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NASA ContractorReport 174838

NASA-CR-174838

19850007419

lhe Structureof Dilute CombustlngSprays

3-S. Shuen, A.S.P. Solomon,and G.M. Faeth

The PennsylvaniaState University

UniversityPark, Pennsylvania

[!BIIAflV I OP\'

3anuary 1985

SEP2 0_95

LAr,GLEY ffESE_RCH CENIER

LI_I_ARy,IIASA

Preparedfor

i NATIONALAERONAUTICSAND SPACE ADMINISTRATION

Lewis ResearchCenter

," Under Grant NAG 3-190

TABLE OF CONTENTS

Page

NOMENCLATURE .......................... iii

SUMMARY ............................ I

I. INTRODUCTION........................ 2

2. EXPERIMENTAL METHODS .................... 4

2.1 Test Arrangement ................... 4

2.2 Test Conditions.................... 7

2.3 Instrumentation.................... 10

2.3.1 Gas Velocity .................. 10

2.3.2 Drop Velocity ................. 10

2.3.3 Drop-Size Distributions ............ 12

2.3.4 Drop Number Flux................ 14

2.3.5 Mean Gas Temperature.............. 14

3. THEORY ........................... 18

3.1 General Description.................. 18

3.2 Continuous-Phase Analysis.............. 18

3.2.1 Governing Equations .............. 18

3.2.2 State Relationships .............. 22

3.2.3 Computations.................. 26

3.3 Drop Transport .................... 26

3.3.1 Drop Transport Analysis ............ 26

3.3.2 Drop Transport Calibrations .......... 32

3.4 Deterministic Separated Flow Model .......... 35

3.5 Stochastic Separated Flow Model............ 36

4. RESULTS AND DISCUSSION ................... 38

4.1 Introduction ..................... 38

4.2 Initial Conditions .................. 39

4.3 Scalar Structure of the Test Flame .......... 39

4.4 Structure of the Spray Flames............. 47

4.4.1 Mean Phase Velocities ............. 47

4.4.2 Fluctuating Phase Velocities .......... 52

4.4.3 Drop Number Flux................ 54

4.4.4 Drop-Size Distributions ............ 61

5. SUMMARY AND CONCLUSIONS .................. 61

5.1 Summary........................ 61

5.2 Conclusions...................... 64

APPENDIX A: EXPERIMENTAL UNCERTAINTIES ............ 66

A.I Phase Velocities ................... 66

A.2 Drop-Size Distribution ................ 69

A.3 Drop Number Fluxes ................ 71

A.4 Mean Gas Temperatures ................. 72
APPENDIX B: DROP NUMBER FLUX MEASUREMENTS ........... 74

B.I Pulse Counter ..................... 74

B.2 Calibration of Measuring Area ............. 74

APPENDIX C: CORRECTION OF TEMPERATURE MEASUREMENTS

FOR RADIATION ................... 77

APPENDIX D: DROP TRANSPORT PROPERTIES ............. 79

D.I Mixture Thermal Conductivity ............. 79

D.2 Mixture Viscosity ................... 79

D.3 Mixture Mass Diffusivity ............... 79

D.4 Mixture Specific Heat ................. 80

D.5 Properties of Methanol ................ 80

APPENDIX E: DROP TRANSPORT CALIBRATION ............ 83

E.I Experimental Method ................. 83

E.2 Drop-Life-History Data ................ 86

APPENDIX F: FLAME STRUCTURE DATA ............... 87

F.I Mean Gas Temperatures ................. 87

F.2 Gas Velocities .................... 90

F.3 Drop Velocities .................... 95

F.4 Drop Number Fluxes .................. 105

F.5 Drop Size Distributions ................ 109

REFERENCES ........................... 113

ii
NOMENCLATURE

Symbol Description

a acceleration of gravity

A total surface area of drops in a sample

AF cross-sectional area of drop number flux measuring volume

BO,BY mass transfer driving potentials, Eqs. (3.20) and (3.21)

CD drag coefficient

Ci parameters in turbulence model

Cp specific heat at constant pressure

d injector diameter

di diameter of i'th drop

dk k = I, 2, etc., moments of drop-slze distribution,

Eq. (A.10)

dp drop diameter

dtc diameter of thermocouple junction

D mean mass diffusivity

Dij binary diffusivity

e fluctuating signal amplitude

E signal amplitude

f mixture fraction

g square of mixture fraction fluctuations

h heat transfer coefficient

hi enthalpy of species i

hfg enthalpy of vaporization

hfgT total enthalpy of gasification, Eq. (3.27)

k turbulence kinetic energy

k' Boltzman constant, Appendix D

K LDA calibration factor, Eq. (A.5)

half-width of LDA measuring volume

L distance between drop generator and burner exit,

length of drop number flux measuring volume

Le dissipation length scale

m drop mass

mass flow rate

_" mass flux at drop surface

Mi,M molecular weight of species i, of mixture

n number of drop groups, total number of drops sampled

total drop count rate

hi number of drops per unit time in group i

_" drop number flux

Np,NS convection correction, Eq. (3.24)

p pressure

_v vapor pressure

P(f),P(f) time- and Favre-averaged probability density function

of f

PDF probability density function

Pr Prandtl number

Qr lower heat of reaction per mass of oxygen

r radial distance

R ideal gas constant

Re Reynolds number

iii
Sc Schmidt number

S¢ source term

SMD Sauter mean diameter

t time

te eddy lifetime

T temperature

Tcr critical temperature

Tr reference state

u axial velocity

Up drop velocity vector

v radial velocity

vi generic quantity, Appendix A

V generic function, Appendix A; total drop volume in a

sample

Vj volume of computational cell j

w tangential velocity

W width of drop number flux measuring volume

x axial distance

Xp drop position vector

Xi mole fraction of species i

Yi mass fraction of species i

_. average property factor, Eq. (3.28)

AXp path length of drops in an eddy

At residence time of drops in an eddy

rate of dissipation of turbulence kinetic energy,

gray-body emissivity

€' characteristic molecular energy, Appendix D

A thermal conductivity

laminar viscosity, location of maximum probability

Ut turbulent viscosity

kinematic viscosity

VFO stoichiometric mass of fuel per mass of oxygen

p density

o standard deviation of PDF, Stephan-Boltzman constant

o' characteristic molecular length, Appendix D

Odp standard deviation of drop-size distribution

oi turbulent Prandtl/Schmidt number

€ generic quantity, fuel-equivalence ratio

¢c critical fuel-equivalence ratio

¢ij property interaction parameter, Appendix D

Subscripts

a air

avg average value

bf bulk liquid

c centerline quantity

f flame property, reference property

F fuel

g gas-phase property

i drop group or coordinate direction

o burner exit condition

iv
p drop property

s drop surface condition

t measured value of a property

tc thermocouple

ambient condition

Superscripts

(-) time-averaged quantity

(-)' tlme-averaged fluctuating quantity

(~) Favre-averaged quantity

(~)" Favre-averaged fluctuating quantity

(_) vector quantity

v

SUMMARY

A theoretical and experimental study of dilute combusting sprays

is described. The objective of the work was to assist development of

spray combustion models by providing data for well-defined experimental

conditions; and initiating evaluation of models of combustlng sprays,

typical of current practice, using the new measurements. Both test

conditions and analysis were chosen to emphasize effects of interphase

transport of mass, momentum and energy as well as drop-turbulence

interactions.

Measurements considered ultra-dilute combustlng sprays to minimize

uncertainties in continuous-phase properties and experimental results.

The test arrangement was a turbulent, methane-fueled diffusion flame

burning in still air. Monodlsperse (initial diameters of 105 and 180

wm) streams of methanol drops were injected along the axis of the

flame, at its base. Drop mass flow rates were low so that flame

structure was not influenced significantly by drop combustion and the

mean and turbulent properties of the flame were known from earlier work.

Present structure measurements included: mean and fluctuating phase

velocities, mean drop number flux distributions, drop-slze

distributions and mean gas temperatures. Initial conditions were known

from measurements at the burner exit, while ambient conditions of the

flame were well-defined. The transport properties of individual drops

were calibrated by auxiliary measurements using drops supported in the

post-flame region of a flat-flame burner.

Analysis of the combusting sprays was undertaken to help interpret

the measurements and to initiate evaluation of models of the process.

Two approaches were considered: (I) a deterministic separated flow

model, where effects of finite interphase transport rates are

considered but drop-turbulence interactions are ignored; and (2) a

stochastic separated flow model, where effects of finite interphase

transport rates and drop-turbulence interactions are considered using

random sampling for turbulence properties and random-walk computations

for drop motion. Drop combustion was also treated by taking limits,

either considering or ignoring the presence of envelope flames around

individual drops.

The deterministic separated flow model was not very successful for

present test conditions, since neglect of drop-turbulence interactions

caused drop spread rates to be underestimated. The stochastic

separated flow model yielded encouraging predictions with all empirical

parameters either fixed from earlier work in noncombusting flows or set

by the independent calibration tests. The distinction between the

presence or absence of envelope flames did not influence predictions

appreciably, since the drops primarily evaporated in the core of the

- flow where oxygen concentrations are low. The present experiment was

useful for studying drop transport and drop-turbulence interactions and

should be considered by others. The parabolic flow facilitates

numerically--closed computations, initial conditions are readily

measured, boundary conditions are well-defined, and flow properties are

conducive to reasonably accurate measurements.

1
I. INTRODUCTION

The primary objective of this investigation was to complete new

measurements of the structure of dilute combusting sprays, useful for

evaluating models of the process. Model evaluation was also

initiated, considering several methods typical of current eombusting

spray analysis. This research was motivated by the widespread

application of combusting sprays in aircraft and rocket propulsion

systems. The availability of reliable models of spray combustion

processes would be of great value in reducing the need for costly and

time-consumlng, cut-and-try testing during combustor development.

Past work on spray flames, and related processes of particle-laden

jets, was recently reviewed by one of us; therefore, the details wlll

not be repeated here [1,2].* It was concluded that the most

pressing current need was for additional data to support spray model

development--particularly for test conditions where boundary conditions

can be well-defined and initial conditions for both phases can be

specified. The present study is the final phase of an investigation

which sought to contribute information of this nature. Earlier phases

of the study considered particle-laden jets [3-7], nonevaporating

sprays [8-11] and evaporating sprays [12]. A brief report of current

findings for combusting sprays can be found in Ref. [13]. More

complete details and complete tabulations of data for noncombusting

flows, can be found in previous reports and theses issued as part of

this study [14-19]. The present report presents similar results for

the combusting sprays.

Experience during earlier phases of this study showed that it is

very difficult to provide adequate data using practical spray

injectors--even in very simple flow situations, such as sprays injected

into stagnant air. The main difficulty involves the dense-spray region

near the injector, where current instrumentation is difficult to apply

due to obscuration by drops, the presence of liquid sheets and

ligaments, and the small dimensions of the region which causes problems

in obtaining adequate spatial resolution. Furthermore, it is difficult

to present results for polydisperse sprays, even in regions where

reliable measurements can be made. The information required to

characterize the flow is vast, including all continuous-phase

properties, drop-size distributions, and both mean and fluctuating

velocities as a function of drop size, among others.

In order to obtain a more tractable experiment, the present test

configuration was simplified considerably. This involved creating the

combustion environment with a methane-fueled diffusion flame burning in

still air. Ultra-dilute sprays were studied in this environment by

injecting monodlsperse streams of drops (105 and 180 pm initial

diameter) at the base of the flame--along the axis. The flow was

lightly-loaded with drops; therefore, flame structure was controlled by

*Numbers in brackets denote references.
methane combustion and could be studied once-and-for-all with no drops

present. This same flame configuration was studied during earlier work

in this laboratory; therefore, a detailed picture of its structure was

known, e.g., profiles of mean and fluctuating velocities, mean

temperatures, and the mean concentrations of major gas species [20-22].

A portion of these measurements were repeated during the present

investigation to provide more detail in the drop-contalning region,

e.g., mean and fluctuating velocities and mean gas temperatures. In

addition, the following measurements of drop properties were made:

mean and fluctuating drop velocities, drop number flux distributions,

and drop-size distributions. Present measurements included careful

characterization of the properties of both phases at the burner exit;

therefore, the test results should be useful for evaluating models of

sprays.

The experimental results were analyzed to help interpret the

measurements and to initiate evaluation of spray models. Two methods

typical of current practice were considered: (I) a deterministic

separated flow (DSF) model, where effects of finite interphase

transport rates are considered but drop-turbulence interactions are

ignored; and (2) a stochastic separated flow (SSF) model, where both

finite interphase transport rates and drop-turbulence interactions are

considered using random-walk computations for drop motion and transport.

The former method is typical of most current spray models [I]. The

latter method is based on a proposal by Gosman and Ioannldes [23],

which yielded encouraging results during the earlier phases of this

investigation considering noncombusting flows [I-19].

During past work [I-19], the locally homogeneous flow (LHF)

approximation for spray analysis was also examined. With this

approach, transport rates between the phases are assumed to be

infinitely fast, which implies that drop and gas velocities are the

same and that local thermodynamic equilibrium is maintained in the flow.

The LHF approximation, however, is only useful when drop diameters are

small--generally less than 10 _m in diameter [I]. Since present test

conditions were chosen to provide significant effects of finite

interphase transport, it was not worthwhile to pursue LHF calculations

in this study.*

All turbulent sprays and particle-laden flows have the potential

for interesting drop (particle)-turbulence interactions. A new element

appearing in combusting flows, however, is the possible existence of

envelope flames around individual drops when they contact

oxygen-containing regions in a turbulent flame environment [I]. This

problem was studied during the present investigation by conducting

calculations for the limiting conditions where envelope flames are

either considered or ignored. Analysis of single-drop transport was

*In a sense, results for the gas phase are equivalent to LHF results,

since the drop loading was very small during present tests.

3
calibrated for both conditions, using data from drops supported in the

post-flame region of a flat-flame burner.

In the following, experimental and theoretical methods are

described first. The structure of the diffusion flame is then

considered. The report concludes with discussion of spray flame

predictions and measurements. All data are tabulated in the

Appendix.

2. EXPERIMENTAL METHODS

2.1 Test Arrangement

A sketch of the test apparatus appears in Fig. I. The burner flow

is directed vertically upward. The combustion products are removed

near the ceiling of the test cell using a hood and blower. The

test-cell dimensions were: 5 m wide, 7 m long, and 5 m high.

The flame was contained within a screened enclosure to minimize

effects of room disturbances. The enclosure dimensions were I m square

cross-section, 2.5 m high, with a single layer of screen (630 wires/m,

square pattern, 0.25 mm wire diameter). Rigidly-mounted optical

instrumentation was used for some measurements; therefore, the entire

cage assembly was traversed, using a bearing track, to measure radial

profiles. Vertical traversing was accomplished by another track in

conjunction with a jack. Transverse motion, largely used to trim the

position to find the centerline, was accomplished using a linear

positioner. Transverse positions could be located within 0.10 mm,

while vertical positions could be located within 0.25 mm.

The burner assembly was a modified version of the design of Jeng

and coworkers [20-22]. The burner had provision for attaching the

flame at the burner exit and for injecting the drops vertically into

the base of the flow. A sketch of the burner appears in Fig. 2. The

burner was constructed of brass. The top surface of the burner was

coated with a radiation-absorbing paint (Rust-Oleum, type 4279) having

an emissivity of 0.96. A mixture of methane and natural gas entered a

baffled chamber at the bottom of the burner passed along the exit port

of the drop generator, and then flowed out of the burner through a

contraction section. The diameter at the inlet of the contraction was

25 mm and the burner exit diameter was 5 mm. The contractionwas shaped

according to the prescription of Smith and Wang [24], in order to

obtain a uniform exit velocity.

The top surface of the burner was cooled with water which flowed

through a passage (not shown in Fig. 2) concentric with the burner exit.

