSF model at smaller vaIues of

x/d for the case I spray, and where data is available for the case 2

spray, may probably be attributed to errors in the measurements. In

spite of the fact that a shielded thermocouple was used for the

measurements, the smaller drops could impinge and subsequently vaporize

on the thermocouple bead--due to the lower collection efficiency of the

shield for the smaller drops, cf., Section 3.3.1.2.

Predicted (DSF and SSF models) mean liquid flux along the axis of

the two evaporating sprays is illustrated in Figure 25. The predicted

centerline liquid fluxes are normalized by the initial condition values

at x/d = 50. Both models predict similar results up to x/d = 250 for

the case I spray. However, the SSF model predicts a slightly more

rapid decrease in liquid flux in the remaining downstream region of the

flow. For the case 2 spray, the DSF model predicts a more rapid

decrease of the centerline liquid flux than the SSF model. However, as

will be seen later, the DSF model predicts peaked radial profiles,

suggesting that DSF model predictions of centerline liquid flux are

largely dominated by initial conditions of drop properties.

4.4 Radial Variation of Mean Spray Properties

Predicted (LHF and SSF models) and measured radial profiles

of mean gas-phase velocity are illustrated in Figure 26. In this and

the following figures, radial distances are normalized by distance from

the injector (which is the similarity variable for fully-developed

constant density single-phase jets [I]) so that model predictions of

flow width can be seen directly. Unlike most particle-laden jets [I],

the flow-widths of these sprays are generally greater than predictions

of the LHF model due to enhanced dispersion of drops by turbulence.

This behavior, however, was much more pronounced for the nonevaporating

sprays investigated earlier [I0,11]. The effect is reduced here, since

drops evaporate quite rapidly as they reach nearly pure air near the

edge of the flow--tending to limit their radial dispersion as drops.

Predicted and measured radial profiles of total (gas and liquid)

mean Freon-11 concentration are illustrated in Figure 27 for both

sprays. Predictions of all three models are shown (the LHF prediction
54

- :57.5 I I I I I I I I I I I

CASE I CASE 2

25.0- x/d= 50 x/d = 50 _ "

SMD=31.3pro SMD=59.7pm

12.5-

0.0---- I=- ,

IOO IOO

"" 31.5pm 59.5 pm

12.5--

_. 0.0 F

cy I"- 150 150

= 29.6 pm -'r-t'-r- L 60.2 pm

',.=, , 12.!-; i q -_ V _._ -

::> 250 250

z I _1, 28.7 pm .___'L_ 62.1pm

IJJ

_>

oo F

-J 400 "'

12.5- ,_

-'-L --

0.0 ['-'

500

12.5- --

0.o I I I I I F I i i u.4 i

I0 20 30 40 50 60 I0 :30 50 70 90 I10 130

DROPLET DIAMETER (pro)

Figure 23. Drop-size distributions along the axis of

the c_se 1 and ease 2 evaporating sprays. _

I
300 I i m m m ; m_ I J m t m m mmi

- CASE 2 f/I -

J

J

280- / A A -

-- I

v 1 CASE I

\

260 - N \

ii_U \ \

\ \ /

- \ \ I

\ \ / / DATA CASE

240- O I -- THEORY

. _ LHF A 2 _

SSF

220 t m , m mI i_1 , , , m i i t_

10 50 I00 500 IOOO J

x/d

Figure 24. Predicted and measured mean gas-phase temperature along the axis of the evaporating sprays.

Ln

L_
56

0o0001 I I I II I I I I

I0 I00 I000

x/d

Figure 25. DSF and SSF model predictions of mean liquid

flux along the axis of the evaporating sprays.
57

1.2o; z_ z_lz_ A I I I I

1.00_0 0 0 A

0 A

. 0.75 - 0 Z_ O

o o- o o

CASE DATA THEORY

0.25 , o .. R 8

0.00 2 Z_ a

xld = 50

1.0( A Z_

Z_

0.75 _ n SSF

0.50

0.25 L HF

A _

t::} x/d : 100

_. 1.0(

0.75 SSF

0.50

0.25 LH F

0.00

x/d :250

0.75

SSF

0.50

0.2,i L HF

x/d =500

D.q I

" 0.00 004 0.08 0.12 0.16 0.20 0.24

r/x

Figure 26. Predicted and measured radial variation of mean

gas-phase velocities in the nonevaporating sprays.
58

1.00_ _ Rt P, O I I I I

0.50

0.25 CAS-E-DAT-AT-HE-0RY g A

O A A o _/d_S0o

0.00 - 2 A

1.00 DSF --

0.75

0.50

SSF

_>-"°025

0.00 DSF

LH F

x/d = I00 _,:"

0

\

,...--'" 0.75 \ --

s -,,,-

LHF

1,4- 0.50L

SSF

0.25 --

A

0.00

DSF x/d= 250

SSF

0.75 0

0.50

0 x/d = 500

0.25 o

o.oo I I

0.00 0.04 0.08 0.12 0.16 0.20 0.24

r/x

Figure 27. Predicted and measured radial variation of

mixture fraction (LHF) or total Freon-ll

mass fraction (SSF) for the evaporating sprays.
59

formally being f/fc as before). The DSF model yields a peaked

profile due to neglect of turbulent dispersion of drops, while the LHF

and SSF models provide better agreement with measurements. In general,

discrepancies between the LHF and DSF models and measurements are

smaller than comparable measurements in the nonevaporating sprays,

since Freon-11 vapor tends to dominate the concentration measurement

for present test conditions. Turbulent dispersion of drops, however,

increases the width of the flow in comparison to single-phase jets

ill--an effect which decreases at large x/d where the drops have

evaporated.

Predicted (LHF and SSF models) and measured radial variation of

the normalized gas-phase temperature decrement for the two sprays are

illustrated in Figure 28. The data at x/d = 250 in the case I spray

and x/d = 500 in the case 2 spray show some evidence of bias in the

measurements, due to drop impingement on the thermocouple at the center

of the spray. Far downstream at x/d = 500 in the case I spray, where

all the drops have evaporated, the profile is reasonable and agrees

well with the predictions--particularly the SSF model.

Predicted (DSF and SSF models) radial variation of mean liquid

flux at various axial locations in the two sprays are illustrated in

Figure 29. Similar to the results obtained for the nonevaporating

sprays, the DSF model predicts peaked profiles and narrower flow widths

than the SSF model, due to the neglect of turbulent dispersion of drops.

The comparison between the results of the DSF and SSF models shown in

Figure 29, in conjunction with those shown in Figure 25 for the axial

variation of liquid flux emphasizes the effect of turbulent dispersion

on interphase transport rates.

4.5 Radial Variation of Gas-Phase Turbulence Properties

Figures 30 and 31 illustrate results for gas-phase turbulence

kinetic energy and Reynolds stress for the two evaporating sprays.

Both these quantities are quadratic, which amplifies discrepancies

between predictions and measurements. The comparison between

predictions and measurements is reasonably good for the case I spray,

but poorer agreement is observed for the more heavily-loaded case 2

spray. This trend could be due to effects of turbulence modulation,

discussed by AI Taweel and Landau [28], which were ignored during the

present calculations. Unusually low values of Reynolds stress are

observed for the more heavily-loaded case 2 spray at x/d = 100 and 250.

This effect could be due to bias of the measurements by drops, since

fluctuating radial particle velocities are significantly smaller than

radial gas fluctuations in two-phase jets [7,8].

Effects of the presence of drops on turbulence properties are more

evident when individual components of velocity fluctuations are

examined. Measured radial profiles of u', v' and w' are illustrated in

Figures 32 and 33 for the case I and case 2 sprays. Predictions of the

• SSF model were obtained assuming (_,,2:_,,2:_,,2)= (1:0.5:0.5) k,

which is approximately observed in the fully-developed region of

single-phase round jets [29,30]. The results are similar to those
60

Figure 28. Predicted and measured radial variation of mean

gas-phase temperature in the evaporating spray.
61

1.2 I I I I I

THEORY

1.0 DSF .... _

° \ SSF

x/d

 ,oo -

\

o.4- \ / \

500 ._ I \

/-, \

|(.._ 0.2-- I \ \ CASE I _

I

o.o- I \

X

::) \

,, I \ \

L2 \ \

(3

D

0 1.0

- \

\

O.S \ \

I \ x/d

0.6 I00

\ \

\ \

,.500 \ \ CASE 2

\ \

\

\

0.00 0.04 0.08 0.12 0.16 0.20 0.24

• r/x

Figure 29. DSE and SSF model predictions o£ the radial variation

of mean liquid flux in the evaporating sprays.
62

0.075 I I I I I

0.050 -- A --

o oo o,,_ oo_ 0... L . A w

°'°25, A a _C-ASE.....DA f_R - TATHEORY

- -7- _ ___/5ode0.000 ; 2 z_ .... _•/_"