Water flow rate was adjusted to keep the top surface of the burner

within 0.5 K of the room temperature, in order to avoid the formation

of a natural convection plume which would disturb the flame flow field.

The temperature of the top surface of the burner was measured using 26

gauge chromel/alumel thermocouples, which were cemented directly to the

surface.
S EXHAUST HOOD

--_ EXHAUST

/- UPPER OPTICAL PLANE MOVABLE BURNER /__

,.OmLOWER OPTICAL PLANE OPTICS

50mW He-Ne LASER

I.Im ×x_

£DED BURNER GAS

LINEAR POSITIONER ENCLOSURE TRACK

Fig. I. Sketch of the test apparatus.
o

o FFUSION FLAME

o

o

o o

o

o 0

o

o

o

o

o o

o o MONODISPERSE DROPS

o (70-200 pm)

o o o

o

_ H2 GAS

o

o

o o

°o , , _ METHANE GAS

l II

JI

_DROP GENERATOR

LIQUID

METHANOL'-_L

Fig. 2. Sketch of the burner assembly.
The flame was stabilized at the burner exit using a small annular

flow of hydrogen. The hydrogen entered the flow through a 2 mm high

slot, whose upper edge was 1.2 mm below the burner exit.

The monodisperse stream of drops was produced using a commercial

vibrating orifice Berglund-Liu monodisperse drop generator (TSI, model

3050). The generator was removed from the manufacturer's cabinet and

mounted directly on the lower end of the burner, with an adaptor which

could be adjusted to center the generator orifice. A dispersing gas

flow of methane was supplied to the generator, to eliminate coalescence

of the drop stream. The stream of drops and dispersing gas flowed up a

cylindrical tube (9.5 mm outside diameter, 1.8 mm wall thickness, 19 mm

long) which ended 6.4 mm below the inlet of the contraction section.

Operation of the drop generator was checked using the flash

photography system of Solomon [19]. This was a useful check since

small errors in generator settings resulted in drop coalescence which

destroyed drop uniformity.

The flow rate of methanol was obtained directly by timing the

motion of the syringe pump used to feed the fuel to the generator. The

flow rate of natural gas was measured using a laminar flow element

(Merriam, model 50MW20-I) which was calibrated according to its

pressure drop (which was measured with an inclined manometer). The

flow rate of methane dispersing gas was measured using a Matheson model

603 rotameter. A second methane flow rate was used to provide seeding

particles in the burner flow during gas velocity measurements; this

flow was measured with a Matheson model 604 rotameter. The flow rate

of hydrogen was measured using a Matheson model 603 rotameter. All gas

flow instruments were calibrated using Precision Scientific Company

wet-test meters (0.10 and 1.0 cu. ft. per revolution).

2.2 Test Conditions

The properties of the test gases are summarized in Table I. The

natural gas composition is only typical and can vary depending on the

product mix of the supplier. Since the natural gas contained nearly

95% methane, and was supplemented with additional methane flows for the

drop generator dispersing gas and the particle seeder, the fuel will be

referred to as methane in the following.

The turbulent flame test conditions are summarized in Table 2.

Only one burner gas flow condition was considered; corresponding to the

highest Reynolds number flame studied by Jeng and coworkers [20-22].

This flame had an initial Reynolds number of 11,700 and was fully

turbulent over its length with the region of luminosity extending

400-600 mm. Effects of buoyancy were also relatively small over the

luminous region of the flame [20-22], which corresponded to the region

of interest for the present multiphase flow tests. The hydrogen

stabilizing flow was 2.8% (by mass) of the burner flow; therefore,

flame properties were primarily those of a methane-fueled flame in the

absence of drops (although the flame would be lifted without the

hydrogen flow).
Table I. Composition of Test Gases

Percent

by

Species Source Volume

Methane Matheson, Commercial Purity 99.0

Hydrogen Matheson, Extra-Dry Purity 99.9

Natural Gas Columbia Gas Co., Typical Composition

Methane 94.863

Ethane 3.753

Propane 0.266

iso-Butane 0.039

n-Butane 0.047

iso-Pentane 0.019

mono-Sulfur 0.009

di-Sulfur 0.012

Mercaptans 0.016

n-Pentane 0.016

Hexane 0.084

Nitrogen 0.408

Carbon Dioxide 0.423

neo-Pentane 0.006

Hydrogen Sulfide O.O19

Hydrogen 0.020

8
Table 2. Summary of Turbulent Flame Test Conditions

Nominal Drop Diameter (_m) 105 180

Liquid Volume Flow Rate (_/s) b 12.21 24.48

Generator Frequency (kHz) 20 7.96

Generator Orifice Diameter (wm) 50 100

aNatural gas and hydrogen flow rates of 520 and

14.6 mg/s; burner exit diameter of 5 mm; initial

Reynolds number of 11,700; initial centerllne

velocity (x/d = I) of 52.8 m/s; ambient temperature

and pressure of 300 ± 2 K and 97 kPa.

bMethanol (laboratory grade).
Two spray conditions were examined, corresponding to initial drop

diameters of 105 and 180 _m. The maximum mass flow rate of methanol

was less than 0.004% of the burner gas; therefore, the methane flame

was influenced by the drops to a negligible degree.

2.3 Instrumentation

2.3.1 Gas Velocity

Present structure measurements included: phase velocities,

drop-number flux, drop-slze distributions, and mean gas temperatures.

Each of these measuring systems will be described in the following.

Mean and fluctuating velocities were measured using a dual-beam,

single-channel, frequency-shlfted laser Doppler anemometer (LDA). The

components of the LDA are summarized in Table 3. Two sets of sending

and receiving optics were used yielding measuring volume dimensions of

100, 120 _m (x/d _ I) and 247, 720 _m (x/d > I).

The LDA actually measures the velocity of small seeding particles

in the flow. Aluminum oxide particles having a nominal diameter of

0.5 um were employed for seeding. Both the burner gas and the air

surroundings were seeded using reverse-cyclone seeders described by

Glass and Kennedy [25]. Operation of the seeders yielded particle

densities on the order of 109 particles/m3.

Mean and fluctuating velocity components of the gas phase were

measured at various axial and radial locations in the test flame. 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 flow andcomponents 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

(_,2)12 were made with a separate traverse in the third direction.

Reynolds stress measurements were made near the centerline in order to

find the flow axis (since Reynolds stress is zero at the centerline and

doesn't exhibit the broad maxima encountered for other variables).

Potential errors and uncertainties in the LDA measurements are

discussed in Appendix A. Uncertainties (95% confidence interval) in

mean and fluctuating velocity components were 5% while uncertainties in

k were 10%. All measurements were repeatable within these limits.

2.3.2 Drop Velocity

Drop velocities were measured using the same LDA arrangement as

the gas velocity measurements. In this case, gain settings of the

photomultiplier and counter were set to low values so that only strong

scattering signals from large particles were recorded. The processor

output was collected with a MINC 11/23 minicomputer and processed to

yield mean and fluctuating drop velocities (finding number-averaged

velocities). When these tests were run, the gas phase was not seeded,

to reduce the potential for bias errors with small drops. Various

i0
Table 3. Summary of LDA Components

Component Manufacturer Model Specification/Function

Hellum-Neon Laser Spectra 125A TEM_ mode,

Physics 632.8 nm wavelength,

2.0 mm beam diameter,

50 mW power

Polarization Rotator TSI 9102-2

Beam Splitter TSI 9115-2 50 mm beam spacing

Frequency Shifter TSI 9180-2 Bragg cell, 2 kHz -

40 MHz shift frequency

Transmitting Lens a TSI 9118 241 & 600 mm focal length,

60 mm clear aperture

Receiving Assembly TSI 9140

Detector Lens TSI 920 200 mm focal length

60 mm clear aperture

Photodetector TSI 9160 photomultiplier with

0.25 mm diameter aperture

Filter TSI 9157 632.8 nm central wavelength, 10 nm bandwidth,

60% peak transmittance

Duel Beam Oscilloscope Tektronix 912

Frequency Tracker TSI I090-IA 2 kHz - 50 MHz bandwidth

Burst Counter TSI 1980-A 100 MHz bandwidth

Digital/Analog Converter TSI 1988 used for analog output

from burst counter

True RMS Voltmeter TSI 1076

Integrating Digital Hewlett- 240IC

Voltmeter Packard

aonly one set having equal focal lengths for focusing and collecting

used at a time.

ii
components of drop velocity were measured in the same manner as the gas

phase.

Errors and uncertainties in mean and fluctuating drop velocities

were the same as to the gas velocity measurements, cf. Appendix A.

These measurements were also repeatable within these limits during the

period of testing.

2.3.3 Drop-Size Distributions

The sprays were so dilute that flash photography was not effective

for determining drop-size distributions, e.g., the number of in-focus

drops on each photograph was too small to make this method economically

feasible. As an alternative, the slide impactlon method of Shearer et

al. [26] was used, similar to earlier phases of the present

investigation [I0,11].

Figure 3 is a sketch of the slide impactor. Small glass slides,

coated with a layer of magnesium oxide, were exposed to the flow for a

timed period. The drops leave a crater in the coating upon impact,

which can be related to initial drop size even though they subsequently

evaporate.

May [27] presents results indicating that the crater diameter

varies with slide and drop properties; therefore, the ratio between

crater and drop diameters was calibrated. Streams of drops, having

various initial diameters, were produced by the monodisperse drop

generator and impacted on the slides. The initial drop size was

measured using the flash photography system of Solomon [19], while

crater size was measured using a microscope (the general practice for

data reduction from the slides). It was found that the crater diameter

varied with both drop diameter and velocity; therefore, a calibration

of these effects was used to reduce present measurements.

The raw drop-size distribution is influenced by the collection

efficiency of the impactor, which varies with both drop size and

velocity [28]. For present tests, the drop size ranges at a point were

relatively narrow since the drops were initially monodisperse;

therefore, the correction factors of the distribution were essentially

unity (or zero). As a result, the distributions were not corrected and

are reported as measured. This practice is adequate, except in regions

where drops are small (SMD < 30) where present SMD values are biased

upward since small drops were not collected.

The slide impactor required long sampling times to gather drops

since the spray was very dilute. Therefore, SMD was evaluated using

roughly 200 drops in the sample. While this sample is small, in

comparison to drop counts used for SMD in polydisperse sprays, the

uncertainty in SMD was comparable since the drops were initially

monodisperse and drop-slze distributions were relatively narrow, except

at the flame tip. Errors and uncertainties of the slide impactor are

discussed in Appendix A. For SMD values greater than 30 pm, the

uncertainty in SMD (95% confidence interval) was less than 10%.

12
r SUPPORT ROD 6.55 DIA.

6.35

b

DIRECIION _ )'_,---TOAIR t-'

1 OF TRAVEL SUPPLY

!= 101.6 _! GUIDE ROD

6.55 O.D. TUBE

Fig. 3. Sketch of the sllde [mpactor.
2.3.4 Drop Number Flux

Drop number fluxes were measured using the Mie-scattering system

illustrated in Fig. 4. The equipment llst for this system appears in

Table 4. The beam from a 50 mW HeNe laser was passed through a beam

expander and round-hole aperture to yield a relatively

uniform-lntenslty beam. Aperture dimensions were varied to increase

spatial resolution near the burner exit and to reduce sampling times in

regions of low drop concentrations far from the burner exit. A

cylindrical lens system then focussed the beam into a flat (waist

height 78-156 _m, depending on the aperture used) sheet whose plane was

normal to the streamwise direction.

Drops passing through the light sheet generated scattered-light

pulses which were observed from an angle of 90° to the laser beam in

the plane of the light sheet. The collecting and detector lenses and

the aperture of the photodetector defined the measuring area. A

laser-llne filter was placed in the path of observation, to reduce

effects of flame luminosity and increase slgnal-to-nolse ratios.

The output of the photodetector was observed on an oscilloscope.

Each drop passing through the measuring volume yielded a light pulse

which was recorded and counted using a pulse counter constructed in

this laboratory, cf. Appendix B for a description of the pulse counter.

Generally, more than 1000 drops were counted in order to obtain the

mean number flux.

The cross-sectional area of observation varied with drop size.

This effect was calibrated over the size range of interest and the

different aperture sizes--as described in Appendix B. The maximum

cross-sectional areas of observation were for 180 _m diameter drops, as

follows: 0.2 mm2 for x/d _ 12 and 2.9 mm2 for x/d > 12. The raw data

was corrected for the drop-size effect, using the measured drop-size

distributions.

Uncertainty analysis for these measurements is described in

Appendix A. The major source of uncertainty was the calibration of the

cross-sectional area of observation as a function of drop size.

Estimated uncertainty in drop number flux measurements is less than 15%

(95% confidence interval).

2.3.5 Mean Gas Temperature

The thermocouple probe used for mean gas temperature measurements

is illustrated in Fig. 5. The thermocouple junction was constructed by

butt-welding 75 _m diameter Pt/Pt-10% Rh wires. The wires were

attached to heavier lead wires of the same materials, having diameters

of 750 _m and spaced 12.7 mm apart. The wires were coated with silica,

to eliminate catalytic effects. The thermocouple probe was mounted in

a linear positibner, accurate to I mm.

The output of the thermocouple was sampled and processed using a

DEC MINC 11-23 minicomputer to yield time-averaged mean temperatures.

14
DETECTOR

PULSES COUNTER OSCILLOSCOPE

II IIII II _ DETECTOR

LENS

COLLECTING

LASER LINE LENS

' FILTER I

I

I I

I -- TWFLOWO - PREGION HASE

He -Ne APE

LIGHT SHEET

CYLINDRICAL LENS

EXPANDER _ SPATIAL FILTER

Fig. 4. Sketch of tile drop number flux system.
Table 4. Summary of Drop Number Flux Components

Component Manufacturer Model Specification/Function

Helium-Neon Laser Spectra 125A TEM, mode,

Physics 632.8 nm wavelength,

2.0 mm beam diameter,

50 mW power

Beam Expander Spectra 15 mm output beam

Physics diameter

Aperturea in-house -- 3.1 and 6.2 mm diameter

apertures

Cylindrical Lens unknown -- 600 mm focal length

Collecting Lens TSI 9119 595 mm focal length

60 mm clear aperture

Detector Lens TSI 920 200 mm focal length

60 mm clear aperture

Filter TSI 9157 632.8 central wavelength,

10 nm bandwidth,

60% peak transmittance

Digital Oscilloscope Nicolet Explorer 20 MHz sampling rate

III

Photodetector TSI 9160 photomultiplier with

0.25 mm diameter aperture

Pulse Counter in-house -- 12 V max voltage,

2 V threshold adjust,

I MHz response

asmall aperture for x/d _ 12, large aperture otherwise.

16
STAINLESS STEEL

TUBE

CERAMIC INSULATOR

52 LEAD WIRE

0.75 mm DIA.

PT/PT-I0 % RH

THERMOCOUPLE WIRE •--,,.16mm 0.076 mm DIA.

PT/PT-I0 % RH

Fig. 5. Sketch of the temperature probe.

17
The raw data was corrected for radiation errors following the procedure

described in Appendix C. The uncertainty of these measurements is

estimated to be less than 5% of the local mean temperature difference

between the gas and the surroundings, cf. Appendix A.

3. THEORY

3.1 General Description

Two theoretical models of spray processes were considered: (I) a

deterministic separated flow (DSF) model, where finite interphase

transport rates are considered, but effects of drop-turbulence

interactions are ignored, i.e., the drops are only assumed to interact

with the mean flow; and (2) a stochastic separated flow (SSF) model,

where effects of flnite interphase transport rates and drop-turbulence

interactions are treated using random sampling for turbulence

properties in conjunction with random-walk computations for particle

motion. In both cases, analysis follows past work in this laboratory

on noncombusting particle-laden Jets and sprays [I-19]. The main

theoretical extension of the present investigation involves treating

effects of combustion with respect to both the drops and the gas phase.