0.07 5

o.O_-__ Oo.o__ - -"_

o.ooo_,

,) x/d =I00 _,

0.I00"- SSF _//

_'_ 0 0 o 0

0.07 5 o --

_' o

0.050 _ _ _ A

Z_

LHF Z_

0.025

0.000

SSF x/d=250 /_

o._ 2_

o u _, t_

0.075

0

0.050 o _

LHF

0.025 _, xld-500 --

o.ooo I I I I

0.00 0.04 0.08 QI2 0.16 0.20 0.24

r/x

Figure 30. Predicted and measured radial variation of turbulent

kinetic energy in the evaporating sprays.
63

0.020

I I I A _1 I

0.015-- A Z_ O O

Z_ O O

o.olo- 9 9, - O

0.005 - _ _. CASE DATATHEORY

I O , '_' -

O.000 _- 2 Z_....

x/d =50 -- J

0.020"- o o -

0.015 O SSF _

/

0.010 / A A

A A Z_

0.005 0 -

N o

{:::} 0.000 LHF

0.02 x/d = I00, (

=

0.015

Z_ o SSF

0.010 A A

p,

0.005 ,x LH F O -

O

0.000

0.02( SSF x/d - 250_///

0.005 L H F -

x/d=500

o.ooc I I

0.00 0.04 0.08 0.12 0.16 0.20 0.24

r/x

Figure 31. Predicted and measured radial variation of

Reynolds stress in the evaporating sprays.
64

0.16 0.20 0.24

__----..Ll..~O~O~0 CASE I

000 A

BHR~

......

'" 0x/d: 250

-...... ............ ......

~-OQno~~~A-~f;~

DATA THEORY(SSF) (IN ITIAL

O~/uc (k/u~)1/2 CONDITIONS)

6.-Jv·-/.uc r=.2- - } -2 1/2 x/d: 50

r=:; --- (k /2u ) O.JWI~UC c

o

O.

0.0L----l---~_-L __....l.__~___1

0.00 0.04 0.08 0.12

r/x

0.1

0.0

0.1

o.

Figure 32. Predicted and measured radial variation of velocity

fluctuations for the case 1 evaporating spray.
i

65

o.3 I I j i I

o o (INITIAL CASE 2 O O

-_ _ oCONDMONS)

o.=o;oS-f o -

DATA THEORY(SSF) []

o.o- o_--/i c --( k/._c),2/2 n _,

o._- A4;,2]_c]...._,/2

0.2_0

o.o

0._/_ _;

BBFI

0.2

_ xld =500

0.I- \\ _, --

o.o I I I I I

0.00 0.04 0.08 0.12 0.16 0.20 0.24

r/x

Figure 33. Predicted and measured radial variation of velocity

fluctuations for the case 2 evaporating spray.
66

observed in the nonevaporating sprays [I0,11]. Predictions constructed

in this manner are in fair agreement with the measurements--

particularly in the region far from the injector. A notable feature of

the results, however, is that levels of anisotropy are rather high for

positions near the injector and generally exceed levels observed for

comparable values of x/d in single-phase jets [68,69]. Since this

region abuts the dense-spray portion of the flow, it seems likely that

the presence of drops are responsible for the higher degree of

anisotropy since effects of sllp are preferentially transmitted into

the streamwise velocity component. High levels of anisotropy are also

of concern regarding the prescription of eddy properties in the present

SSF model, since this approach is based on the assumption of isotropic

turbulence. This suggests that multistress models of particle-laden

flows might profitably be examined in order to gain more insight

concerning effects of particles on turbulence properties.

4.6 Sensitivity Study

Early in the preceding discussion, it was noted that

specification of initial conditions is of vital importance to

predictions using separated flow models. In the present study, care

was exercised in obtaining well-deflned initial conditions of all

necessary flow properties, at a position as close as possible to the

injector exit, viz. x/d = 50. However, while measurements of initial

conditions of gas-phase mean and turbulence properties were considered

sufficiently accurate, initial conditions of mean and fluctuating axial

and radial drop velocities were estimated to contain uncertainties that

could be beyond acceptable limits of experimental error.

Uncertainties exist in the measurements of mean and fluctuating

axial drop velocities due to the grouping of data into finite diameter

slze-ranges and the use of insufficient sample sizes, especially for

the larger drops in the size distribution. Initial conditions of mean

and fluctuating radial drop velocities are also of concern. These drop

properties were not measured but were estimated from the measured

values of the corresponding axial drop velocities and the spray angles.

Due to these uncertainties regarding measurements of initial

conditions of drop properties, the sensitivity of the SSF model

predictions to the variation of these parameters was examined. The

results of this study are presented in Tables 5-7 and Tables 8-10 for

the case I and case 2 evaporating sprays. The entries show the

fractional change in the predicted variable caused by increasing the

input variable (at x/d = 50) by 25%--with all other variables

unchanged.

In general, gas-phase properties and SMD are relatively

insensitive to changes in the input variables. The total Freon-11 (gas

and liquid) concentration YF, is also relatively insensitive since

Freon-11 vapor dominates in the predictions for the present test

conditions. The most sensitive variable is the liquid mass

flux--partlcularly for changes in mean and radial drop velocities.

Next in importance are mean axial drop velocities, which are mostly

sensitive to their own initial conditions. These effects are more
67

Table 5. Summary of Results of Sensitivity Study for

the Case I Evaporating Spray at x/d = I00a

Input Variables

Output u (u"2) I/2 v (v 2)I/2

Variables p p p P

Uc .03 ~.00 ~.00 ~.00

2

kc/_ c -.02 ~.00 ~.00 ~.00

~

Yfc ~.00 ~.00 -.03 .01

Gc .16 -.01 -.10 .05

SMD c 02 -.01 .02 .01

~

u

Pc

Dp (um) = 17.5 .08 -.O3 .O4 .06

32.5 .14 .01 .02 -.02

52.5 .17 .02 ~.00 ~.00

aEntries show fractional change in predicted output variable by

raising input variable at x/d = 50 by 25%.
68

Table 6. Summary of Results of Sensitivity Study for

the Case I Evaporating Spray at x/d = 250

Input Variables

Output - (u 2 I/2 - (v )

Variables Up P ) Vp p2 I/2

u .03 ~.OO ~.00 ~.OO o

k /_ 2 .02 ~.00 -.01 ~.00 O C

Yfc -.02 -.02 -.04 -.02

Gc .06 -.08 -.18 -.09

SMD .02 ~.00 -.04 ~.00 e

u

Pc

Dp (_m) = 17.5 -.03 -.01 -.10 -.04

32.5 .09 .04 .05 -.04

52.5 .05 ~.00 -.02 ~.00
69

Table 7. Summary of Results of Sensitivity Study for

the Case I Evaporating Spray at x/d = 500

Input Variables

Output

Variables u (u 2 I/2

p ; ) Vp (V ; 2 ) 1/2

Uc .02 -.00 ~.00 ~.00

k/G 2

o o .oi -.oo ~.oo ~.oo

Yfe -.03 ~.00 .01 ~.00

Gc .45 -.02 -. I0 .03

SMD c .03 -.01 .01 .02

~

U

Pc

Dp (um) = 17.5 -.I0 -.18 ~.00 -.05

32.5 -.02 -.05 -.o3 -.o3

52.5 ........
7O

Table 8. Summary of Results of Sensitivity Study for

the Case 2 Evaporating Spray at x/d = 100

Input Variables

Output U (U 2)I/2 ~ (V,,2)I/2

Variables p _ Vp P

.03 ~.00 ~.00 ~.00 o

k /_ 2 .03 ~.00 -.01 ~.00 e e

~

Yfc .01 -.01 -.03 .03

Gc .25 -.04 -.15 .13

SMD -.01 -.01 - 01 - 02 e = "

~

U

Pc

Dp (_m) --15 .02 -.06 -.04 -.02

55 .15 ~.00 .01 -.02

95 .20 .01 .01 .01
7]

Table 9. Summary of Results of Sensitivity Study for

the Case 2 Evaporating Spray at x/d --250

Input Variables

Output - ~

Variables uP (u;2)I/2 _p (V;2)I/2

uc .04 ~.00 ~.01 ~.00

k /u 2

o e .11 ~.00 -.02 ~.00

~

Yfc .03 -.01 -.07 ~.00

Gc .26 -.04 -.22 ~.00

SMD c .01 ~.00 -.04 .01

~

u

Pc

Dp (um) = 15 .06 ~.00 .05 .02

55 .07 ~.00 ~.00 .01

95 .14 -.01 -.01 .01
72

Table 10. Summary of Results of Sensitivity Study for

the Case 2 Evaporating Spray at x/d = 500

J

Input Variables

Output U (U"2) I/2 - (V 2 I/2

Variables p P Vp ; )

uc .03 .00 .00 .00

k

e

/u

e

2 .09 .00 -.02 ~.00

Yfc .01 .01 -.02 .02

Gc .21 .03 -.16 .07

SMD c -.04 -.03 -.04 -.02

u

Pc

Dp (um) = 15 .13 .07 .13 ~.00

55 .o4 .o5 -.o3 -.01

95 .09 -.01 ~.00 ~.00
73

important for the case 2 spray where a greater proportion of large

drops, which tend to maintain the properties at the inlt_al state due

to their greater mass, exert a strong influence on flow properties.

These findings are similar to the results obtained for the sensitivity

study in the nonevaporating sprays [I0,11].

5. SUMMARY AND CONCLUSIONS

5.1 Summary

t

Comprehensive measurements of the structure of fine and

coarse evaporating sprays were completed to aid in the understanding of

effects of drop size, coalescence, turbulence modulation and turbulent

dispersion on spray properties. Sprays having nominal Sauter mean

diameters of 31 and 58 microns were considered. These measurements

included mean and fluctuating gas-phase velocities, liquid fluxes,

drop-size distributions, mean and fluctuating axial drop velocities,

mean concentration of injected fluid and mean gas-phase temperatures.

Initial conditions of spray properties were measured at a location as

close to the injector exit as possible, viz. x/d = 50, to provide

appropriate initial conditions for separated flow models of spray

processes. Uncertainties in proper average properties to determine

drop transport were mlnlmized by calibrating procedures using

measurements stream. of life histories of single drops supported in an air

Measurements of the structure of the evaporating sprays were used

to evaluate the predictions of three theoretical models, as follows:

(I) a locally homogeneous flow (LHF) model, where slip between the

phases is neglected; (2) a deterministic separated flow (DSF) model,

where interphase slip is considered but turbulent dispersion of

particles is neglected; and (3) a stochastic separated flow (SSF)

model, where effects of interphase sllp, turbulent dispersion and

turbulent fluctuations are considered using random sampling for

turbulence properties in conjunction with random-walk computations for drop motion.

The theoretical description of the continuous phase for all three

models was based upon the Favre-averaged form of the conservation

equations writte n in Eulerian coordinates. The dispersed phase was

treated, for the separated flow models, by solving Lagrangian equations

of motion for the particles. A modified version of the GENMIX program

[26] combined with a second-order Runge-Kutta ordinary differential

equations. equation solver for drop motion were used to solve the governing
74

A sensitivity study was conducted to i_nvestigatethe influence of

uncertainties in specification of initial conditions of drop properties

on model predictions. The results are useful in identifying potential

sources of error for both predictions and measurements.

5.2 Conclusions

The major conclusions and observations of this study are as follows:

I. The present measurements in nonevaporating sprays showed

significant effects of slip between the gas and liquid phases.

The rate of development of the coarser spray, having a higher

loading ratio, was slower than that of the more finely atomized

spray with a lower loading ratio. Present measurements were

limited to the dilute portion of the flows, where void fractions

were greater than 99.1%. In this region, drop coalescence and

major effects of drops on turbulence properties were not observed.

As the dense flow region was approached, however, gas-phase

turbulent velocity fluctuations exhibited increased

anisotropy--suggestlng a significant modification of turbulence

properties by drops. Additional measurements in the dense spray

region would be required to confirm these effects. Turbulent

dispersion of drops was observed as a significant phenomena in

both sprays; yielding spray widths that were generally larger than

most fully-developed, slngle-phase jets. Effects of dispersion

were smaller than observed for nonevaporating sprays [I0-11], due

to decreasing mass of the dispersed phase by evaporation.

Counteracting effects of turbulent dispersion and evaporation also

caused the SMD to remain relatively uniform along the centerline

of the sprays.

2. The LHF model generally overestimated the rate of flow development

of the sprays, similar to past experience with this model [15-17].

However, the LHF model underestimated flow wldths--unllke the

results of earlier work in particle-laden jets [7,8]. Such

enhanced turbulent dispersion of drops, for certain ranges of

turbulence and drop properties, is often observed in multiphase

flows. The effect was more evident for the present sprays than

for the partlcle-laden jets due to the smaller density of the

liquid, which allowed the drops to respond more readily to

turbulent fluctuations; and greater initial slip and rates of

deceleration in the sprays; due to smaller injector dimensions.

Due to the possibility of preferential dispersion under some

conditions, it may be concluded that the LHF model does not always

provide an upper bound on the rate of development of sprays, as
75

suggested in the past [I]. In spite of these shortcomings, it is

felt that the LHF model is still useful as a design tool, since it

provides a reasonable first estimate of spray properties with much

reduced requirements for defining initial conditions than

separated flow models.

3. Differences between measurements and predictions of the DSF and

LHF models were smaller than observed for nonevaporating sprays

[I0-11], since decreasing mass of the dispersed phase by

evaporation causes the flow to approach a single-phase flow, where

all models considered here are identical. The DSF model generally

underestimated drop dispersion for the present measurements. This

approach appears to have limited utility for modeling practical

two-phase flows. Gosman and Ioannldes [22] note, however, that

uncertainties in initial conditions for multiphase flows are

potentially a greater source of error than neglecting particle dispersion.

4. In contrast, the SSF model yielded reasonably good results for the

present measurements. The SSF model also provided adequate

treatment of enhanced drop dispersion in the sprays with no

modification of the model from its original calibration (where

effects of enhanced dispersion were not observed). While this is

encouraging, additional evaluation of the model is needed--

particularly considering improved specifications of initial

conditions. Predictions of the SSF model showed greatest errors

for axial drop velocities in the near-injector region; however,

sensitivity analysis showed that this property is strongly

influenced by specification of initial drop velocities, where

experimental uncertainties are greatest.

The SSF model, which employs assumptions of isotropy performed

reasonably well in spite of effects of anlsotropy exhibited by

measurements near the dense regions of the sprays. However,

further consideration of effects of anisotropy, perhaps using a

multlstress turbulence model, would be desirable. The SSF

approach, however, appears to provide an attractive formulation

for treating nonlinear interphase transport processes in

drop-laden turbulent flows.

5. In general, present model predictions are relatively insensitive

to the specification of gas-phase initial conditions. The

specification of drop properties, however, exerts much more

pronounced effects on predictions. This emphasizes the importance

of measurements of initial condition of drop properties in order

to obtain a convincing evaluation of separated flow models.

/
76

Potentialproblems in obtainingreliable initialconditions

includedifficultiesin carryingout measurementsin the dense

spray regions and lack of understandingof the atomizationprocess

in sprays.
77

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1978.

20. Boyson, F. and Swithenbank, J., "Spray Evaporation in Recirculating

Flow," Seventeenth Symposium (International) on Combustion, The

Combustion Institute, Pittsburgh, 1979, pp. 443-453.

21. Yuu, S., Yasukouchl, N., Hirosawa, Y. and Jotaki, T., "Particle

Turbulent Diffusion in a Dust Laden Round Jet," AIChE J., Vol. 24,

1978, pp. 509-519.

22. Gosman, A. D. and Ioannides, E., "Aspects of Computer Simulation of

Liquid-Fueled Combustors," AIAA Paper No. 81-0323, 1981.

23. Lockwood, F. C. and Naguib, A. S., "The Prediction of the

Fluctuations in the Properties of Free, Round Jet, Turbulent,

Diffusion Flames," Combustion and Flame, Vol. 24, 1975, pp.

109-124.

24. Bilger, R. W., "Turbulent Jet Diffusion Flames," Prog. Energy

Combust. Sci., Vol. I, pp. 87-109, 1976.

25. Jeng, S. M. and Faeth, G. M., "Species Concentrations and

Turbulence Properties in Buoyant Methane Diffusion Flames,"

submitted to J. of Heat Transfer.

26. Spalding, D. B., GENMIX: A General Computer Program for

Two-Dimensional Parabolic Phenomena, Pergamon Press, Oxford, 1978.
79

27. McCreath, C. G., Roett, M. F. and Chigier, N. A., "A Technique for

Measurement of Velocities and Size of Particles in Flames," J.

Physics E: Scientific Instruments, Vol. 5, pp. 601-604, 1972.

28. AI Tawell, A. M. and Landau, J., "Turbulence Modulation in

Two-Phase Jets," Intl. J. Multiphase Flow, Vol. 3, Pp. 341-351,

1977.

29. Wygnanski, I. and Fiedler, H., "Some Measurements in a Self

Preserving Jet," Journal of Fluid Mechanics, Vol. 38, pp. 577-612,

1969.

30. Rodi, W., "The Prediction of Free Turbulent Boundary Layers by use

of a 2-Equation Turbulence Model," Ph.D. Thesis, University of

London, 1972; also cited in Launder, B. E. and Morse, A.,

"Numerical Prediction of Axisymmetric Free Shear Flows with a

Reynolds Stress Closure," Turbulent Shear Flows I, (F. Durst et

al., ed.), Springer-Verlag, Berlin, 1979, pp. 279-294.

31. Reid, R. C., Prausnitz, J. M. and Sherwood, T. K., The Properties

of Gases and Liquids, 3rd Edition, McGraw-Hill, New York, 1977.