Since the sprays were extremely dilute, the structure of the gas

phase turbulent diffusion flame was not appreciably influenced by

drops; therefore, source terms due to drops and the volume of the drops

were ignored in the governing equations of the continuous phase. The

continuous-phase analyses employed a k-E-g turbulence analysis, since

this approach has been effective during earlier work in this laboratory

[I-22].

We average over flow variations on the scale of drops and consider

analysis of drop transport in the flame environment. Given the results

of the gas phase analysis, drop motion and transport is computed over

the lifetime of a drop using a Lagrangian formulation.

In the following, the gas phase solution is described first. Then

drop transport calculations and their calibration with single-drop

experiments are discussed. The section concludes with descriptions of

the DSF and SSF models.

3.2 Continuous-Phase Analysis

3.2.1 Governing Equations

The continuous-phase analysis treats a steady, axisymmetric

turbulent diffusion flame in an infinite stagnant environment. The

analysis follows procedures proposed by Lockwood and Naguib [29], but

with extensions due to Bilger [30,31] and Liew et al. [32]. This

involves solution of the mass-weighted (Favre)-averaged governing

equations using a k-_-g turbulence closure. Scalar properties are

found from the conserved-scalar (mixture fraction) formalism, in

conjunction with the laminar flamelet technique for prescribing

instantaneous scalar properties. This approach has provided

encouraging predictions of the structure of turbulent, gas-fueled,

diffusion flames (including the current test flame) during recent work

18
in this laboratory [20-22,33]. Agreement with measurements was

obtained using fixed empirical parameters in the turbulence

model--based on measurements in noncombusting constant and variable

density jets.

Major assumptions of the continuous-phase analysis were: boundary

layer approximations apply; since gas velocities were low, viscous

dissipation and the kinetic energy of the mean flow were ignored;

typical of most turbulence models, the exchange coefficients of all

species and heat were assumed to be the same; the contribution of

buoyancy to turbulence quantities was neglected, since this

approximation yielded reasonably good predictions of mean and turbulent

flame structure in the present slightly-buoyant flame in the past

[20-22]; and effects of radiation were neglected, since the present

flame only lost roughly 14% of its chemical energy release by this

mechanism.

Under these assumptions, the gas-phase flow structure can be found

by solving governing equations for conservation of mass, mean momentum,

mean mixture fraction, turbulent kinetic energy, rate of dissipation of

turbulent kinetic energy and the square of mixture fraction

fluctuations, as follows:

aa--_(pu¢) -~ + _I a (rp_¢) = Ir aar (r_eff'€ _-r) a¢ + s¢ (3.1)

where

= -_/P (3.2)

is a Favre-averaged quantity. ¢ is a generic quantity denoting I (for

conservation of mass), u, f, k, E or g. The expressions for _eff,¢

and S€ appearing in Eq. (3.1) are summarized in Table 5, along with the

appropriate empirical constants. The turbulent viscosity, _t, is

calculated from the turbulent kinetic energy and its rate of

dissipation, as follows:

_t = C pk2/€ (3.3)

The boundary conditions for Eqs. (3.1) are

a_

r = 0 , _ = 0 ; r . = , € = 0 (3.4)

The condition at r = 0 is only applied beyond the end of the potential

core.

Initial conditions were specified by assuming uniform properties

across the burner exit, except for a shear layer having a thickness

equal to I% of the jet radius. For the present flame, 0o and ko

were measured, while co was estimated by matching the variation of k in

19
Table 5. Source Terms in Equation (3.1)

_eff,¢ S¢

I ---- 0

_ + _t a (p_ - _)

(_/Sc) + (pt/of) 0

2

k

P + (Pt/Ok) Pt (-_) -pc

-2

€ _ + (pt/oc) (OElnt(___) - O 2_€)(c/k )

g (_/Sc) + (Ut/Og) Cg1_tt_-_) - Cg2_gc/k

C C_I CgI Ce2--Cg2 ok o of=Og Sc

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

2O
the potential core (noting that all radial gradients of flow properties

are zero in this region). Furthermore, _o = I and go = O,

by definition. Thus the initial condition for the major portion of the

- flow is as follows:

x --0 , 2r/d < 0.99 ;

Uo' ko = measured, _o = matched, fo = I, go = 0 (3.5)

Flow properties in the shear layer were found from the governing

equations after neglecting convection and diffusion terms. Subsequent

boundary conditions along the inner edge of the shear layer were

determined by solving the transport equations within the potential

core.

The conserved scalar formalism was used to find _, needed to

solve Eqs. (3.1), as well as other scalar properties, e.g., mean

temperature and mean mass fractions of major gaseous species (CH4, 02 ,

N2, CO, CO2, H20 and H2). Under present assumptions, the instantaneous

values of all scalar properties are only functions of the instantaneous

mixture fraction--termed the state relationships. Specification of

state relationships, ¢(f), will be considered in the next section; for

the present, these quantities will be assumed to be known.

Given the @(f), the Favre-averaged mean and variance of scalar flow

properties are found from the mass-averaged probability density function

(PDF) of f, P(f), as follows [30]

Z fl° (36

P

P

In the same manner, Bilger [30], shows that time-averaged means and

variances are:

= P I_ (¢(f)/P(f)) P(f) df (3.8)

= SloI (¢(f) _ _(f))2 _(f) df (3.9)

The value of _ can be found by setting ¢ = I in Eq. (3.8).

A functional form must be assumed for P(f), although

predictions have a relatively weak sensitivity to the specific form

21
chosen. Foll£wing past practice [21-23,33] a clipped-Gausslan function

was used for P(f). This function has two parameters which

must be specified: _, its most probable value; and c, its standard

deviation. These quantities can be found by noting [29]:

= S_ f P(f) df (3.10)

g = S_ (f _ _)2 _(f) df (3.11)

Both f and g are known from solving Eq. (3.1); therefore,

Eqs, (3.10) and (3.11) provide two implicit equations to find _ and c.

These computations can be time-consuming; therefore, Eqs. (3.10)_and

(3.11) were solved once the results tabulated as a functions of f

and g to facilitate a table look-up procedure on the computer, cf.

Shearer et al. [26].

Given P(f) and ¢(f), time- and Favre-averaged values of all

scalar properties can be found by solving Eqs. (3.6) and (3.8).

3.2.2 State Relationships

Methods for constructing state relationships required by the

conserved-scalar approach have received a great deal of attention. The

earliest methods assumed local thermodynamic equilibrium

[1,21,11,16,19,30,34,35]. Under present assumptions, this implies

that the properties of the flow at each mixture fraction are equivalent

to the properties of an adiabatic flame having the same mixture ratio

and initial conditions of the fuel and air streams. With this approach,

state relationships can be constructed routinely, using a standard

chemical equilibrium computer package routine, e.g., CEC76 described

by Gordon and McBride [36].

The thermodynamic equilibrium method yields reasonably good

results for mixture fractions corresponding to lean fuel-air ratios,

but yields large errors at fuel-rich conditions. For rich mixture

ratios, low gas temperatures cause slow rates of chemical reaction

which prevents equilibration of the mixture. A "partial equilibrium"

method has been proposed to rectify this problem [I].* The partial

equilibrium assumes thermodynamic equilibrium only up to a critical

mixture fraction, fc, or critical fuel equivalence ratio, ¢c- For

higher fuel equivalence ratios, mixture properties are found assuming

adiabatic mixing of the pure fuel stream and the equilibrium mixture at

¢c. The approach is useful to the extent that ¢c is relatively

universal, in fact, evidence to date suggests €c = 1.2 provides

reasonably good results [22].

*This is poor choice of terminology and does not correspond to

conventional use of the term "partial equilibrium" in the chemical

kinetics literature, where it implies that a portion of the reversible

reactions at a point are in equilibrium.

22
Most flames exchange energy by radiation, however, this is not

very significant for typical combustion chamber conditions; therefore,

- radiation effects are generally treated as a perturbation. The state

relationships are then obtained by allowing for the loss of a fixed

fraction of the combustion energy release by radiation.*

A more recent approach for constructing state relationships, which

was adopted here, is the laminar flamelet method first proposed by

Bilger [31] and subsequently developed by Liew et al. [32]. This

follows from the observation that measurements of temperature and the

concentration of major gas species provide nearly universal functions

of mixture fraction for a wide range of shear rates and positions in

laminar flames. State relationships are then found directly from these

correlations, assuming that properties in a turbulent flame are the

result of a succession of laminar flamelets sweeping past a given

position. This implies a wrinkled-flame picture of a turbulent flame

as well as a quasi-equilibrium structure for diffusion flames which is

invarlant for both laminar and turbulent conditions. Regions of

attachment of laminar flames, where such invarlance is not observed,

cannot be used for constructing state relationships. Furthermore,

turbulence scales must not be too small in comparison to the

characteristic diffusion flame thickness. Finally, radiant heat loss

fractions must be roughly the same for both the laminar and turbulent

flame, a condition which must be checked on a case-by-case basis. In

spite of these limitations, however, the laminar flamelet technique has

provided reasonably good predictions of mean scalar properties in

turbulent flames [20,22,32,33,37,38] and it represents the best

approach currently available to treat turbulent diffusion flames.

State relationships for methane diffusion flames burning in air

(both initially at normal temperature and pressure) are illustrated in

Figs. 6 and 7. The temperature and mass fraction of major gas species

(CH4, 02, N2, CO2, H20, CO and H2) are plotted as a function of local

fuel equivalence ratio for both the laminar flamelet and partial

equilibrium (¢c = 1.2) methods. The laminar flame data of Tsujl and

Yamaoka [39-41] and Mitchell et al. [42] are shown on the figures.

These results involve rather different flame configurations: Tsujl and

Yamaoka considering an opposed flow diffusion flame; Mitchell et al.

considering coflowing streams of methane and air. Clearly, nearly

universal correlations of the data are obtained as a function of

mixture ratio. Use of €c = 1.2 in the partial-equillbrlum method

yields results which are comparable to the measurements.*_ Similar

results have been obtained for propane/air [20,33] and n-heptane/air

[31] diffusion flames. Current work in this laboratory suggests that

*The radiant heat loss fraction of the flame must be found by other

means. Methods of computing this loss for nonluminous flames are

discussed by Jeng and coworkers [20,37,38].

_*The partial-equilibrium method is mainly useful for the many instances

where laminar flame data are not available for direct correlation.

23
_2400 '' '"'"A ' '''""I ' '

i,i

nT

1200 n,-

I,U

ul o

I-. /

I.O0- LAMINAR METHANE FLAME DATA

0 TSUJI AND YAMAOKA

- MITCHELL ET AL. .Z_"'OZ (mm) ,,D"

0.50 -- O 12 CH_,.O"/ --

0 24 _0_ O 5o

/ A CENTERLINE, 12-50 /

Q24

(_ SYMBOLFLAMELET DESCRIPTION

PARTIAL EQUIL. (_c= 1.2

"_ O.12 ADIA.

n- 20 % RAD.

LL.

¢f)

€/) oa

_; 1.00

m

Q50

0.00- , ,,,,,,,l, ,, ,,,,,I , ,, ,,,,,II I ,,,,,-[

IO-2 I0-' IO° IO' IO2

LOCAL FUEL EQUIVALENCE RATIO

Fig. 6. State relationships for methane/air diffusion flames.

24
0.20 '' '''"'I '' ''""I ' '' ''"'I , i i,,,l,i

0 m

0.I0

0.1(

SYMBOL DESCRIPTION

FLAMELET

PARTIAL EQUILIBRIUM

_) 0.05 ADIA.

COo

n,- 0.20 I,i.

_ H20

/ I

o.o;

LAMINAR METHANE FLAME DATA

O TSUJI AND YAMAOKA

MITCHELL ET AL.

0.01 Z (mm)

0 12

D 24 H_

- O 50 o "

i0-z i0-I i00 i01 i02

LOCAL FUEL EQUIVALENCE RATIO

Fig. 7. State relationships for methane/air

diffusion flames (continued).

25
H2/air and CO/air flames can be correlated as well; therefore, the

flamelet technique seems to have sufficient generality for practical

use--until such time when problems of predicting chemical reactions in

turbulent flames have been resolved.

Natural gas was used to fuel the present burner so that while the

fuel was predominantly methane, several other fuel species were

involved, cf. Table I. To allow for this, structure measurements were

made in a laminar flame using the local natural gas [43]. The test

arrangement involved coflowlng streams of fuel and air, similar to

Mitchell et al. [42]. The results of these measurements are

illustrated in Figs. 8 and 9. Clearly, a nearly universal correlation

of the concentrations of major gas species is achieved, which was used

for the present state relationships.

3.2.3 Computations

Calculations for the continuous phase were completed using a

modified version of GENMIX [44]. The computational grid was similar to

past work; 33 cross-stream grid nodes; and streamwise step sizes

limited to 6% of the current flow width or an entrainment increase of

5%--whichever was smaller. A convergence check of the numerical

solution was performed by comparing the mean mixture fraction flux

between the exit of the injector and the downstream positions. If

differences were greater than I%, the calculation was redone using more

cross-stream nodes and smaller streamwise steps.

3-3 Drop Transport

3.3.1 Drop Transport Analysis

Methods for calculating transport between drops and the continuous

phase have been extensively discussed elsewhere [I]; therefore, the

following discussion will be brief since current methods are

essentially the same. A major assumption of the analysis is that we

integrate over small features like drops; therefore, drop properties

are computed by a Lagrangian calculation following their motion, using

empirical expressions to evaluate the interphase transport of mass,

momentum and energy.

The main assumptions of the drop-trajectory calculations were as

follows: dilute spray with drop transport the same as for a single

drop in an infinite environment and negligible drop shattering and

collisions; quasisteady drop flow field, e.g., transport rates are

found from steady flow conditions for the same boundary conditions

while the radial velocity of the drop surface, due to evaporation, is

neglected; empirical treatment of drag and forced convection; liquid

surface in thermodynamic equilibrium with effects of drop curvature and

surface tension on equilibrium neglected; negligible radiation; only

concentration diffusion with equal binary diffusivities of all species;

ideal gas mixture with constant average properties and unity Lewis

number;negligible solubility of the ambient gases in the liquid phase;

negligible virtual mass and Basset history forces; and transport within

the liquid analyzed using the "thin skin" approximation [I]. These

26
I.O I I I

Ne

o.8-o

00.

.64---- __ a--_

A

° 2 B m

z

o 0.0- _ "_

CH 4

,, 0.4 _ -

_ 0.0 o.z--- o oi:3,, _AI:Djo _

0._ vn2 TRAVERSE x(mm) Re 1

- 0 RADIAL I. I 38

A RADIAL I. I 52

0.2 -- 0 0 O RADIAL 3.5 38 --

0 RADIAL 3.5 52

0.I Q_,_ 0 AXIAL -- 38

o.o- I o___ _

10-2 I0-I i0° I01 I0a

LOCAL FUEL EQUIVALENCE RATIO

Fig. 8. State relationships for natural gas fueled flames.

27
0.06 I I I

CO

Q04 --

LOCAL FUEL EQUIVALENCE RATIO

Fig. 9. State relationships for natural gas fueled flames (continued).

28
assumptions are common to most spray models, their justification and

limitations are fully discussed elsewhere [I].

The thin skin approximation was adopted to avoid substantial

complications required to treat transport within the drop. This

involves the assumption that the drop surface adapts immediately to

changes in local ambient conditions, while the bulk liquid remains at

its initial state. This approximation yields results for transient

drop effects which are comparable to the more widely used uniform

drop-temperature approximation [I].

A key issue with respect to combusting sprays concerns the

presence or absence of envelope flames around individual drops [I].

This had to be considered, since drops penetrated oxygen-contalnlng

regions during the present tests. Existing methods for estimating

conditions where envelope flames are present are controversial and

don't treat environments representative of turbulent flames [I]. These

uncertainties were avoided by considering two limiting cases: (I)

ignoring the presence of envelope flames in all regions of the flow;

and (2) assuming that envelope flames were present whenever the local

environment contained oxygen. Past work in this laboratory suggests

that the differences between these two limits is not large until the

local fuel equivalence ratio becomes less than 0.9 [45].

Two limits were also adopted with respect to drop-turbulence

interactions: (I) the DSF approach, where drop transport is only

controlled by local mean properties; and (2) the SSF approach where

drops transport is computed for local instantaneous properties (which

are estimated by random sampling of the continuous-phase solution). A

generic formulation will be used in the following, applicable to both

cases, i.e., gas properties will not be designated as either mean or

instantaneous since either can apply depending on the spray model.

In both spray analyses, 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 .

Xpi = Xpoi + Jo upi dt ' i = 1,2,3 (3 12)

The mean drop velocity is determined by integrating the equation for

conservation of momentum

dUpi d2 I. . I (Upl-Ui) m d---_-= - (_/8) P p CD Up-U + ai , i = 1,2,3 (3.13)

The standard drag coefficient for solid spheres is employed in the

calculations, approximated as follows [I]:

29
Re2/3

CD = R-e24(I + 6 ) , Re < I000

= 0.44 , Re > 1000 (3.14)

where, Re = P P (3.15) V

The size and mass of the drop are related as follows:

d3

m = (_/6) Pbf p (3.16)

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

injected condition under the assumptions of the thin skin model.

The rate of change of drop diameter is given by

dd

dtp = - 2m"/Pbf (3.17)

Heat and mass transfer rates to the drop are influenced by the

presence or absence of envelope flames. The following expressions can

be used for both cases.

_" dp/(pD) = 2NS £n [(I + By)(1 + BO) ] (3.18)

h dP/_ = 2 Np £n [(I + By)(1 + BO)]/B Y (3.19)

where

By = (YFs - YF_)/(I - YFs) (3.20)

and

BO = vFO YO_ (3.21)

The stoichiometric parameter, VFO , is the mass of fuel consumed per

unit mass of oxidant at the flame front. The heat transfer

coefficient, appearing in Eq. (3.19) is based on the temperature

difference between the envelope flame and the drop surface, e.g.,

aT

h = _ (_)s/(Tf - Ts) (3.22)

Neglecting dissociation in the flame, the flame temperature can be

found from

30
T _Ts -- I + Cp (T -Ts)_ / I + _yy (By + B (3.23)

where Qr is the chemical energy released by combustion per unit mass of

oxidant. The correction factors for _" and h due to forced

" convection are found from the following expressions:

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

Np or NS = I + (3.24)

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

Equations (3.18)-(3.23) are used directly when envelope flames are

considered. If YO_ = 0 at the current drop position, this

formulation becomes equivalent to results for simple drop evaporation

in a heated environment without combustion, e.g., BO _ 0 from Eq.

(3.21) and Tf = T_ from Eq. (3.23). Thus, calculations at the limit

of no envelope flame present were conducted by the simple expedient of

setting YO_ = 0 in the formulation, even in regions where finite

concentrations of oxygen were present.

In order to complete the solution, the drop surface temperature

and the fuel mass fraction at the drop surface must be known. The two

equations required to solve for these quantities are provided by the

fuel vapor pressure relationship and the energy balance at the liquid

surface. The vapor pressure relationship has the form

YFs = f(Ts' p' Yis) (3.25)

Applying the thin-skin approximation, the energy balance at the surface

becomes

h (Tf - Ts) = m" hfgT (3.26)

where hfgT allows for both the enthalpy of vaporization and the heat

up of the liquid from its initial temperature (the bulk liquid

temperature) to the surface temperature

hfgT _ hfg + CpF (Ts - Tbf) (3.27)

The vapor pressure relationship and other properties used for the

liquid and gas phases, along with mixing rules used, are summarized in

Appendix D. Gas-phase transport properties are found at a reference

state, representing average conditions for the flow around the drop.

The reference state was defined as follows:

Cavg = a Cgs + (I - _) ¢g_ (3.28)

where ¢ is a generic quantity representing either mass fraction or

temperature, and 0 _ e _ I. The value of e was selected to best match

31
computations using the present model and the single drop calibration

experiments discussed in the next section.

Drop-life-history calculations were carried out using a

second-order Runge-Kutta algorithm.

3.3.2 Drop Transport Calibrations*

It is well-known that a priori calculations of drop-life histories

are very uncertain, when using constant-average-property models, due to

the large variation of properties in the flow field [I]. Calibration

tests were undertaken in the post-flame region of a flat-flame burner

in order to reduce thls uncertainty. The test results were used to

match measurements and predictions by selecting an optimum value of

in Eq. (3.28).

Test methods for the calibration tests, along with a tabulation of

data, are provided in Appendix E. Single methanol drops, supported on

a quartz fiber, were rapidly immersed in the post-flame region of the

burner. The drops were backlighted and photographed, with timing marks

placed on the motion picture film. The film was processed using a

motion analyzer to yield drop size as a function of time.

. Gas properties at the test drop location were found as follows:

gas composition, by sampling and analysis wlth a gas chromatograph; gas

temperature, using the radiation-corrected thermocouple described in

Section 2.3.5; and gas velocity, by computations assuming

one-dimensional flow (knowing the burner flow rate and cross-sectional

area, as well as the burned-gas density from the other measurements).

Test conditions for the drop-life-history calibrations are

summarized in Table 6. The burner was fueled with methane/air mixtures

having various fuel-equivalence ratios; therefore, the test gases were

representative of the turbulent flame. Drop diameters for the

calibration tests were large, however, Reynolds numbers are comparable

to the turbulent flame conditions, due to the low velocities of the

flat-flame-burner gases. Finally, the flow in the flat-flame burner

was laminar; eliminating uncertainties due to drop-turbulence

interactions.

Predicted and measured drop-life histories are illustrated in Fig.

10. The period considered corresponds to steady-burning after initial

drop heat up is complete. Test conditions were all for fuel

equivalence ratios less than unity; therefore, predictions are shown

for the limiting cases of envelope flames both present and absent.

Envelope flames were observed for the test conditions; therefore, the

data is matched to this limit. The results yielded an optimum value of

= 0.3, in Eq. (3.28). This value is not a universal, since it

depends on the assumptions of the drop transport analysis, the method

*The authors wish to acknowledge the help of J. T. Holl in carrying out

these calibrations.

32
Table 6. Summary of Drop-Life-History Test Conditions

Fuel Equivalence Ratio 0.65 0.82 0.97

Initial Drop Diameter (wm) 2293 2786 2954

Gas Temperature (K) 1500 1690 1690

Gas Mass Fractions

02 0.076 0.038 0.000

N2 0.755 0.744 0.778

H20 0.077 0.098 0.099

CO 0.004 0.000 0.001

CO2 0.088 0.120 0.122

Initial Drop Re 19 21 28

aMethanol drops supported in the post-flame region of

a flat-flame burner fueled with methane-air mixtures.

33
1.2 I I I I I

o DATA

EVAPORATIONTHEORY

0.8 "0. COMBUSTIONTHEORY -

Oo 2 m

0.0 I I I I I

0.0 !.0 2.0 3.0 4.0 5.0 6.0

TIME (sec)

Fig. 10. Drop-life-history calibrations.

34
of computing average properties, and the correlation of transport

properties in the calculations. Values of _ in the range 0.3-1.0 have

been found during past work [1,17,19,26,34,35,45]. The value selected

here, however, provides excellent agreement between predictions and

measurements in Fig. 10.

r Differences between computations considering and ignoring envelope

flames are not very large for the highest fuel equivalence ratio

considered in Fig. 10 and, of course, are irrelevant for fuel

equivalence ratios greater than unity where ambient oxygen

concentrations are negligibly small, cf. Figs. 6 and 8. Differences

between the two methods progressively increase, however, as the fuel

equivalence ratio decreases, since the presence of the envelope flame

enhances combustion both due to increased flame temperature (in

comparison to the surroundings) and due to its consumption of fuel

vapor before the edge of the flow field around the drop is reached.

These trends are similar to those observed by Szekely and Faeth [45].

The greatest uncertainty, based on current knowledge, involves a

reliable criterion for predicting the presence of envelope flames [I].

3.4 Deterministic Separated Flow Model

The most stringent assumption of the DSF model is that drops only

interact with the mean flow; therefore, turbulent dispersion of drops

and effects of turbulent fluctuations on drop transport properties are

ignored. Neglecting turbulent dispersion implies that drops follow

deterministic trajectories in the flow, prescribed by their initial

conditions. Drops are generally much smaller than the smallest

turbulent scales in the present flow [I]; therefore, the influence of

turbulent fluctuations on drop transport properties pertains to drops

interacting with relatively large eddles--from the perspective of the

drop. Use of mean properties in this instance is only true when the

transport rate is a linear function of property differences between the

drop surface and its local surroundings. This is never strictly true,

and is particularly in error for drag, which is quadratic in the sllp

velocity for Reynolds numbers typical of drops in sprays (values ca. 100).

While Favre-averages are convenient for computations of

continuous-phase properties, only time-averaged properties are relevant

for defining the flow along a drop trajectory. This represents no problem

for scalar properties, since time-averaged scalar properties can be

computed from Eq. (3.8).

Time-averaged mean gas velocity must also be known for trajectory

computations with the DSF model. However, to obtain the tlme-averaged

velocity from the computed Favre-averaged velocity, the correlation

between fluctuating density and fluctuating velocity must be known,

since [30], e.g.,

m

U = U - p'u'/p (3.29)

Density fluctuations and velocity fluctuations are neither satistically

independent nor perfectly correlated in jet diffusion flames;

35
therefore, an extension of the basic model of Section 3.2 would be

required to predict p'u". This was beyond the scope of the present

study; therefore, we chose to assume statistical independence--setting

Favre- and time-averaged velocities equal. Fortunately, existing

evidence suggests that the two methods of averaging are not very

different for jet flames, with differences of ca. 5% [22].

Initial conditions for the DSF model were defined at the burner

exit,* where drop size, velocity, direction and number density were

known as a function of position. At this location, drops were placed

in n groups according to these properties, and the motion of each group

was tracked through the flow field. This involved numerical

integration of Eqs. (3.12)-(3.27), using the second-order algorithm in

conjunction with mean gas properties found from the continuous-phase

solution.

When calculating drop properties in the flow field, for

comparison with measurements, the properties of each group were

weighted to satisfy their initial number flux. The trajectories of 100

groups were computed in order to obtain a statistically-significant

representation of drop-phase properties.

3.5 Stochastic Separated Flow Model

The DSF model considers only deterministic trajectories for drop

groups. The stochastic separated flow (SSF) model, however, includes

effects of turbulent fluctuations on drop dispersion and interphase

momentum transport rates by using a technique proposed by Gosman and

Ioannldes [23] and subsequently developed in this laboratory [I-19].

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--utillzing 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.

Properties within a particular eddy were assumed to be uniform,

but to change in a random fashion from eddy to eddy. The trajectory

calculation was the same as the DSF model, involving solution of Eqs.

(3.12)-(3.27). Mean-gas properties in these equations, however, 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 Gaussian PDF having a standard deviation of (2k/3)I/2

and mean components _, 7, O. This ignores the distinction

between Favre- and time-averaged velocities (the latter being the

quantity that should be sampled), similar to the DSF analysis where

Favre- and timed-averaged velocities were assumed to be the same. The

*Formally, x/d = I.

36
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. This

corresponds to random choices of velocity which satisfy the assumed

forms of the velocity PDF's.

" The instantaneous scalar properties of each eddy were computed in

a similar manner. Scalar properties are only a function of mixture

fraction, under present assumptions; therefore, only a random selection

of mixture fraction had to be made. Given the mixture fraction, the

state relationships provided all scalar properties, e.g., Figs. 8 and 9.

Only the tlme-averaged PDF of mixture fraction is relevant for sampling.

This was constructed from the known Favre-averaged PDF at each point,

by noting [30]

P(f) P(f) --P PCf) (3.30)

The time-averaged cumulative distribution function of f was then

constructed and sampled to find the instantaneous value of f. A random

number in the range 0-I was selected and the instantaneous f became the

value of f that yielded this value of the cumulative distribution

function. Values of f chosen this way yield a random distribution

which satisfies the clipped-Gaussian PDF.

Similar to past practice, a drop was assumed to interact with an

eddy for a time which was the minimum of the eddy lifetime and the time

required for the drop to traverse the eddy. The specification of eddy

lifetime and size is somewhat ad hoc, however, present methods have

been extensively calibrated and evaluated for particle laden jet flows

and noncombusting sprays, yielding excellent results [I-19].

The characteristic size of an eddy was taken to be the dissipation

length scale from the k-_ model, e.g.,

Le --C_3/4 k3/2/_ (3.31)

The eddy lifetime was computed from thls length scale and the velocity

fluctuations, taken to be isotropic, as follows:

te = Le/(2k/3)I/2 (3.32)

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:

At < te , IA_pl <" Le (3.33)

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.

37
The remaining computations are similar to the DSF model. More

drop trajectories must be considered to obtain statistically

significant drop properties than the DSF analysis (generally 5000-6000

trajectories were used). A by-produc_ 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.

4. RESULTS AND DISCUSSION

4.1 ,|Introduction

In the following, measurements of the turbulent test flame and the

two test sprays will be described, cf. Table 2 for operating conditions.

In addition, the DSF and SSF model predictions will be used to help

interpret the measurements. Naturally, this also provides an

opportunity to evaluate these models for reasonably well-deflned test

conditions.

Time-averaged mean and fluctuating velocities were measured but

are compared to Favre-averaged predictions--for lack of an alternative

without extending the continuous phase analysis. As noted earlier,

these properties are not very different for turbulent jet flames;

therefore, the distinction is not important in comparison to present

experimental uncertainties [22].

Mean concentrations were measured by isokinetic sampling for the

test flame [22]. While this was thought to yield Favre-averaged

properties originally [30], recent work suggests that measurements are

between Favre- and time-averaged properties [46]. In fact, the average

obtained depends very much on the flow properties and response of the

sample probe and its flow system--which is not known very well.

Therefore, for lack of a definitive alternative, Favre-averaged

predictions are compared with measurements of species concentrations.

Differences on the order of 5% for mean concentrations can be expected

for these two methods of averaging in jet flames [22]; therefore, the

distinction is not large in view of experimental uncertainties.

Temperatures measured with small thermocouples having fast

response, and time-averaged, yield time averages. However, large

thermocouples yield values between time and Favre averages with

currently unknown effects of radiation and radiation corrections on the

average actually obtained. Since potential differences are less than

uncertainties in the radiation correction [20], Favre averages will be

compared with measurements in the following.

Drop velocities were particle-averaged over all sizes during the

measurements. The following predictions were obtained by averaging in

the same manner for consistency.

Drop number fluxes were time-averaged over all sizes (after

correcting for the variation of capture area with drop size). The same

procedure was used for computed results.

38
Slide impactors obtain tlme-averaged drop size distributions, as

opposed to spatial averages yielded by flash photography methods

[I0-12,19]. This quantity, as well, was computed in a consistent

. manner for the predictions.

In the following, initial conditions will be described first,

followed by a discussion of the properties of the test flame. Then the

results for sprays will be considered. All data are tabulated in

Appendix F.

4.2 Initial Conditions

Due to the LDA and burner configurations it was not possible to

make measurements of mean and fluctuating phase velocities closer than

x/d = I; therefore, burner initial conditions were obtained at this

position as discussed earlier. The burner flow was seeded, however,

the hydrogen coflow was not; therefore, traverses in the radial

direction were limited to r/x _ 0.6, since seeding levels were too low

(and results would be biased to the burner flow gas depending on

mixing) at larger radial distances.