32. ASHRAE Thermodynamic Properties of Refrigerants, American Society

of Heating, Refrigerating and Air-Conditioning Engineers, Inc.,

New York, 1969.
8O

APPENDIX A

SUMMARY OF PROPERTIES OF THE SPRAY FLUIDS

A.I Freon-11

M = 137.37 kg/kg mole

Cpg = 0.520 kJ/kg K

Cpf = 01879 kJ/kg K

hfg = 181.32 kJ/kg (at T o = 298 K)

pf = 2143.7-2.235 T kg/m3 (T in K)

log10 pg = A''B'/T kPa (T in k)

A' = 6'7828

B' = 1416'I

A.2 Air

M = 28.97 kg/kg mole

Cp = 1.005 kJ/kg K

A.3 Evaluation of Mixing Rules for Gaseous Mixture

A.3.I Thermal Conductivity

The thermal conductivity of the gaseous mixture was

calculated with the Mason and Saxena formulation of the Wassiljewa

Equation [31].

= 7. N (A.I)

Im 1--I j_1"=xj _i

where,
81

with CLj = I when i = j

A.3.2 Viscosity

The mixture viscosity calculations employed the method of

Wilke as described in Reference [31].

For a mixture of N components

Nixij )am = _ i (A.3)

i=I xj 01 --I J

where eli is given by Equation (A.2).

The Freon-11 vapor thermal conductivity and viscosity were

obtained from Reference [32].
82

APPENDIX B

STATE RELATIONSHIPS FOR

LHF PREDICTIONS OF THE EVAPORATING SPRAYS

The relationship between mixture enthalpy, composition,

temperatureand density and the mixture fraction is provided by the

state relationship. The experimental results to be compared with the

analysis were all obtained at relatively low pressures; therefore, all

gases are assumed to be ideal gases. Since combustion is not treated,

chemical reaction is ignored. Finally, it should be recalled that the

mixing process is adiabatic and occurs at constant pressure, under the

assumptions of the present analysis.

Considering N species in the flow, the expression for the

composition of the mixture is:

Yi = Yio f + Yi_ (I - f) , i=I, ...N (B.I)

where each species may exist in both the gaseous or liquid state

Yi = Yfi + Ygi (B.2)

The total enthalpy of the flow during the mixing process can be

expressed as

h = ho f + h_ (l-f) (B.3)

where at any condition

h = [ (Yfi hfi + Ygi hgl) , i=I, ...N (B.4) N

The density of the mixture is given by

P = (gfi + , i = I, ...N (B.5)

where vfl and Vg i are the partial specific volumes of species i in the

liquid and gas phases.

Given the relationships between enthalpy and density of each

species and the composition, temperature and pressure, Equations

(B.I)-(B.5) are sufficient to describe the composition, temperature and

density of the mixture. The relative composition of the gas and liquid

phases is obtained from Equation (B.2) and the requirement that the

chemical potential of each species must be the same in both phases.
83

For the present test conditions, both air and Freon-ll liquid and

vapor leave the injector exit, while the surroundings contain no

Freon-11. Properties of the _pray fluids used in the present

calculations are summarized in Appendix A. Figure 34 shows the state

relationship for the case 2 evaporating spray. The total mass

fractiods of air and Freon-ll are linear. The presence of liquid

. causes the mixture temperature to vary more slowly than in the region

where only gases are present, due to heat of vaporization requirements.

The mass fraction of Freon-11 vapor reaches a maximum at the point

where the liquid disappears.

The state relationship for the case I evaporating spray can be

obtained from the case 2 results, by shifting the abscissa of Figure 34

by the ratio of the initial Freon-11 mass fractions, (YFo)case I/

(YFo)case 2 : 0.941. The results are shown in Figure 35.
84

0.2

YFg

0.0 I I

0.0 o.2 o.4 o.6 0.8 _.0

MIXTURE FRACTION f

Figure 34. State relationship for the case 2

evaporating Freon-ll spray (LHF model).
85

0.8

1

I- 0.6

Q::

LI.

0.4

0.2 YFg

0.0 I I

•0.0 0.2 0.4 o.6 0.8 I.O

MIXTURE FRACTION f

Figure 35. State relationship for the case 1

evaporating Freon-ll spray (LHF model).
86

APPENDIX C

DROPLET LIFE HISTORY CALIBRATION TESTS

C.I Calibration Apparatus

The purpose of the calibration tests was to establish the proper

reference condition to evaluate the fluid properties in Equations

(2.13)-(2.21), as defined by Equation (2.24). The calibration

experiment provided a well-deflned test condition to evaluate the drop

evaporation model, by providing a convective environment for the

observation of a stationary evaporating drop.

A schematic of the overall experimental apparatus is shown in

Figure 36. Motion pictures of the droplet evaporation process were

taken to record the variation of droplet size with time. The droplet

. was suspended on a quartz probe of diameter approximately 150 _m. A

pitot-static velocity probe was used to measure the velocity of the

surrounding gas. The probe was connected to a Meriam model 34FB2

micromanometer in order to measure the difference between the static

and stagnation pressure.

Turbulent air flow at the exit of a pipe provided the convective

flow field for the droplet evaporation process. Fully-developed

turbulent pipe flow was obtained from a pipe 32 mm in diameter and 610

mm in length. Four 16-mesh screens were placed near the pipe inlet to

assist in developing the flow. Oil-free, dry air was supplied by a

compressor. The air flow was controlled by a Matheson model 4

regulator and metered with a calibrated critical-flow orifice.

A Photosonic I-B motion picture camera driven with a Kepco SM 36-5

AM d.c. power supply was used to record the variation of droplet size

with time. The film speed was indicated by a timing light on the

camera activated by an Adtrol Electronics pulse generator, model 501.

Kodak Plus-X reversal film was used for all the tests. Backlighting

for the photographic measurements was supplied by a conventional, 75

watt tungsten bulb. A diffuser screen was employed to obtain equal

background intensity from the bulb.

Separate measurements of the drop temperature variation Wlth time

were made in order to estimate the wet-bulb temperature of the

evaporation process. For these tests, the drop was suspended on the

junction of a flne-wire thermocouple. The thermocouple was made from

0.076 um chromel-alumel wire with a bead diameter of 0.2 mm. The

reference junction was placed in an ice bath. A Hewlett-Packard X-Y

plotter, model 7044A, was used to record the droplet temperature

variation with time.

The temperature trace consisted of three regions; first a region

of rapidly decreasing temperature; second, a constant temperature

region; and third, a region where the temperature increases back to the
COMPRESSED AIR -SSURE GAGE

CRITICAL FLOW ORIFICE

PLASTIC TUBE

VALVE REGULATOR FILTER 32 mm I.D.

LENGTH 610mm

QUARTZ PROBE OR I / !

THERMOCOUPLE PROBE

CHROMEL- ALUMEL

0.0762 mm DIA

PITOT-STATIC TUBE MICROMAN

ICE BATH REFERENCE JUNCTION

Figure 36. Schematic diagram of the drop life history calibration apparatus.
88

ambient gas temperature. The constant temperature is the wet-bulb

temperature for the evaporation process. At this condition, all of the

energy transferred to the drop is used to vaporize the liquid.

The analysis of the droplet size variation with time from the

motion pictures was confined to the constant temperature region, by

disregarding frames for an initial time period estimated from the

droplet temperature tests. The films were analyzed using a Vanguard

motion picture analyzer to view the film and measure the size of the

droplet in each frame.

C.2 Theoretical Model of Droplet Life History Calibration Tests

The measurements of the life history of a stationary droplet in a

well-defined environment were used to calibrate the drop evaporation

model given by Equations (2.17)-(2.21). In this manner, errors in the

drop life history calculations for the separated flow models (due to

uncertainties in selecting proper average properties for transport

parameters) were minimized.

All the assumptions outlined in Section 2.3.1, apply in the

calculations for the calibration tests. Since the droplet is

stationary, the drop momentum Equations (2.12)-(2.14) are not required.

The governing equations are given by Equations (2.16)-(2.21) and (2.15)

with only miner modification. Equation (2.16) is transformed to a

function of time by noting that

d d

U _ _

p dx dt (C.I)

The ambient velocity, concentration and temperature are constant with

time. Equations (2.16)-(2.21) are sufficient to solve for the surface

temperature and diameter of the droplet as a function of time.

Equation (2.16) is integrated numerically, where _" is given

by a simultaneous solution of Equations (2.17) and (2.18). Average

properties were computed at a mean state defined by Equation (2.26).

The mixing rules employed are summarized in Appendix A.

C.3 Calibration Test Results

Several test conditions were considered with ambient velocities

from 3 m/sec to 6 m/sec. This velocity range was selected so that the

drop Reynolds numbers in the calibration experiment spanned the range •

encountered in the evaporating spray experiments.

The theoretical and experimental results for the variation of

droplet size were examined. The closest agreement between predictions

and measurements was achieved when a value of e = 0.75 was used in

Equation (2.24) to compute average gas-phase properties. Figure 37 is

an illustration of some typical theoretical and experimental results.