Figure 11 is an illustration of mean and fluctuating velocities of

the burner gas. Mean velocities are relatively uniform for r/x < 0.4

and then decrease as the shear layer at the edge of the potential core

is encountered. Velocity fluctuations and the turbulence kinetic

energy are also relatively uniform in the core, but then increase due

to turbulence production in the shear layer. The main difference

between the present burner and that of Jeng [20] is that turbulence

kinetic energy is more than an order of magnitude higher, probably as a

result of the drop generator inducing disturbances in the burner flow.

Drop sizes were essentially constant at the burner exit, with

initial diameters of 105 and 180 _m. Distributions of mean and

fluctuating drop velocities and drop number fluxes across the burner

exit are illustrated in Figs. 12 and 13 for the two sprays. Mean drop

velocities are essentially constant (within 2%) over the region where

they could be measured. Drop velocity fluctuations are on the order of

2% of the mean drop velocity of dpo = 105 _m, primarily due to the

operation of the drop generator. Drop velocity fluctuations are nearly

constant over the exit, except near the shear layer for dpo = 105 um,

where _ are increasing (V_ and _ to a lesser degree) in response

to higher gas-phase turbulence levels. In contrast, drop number fluxes

decrease rapidly with increasing radial position, since turbulent

dispersion has had little time to act and the drop generator delivers

the drops along the centerline. Few drops were observed for r/x > 0.4.

The spray with the larger drops, dpo = 180 um, is less dispersed at

this position, due to the larger inertia of these drops which makes

them less responsive to turbulent dispersion.

4.3 Scalar Structure of the Test Flame

In this section, the scalar structure of the test flame will be

discussed. The main features of this are comparison of present

measurements with earlier work by Jeng and coworkers [20-22] for

39
I I I I I

1.0 _- 0 0 0 0

- _"/'dc 0 -

(

0.5-

_c = 52.8 m/s

/

0.2_4 -

0 "u'/-Uc

A V'/_c 0

0.1 6 -- [] i,/0 c -'()

0.08 - 0 A

[] _ _p _o _ [] _E_

0

L 0.016 -

0.OO8 - 0 -

.0 0 0 x/d= I

o I I I I I

0 0.2 0.4 0.6

r/x

Fig. ii. Mean and fluctuating gas velocities at x/d = i.

4O
I I I I I

1.0 _- 0 0 0 0 -

I

0.5 - _p/Upc

U'pc = 15.6 m/s

m I

O

Q024 -

)

0.016 -

0 "UI_/ "Upc 0.008-

A V--_/ U'pc

[] WI_/'Upc

0 --

1.0

O

- x/d = I '

0.5 - 0 dpo= 105 pm

II II

h"/ nc hc =3769xlO6/rn_s

0

o I I I Q I

0 0.2 0.4 0.6

r/x

Fig. 12. Drop properties for d = 105 _m at x/d = i.

po

41
1 I I I I

1.0(- 0 0 0 0

0.5 -- _P / EPC

"Upc= 12.0 rn/s

m m

0.06 -

0 _'I;/_pc

0.02 -

Z_ -' /- Vp Upc

[] Wp/U'pc

0 --

i.O _-

0

- x/d = I --

i

0.5 -- 0 dpo= 180 IJm --

• ,, ,._6 2

• ,, .,, n = 1826xlu/ms

_ n /n c c _

0

o I I I 6 I

0 0.2 0.4 0.6

r/x

Fig. 13. Drop properties for d = 180 _m at x/d = i. *

po

42
essentially the same flame. The comparison between continuous-phase

predictions and the measurements will also be discussed. Mean and

fluctuating velocities of the continuous phase will be considered

subsequently, when spray properties are presented.

Figure 14 is an illustration of measured and predicted mean gas

. temperatures along the axis. Present measurements are shown along with

the earlier results of Jeng and coworkers [20-22]. Both sets of

measurements are virtually identical, indicating excellent

reproducibility of the earlier work. This occurred in spite of

increased turbulence intensities at the burner exit for the present

flame, since the measurements were confined to x/d _ 20, where mean

properties are relatively insensitive to initial conditions.

Predictions are also in reasonably good agreement with measurements,

corresponding to earlier performance with essentially the same

continuous-phase model. The computations of Jeng and coworkers [20-22]

provide virtually the same mean temperature predictions along the axis

as the present study. This implies that the increased turbulence

intensity at the burner exit had little effect on the results in Fig.

14 as well.

In Figure 14, the maximum temperature along the axis is reached at

x/d = 100-120. In the same region, the mean concentration of fuel

approaches zero and we will refer to this as the flame tip. This is

also roughly the mean axial extent of flame luminosity, although

turbulent fluctuations cause the luminous flame region to extend up to

40% farther from the burner exit at times.

Radial profiles of mean gas-phase temperature, in the region of

two-phase flow, x/d _ 100, are illustrated in Fig. 15. Present

measurements, the earlier results of Jeng and coworkers [20-22], and

present predictions are shown. Radial distances in this, and all

subsequent plots, are given as r/x, which is the radial similarity

scale for turbulent jets, in order to indicate capabilities to predict

flow widths directly. Near the burner exit, the maximum temperature

position, which is representative of the flame position, is off-axis

and only closes to the centerline near the flame tip. This is the

normal structure for a turbulent diffusion flame or combusting spray

[I]. Present measurements indicate a broader profile near the burner

exit than Jeng et al. [21], probably due to the higher turbulence

intensity at the burner exit. Predictions are in fair agreement with

measurements.

Jeng and coworkers [20-22] completed composition measurements and

compared them with predictions for the present flame. Since similar

measurements were not made during this study, we will consider results

drawn from Ref. [21], to provide a more complete picture of the flame

structure and the performance of the continuous-phase analysis.

Predicted and measured variations of mean temperature and the mean

mass fraction of major gas species (CH4, N2, 02 , CO2, H20, CO and H2)

along the axis appear in Fig. 16. Predictions are shown for both the

partial equilibrium and laminar flamelet state relationships, however,

43
0 l _ _ , i i ill I t t t t I ttl I

2 4 6 8 I0 20 40 60 80 I00 200

x/d

Fig. 14. Mean gas temperatures along the axis.
1800 I I I I

c_

Z_

OA

I000 OAA -

oA

Ozx

( 0 --

x/d = I00

200 --,

z_ A

_ ' AO °

I000

z_ o

z_ O

_ zx __

200_ xld = 50 A Z_b_ ;,

- 00_ --

oy

I000 _ _0 --

- 0 0

o PRESENT

- A JENG \ --

X/

\

d = 20 _... PREDICTION

200 I I I I I

0 0.0 8 O.16 0.24

r/x

Fig. 15. Radial variation of mean gas temperature

in the two-phase flow region.

45
H20

- - -

I::::) 1200 --_- J//_- _%_ O.I0 -__'--" -

I III I.. 0.00 I/ I I ! IIIIII I I TIIIII

Oi\ 'i I1 11li 'lillilI11 11 I,j.I , , , : 0.24 I CO I I I I I I111 i I , i i Ill

I-- I

I"_7 _\ OH40 _ N2 ' _ _ L ___. ___ PPARTIAL RED.FLAMEQUl ELLE.T¢--1.2 ADIA-- --.-- 20 % RAD. ';

O.OOP_ i ,% ^i _ i i i i , , ,il .00 0.001 . i i i , , 1,,

CO21 I i i Jill I i , H2 i I I i jill I i i i I ,Ill

_ Re = I I TO0

O METHANE FLAME

0.10 -- 0.01 -- 0 o -

-- 000 -

0 0 0

0.00 0.00 _ I I i ' I ill

I0 I00 I000 I0 I00 I000

x/d

Flg. 16. Mean temperatures and species concentrations along the axis.

From Jeng and Faeth E22].

o • v •
there is not much difference between these methods. The turbulent

diffusion flame structure is evident with both mean fuel and oxygen

concentrations overlapping somewhat near the flame tip, due to lack of

complete mixing. The comparison between predictions and measurements

is good, except for hydrogen concentrations which are underpredlcted

near the burner exit. This behavior is not a defect of the analysis,

however, but is due to neglecting the presence of the hydrogen coflow

" required to attach the flame [21].

Radial variations of scalar properties, drawn from Ref. [21], are

illustrated in Figs. 17 and 18 for axial stations x/d _ 52.2 and 100.

The comparison between predictions and measurements is fair, with a

continued tendency to underestimate hydrogen concentrations, and to a

certain extent, flow widths.

Comparison of predicted and measured scalar structure of the test

flame, illustrated in Figs. 14-18, suggests reasonable capabilities for

predicting flame structure. With this baseline established, we now

proceed to consideration of the spray flames.

4.4 Structure of the Spray Flames

4.4.1 Mean Phase Velocities

The DSF analysis generally did not provide very good predictions

for present test conditions. In order to avoid cluttering the figures,

the DSF results will only be considered on a few plots, just to

demonstrate its performance quantitatively. Similarly, the two

versions of the SSF model, with and without envelope flames, yielded

nearly the same results; therefore, only the latter result has been

plotted, since it involves less empiricism.

Mean gas and drop velocities along the axis are illustrated in

Fig. 19. Drop velocities for both sprays are shown along with SSF

predictions ignoring envelope flames. The comparison between

predictions and measurements is very good. Gas velocities are

substantially greater than drop velocities at the burner exit, however,

they rapidly decrease due to mixing with the surroundings. Near the

injector, the drops have significant inertia and their velocities only

gradually increase in response to the higher gas velocities. Near the

tip of the flame (maximum temperature location at ca. x/d = 100-120,

cf. Fig. 14), however, drop sizes are small and their velocities

approach gas velocities. Drops in both sprays penetrate beyond the

flame tip; therefore, the presence or absence of envelope flames should

be a factor. However, this was found to have little effect on present

computations. Use of the locally homogeneous flow (LHF) approximation,

where slip between the phases is neglected [I], would be clearly

inappropriate for present test conditions.

Radial profiles of mean phase velocities are illustrated in

Fig. 20. The comparison between SSF model predictions and the

measurements is good. Slip between the phases is most important for

large drops near the injector and becomes small near the flame tip.

Drop velocity measurements could only be undertaken where reasonable

47
_' 2400 I , , _ I , I 0.20 I I I I i I ,

_'LLI H20

._ Oo

1200 o 0.10 ) o o

_ 0 _ 0.00 t t oot t

I I t i t I I I I I I I I I

N2 _ CO _

z 0.50 12 0.10- -

---- o

oo _ CH4 A A

I-- u

,Y 0.00 0.00 0.00 )-O t

O o I o

t.L I i i I t I i I I I I t I I

CO2 --"-- PRED. FLAMELET H2 Re = I170 0

{'/) - O0 A DATA - - x/d = 52.2 -

u) 0 0

<:1: METHANE FLAME

0. I0 0 _ - 0.01 -

0 0 0

- 0 010 i_1 - )0 0 _

o

0.00 I I I I 0.00 I I T"_ t t

0.00 005 0.10 0.15 0.20 0.00 005 0.10 0.15 0.20

r/x

Fig. 17. Radial variat£on or mean temperature and species concentrations

at x/d = 52.2. From Jeng and Faeth [22].
A

v 2400 I , I I 1 , , 0.20 i , i i I I

_I.LI H20

,2oo o.,o_ -

0 0.24 0.00 .. t

0.00 , ,i°0.00 ';'0.00 o,o __ I._ I I I I t I I I I I I I I I

C02 PRED. FLAMELET H2 Re = I I 7OO

re, f) oOA DATA x/d =1OO

<_ METHANE FLAME

0. I0 0.01 :L _

0 0

-- 0

0

0.00 0.00--,_-_ l l , ,

0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20

r/x

Flg. 18. Radial variation of mean temperature and species concentrations

at ×/d = 100. From Jeng and Faeth [22].
200.0 _ _ I J I I I t J I J '

dpo (pro) DATA THEORY

100.0

80.0 - uc -- o _

600 _-Pc 105 r_ _

zoo - ._.....o.-_ - _._.,_._.._;,,_-__.

,.-_ _.._.-__,_ ,,_,,,-__

_> I°°t . -_

0_"

I.o v I I , ! I ! ifl i i

I 2 4 6 8 I0 20 4.0 60 80100 200 4.00 600

x/d

Fig. 19. Mean phase velocities along the axis.

5O
0.6 -

0.4

0.2

0.0- /

//,

1.0

0.8

/x

0.6

0.4 o x/d : 50 -- 0

0

0.2 o -

0.0 dpo(pm)DATA THEORY _ _'

I

o _ l_c --

0

0.8 z_ - -

0 U'p/Upc 105 [] ....

0

0.6 - /Epc 180 Z_ __.-- -

0.4- --

o.o

0.00

I

0.08

I I

0.16

I

0.-24

r/x

Flg. 20, Radial profiles of mean phase velocities.

51
numbers of drops were present; this region is roughly bounded by the

flame zone since drop vaporization is high in this region, cf. Figs.

15, 17 and 18.

The overall picture that emerges from the measurements thus far is

that drops are confined to the cool core of the flow and tend to

evaporate quickly as the flame region is approached. Effects of slip

are important in this core region, due to relatively large drop inertia.

As the drops become small in the flame, however, they are more

responsive and slip is less important. For present conditions, the

large drops penetrate through the maximum temperature region to

locations where oxygen is present.

4.4.2 Fluctuating Phase Velocities

Predicted and measured phase velocity fluctuations along the axis

are illustrated in Fig. 21. Gas velocity fluctuations were estimated

from the predictions assuming the anisotropy ratios generally

associated with jets, e.g., _,2:_,2 _ k:k/2 [47]. It is evident from

the gas phase measurements illustrated in Fig. 21, that similar ratios

were observed in the test flame. Predictions for the drop phase were

found directly from the SSF analysis. Measured drop velocity

fluctuations and the predictions were obtained by averaging overall

drop sizes at a particular point; therefore, these values are higher

than for any single size.

Predicted gas velocity fluctuations are generally within 20% of

the measurements in Fig. 21, which is reasonably good in view of the

relative simplicity of the continuous phase turbulence model. Velocity

fluctuations decay slightly in the potentia! core, but then increase

rapidly due to turbulence production when the shear layers merge to end

the potential core region. Turbulence intensities reach a plateau as

this initial development of turbulence properties ends for x/d 10-20,

but then increase once again as the flame tip is reached, ca. x/d _ 100.

In this region, and beyond, effects of buoyancy become important in the

flow [20-22].

Drop velocity fluctuations illustrated in Fig. 21 behave somewhat

differently than the gas phase. Radial drop velocity fluctuations are

predicted reasonably well, which is important if turbulent dispersion

of drops is to be represented accurately. Streamwise velocity

fluctuations, however, are underestimated. This is similar to past

observations with the SSF model and is felt to be due to the assumption

of isotropic eddy properties within the SSF computations of drop/eddy

interactions [I-19]. Extension of the analysis to consider anisotropy

would be desirable, but would be most appropriate in conjunction with a

multistress analysis of the continuous phase. This would require

extensive modification of the present continuous phase analysis, and

additional empiricism and model evaluation; therefore, this step was

beyond the scope of the study.

Near the injector, the drop velocity fluctuations are small in

comparison to gas velocity fluctuations for the results appearing in

52
I

I 4 I0 40 I00 400

xld

Fig. 21. Fluctuating phase velocities along the axis.

53
Fig. 21. This is due to the inertia of the drops, which limits their

response to both mean and fluctuating gas-phase velocities. Near the

flame tip, however, the drops become small due to evaporation and in

the final stages of their lifetime, drop velocity fluctuations increase

rapidly--approaching levels and degrees of anisotropy seen in the gas.

Even under the assumption of isotroplc eddy properties for computing

drop/eddy interactions with the SSF model, predictions show anisotropy

of drop velocity fluctuations. This behavior is due to effects of

turbulent drop dispersion, which causes slower moving drops in the

off-axis flow to reach the centerline. Averaging calculations over all

drops sizes at a point also tends to increase predicted levels of

anisotropy--behavior which is also a factor in the measurements•

Predicted and measured radial profiles of gas and drop velocity

fluctuations are illustrated in Figs. 22-24. The comparison between

predictions and measurements is reasonably good, except that streamwise

drop velocity fluctuations are underestimated--as noted earlier•

Another defect is that drops having an initial diameter of 105 _m were

predicted to disappear prior to x/d = 100; therefore, no predictions

can be shown for this position• In contrast, measurements showed that

drops were present as shown in the figure.

The gas velocity fluctuations illustrated in Fig. 22 tend to be

similar to observations in noncombusting jets [47]. Maximum

fluctuations are observed off-axis, where turbulence production rates

are highest, and decrease slightly as the axis is approached. For a

jet in still air, velocity fluctuations decay continuously near the

edge of the flow, where mean velocities are low. Turbulence levels at

the axis tend to increase near the flame tip, however, due to effects

of buoyancy•

In contrast, drop velocity fluctuations increase monotonically

with increasing radial distance, cf. Figs. 23 and 24• This occurs

since drops are smaller and more responsive near the edge of the

two-phase flow region. Typical of the continuous phase, drop velocity

fluctuations in the radial and tangential directions are nearly the

same and are generally smaller than streamwise drop velocity

fluctuations.

4.4.3 Drop Number Flux

Predicted and measured mean drop number fluxes along the axis are

illustrated in Fig. 25 for both sprays. In this case, predictions are

shown for both the DSF and SSF models (both for no envelope flames

present). The SSF analysis is in quite good agreement with the

measurements, except for a tendency to underestimate the length of the

drop-containing region for dpo = 105 um, as noted earlier. This is

very encouraging, since particle/drop fluxes are a sensitive indicator

of the performance of dispersed flow models [6,10-12].

In contrast, the DSF model yields rather poor predictions of

measured drop number fluxes in Fig. 25. The DSF approach vastly

overestimates number fluxes along the axis, beyond the end of the

54
03 I l I I I I

r/x

Fig. 22. Radia! profilesof gas velocityfluctuations.

55
I I I I I

0.2 -- x/d : 20 --

,tO O.l -

00000 000 O0

0.0-- -

,f' _¢

- 0 --

o o x/d : 50

0.1 -- o o°

_- ffl-'zT_

0.0 i- -i,

0 -

o o 0 x/d : I00 _ 0.5--

_ 0

dpo : 105 pm

0.2 -

DATA THEORY

m

1 n

u_,/Upc o

O. I -- T_ /_pc A --

_ wl_ /Upc [13 _

o.o I I I I I

o.oo 0.OB O._6 0.24

r/x

Fig. 23. Radial profiles of drop velocity fluctuations,

dpo = 105 Urn.

56
I I I I I

dpo= 180 pm

O.2-

x/d = 20 o DATA THEORY

-- O --

ooo °-_/;.o o

0. I -- o o --v_ _ A -- o o o o /_P0

WI_ /Upc i"1

0.0- --

/

O° 2 I m

x/d : 50

I m

0. I-- o o o o o

( 0 0 0

0.0E_" "_"'_--_-"_'-'B"'_---

S, -I

x/d : I00

0.2 --

0

0

0 0 0

0

0.I _-o o

_

o.o-_"___-"__" I I I

0.00 0.08 0.16 0.24

r/x

Fig. 24. Radial profiles of drop veloclty fluctuations,

dpo = 180 _m.

57
1.0_ i i i I i i I.i I I , i i_

dpo= 105 pm

\

\ \ dpo= 180 pm

\

\

Fig. 25. Mean drop number fluxes along the axis.

58
potential core. The reasons for this behavior is that turbulent

dispersion of drops is ignored by the DSF approach, while this

phenomenon is clearly important for present test conditions. With the

DSF approach, drops only move radially due to their initial radial

velocity, or from radial drag due to the mean radial velocity of the

flow. Both of these radial velocities are small in comparison to the

radial gas-phase velocity fluctuations which are the prime contributor

to effects of turbulent dispersion in this flow.*

A surprising, secondary feature of the data illustrated in

Fig. 25, is that i.c.._co_"_" remains somewhat higher along the axls for

the smaller initial drop size, in spite of effects of turbulent

dispersion.** This is a result of turbulent dispersion from the

initially wider number flux profile for the smaller slze (cf. Figs. 12

and 13), allowing drops to diffuse to the centerllne from initially

off-axis positions. In contrast, the initially more concentrated large

drops tend to diffuse predominantly outward in the radial direction and

their concentration at the axis decreases more rapidly. This effect,

due to turbulent dispersion, could hardly be anticipated (in fact, the

DSF analysis gets the trend entirely wrong), but is a natural outcome

of the SSF analysis when accurate initial conditions are available.

Predicted and measured radial profiles of mean drop number fluxes

are illustrated in Fig. 26. Predictions are shown for both the DSF and

SSF analyses, the former exhibiting poor comparison with measurements

due to neglect of turbulent drop dispersion. The SSF analysis

somewhat underestimates the radial spread of the drops, similar to its

underestimation of streamwise drop penetration which was noted earlier.

Mean drop velocities and radial drop velocity fluctuations are

estimated reasonably well; therefore, this behavior is not felt to be

primarily due to underestimation of turbulent dispersion. Since both

the length and width of the two-phase flow region was underestimated, a

more probable source of error is overestimation of drop gasification

rates in the flame zone.

An interesting feature of the results illustrated in Fig. 26, is

that the radial profile of drop number flux for dpo = 180 pm is

somewhat broader than for dpo = 105 pm. This behavior is not expected

from turbulent dispersion considerations alone, where smaller drops

would be expected to disperse more rapidly. In the present case, more

rapid dispersion of small drops is counteracted by their more rapid

*Furthermore, the mean radial velocity is zero at an off-axls position

(r/x ca. 0.08), stably, i.e., _ < 0 for r greater than this

position and _ > 0 for r less than this position. This causes

drops to accumulate at this radial location if the multiphase flow

persists long enough [I], but the effect of accumulation is not large

for present test conditions.

**Until the region near the flame tip where the smaller drops disappear

more rapidly by evaporation.

59
I.O I I I I

0.8 DATA dpo(Hm) _

= 105 pm A 105

0.6 o 180 --

dpo = 180 pm

0.4 THEORY -

SSF

0.2 DSF --

0.0 _ x/d = 20 --

1.0 --

dpo= 105 pm

0.8

0,6

- tJ

.t'-

0.4 = 180 pm _

.C::

0.2

0.0 x/d = 50 _

1.0 -

0.8 --

dpo : 180 pm

0.6 _

0.4 0.2 _o A o

\ "_Q x/d = I00

0.0 \ I _ I I I

0.00 0.08 0.16

r/x

Fig. 26. Radial profiles of drop number flux.

60
evaporation and disappearance in the flame zone. This trend is

represented reasonably well by the SSF predictions.

4.4.4 Drop-Size Distributions

Predicted (SSF analysis) and measured SMD along the axes of the

two sprays are illustrated in Fig. 27. For the present, initially

monodisperse, sprays, SMD decreases monotonically with increasing

distance from the burner exit. This is not generally the case for

polydlsperse sprays, where more rapid evaporation and turbulent

dispersion of small drops in the distribution generally causes the SMD

to increase for a time along the axis [I0-12]. The agreement between

predictions and measurements is reasonably good for dpo = 180 _m, but

drop size is underestimated near the tip of the flame for dpo = 105 _m,

as noted earlier.

Predicted (SSF analysis) and measured radial profiles of SMD for

the two sprays are illustrated in Fig. 28. Two positions are

considered, x/d = 50 and 100. Predictions are satisfactory at x/d _ 50.

At x/d = 100, however, drop sizes are overestimated near the edge of

the flow for dpo = 180 _m, while no drops are computed to be present

for dpo = 105 um, in spite of observations to the contrary.

The discrepancies between predictions and measurements in both the

streamwise and radial directions are largely associated with the region

of the flame. Temperatures, and thus gasification rates, are highest

in this region. Furthermore, drop vaporization rates increase rapidly

with decreasing drop size, tending to make SMD a very sensitive

indicator of model performance in this region. On balance, the present

predictions are encouraging in view of the complexities of these

spray-flame processes, however, additional consideration of drop

transport in the region of a flame is needed to obtain more reliable

predictions.

5. SUMMARY AND CONCLUSIONS

5.1 Summary

A combusting spray apparatus, operating at the limit of a dilute

spray, was developed during this study. This arrangement involved a

turbulent, methane-fueled diffusion flame burning in still air.

Monodlsperse streams of methanol drops were injected vertically upward

along the axis of the flame at its base. The drop loading was

sufficiently low so that flame properties were essentially unaffected

by drop combustion. This configuration has a simple geometry, amenable

to numerically-closed computations; initial and boundary conditions

were well-defined; extensive information was available concerning the

structure of the test flame; and results were available to calibrate

drop transport analysis.

Test conditions were chosen to provide significant effects of

- finite interphase transport rates, turbulent dispersion of drops, and

drop interactions with the flame zone. Two drop sizes were considered,

61
240 I I I I I

dpo(Pm)DATA THEORY

_ 105 A _

180 0

160

C_ _ 0 0 --

oo _--.

eo - -_._.

z_

0 I I I I I i

0 50 I00 150

x/d

Fig. 27. SMD along the axis.
180 I I I I I

o o

B m

120 -

m I

...... _ ....... -- L__ _..

60 x/d = 50 --

_ dpo(Pm) DATA THEORY

E 105 z_

=L 180 0

0 i

_; 180 -

g'J

120 =------

O

0 m- i

z_

m A

x/d = I00

o I I I I I

0.00 0.02 0.04 0.06

r/x

Fig. 28. Radial profiles of SMD.

63
having initial diameters of 105 and 180 um. Present structure

measurements included: mean and fluctuating phase velocities, mean

drop number flux distributions, drop-size distributions, and mean gas

temperatures. All structure measurements, as well as properties at the

burner exit, are tabulated in Appendix F.

Data for calibrating transport of individual drops were obtained

from single drops supported in the post-flame region of a laminar

flat-flame burner. Burner reactants were methane and air; therefore,

gas properties during the single drop tests were representative of the

turbulent flame environment, but simplified, since effects of

turbulence were absent. Drops in these tests had initial diameters in

the range 2000-3000 _m. While these sizes were much greater than in

the turbulent flame tests, drop Reynolds numbers for the calibration

tests and the sprays were comparable.

Analysis of the combusting sprays was undertaken to help interpret

the measurements and to initiate evaluation of models of the process.

Two methods typical of current spray analysis were considered: (I) a

deterministic separated flow (DSF) model, where effects of finite

interphase transport rates are considered, but drop-turbulence

interactions and turbulent dispersion of drops are ignored; and (2) a

stochastic separated flow (SSF) model, where effects of finite

interphase transport rates, drop-turbulence interactions, and turbulent

dispersion of drops are considered using random sampling for turbulence

properties in conjunction with random-walk computations for drop

motion.

Analysis of the continuous phase for both spray models was based

on a k-_-g turbulence model, which provided a reasonably good

description of the structure of the test flame during earlier work in

this laboratory [20-22]. The governing equations were in

Favre-averaged form. The conserved-scalar method was used to find

scalar properties, along with the laminar flamelet method for relating

scalar properties to mixture fraction in turbulent flames.

5.2 Conclusions

Major conclusions of the study are as follows:

I. The DSF model, which ignores drop-turbulence interactions, was

not very successful for present test conditions. The main

defect was a significant underestimation of drop spread rates

due to neglect of turbulent dispersion of drops. In spite of

its popularity [I], this approach appears to have limited

value for analyzing practical combusting sprays.

64
2. The SSF model gave encouraging predictions of current test

results, with all empirical parameters used in the turbulence

model fixed (based on earlier measurements for noncombusting

jets) and drop transport calculations calibrated by

single-drop tests. Largest discrepancies involved streamwise

drop velocity fluctuations, which were underestimated, and the

transport rates of small drops in the flame zone, which were

overestimated. Extension of current methods to consider

anisotropic continuous-phase turbulence properties and further

study of drop transport rates in flames appears warranted.

Based on encouraging results for particle-laden Jets [2-7],

nonevaporating sprays [8-11], evaporating sprays [12] and now

combusting sprays, the SSF methodology appears to be an

effective method for analyzing turbulent sprays. Continued

development of this method appears to be justified.

3. The distinction between the presence or absence of envelope

flames did not modify predictions appreciably since drops

primarily evaporated in the core of the flow where oxygen

concentrations are low. Further study of envelope flame

effects is needed, however, since present work is not

definitive and drops penetrated the flame zone for present

test conditions.

4. The present experiment proved to be useful for studying drop

transport and dispersion in turbulent flames and should be

considered by others. The parabolic flow is attractive for

numerically-closed computations, initial conditions are

readily measured, and flow properties are conducive to

reasonably reliable measurements. Newly-available methods for

simultaneous drop size and velocity measurements could be

fruitfully exploited in this flow.

65
APPENDIX A

EXPERIMENTAL UNCERTAINTIES

A.I Phase Velocities

There are two main sources of uncertainties in the LDA

measurements of phase velocities: bias errors, and general

experimental uncertainty. Each error source will be considered in the

following.

Bias Errors

Bias errors in velocity determinations using LDA arise from

several sources [48]: (I) directional ambiguity, due to the inability

of a stationary or slowly translating fringe pattern to provide an

indication of the direction in which particles are crossing the

fringes; (2) directional bias, due to particles crossing the measuring

volume at a small angle with respect to the plane of the fringes so

that an insufficient number of fringes are crossed to be processed; (3)

concentration bias, due to varying particle concentrations in

components of a mixing flow; (4) velocity bias, due to the fact that

for uniform seeding, more high velocity particles cross the measuring

volume than low velocity particles; and (5) gradient bias, due to

variations in flow velocity. Each of these sources of biasing are

considered in the following.

The present tests employed frequency shifting which eliminated

errors due to directional ambiguity. The effective frequency shift

level, after electronic mixing, was set at each location so that even a

particle moving upstream at the maximum local velocity would be crossed

by fringes which move even faster in the upstream direction. Operated

in thls manner, frequency is a single-valued function of velocity over

the range of interest and no directional ambiguity occurs [48].

Directional bias was also eliminated by frequency shifting. The

worst case is a seeding particle moving somewhat upstream to the fringe

plane while crossing the measuring volume. However, since the fringes

are effectively moving upstream at velocities high enough to prevent

directional ambiguity, sufficient fringe crossings were available at

each point in the flow to yield a detectable signal (8-32 fringe

crossings were used for processing).

Concentration bias was not a factor for drop velocities, since

only drop velocities were sought and measured. Concentration bias can

influence gas velocity measurements, if the burner and ambient gas are

not seeded to the same degree. This was a problem near the burner

exit, since the hydrogen coflow was not seeded, however, measurements

in this region related primarily to burner gas properties so the effect

does not materially influence present results. The tactic used to

reduce effects of concentration bias was to seed both burner and

ambient gas. Similar to past practice [I-18], the detector output was

observed and ambient seeding was adjusted to eliminate any observed

66
effects of signal intermittency due to lack of particles in the ambient

flow.

Velocity bias can occur when particles averages are used, since

more hlgh-velocity particles pass through the measuring volume per unit

time. This effect was eliminated for gas velocities by operating the

- system at high signal rates (500-5000 Hz) and tlme-averaglng the

output, as discussed by Durst et al. [48]. Partlcle-averages were

measured for drops; therefore, drop velocities have velocity bias.