The drop diameter variation is plotted as a function of time for two

different gas velocities. The agreement between predictions and
89

1.0 I I I

0.8

0.6

v 0.4

DATA uoo(m/s) TwB(K) TWB,PRED(K)

o :3 246 240

0.2--

6 246 240

Do=990 pm Too= 293 K

o.o I I I

0 I 2 3 4

TIME (s)

Figure 37. Drop life history calibration results.
90

measurements, with a = 0.75, is seen to be quite good. The wet-bulb

temperature of the drop is not a strong function of drop size or

velocity. The predicted value is within 5°C of the measured value,

which is satisfactory for present purposes.

Based on the results of the calibration experiments, a value of

= 0.75 was employed in Equation (2.24) to compute average gas-phase

properties. No universality of this reference condition should be

implied. The uncertainties in average properties and the transport

correlations are such that calibration should be undertaken for each

system to be investigated [I].
91

APPENDIX D

INITIAL CONDITIONS OF MEAN GAS-PHASE FREON-11 MASS FRACTION (YFK)

AND SQUARE OF MASS FRACTION FLUCTUATIONS (gFg) AT x/d = 50

FOR THE SF MODEL PREDICTIONS OF THE EVAPORATING SPRAYS

Profiles of mean gas-phase Freon-11 mass fraction, YFg, were

needed at x/d = 50 to initiate both DSF and SSF model calculations for

the case I and case 2 evaporating sprays. This information was deduced

from measurements, at x/d = 50, of liquid flux (using slide impaction),

mean axial drop velocities (using double-flash photography), and total

Freon-11 concentrations (using isokinetic sampling and

gas-chromatography). In the following, the analysis and assumptions

used to compute YFg at x/d = 50 is outlined.

Freon-11 liquid, vapor and air exist in the two-phase mixture, so

that conservation of species implies

YF + Ya = I (D.I)

where,

l !

YF = YFf . YFg (D.2)

The density of the mixture is given by

p : (Y_f/pf + Y_g/pg + ya/Pa)-I (D.3)

Let the drop concentration in a unit volume in the flow be denoted by

Cf, then

i

!

Cf = p YFf (D.4)

and the mass fraction of total Freon-11 (liquid + vapor) is given by

Cf + p Y'Fg

YF = p (D.5)

The quantity Cf can be computed from the liquid flux, Gfi, and the

velocity, Upi , of each drop Size group i at a given radial location at

x/d = 50 as follows:

N

Cf = 1=I fi/ ")

(D.6)
92

Gfi is known from slide impaction measurements, cf., Section 3.3.2.3

while Upi is known from the drop velocity measurements, cf., Section

3.3.2.2.

A direct measurement of YF in Equation (D.4) is obtained from

isokinetlc sampling and gas-chromatography measurements of total

concentration of injected Freon-11 described in Section 3.3.3.1.

It now remains to specify the temperature of the mixture so that

the densities of each of the species can be calculated. This part or

the analysis parallels that used for the equation of state computations

for the SF models described in Section 2.3.2.2. The temperature of the

drops is assumed to remain constant at the injected state, while an

adiabatic mixing process is assumed for the gas phase. Therefore,

assuming ideal gas behavior, the energy balance is given by Equation

(2.31) as follows:

Y_g {hfg o + Cpg (To-T)) + Ya Cpa (To-T) = 0 (D.7)

The densities of Freon-11 vapor and air can be found, using the ideal

gas law, at the total pressure of the mixture

pg = p Mg/R o T (D.8)

Pa = P Ma/Ro T (D.9)

Equations (D.I)-(D.3), (D.5) and (D.7) provide five equations for the ! I

five unknowns YFg, YFf, Ya, P and T. The mass fraction of Freon-11

vapor in the gas-phase is then computed from

y,

~ Fg

YFg = y, + y

(D.IO)

Fg a

Tabie D.I lists YFg as a function of radia! location at x/d = 50 for

the case I and case 2 evaporating sprays.

Profiles of the square of Freon-11 vapor mass fluctuations, gFg,

were also needed at x/d = 50 to initiate SF model predictions for the

evaporating sprays. A direct or indirect measurement of this quantity

was not made; therefore, an estimate of the fluctuation intensity

(gFg)I/2/(YFg) c- was made from (g)I/2/f c predictions at x/d = 50 of

the LHF model. These values are listed in Table D.2 for the case I and

case 2 evaporating sprays.
93

Table D.I. Initial Conditionsof Mean Gas-Phase

Freon-11Mass Fractionat x/d = 50 for

the Case I and Case 2 EvaporatingSprays

YFg

r/x Case I Case 2

0.00 0.306 0.447

0.05 0.251 0.352

0.10 0.134 0.238

0.15 0.013 0.126

0.20 0.019 0.000
94

Table D.2. Initial Conditions of Gas-Phase Freon-11

Mass Fraction Fluctuations at x/d = 50 for

the Case I and Case 2 Evaporating Sprays

GFg/(gFg)c

Case I Case 2

112 - ~

r/x (gFg)c /(YFg)c = 0.209 (gFg)l/2c/( YFg)c = 0.210

0.000 1.00 1.00

0.007 I.02 I .01

0.014 1.05 I.04

0.021 I.09 I.I0

0.028 1.15 1.16

0.035 1.22 1.23

0.042 1.28 1.31

0.049 .34 1.36

0.056 .38 1.40

0.063 .42 1.43

0.070 .45 1.44

0.077 .45 1.43

0.084 .43 1.41

0.091 .40 1.37

0.099 .35 1.31

0.106 .29 .23

o.113 .22 .14

0.120 .12 .03

0.127 .00 0.90

0.134 0.88 0.76

0.141 0.67 0.61

0.148 0.45 0.46

O.155 0.22 0.30

0.162 0.12 0.00

0.169 0.10 0.00

0.176 0.06 0.00

0.183 0.00 0.00

0.190 0.00 0.00

0.197 0.00 0.00

0.204 0.00 0.00

0.211 0.00 0.00

0.218 0.00 0.00
95

APPENDIX E

DATA FOR THE EVAPORATING SPRAY (CASE I)

E.I Gas-Phase Properties

Table E.I.1. Axial Variation of Centerline Velocity

x/d u /u

c o

40 0.428

50 0.370

70 0.284

100 0.222

150 0.170

250 0.113

400 0.062

500 0.052
96

Table E.I.2. Radial Variation of Quantities

x/d = 50

rlx ulu u'v'/u 2 i u'21u i v'21u i w'2/u _</u 2

C C C C C C

0.0 I.0 0.0 0.193 0.095 0.094 .0276

0.0168 0.994 .00124 0.217 0.097 0.100 .0332

0.0335 0.996 .00505 0.221 0.110 0.111 .0366

0.0503 0.951 .00632 0.219 0.111 0.112 .0364

0.0670 0.895 .0105 0.221 0.114 0.117 .0373

0.0838 0.809 .01221 0.221 0.114 0.115 .0375

0.1005 0.725 .011 6 0.223 0.118 0.114 .0383

0.1173 0.625 .01268 0.200 0.120 0.114 .0337

O.1340 0.555 .01692 0.204 O.120 0.110 .0341

0.1508 0.496 .0164 0.219 0.116 0.103 .0360

0.1675 0.406 .0139 0.206 0.115 0.098 .0326

0.1843 0.309 .0105 0.175 0.106 0.095 .0254

0.2010 0.216 .0087 0.150 0.101 0.094 .0208

0.218 0.095 .00258 0.084 0.075 0.079 .0095
97

Table E.I.3. Radial Variation of Quantities

x/d = 100

•r/x u/u u'v'/u 2 / u'2/u / v'2/u / w'2/u [</u 2

c c o c c c

0.0 1.0 0.0 0.238 0.165 0.164 0.0554

0.0168 0.971 0.00356 0.237 0.166 0.162 0.0549

0.0335 0.940 0.0100 0.238 0.167 0.167 0.0562

0.0503 0.892 0.0146 0.238 0.166 0.173 0.0571

0.0670 0.858 0.0158 0.242 0.167 O.179 0.0592

0.0838 0.794 0.0181 0.242 0.168 0.180 0.0596

0.1005 0.690 0.0194 0.243 0.169 0.179 0.0598

0.1173 0.554 0.0193 0.239 0.161 0.159 0.0542

0.1340 0.463 0.0146 0.213 0.138 0.135 .0413

0.1508 0.377 0.0128 0.194 0.124 0.115 0.0331

0.1675 0.274 0.01026 0.156 0.096 0.088 0.0206

0.1843 0.135 0.0052 0.121 ......