This represents no problem, however, since theoretical results were

obtained in the same manner.

The final source of biasing is gradient biasing, which could

introduce errors in present measurements. These biases can be

estimated using the analysis reported by Kreld [49]. For this

analysis, only velocity gradients in the radial direction are

considered and all seeding particles crossing the measuring volume are

assumed to be recorded--independent of any directional bias, which has

already been shown to be small. The measuring volume is assumed to be

small, so that higher-order terms in the Taylor series expansion of

mean velocity (expanded from the center of the measuring volume) can be

ignored. Then the difference between the measured mean ann fluctuating

velocities, ut and u_, and the actual values of the flow, u and

u' are

Iu _ u i_ _2 _2u (A.I)

t 6 _r2

_ '_r (A.2)

where _ is the half-width of the measuring volume in the radial

direction.

Applying Eqs. (A.I) and (A.2), after estimating gradients from the

measurements, indicates gradient broadening errors less than I% for

present tests--for both phases.

Jeng [20], extended considerations of gradient broadening to

consider this effect for two othogonal gradlents--neglecting only the

gradient in the streamwise direction, since it is small. He reached

the same conclusion for the gas phase, e.g., gradient broadening errors

were less than I%.

Uncertainty Estimates

The uncertainty analysis procedures of Moffat [50] are adopted to

estimate experimenta! uncertainties. In this case, we consider an

output variable V, which is a function of several, n, measured

variables, vi, as follows:

67
V = V(v I, v2, ..., vn) (A.3)

The vi are subject to uncertainties, Avi, and we wish to determine the

resulting uncertainty in V, e.g., AV. The Avi and AV are defined

somewhat arbitrarily, but consistently. They can be the expected

standard deviation of these quantities or some percentage of the

confidence interval for these quantities, e.g., the 95% confidence

interval is most frequently chosen [50]. In the following, we will use

the latter definition. Based on these definitions, Moffat [50] finds

-V= i=I vinavi)1 (A.4)

Equation (A.4) will be used to estimate relative uncertainties in the

following.

In considering uncertainties in gas velocity measurements, we

ignore positioning errors, since this only influences the position

where points are plotted and this accuracy has been stated already.

Furthermore, all orientations of the laser beams were measured with

positions of the experiment and optics fixed. It is felt that optical

alignment was sufficiently good so that rotation of the laser beams did

not shift the location of the measuring volume significantly, e.g., the

detector was fixed and optical alignment was optimized to maintain good

slgnal-to-noise ratios at all beam angles. As a result, the mean

velocity measurement only depends on the overall calibration factor, K,

between the electrical signal and velocity and the time-averaged

electrical signal itself, E, allowing for frequency shift, e.g.,

u --K E (A.5)

Applying Eq. (A.4) to Eq. (A.5) yields

1/2

The overall calibration factor K was checked using a rotating disk and

is estimated to have a relative uncertainty of 2%. The uncertainty of

E was estimated from measurements of several samples at a worst-case

condition using representative operation procedures. The uncertainty

is taken as two times the standard deviation of these samples (roughly

the 95% confidence interval) to yield an estimate of 3%. Substituting

these estimates into Eq. (A.6) then yields an uncertainty for mean

velocities of 4%.

68
Similar considerations hold for velocity fluctuations, except that

in this case processing differed since the true rms meter was in the

circuit. Then

u',v,,w' = K (_u'ev' _w)

(A.7)

where _i is the averaged output of the true rms meter. The

uncertainty in K is unchanged while the worst-case estimate of the

uncertainty in _i is 5%. This yields an uncertainty in individual

velocity fluctuations of 5%.

Errors in quadratic quantities, llke k are larger. In the case of

k we have

IK2 2+ e2+ e2 )

k = _ (eu v w (A.8)

Applying Eq. (A.4) to Eq. (A.8) then yields

_ _ wl I/2

Ak AK 2 e 2 Ae 2 + e 2 Ae 2 + e-2 Ae

_-= 2 (_--) + u u v v w (A.9)

(_2+e2+- -e 2)2

U V W

Based on the uncertainties in K and the _i, discussed above, the

uncertainty in k is roughly 9%.

Considerations for drop velocities are similar to those of gas

velocities, except the results for individual drops were summed to find

appropriate averages. Based on several samples at typical operating

conditions, the uncertainties in E and _ were 3 and 5%

(two times the standard deviation). This yields uncertainties in

streamwlse mean and fluctuating drop velocities of 4 and 5%, as

before.

A.2 Drop-Size Distribution

Various characteristic sizes can be used to represent the

distribution of drop sizes. They are, essentially, different moments

of the drop-size distribution. For example, for a sample of n drops,

we have

n

dkk = _ d.k1 /n (A.10)

i=I

where d i is the diameter of the i'th drop. Then dI is the number mean

drop diameter, d2 is the area mean drop diameter, etc.

Drop size data in this report is presented as the Sauter mean

diameter, which is the drop size that has the same surface area to

volume ratio as the spray as a whole, at the point sampled. Thus

69
SMD = 6V/A (A.11)

where

V = _n d33/6 ; A =n _n d22 (A.12)

To find the uncertainty in the SMD, we first apply Eq. (A.4) to Eq.

(A.11) to yield

ASMD I'AV" 2 A--AAI I/2

= t--_) + ( ) (A.13)

The uncertainties in V and A are primarily due to the uncertainties in

the diameter of each drop in the sample and the finite sample size. To

find these quantities, we first take the partial derivatives of V and A

with respect to di, obtaining the arguments of Eq. (A.4), as follows:

2

Adi _V 3 di Adi

= (A.14)

V _d. e

1 n d3

Ad. 2 d. Ad.

i _A i I (A.15)

A _di n d22

The total uncertainties in V and A are obtained by summing the squares

of Eqs. (A.14) and (A.15) over all drops in the sample

2 2

AV2 n 3 d Adi

V--) = _ (. i _ ) (A.16)

i=I n d3

2

AA2 _ 2 d. Ad. A--) = ( i 21) (A.17)

i=I n d2

During present work, drops were grouped into size ranges having

the same width, thus the uncertainty Adi was constant, cf. data

presented in Appendix F.5. Then noting the various mean diameters

defined by Eq. (A.IO) we have

dI 6 Ad. 2

AV 2 9 (d_)4() (#) (A.18)

7O
h AA I 2 4 dI 2 Ad. 2

( ) (-_-_) (A.19)

uI

Now, the present size distributions are only roughly Gausslan, due to

the propensity for smaller drops in the distribution to evaporate more

rapidly than large ones. However, for present purposes, it is

reasonable to assume Gausslan distributions, whereupon, it can be shown

that

(d_)4(_3)6 < I ; (-_2) dl 2 < I (A.20)

Conservatively setting these quantities equal to unity and substituting

Eqs. (A.18) and (A.19) into Eq. (A.13) yields the following expression

for the uncertainty in SMD

ASMD 13 I/2 _Ad"

SMD = (--_) (--d_.) (A.21 )

I

During current tests, n = 200. The factor (Adl/dI) varied from

values on the order of 0.01 at the burner exit to values as high as

0.33 near the end of drop llfe. Taking the latter condition for

specification of the maximum uncertainty we find ASMD/SMD < 10% from

Eq. (A.21).

A.3 Drop Number Fluxes

Uncertainties in the drop number flux are due to flnite-length

drop counts, the calibration of the cross-sectional area of

measurement as a function of drop size and the uncertainty of the

drop-size distribution when the raw data was corrected. For much of

the flow, the latter correction is small (cf. Appendix F.4) and can be

related to the uncertainty in mean drop diameter; therefore, this

approximations will be used here.

The basic expression for drop number flux, under the present

approximation, is

_" _ _/AF (dp avg) (A.22)

AF (dp avg) is the flux area at the mean drop size

AF (dp avg) _ w (dp avg) L (dp avg) (A.23)

where W and L are found from the flux area calibrations described in

Appendix B.2.

Applying Eq. (A.4) to Eqs. (A.22) and (A.23) yields the following

expression for the uncertainty.

71
I_n)2 -P avg)_ I/2

A_" " AW 2 .AL.2 _ _n AF Adp (A.24)

More than 1000 drops were generally counted; therefore, the

uncertainty in _ is small--less than 0.1%--and can be ignored.

The uncertainty in W and L is conservatively estimated to be the region

of cut-off of the count signal near the edge of the measuring region as

discussed in Appendix B.2. This is roughly 10% of the mean dimension.

The parameter _ _n AF/_ _n dp is roughly unity, from the present

calibration measurements. The relative uncertainty in dp avg (95%

confidence) is given by

A I/2

dp avg/dp avg = 2 0d /(dp avg n ) (A.25)

P

where 0d is the standard deviation of the drop-size distribution

for n dr_ps counted. From Appendix F.5, 0d /dn avg is never

greater than I/2 for the data reported here_ w_ile n : 200.

Substituting these estimates into Eq. (A.24) yields an uncertainty (95%

confidence) of less than 16% in the drop number flux measurements.

A.4 Mean Gas Temperatures

The uncertainty in mean gas temperature, to the scale plotted in

the present report, is greatest in the region of flame. The

measurement of the mean thermocouple EMF had an uncertainty less than

I% in this region; therefore, the uncertainty in the temperature

measurement is dominated by the radiation correction.

The radiation correction is described in Appendix C. For present

conditions, T_ has little influence on the estimate of radiation error

and the Reynolds number of the junction was sufficiently high so that

the heat transfer coefficient is dominated by forced convection. At

this limit, use of Eq. (A.4) yields the following expression for the

uncertainty in the radiation error estimate.

A(T-Ttc) F.AE)2 Akf 2 Adtc 2 Au)2

= L dtc) +

(T_Ttc) £_-- + (-_-f) + (0.38_ (0.62 u

A_f)2 ATtc _ I/2

* (0.62 (4 _tc ) (A.26)

where the small uncertainty in the Stephan-Boltzman constant has been

ignored.

72
The uncertainty in thermocouple emissivity is large, due to the

practical problems of preventing accumulations of soot on the probe,

and is taken to be 100%., Uncertainties in other quantities are

estimated as follows: gas properties, 20%; junction diameter, 10%; gas

velocity, 20%; and junction temperature reading, I%. Substituting

these estimates into Eq. (A.26) yields an uncertainty in the radiation

correction of 104%.

With a maximum radiation error correction of 57 K, at a mean

temperature of 1700 K, the above uncertainty becomes roughly 5% of the

difference between the indicated and ambient temperatures. Estimates

at other points in the flow, where temperatures are reported here,

indicate comparable levels of uncertainty.

73
APPENDIX B

DROP NUMBER FLUX MEASUREMENTS

B.I Pulse Counter

The pulse counting device used for the drop number flux

measurements was designed and fabricated by Electronic Design Services,

College of Engineering, The Pennsylvania State University. The device

was designed to count electrical impulses for any desired interval from

I to 999s. The count value is displayed on a seven digit display as a

decimal integer value. The device will count pulses for any electrical

signal that ranges from 0 to -12 V and has a frequency range of 0-I MHz.

A threshold adjustment allows setting of a DC level from 0 to 2 V,

which determines the minimum amplitude of a signal which will be

accepted as a pulse. The device was designed as a

mlcro-processor-based system.

The amplified signal from the photodetector was fed to the pulse

counter. The threshold adjustment was set to the lowest value possible

where no counts were registered with the drop generator off. Drops

were then produced and their counts recorded, generally setting the

time of counting to record roughly 1000 drops or to count for more than

100s--whichever was the limiting factor.

Complete description of the device requires the circuit diagram

and the program used to control the micro-processor. In the interest

of brevity, these details are not included in the present report, but

can be obtained from the senior author (GMF) upon request.

B.2 Calibration of Measuring Area

Facility limitations required that scattered light signals be

observed from the same plane as the light sheet, cf. Fig. 4. This was

undesirable, to some extent, since the region of observation could not

be strictly controlled by the detector aperture and depended on drop

size more than would be the case for off-plane observations. As a

result it was necessary to calibrate the measuring area as a function

of drop size. The method of calibration and some typical results will

be presented in the following.

The monodisperse drop generator was used to calibrate the

measuring area of the drop number flux system. The exit of the

generator tube was positioned a short distance below the measuring

plane (4 mm). The generator was operated with a slow flow of

dispersing gas so that the drop stream was essentially collnear. The

generator was mounted on two orthogonal traversing systems, each fitted

with dial gauges accurate to 25 wm. Varying the generator orifice and

operating conditions yielded monodisperse drop streams having diameters

in the range of interest for the drop number flux measurements

(36-180 um). The pulse-counter threshold and detector gain were set as

described in Section B.I and kept at this condition during calibration,

since the calibration was influenced by these parameters. The

calibration tests consisted of traversing the generator across the

74
measuring volume in the two directions and recording the drop pulse

rate as a function of position.

Some typical results of the calibration are illustrated in Fig.

B.I. Results for two different drop sizes and for traverses along and

normal to the optical axis (both centered on the measuring volume) are

shown. The observed counts drop off reasonably fast at the edge of the

measuring volume, but the stronger scattering signal from the larger

drops causes the threshold on the detector to be crossed at a larger

distance from the center of the measuring volume. The region of

decreasing signal represents the uncertainty in the cross-sectlonal

area; this was generally less than ±10% of the mean dimension of

observation. Off-axls traverses indicated that the measuring region

was roughly rectangular and this was assumed for both the flux area

calibration and the analysis of uncertainty of the flux measurements.

The calibrations are not given here, since they are specific for the

present gain and threshold settings and would be of little general

value.

75
TRAVERSE DISTANCE (mm)

Fig. B.I. Drop number flux calibration.

76
APPENDIX C

CORRECTION OF TEMPERATURE MEASUREMENTS FOR RADIATION

Radiation errors for the thermocouple were estimated considering

heat gain by convection from the local gas flow and heat loss by

radiation to the room, through a transparent flame. This ignores

radiation from the flame to the thermocouple, which tends to increase

its indicated temperature from the estimates made here. We also

neglect heat transfer to the thermocouple leads, since the present

configuration had fine-wlre leads, with relatively large

length-to-diameter ratios, cf. Fig. 5.

Conservation of energy for the thermocouple lead yields

Ttc + (ca/h)(Ttc4 - T_ 4) (C.I)

T

where _ is the thermocouple emissivity, _ is the Stefan-Boltzmann

constant and h is the convection heat transfer coefficient to the bead

of the junction.

The thermocouple junction was formed by butt-weldlng two 76 um,

Pt/Pt-10% Rh wires together. The junction was then coated with silica

to minimize catalytic effects. The final diameter of the bead was

measured with a microscope to be 225 um.

The emissivity of the thermocouple bead was taken to be equal to

the emissivity of platinum, given by Caldwell [51], as follows

E : 9.6 x 10-5 Ttc + 0.056 (C.2)

where Ttc is in K. The coating is essentially transparent to

radiation.

The flame gases have a Prandtl number of nearly 0.7, since the

mixture is dominated by nitrogen. In this case, the Nusselt number for

a thermocouple bead can be obtained from the following formula from

Becker and Yamazaki [52].

hdtc/A = 2 . 0.31 (Udtc/V)0"62 (C.3)

where dtc is the bead diameter, u is the relative gas velocity, A is

the thermal conductivity and _ is the kinematic viscosity. Properties

are evaluated at the average temperature of the thermal boundary layer,

Tf.

Properties of the gas mixture were approximated as pure air, with

density obtained under the assumption of an ideal gas. The gas

viscosity was computed from [53]

77
uf(Ns/m2) = 0.40201 + 0.74582 Tf - 0.57171Tf 2

. 0.29928 Tf3 - 0.62524 Tf4 (C.4)

where Tf is in K. The thermal conductivity was obtained from [52]

Af(W/mK) = 264.6 x 10-5 Tf3/2/(Tf + 245 x I0-12/Tf) (C.5)

where Tf is also in K.