0.2010 0.091 0.00170 0.085 ......
98

Table E.I.4. Radial Variation of Quantities

×/d = 250

r/x u/u u'v'/u 2 t u'2/u i v'2/u i w'2/u k/u 2

c c c o c c

0.0 1.0 0.0 0,257 0.209 0,215 0,0779

0.0168 0.993 0.00202 0.259 0.213 0.224 0.0813

0.0335 0.931 0.00897 0.256 0.215 0.228 0.0819

0.0503 0.797 0.01784 0.253 0.212 0.233 0.0816

0.0670 0.688 0.0197 0.247 0.222 0.237 0.0832

0.0838 0.561 0.01868 0.236 0.236 0.241 0.0847

0.1005 0.435 0.0185 0.199 0.229 0.238 0.0743

0.1173 0.357 0.0146 0.188 0.207 0.202 0.0595

0.1340 0.259 0.00894 0.151 0.139 0.139 0.0307

O. 1508 0.186 0.00664 0.128 0.132 0.115 0.0235

0.1675 0.150 0.00497 0.110 0.110 0.100 0.0171

0.1843 0.078 0.00131 0.076 0.0757 0.070 0.0082
99

Table E.I.5. Radial Variation of Quantities

x/d = 500

m

r/x u/u u'v'/u 2 i u'2/u i v'2/u i w'2/u k/u 2

C C C 0 C C _'

0.0 I.0 0.0 0.279 0.221 0.223 0.0882

0.01 68 0.968 0.00585 0.279 0.220 0.223 0.088

0.0335 0.875 0.0151 0.282 0.225 0.231 0.0918

0.0503 0.821 0.01 797 0.286 0.221 0.230 0.0918

0.0670 0.763 0.0202 0.276 0.214 0.226 0.0865

0.0838 0.581 0.0202 0.254 0.204 0.219 0.0770

0.1005 0.501 0.0189 0.231 0.192 0.208 0.0667

0.1173 0.406 0.0136 0.193 0.178 0.199 0.0543

0.1340 0.304 0.00827 0.167 0.147 0.153 0.036

0.1508 0.200 .00602 0.142 0.129 0.131 0.027

0.1675 0.135 .00489 0.122 0'.106 0.119 0.201
100

Table E.I.6. Axial Variation of Mean Gas-Phase

Temperature Decrement and Mean Mixture

Fraction (or Total Freon-11 Concentration,

YFc/YFo ) in the Case I Evaporating Spray

x/d (Tc-T)/(To-T )a -fc/_ob

50 -- 0.420

70 -- 0.31 7

100 -- 0.226

150 -- 0.153

250 - O.508 O.062

300 0.437 --

400 0.254 0.029

500 O.168 0.024

600 O.138 0.01 9

aTo = 261 K

bfo = 1.0
I01

Table E.I.7. Radial Variations of Mean Gas-Phase Temperature

Decrement in the Case I Evaporating Spray

x/d = 250 x/d = 500

r/x

- (T_T)/(Tc_T ) (T-T_)/(Te-T _)

0.0 I .0 I .0

0.01 68 0.970 0.992

O.0335 O.939 O.902

O.0503 O.687 O.869

0.0670 O.603 0.803

O.0838 O.402 0.689

0.1005 0.346 0.623

O. 1173 0.296 O.459

0.1340 0.229 0.344

0.1508 0.156 0.262

0.I 675 0.089 O.197

0.1843 0.0502 O. 131

0.2010 -- 0.0656

0.2176 -- 0.0492
102

Table E.I.8. Radial Variation of Mean Mixture Fraction

(or Total Freon-11 Concentration, YF/YFc )

in the Case I Evaporating Spray

x/d = 50 x/d = 100 x/d = 250 x/d = 500

r/x

f/f f/f f/f f/f

C C C C

0.0 I.0 I.0 I .0 I.0

0.0168 0.987 0.981 0.984 0.984

0.0335 0.946 0.947 0.953 0.967

0.0503 0.880 0.860 0.840 0.915

0.0670 0.786 0.789 0.758 0.851

0.0838 0.731 0.677 0.628 0.760

0.1005 0.627 0.534 0.493 0.669

O.1173 O.506 O. 421 0.411 0.548

0.1340 0.443 0.307 0.335 0.457

0.1508 0.341 0.263 0.269 0.385

O.1675 0.288 0.184 0.207 0.282

0.1843 0.229 O. 121 0.172 0.209

0.2010 0.189 -- ....

0.2180 0.131 ......
103

E.2. Liquld-Phase Properties

Table E.2.1. Radial Variation of Liquid Flux and SMD

at x/d = 50 in the Case I Evaporating Spray

SMD (um) SMD (um)

r/x G/Gc (Slide Impaction) (Photographic)

0.00 1.00 3o.3 31.3

0.05 0.96 30.2 31.2

0.10 0.68 28.7 31.7 ,

0.15 0.42 31.5 29.4

0.20 0.12 30.9 30.4

aGc = 5.332 kg/m2s
o

Table E.2.2. Radial Variation of Drop Size Distributions at x/d --50 _"

for the Case I Evaporating Spray (Slide Impaction Results)

(Entries are Relative Percentage Number Frequency)

Diameter 0.00 6.36 12.72 19.08 25.44 31.80 38.16 44.52 50.88 57.24

Size Range ....................

(_m) 6.36 12.72 19.08 25.44 31.80 38.16 44.52 50.88 57.24 63.60

r/x

0.00 17.9 15.5 22.5 18.8 11.5 9.1 1.8 0.9 0.8 0.3

0.05 20.0 15.0 20.2 19.6 12.5 8.9 I_8 0.8 0.8 0.3

0.10 15.8 13.4 24.6 22.3 11.9 9.2 1.6 0.5 0.6 0.03

0.15 30.4 14.9 17.1 17.3 9.3 4.9 3.4 I .6 0.8 0.1

0.20 41.7 14.6 15.5 14.0 5.0 4.6 2.9 0.5 I .0 0.1
Table E.2.3. Radial Variation of Drop Size Distributions at x/d --50

for the Case I Evaporating Spray (Photographic Results)

(Entries are Relative Percentage Number Frequency)

Diameter 15 20 25 30 35 40 45 50 55

Size Range ..................

(_m) 20 25 30 35 40 45 50 55 60

r/x

0.00 14.7 33.1 26.9 11.3 7.2 4.2 I.5 0.8 0.3

0.05 19.4 29.5 26.4 11.3 7.5 3.1 1.8 0.6 0.4

0.10 17.5 30.4 26.7 11.0 6.5 5.1 1.8 0.7 0.4

0.15 21.8 34.2 26.2 10.6 2.3 2.9 I.3 0.6 0.2

0.20 23.0 33.1 22.4 9.7 4.3 5.8 I.2 0.6 --

I--L

0
106

Table E.2.4. Initial Conditions of Mean Axial Drop Velocities

(m/s) at x/d = 50 for the Case I Evaporating Spray

r/x 0.00 0.05 O.I0 O.15 0.20

Diameter

Size Range

(_m)

15-20 27.20 25.24 19.54 13.60 7.80

20-25 28.51 27.08 20.78 14.19 8.31

25-30 28.50 26.82 21.08 14.70 8.91

30-35 28.41 27.93 21.44 15.20 9.07

35-40 27.52 27.30 22.15 14.92 11.36

40-45 28.32 27.93 21.59 16.70 11.26

45-60 27.78 28.59 22.31 18.22 11.93
107

Table E.2.5. Initial Conditions of Fluctuating Axial Drop Velocities

(m/s) at x/d = 50 for the Case I Evaporating Spray

r/x 0.00 0.05 0.10 0.15 0.20

Diameter

Size Range

(_m)

15-20 2.01 2.45 2.60 2.57 3.05

20-25 2.34 2.78 2.81 2.51 2.90

25-30 2.27 2.85 2.79 3.01 3.82

30-35 2.56 2.09 3.57 3.55 3.56

35-40 2.06 2.96 3.43 2.58 4.59

40-45 2.32 2.24 2.16 1.98 3.20

45-60 1.66 2.18 2.52 2.31 4.65
o

co

Table E.2.6. Axial Variation of Drop Size Distributions Along the Centerline

of the Case I Evaporating Spray (Photographic Results).

(Entries are Relative Percentage Number Frequency)

Diameter 15 20 25 30 35 40 45 50 55

Size Range ..................

(_m) 20 25 30 35 40 45 50 55 60

x/d

100 18.66 29.69 24.74 11.48 8.22 4.41 2.05 0.63 0.12

150 21.87 30.07 25.13 12.26 7.22 2.15 0.86 0.43 --

250 22.72 31.44 25.90 11.53 5.79 1.49 1.12 ....
109

Table E.2.7. Axial Variation of SMD Along the

Centerllne of the Case I EvaPorating Spray

(Photographic Results)

x/d SMD (um) '

100 31.50

150 29.61

250 28.74
110

Table E.2.8. Mean Axial Drop Velocities (m/s) Along the

Centerline of the Case I Evaporating Spray

x/d IO0 150 250

Diameter

Size Range

(_m)

15-20 16.5 12.9 8.1

20-25 16.3 13.2 8.2

25-30 16.8 13.5 8.7

30-35 17.6 14.0 9.4

35-40 18.0 14.7 9.8

40-45 17.8 15.5 9.8

45-60 19.8 16.9 9.9
iii

Table E.2.9. Fluctuating Axial Drop Velocities (m/s) Along

the Centerline of the Case I Evaporating Spray

x/d 100 150 250

Diameter

Size Range

(_m)

15-20 2.60 1.87 1.28

20-25 2.49 1.71 1.14

25-30 2.28 1.69 1.29

30-35 2.00 1.80 1.66

35-40 1.88 1.91 1.91

40-45 1.93 1.99 2.03

45-60 1.56 1.48 2.08
112

f

APPENDIX F

DATA FOR THE EVAPORATING SPRAY (CASE 2)

F.I Gas-Phase Properties

Table F.I.1. Axial Variation of Centerline Velocity

x/d u /u

c o

40 0.590

50 0.538

70 0.495

100 0.419

150 0.307

250 0.234

400 0.117

5OO O.O95
113

Table F.I.2. Radial Variation of Quantities

x/d = 50

m m

- - 2 "/ u'2/u ",/v'2/u ",/w'2/u k/u 2

rlx uluc u'v;lue c c c c

0.0 I .0 0.0 .156 .074 .075 .0177

0.0168 1.104 .00149 .161 .077 .077 .0189

0.0335 1.164 .00385 .162 .074 .077 .0188

0.0503 1.168 .00612 .178 .078 .083 .0223

0.0670 1.072 .00954 .208 .081 .090 .0289

0.0838 1.008 .0125 .239 .086 .093 .0366

0.1005 .885 .0170 .263 .092 .095 .0433

0.1173 .771 .0163 .274 .097 .I03 .0475

0.1340 .657 .0187 .253 .097 .108 .0425

0.1508 .515 .0185 .249 .091 .093 .0395

O. 1675 .463 .0136 .221 .092 .083 .0321

0.1843 .259 .0094 .I69 .093 .077 .0216

0.2010 .142 .0042 .138 .084 .049 .0143

0.218 .091 .0028 .134 .082 .020 .0125
114

Table F.I.3. Radial Variation of Quantities -

x/d = 100

r/x u/u u'v'/u 2 i u'2/u i _'2/u i w'2/u k/u 2

C C e c c c

0.0 1.0 0.0 0.218 0.116 0.117 0.0373

0.0168 0.995 0.00435 0.213 0.120 0.118 0.0368

0.0335 1.017 0.00614 0.214 0.111 0.120 0.0363

0.0503 I.032 0.00752 0.227 0.115 0.124 0.0401

0.0670 0.933 0.00838 0.229 0.117 0.132 0.0418

0.0838 0.828 0.0113 0.236 0.124 0.133 0.0444

O.1005 0.695 0.0102 0.233 O.127 0.127 0.0433

0.1173 0.567 0.00858 0.230 0.132 0.118 0.0421

0.1340 0.437 0.0082 0.209 0.127 0.103 0.0352

0.1508 0.291 0.00783 0.174 0.118 0.090 0.0262

0.1675 0.248 0.00713 0.138 0.117 0.086 0.0201

0.1843 0.172' 0.00556 0.127 0.110 0.082 0.0175

0.2010 0.118 0.00291 0.0995 ......
115

Table F.I.4. Radial Variation of Quantities

x/d _ 250

r/x u/u u'v'/u 2 / u,2/u / v'2/u / w'2/u k/u 2

C C C C O C

0.0 1.0 0.0 0.242 0.153 0.144 0.0514

0.0168 0.926 0.00434 0.232 0.154 0.150 0.0500

0.0335 0.825 0.00787 0.239 0.148 0.162 0.0526

0.0503 0.714 0.0107 0.226 0.146 0.174 0.0513

0.0670 0.621 0.0128 0.228 0.152 0.174 0.0527

0.0838 0.532 0.01022 0.185 0.157 0.143 0.0397

0.1005 0.400 0.00947 0.167 0.144 0.123 0.0319

0.1173 0.320 0.00879 0.159 0.132 0.108 0.0272

0.1340 0.250 0.00559 0.141 0.117 0.100 0.0218

0.1508 0.183 0.00435 0.124 0.108 0.086 0.0172

0.1675 0.118 0.00149 0.082 0.066 0.058 0.00722

0.1843 0.085 0.00078 0.069 • 0.061 ....
116

Table F.I.5. Radlal Varlatlon of Quantities

x/d --500

- - 2 V'u'2/u i/v'2/u _/w'2/u k/u 2

rlx UlUe u--i-_Tv 'lUe e e e e

0.0 1.0 0.0 0.291 0.237 0.248 0.1012

0.0168 0.902 0.00665 0.286 0.238 0.241 0.0983

O.0335 O.840 O.0117 O.265 O.232 O.240 O.0963

0.0505 0.764 0.0141 0.275 0.227 0.241 0.0926

0.067 0.699 0.0186 0.257 0.228 0.235 0.0866

0.0838 0.592 0.0185 0.245 0.215 0.227 0.0789

0.1005 0.45 0.0141 0.218 0.201 0.221 0.0684

0.1173 0.341 0.00978 0.174 0.177 0.181 0.0472

0.1340 0.256 0.00776 0.151 0.155 0.158 0.0359

0.1508 0.156 0.00708 0.141 0.133 0.146 0.0294

0.1675 0.101 0.00452 0.114 0.098 0.115 0.0179
117

Table F.I.6. Axial Variation of Mean Gas-Phase

Temperature Decrement and Mean Mixture

Fraction (or Total Freon-11 Concentration,

YFc/YFo ) in the Case 2 Evaporating Spray

x/d (Tc-T)/(To-T )a _c /_ob

50 -- 0.550

70 -- 0.409

100 -- 0.345

150 -- 0.240

250 -- 0.162

400 -- 0.079

500 0.654 0.063

600 0.617 0.049

aTo = 268 K

bfo = 1.0
118

Table F.I.7. Radial Variation of Mean Gas-Phase Temperature

Decrement in the Case 2 Evaporating Spray

r/x x/d = 250

(T-T)/(To-T _)

0.0 1.000

0.0168 0.900

0.0335 0.797

0.0503 0.651

0.0670 0.589

0.0838 0.495

0.1005 0.432

0.1173 0.380

0.1340 0.339

0.1508 0.260

0.1675 0.234

0.1843 0.177

0.2010 0.130

0.2176 0.093

0.2344 0.067
119

Table F.I.8. Radial Variation of Mean Mixture Fraction

(or Total Freon-11 Concentration, YF/YFc)

in the Case 2 Evaporating Spray

i

x/d = 50 x/d = 100 x/d = 250 x/d = 500 r/x

f/f f/f f/f f/f

C C C C

0.0 1.0 1.0 1.0 1.0

O.0168 O.935 O.992 O.988 O.984

0.0335 0.894 0.979 0.958 0.949

0.0503 0.855 0.920 0.880 0.901

0.0670 0.807 0.810 0.763 0.778

0.0838 0.733 0.726 0.579 0.611

0.1005 0.671 0.640 0.486 0.520

0.1173 0.589 0.535 0.403 0.419

0.1340 0.495 0.404 0.329 0.326

0.1508 0.435 0.305 0,259 0.251

0.1675 0.365 0.252 0.212 0.176

O.1843 0.307 0.184 0.170 0.154

0.2010 0.265 0.130 0.143 --

0.2180 0.191 ......

0.2340 0.127 ......
120

F.2. Llquld-Phase Properties

Table F.2.1. Radial Variation of Liquid Flux and SMD

at x/d = 50 in the Case 2 Evaporating Spray

SMD (_m) SMD (_m)

r/x G/Gca (Slide Impaction) (Photographic)

0.00 1.00 62.6 59.7

0.05 0.92 62.6 60.6

0.10 0.62 58.8 57.6

0.15 0.29 60.2 57.5

0.20 0.13 54.8 59.1

aGc = 7.413 kg/m2s
Table F.2.2. Radial Variation of Drop Size Distributions at x/d = 50

for the Case 2 Evaporating Spray (Slide Impaction Results)

(Entries are Relative Percentage Number Frequency)

Diameter 0.00 6.36 12.72 19.08 25.44 31.80 38.16 44.52 50.88 57.24

Size Range ....................

(_m) 6.36 12.72 19.08 25.44 31.80 38.16 44.52 50.88 57.24 63.60

r/x

0.00 3.2 4.7 7.1 10.0 9.0 11.I 12.0 14.3 8.0 4.9

0.05 3.8 4.1 7.1 9.1 8.0 12.2 13.6 13.2 9.0 5.0

0.10 4.5 5.9 6.8 10.2 9.0 13.1 15.0 12.3 7.4 4.3

0.15 4.2 5.7 6.5 9.0 8.3 14.0 16.0 11.0 9.0 3.0

0.20 5.0 6.2 7.1 10.4 10.0 13.5 16.4 11.8 7.0 3.1

50
(Continued) _o

Table F.2.2. Radial Variation of Drop Size Distributions at x/d = 50

for the Case 2 Evaporating Spray (Slide Impaction Results)

(Entries are Relative Percentage Number Frequency)

Diameter 63.60 69.96 76.32 82.68 89.04 95.4 101.76

Size Range ..............

(urn) 69.96 76.32 82.68 89.04 95.4 101.76 108.12

r/x

0.00 4.1 2.7 I.9 2.0 I .6 I .3 I .I

0.05 3.2 4.0 I .8 2.0 I.8 I.I I .I

0.10 3.0 3.1 I.2 I.7 I.0 I.0 0.5

0.15 4.0 2.5 2.0 I.5 I.7 I.5 0.2

0.20 4.5 I .0 2.0 0.6 0.3 I .0 0.1
Table F.2.3 Radial Variation of Drop Size Distributions at x/d = 50

for the Case 2 Evaporating Spray (Photographic Results)

(Entries are Relative Percentage Number Frequency)

Diameter I0 20 30 40 50 60 70 80 90 IO0 110

Size Range ......................

(_m) 20 30 40 50 60 70 80 90 100 110 120

r/x

0.00 2.85 21 .61 20.23 19.98 18.11 8.26 3.85 2.66 1.73 0.50 0.22

0.05 2.72 13.41 23.17 23.22 16.32 10.46 5.37 3.03 I.47 0.60 0.21

0.10 2.51 20.41 25.64 20.93 14.67 7.46 5.14 I.61 0.93 0.44 0.26

0.15 2.88 31 .91 23.87 16.49 10.94 6.13 3.38 2.45 1.24 0.58 0.13

0.20 4.44 32.22 20.49 12.66 15.66 4.64 6.14 1.42 1.25 0.97 0.09

_o

t_
124

Table F.2.4. Initial Conditions of Mean Axial Drop Velocities

(m/s) at x/d = 50 for the Case 2 Evaporating Spray

r/x 0.00 0.05 0.10 0.15 0.20

Diameter

Size Range

(_m)

10-20 19.80 20.34 14.92 6.67 I.94

20-30 19.97 20.56 15.05 7.10 2.24

30-40 21.15 21.16 15.96 9.29 3.56

40-50 20.68 22.01 16.91 12. I0 4.09

50-60 21.12 22.55 17.41 13.80 5.65

60-70 20.28 21.84 17.70 14.68 6.44

70-80 20.52 21.38 18.02 15.35 7.39

80-90 19.34 20.96 17.91 15.79 8.93

90-100 18.81 20.24 18.33 16.30 10.88

100-120 19.53 19.90 18.26 16.20 11.31
125

Table F.2.5. Initial Conditions of Fluctuating Axial Drop Velocities

(m/s) at x/d = 50 for the Case 2 Evaporating Spray

r/x 0.00 0.05 0.10 0.15 0.20

Diameter

Size Range

(_m)

10-20 2.20 2.14 1.53 2.16 1.08

20-30 2.26 2.19 1.79 2.31 1.25

30-40 1.94 2.08 1.72 2.88 1.95

40-50 1.81 2.29 2.11 3.58 2.03

50-60 1.68 1.83 1.66 3.16 2.63

60-70 1.51 1.83 1.31 2.60 2.88

70-80 1.48 1.66 1.44 3.04 3.11

80-90 1.69 1.65 1.28 1.82 3.02

90-100 1.78 1.26 1.27 1.43 2.51

100-120 1.19 0.92 1.43 1.78 2.42
Table F.2.6 Axial Variation of Drop Size Distributions Along the Centerline

of the Case 2 Evaporating Spray (Photographic Results)

(Entries are Relative Percentage Number Frequency)

Diameter 10 20 30 40 50 60 70 80 90 100 110

Size Range ......................

(um) 20 30 40 50 60 70 80 90 100 110 120

x/d

100 5.66 19.93 19.50 18.11 18.37 9.67 4.27 2.87 0.84 0.53 0.27

150 5.21 17.19 19.34 18.01 19.41 11.41 4.44 3.35 0.95 0.45 0.24

250 6.18 14.47 15.76 19.27 18.79 13.45 6.25 3.64 1.66 0.51 0.04

400 4.00 12.78 12.16 20.45 20.89 14.60 6.81 4.40 2.35 1.56 --

500 6.07 13.96 15.75 20.70 19.58 15.19 7.27 1.34 0.15 ....

r J
127

Table F.2.7. Axial Variation of SMD Along the Centerllne

of the Case 2 Evaporating Spray

(Photographic Results)

x/d SMD (_m)

I00 59.5

150 60.2

250 62.1

400 65.2

5OO 57.8
128

Table F.2.8. Axial Variation of Mean Axial Drop Velocity (m/s)

Along the Centerline of the Case 2 Evaporating Spray

x/d 100 150 250 400 500

Diameter

Size Range

(_m)

10-20 15.6 11.9 7.7 3.9 3.0

20-30 15.8 II.8 7.8 4.3 3.2

30-40 15.9 11.7 8.7 4.7 3.4

40-50 16.0 12.8 8.0 5.1 3.6

50-60 16.8 11.8 8.0 5.5 3.9

60-70 16.0 11.7 8.2 6.0 3.6

70-80 15.9 11.6 8.6 6.3 4.0

80-90 15.1 12.4 8.8 5.8 4.2

90-100 15.7 12.3 8.9 6.9 4.4

100-110 15.7 12.7 9.3 7.2 --

110-120 15.7 13.1 10.1 ....
129

l

Table F.2.9. Axial Variation of Fluctuating Axial Drop Velocity (m/s)

Along the Centerllne of the Case 2 Evaporating Spray

x/d 100 150 250 400 500

Diameter

Size Range

(_m)

10-20 2.61 2.14 1.24 0.98 0.75

20-30 2.48 2.24 1.45 0.92 0.80

30-40 2.53 2.32 1.69 0.88 0.84

40-50 2.26 2.27 1.77 0.89 0.87

50-60 2.37 2.86 1.68 0.94 0.86

60-70 2.00 2.67 1.68 1.07 0.88

70-80 1.84 2.13 1.75 1.26 0.91

80-90 1.70 1.72 1.63 1.38 0.98

90-100 1.86 1.54 1.36 1.44 1.11

100-110 1.55 1.61 1.37 1.49 --

110-120 1.62 1.88 1.57 ....
1. Report No. 2. Government Accession No. 3. Reclplent'e Catalog No.

NASACR-174760

4. Title and Subtitle 5. Report Date

A Theoretical and Experimental Study of Turbulent September 1984

Evaporati ng Sprays 8.Performing OrganizaCode tion

7. Author(s) 8. Performing Organization Report No.

A.S.P. Solomon, J-S. Shuen, Q-F. Zhang and G. M. Faeth None

10.WorkUnit No.

g. Performing Organization Name and Addrese

The Pennsylvania State University 11. Contrect orGrent No.

Mechanical Engineering Building NAG3-190

University Park, Pennsylvania 16802

13. Type of Report Ind Period Covered

12. Sponsoring Agency Name end Address Contractor Report

National Aeronautics and Space Administration

Washington, D.C. 20546 14Spon , sorlng AgencyCode

505-31-42

15. SuDplementaw Noles

Final report. Project Manager, Robert Tacina, Aerothermodynamics and Fuels Division, NASALewis Research Center, Cleveland, OH 44135.

m AbstractMeasurements and analysis limited to the dilute portions of turbulent

evaporating sprays, injected into a still air environment were completed. Mean and

fluctuating velocities and Reynolds stress were measured in the continuous.phase.

Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and

velocity correlation. Initial conditions needed for model evaluation were measured

at a location as close to the injector exit as possible. The test sprays showed

significant effects of slip and turbulent dispersion of the discrete phase. The

measurements were used to evaluate three typical models of these processes: (1) a

locally homogeneous flow (LHF) model, where slip between the phases were neglected;

(2) a deterministic separated flow (DSF) model, where slip was considered but effects

of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow

(SSF) model, where effects of interphase slip and turbulent dispersion were

considered using random-walk computations for drop motion. For all three models,

a k-_ model was used to find the properties of the continuous phase. The LHF and

DSFmodels did not provide very satisfactory predictions for the present measurements

In contrast, the SSF model performed reasonably well--with no modifications in the

prescription of eddy properties from its original calibration. Someeffects of

drops on turbulence properties were observed near the dense regions of the sprays.

Treatment of such dense flow effects will require extension of the present SSF model.

The SSF approach, however, appears to provide an attractive formulation for

treating nonlinear interphase transport processes in drop-laden turbulent flows.

iT. Key Words (Suggested by Author(s)) 18. Distribution Statement

Spray modeling Unclassified - unlimited

Turbulence interactions STARCategory 07 Combustor

19. Security Classlf. (of this report) 20. Security Clesslf. (of this page) 21. No. of pages 22. Price"

Unclassified Unclassified 137 A07

*For sale by the National Technical Information Service, Springfield, Virginia 22161

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