Thermocouple errors were calculated using the measured mean

velocities and temperatures at each location. The maximum magnitude of

the correction was 57 K, at the maximum flame temperature location.

78
APPENDIX D

DROP TRANSPORT PROPERTIES

D.I Mixture Thermal Conductivity

The thermal conductivity of the gaseous mixture was calculated

with the Mason and Saxena formulation of the Wassiljewa equation, cited

in Reid et al. [54]. For a mixture of N components:

N Xil i

_m = _ N (D.I) 1=I

Z XjCij j=1

where

= I Mi)-1/2 (_i)I/2 (Mj)I

The thermal conductivity and viscosity for gases were obtained

from Svehla [55]. Equations (D.I) and (D.2) were evaluated at the

reference state defined by Eq. (3.28).

D.2 Mixture Viscosity

The viscosity calculations of the mixture employed the method of

Wilke, cited by Reid et al. [54]. For a mixture of N components:

_m = _ N (D.3)

=1 3 :j

where ¢i_ is given by Eq. (D.2). The viscosity data used in the

calculat:ons was obtained in the same manner as described in Section

D.I.

D.3 Mixture MassDiffusivity

Since only fuel vapor diffuses through the stagnant mixture, the

diffusion coefficient is given as [54]

= = D (D.4)

=2

Subscript I represents fue! vapor, and j indicates all other gases.

Binary diffusivity calculations employed Chapman-Enskog theory along

79
with Lennard-Jones characteristic energy and length concept cited by

Reid et al. [54]. Values of the characteristic energies and lengths

were drawn from the same source and are summarized in Table D.I.

D.4 Mixture Specific Heat

The mixture specific heat was calculated as a mole fraction

weighted average of the specific heats of each contributing species

N

X

i=I Pi

Cp = M (D.5)

D.5 Properties of Methanol

The fundamental thermochemical properties of methanol are

summarized in Table D.2. Values are drawn from the sources indicated

in the table.

The vapor pressure relationship used for methanol was [54]:

l°g10 Pv (mm Hg) = - 42.629 - 1186.2/T + 23.279 log i0T

- 35.082 (T/1000) + 17.578 (T/1000)2 (D.6)

where T(K).

The heat of vaporization correlation used for methanol was [55]:

hfg (kJ/kg) = 1088 ((Tcr - T)/(Tcr - Tr))0"4 (D.7)

where T(K) and Tr = 337.9 K.

The specific heat of liquid methanol was [55]

Cp (kJ/kgK) = 3.506 - 13.51 (T/tO00) + 34.71 (T/1000)2

+ 0.7067 (T/IO00)3 (D.8)

where T(K).

8O
Table D.I

Properties Used for Binary Diffusivlty Calculationsa

Substance a' (A°) _'/k' (K)

H20 2.641 809.1

CO 3.690 91.7

C02 3.941 195.2

N2 3.798 71.4

H2 2.827 59.7

02 3.467 106.7

CH4 3.758 148.6

CH30H 3.626 481.8

aTaken from Reid et al. [54].

81
Table D.2 Thermochemical Properties of Methanol

Property Value Source

Formula CH3OH [54]

Molecular Weight 32.04 [54]

Normal Boiling Temperature (K) 337.8 [54]

Critical Temperature (K) 513.2 [54]

Critical Pressure (bar) 79.5 [54]

Critical Volume (m3/kg mole) 0.118 [54]

Liquid Specific Heat (kJ/kgK)a 2.54 [55]

Liquid Density (kg/m3)a 790 [55]

Heat of Vaporization (kJ/kg)a 1088 [55]

Heat of Combustion (kJ/kg) 14094 [56]

aAt 25Oc.

82
APPENDIX E

DROP TRANSPORT CALIBRATION

E.I Experimental Method

Drop transport calibration tests were conducted using the

supported drop technique. The drop environment was created by a

laminar flat-flame burner, using methane and air as reactants in order

to simulate the turbulent flame environment. The drops were rapidly

submerged in the post-flame region of the flat-flame burner and

photographed as they evaporated. The films were then measured to yield

drop size as a function of time.

A sketch of the flat-flame burner apparatus appears in Fig. E.I.

The burner construction is described completely by Szekely [57]. Fuel

gas and air flow rates were measured with rotameters which were

calibrated by wet-test meters for each gas used. Fuel gases were mixed

in a 1500 mm long, 10 mm inside diameter tube before entering the

burner assembly. The burner was constructed of 51 mm nominal diameter,

schedule 40, stainless steel welded pipe having a total length of 300

mm. After entering the base of the burner, the gases flowed up the

length of the housing through two 50 mm thick layers of 3 mm diameter

glass beads and one 50 mm thick layer of 2 mm diameter stainless steel

beads. The bead layers were separated by 50 mm long void spaces, and

were supported by 20 mesh stainless steel screens spot-welded to the

sides of the burner housing. Stainless steel screens (100 mesh) were

placed on top of each 20 mesh screen to ensure that no beads would fall

through to the next layer. This burner design provided complete

premixing of the burner gases, and supported a flat flame, roughly 2-3

mm thick, on the top layer of stainless steel beads. A quartz shroud

on top of the burner prevented the burner gases from mixing with the

ambient atmosphere.

Drops were mounted on quartz probes and then centered on the

burner exit with the pneumatically-driven shield, illustrated in Fig.

E.I, in place. Actuating the pneumatic cylinder withdrew the shield

and started the evaporation process.

All flame conditions were characterized by determining the gas

temperature, species concentrations and gas velocity at the drop

position.

Gas temperatures were measured using Pt/Pt-10% Rh thermocouples

with bead diameters of approximately 50 um. The signal from these

thermoeouples was observed with an integrating digital voltmeter. The

reading was then corrected for radiation losses as described in

Appendix C.

Species concentrations were measured at the particle test location

using a stainless steel water-cooled sampling probe having a 0.7 mm

diameter sampling port. Water flow rate through the sampling probe was

adjusted to maintain a probe temperature of about 340 K in order to

83
PROBE SUPPORT

q_ ZERO MARKER

FLAME SHIELD i

-" '-" I---I !

IL,_=_!-_ FLAT FLAME / I

I

L_] F PNEUMATIC SLIDE N2 ACTUATOR

Fig. E.I. Flat-flame burner apparatus.
avoid condensation of water vapor inside the probe. Water vapor in the

sample was removed farther downstream by an ice-bath condenser. The

dry sample was collected in a 125 ml sampling bulb (Supelco, model

2-2161), which was connected to a Welch Scientific duo-seal vacuum

pump, model 1450. Sample flow rates were controlled with a Whitey

regulating valve and metered with a bubble meter to ensure nearly

isokinetic sampling at the probe inlet. The sample was drawn through

the septum of the sampling bulb into a 1.0 ml series C Pressure-Lock

gas syringe, and was analyzed using a Varian model 3720 gas

chromatograph. The gas chromatograph was fitted with a Supelco

carbosleve S, 100/120 mesh, 2.1 m x 3.2 mm stainless steel column, and

was temperature programmed to separate the product gases. An initial

column temperature of 35°C was maintained for 4 minutes, and then

increased to 175°C at a rate of 25OC/minute. The GC was calibrated

with Scott gas mixtures of known concentrations (±2%) of nitrogen,

oxygen, carbon monoxide and carbon dioxide. Helium was used as the

carrier gas, having a flow rate of 0.4 ml/second. Product mole

fractions were determined experimentally on a dry basis, and converted

to a wet basis by conservation of element analysis. Species

concentration measurements for all flame conditions used in this study

were verified with the chemical equilibrium calculation code CEC76

[36].

Gas velocities at the test section were calculated assuming

one-dimensional flow of an ideal gas at the measured gas temperature

and composition. A summary of all flame conditions used in this study

is provided in Table 6. The temperatures listed refer to the maximum

temperatures measured for each flame condition. Average gas

temperatures during testing were I-2% lower than the values tabulated.

Drop diameters were measured as a function of residence time in

the burner gases by means of a 16 mm motion picture camera (Redlake

Locam, model 51), capable of resolution up to 2 milliseconds, but run

at a film speed of roughly 200 pictures per second for present work.

The camera was equipped with an LED timing marker (powered by an

external timing pulse generator). Kodak plus-X reversal film was used

for the tests. Drops were backlighted with a 60 watt light bulb

operated at input voltages which varied between 60-120 V. Photographs

of an Edmund Scientific graticule provided the size calibrations for

the particle diameter measurements. Particle sizes were obtained from

the film records using a Vanguard/Bendix computer digitizing motion

analyzer. Effective particle diameters were calculated as in past work

by approximating the particles as ellipsoids [I]. This approximation

was found to be quite reasonable for the present drops, with typical

particle eccentricities ranging from 1.1-1.4.

85
E.2 Drop-Life-History Data

Table E.I Drop Diameter Squared vs. Time:

dpo = 2293 um, ¢ = 0.65

Time(s) (dp/dpo)2 Time(s) (dp/dpo)2

0.00 I.O0 I.40 0.62

0.10 0.98 I.60 0.54

0.20 0.94 I.80 0.50

0.40 0.90 2.00 0.46

0.60 0.84 2.20 0.39

0.80 0.78 2.40 0.35

1.00 0.71 2.60 0.28

I.20 0.67 2.80 0.24

Table E.2 Drop Diameter Squared vs. Time:

dpo = 2786 _m, ¢ = 0.82

Time(s) (dp/dpo)2 Time(s) (dp/dpo)2

0.00 I.00 I.75 0.65

- 0.25 0.97 2.00 0.59

0.50 0.92 2.25 0.51

0.75 0.88 2.50 0.47

I.00 0.82 2.75 0.45

I.25 0.75 3.O0 0.42

I.50 0.71

Table E.3 Drop Diameter Squared vs. Time:

dpo = 2953 um, ¢ = 0.97

Time(s) (dp/dpo)2 Time(s) (dp/dpo)2

0.00 1.00 2.25 0.68

0.25 0.97 2.50 0.63

0.50 0.94 2.75 0.60

0.75 0.90 3.00 0.56

1.00 0.87 3.25 0.52

1.25 0.84 3.50 0.48

1.50 0.79 3.75 0.45

1.75 0.76 4.00 0.43

2.00 0.72 4.25 0.38

86
APPENDIX F

FLAME STRUCTURE DATA

F.I Mean Gas Temperatures*

Table F.I.1 Mean Temperatures Along the Axis

x/d T(K) x/d T(K)

2O 782 9O 1677

23 858 100 1719

26 935 110 1747

30 1016 120 1730

40 1188 135 1610

50 1325 150 1437

60 1444 170 1153

70 1534 190 939

80 1621 ....

*All mean temperatures are corrected for

radiation heat loss as described in

Appendix C.

87
Table F.I.2 Mean Temperatures at x/d _ 20

r/x T(K) r/x T(K)

0.00 805 0.11 1342

0.01 809 0.12 1457

0.02 822 0.13 1552

0.03 840 0.14 1603

0.04 876 0.15 1619

0.05 905 0.16 1591

0.06 959 0.17 1525

0.07 1020 0.18 1364

0.08 1091 0.19 1248

0.09 1153 0.20 1062

0.10 1265 0.21 877

88
Table F.I.3 Mean Temperatures at x/d = 50

r/x TCK) r/x TCK)

0.000 1324 0.108 1642

0.012 1333 0.120 1568

0.024 1360 0.132 1413

0.036 1403 0.144 1232

0.048 1461 0.156 1074

0.060 1537 - 0.168 932

0.072 1603 0.180 755

0.084 1652 0.192 628

0.096 1678 0.204 518

Table F.I.4 Mean Temperatures at x/d = i00

r/x T(K) r/x T(K)

0.000 1729 O.112 915

O.016 1727 O.128 783

0.032 1702 0.144 625

0.048 1621 0.160 516

0.064 1475 0.176 462

0.080 1297 0.192 378

r

0.096 1115 0.208 300

89
F.2 Gas Velocities

Table F.2.1 Gas Velocities (m/s) Along the Axis

C C C C C C

I 52.80 2.43 2.53 26 18.82 4.08 3.16

2 53 30 2.77 2.61 30 17.59 3.74 3.04

3 53 30 2.98 2.77 40 15.07 3.10 2.56

4 51 80 4.77 3.52 50 13.19 2.57 2.09

5 51 20 6.66 4.15 60 11.63 2.15 1.81

6 48.90 7.34 4.35 70 10.20 2.04 I.59

7 46.60 8.76 4.75 80 9.23 2.00 1.50

8 43.80 9.02 5.08 90 8.55 1.88 1.42

9 40.20 8.80 5.31 100 7.76 1.81 1.36

10 38.20 8.52 5.39 120 7.00 1.73 1.30

12 32.80 7.45 5.18 135 6.23 1.67 1.28

14 29.00 6.35 4.61 150 5.70 1.62 1.26

16 25.20 5.49 4.21 170 5.08 1.45 1.21

20 22.90 4.99 3.76 190 4.64 1.33 1.18

23 20.79 4.41 3.44 ........

9O
Table F.2.2 Gas Velocities,x/d = I

r/x u/u u'v'/u 2 u'/u v'/u w'/u k/u 2

C C C C C C

0.00 1.000 -- 0.040 0.051 0.053 0.0035

0.10 1.001 -- 0.044 0.049 0.054 0.0036

0.20 1.004 -- 0.047 0.055 0.054 0.0041

0.30 0.998 -- 0.051 0.055 0.056 0.0044

0.40 0.960 -- 0.089 0.062 0.057 0.0075

0.50 0.743 -- 0.184 0.090 0.064 0.0230

0.60 0.552 -- 0.162 0.070 0.044 0.0165

91
Table F.2.3 Gas Velocities, x/d = 20

r/x u/u u'v'/u 2 u'/u v'/u w'/u k/u 2

C C C C C C

0.00 1.000 0.0000 0.209 0.161 0.158 0.0473

0.01 0.999 0.0024 0.206 0.163 0.160 0.0473

0.02 0.992 0.0029 0.199 0.157 0.165 0.0457

0.03 0.960 0.0045 0.210 0.161 0.171 0.0496

0.04 0.931 0.0063 0.202 0.162 0.173 0.0485

0.05 0.889 0.0083 0.205 0.163 0.165 0.0479

0.06 0.839 0.0095 0.209 0.160 0.164 0.0481

0.07 0.780 0.0101 0.209 0.163 0.165 0.0487

0.08 0.721 0.0080 0.208 0.162 0.145 0.0453

0.09 0.675 0.0070 0.194 0.147 0.135 0.0387

0.10 0.597 0.0060 0.160 0.131 0.126 0.0293

0.11 0.530 0.0043 0.144 0.108 0.177 0.0230

92
Table F.2.4 Gas Velocities,x/d = 50

r/x ulu u'v'/u 2 u'/u v'/u w'/u k/u 2

e c c c e c

0.000 1.000 0.0000 0.187 0.148 0.150 0.0397

0.012 0.994 0.0033 0.185 0.147 0.152 0.0395

0.024 0.949 0.0061 0.193 0.150 0.158 0.0424

0.036 0.877 0.0095 0.207 0.154 0.163 0.0466

0.048 0.804 0.0109 0.215 0.156 0.165 0.0489

0.060 0.724 0.0112 0.219 0.154 0.167 0.0498

0.072 0.641 0.0106 0.219 0.151 0.169 0.0497

0.084 0.551 0.0084 0.214 0.147 0.160 0.0465

0.096 0.406 0.0076 0.203 0.133 0.151 0.0408

0.108 0.340 0.0060 0.187 0.113 0.131 0.0324

0.120 0.271 0.0047 0.165 0.102 0.112 0.0251

0.132 0.201 0.0046 0.139 0.070 0.099 0.0176

0.144 0.160 0.0028 0.119 0.062 0.086 0.0127

0.156 0.123 0.0020 0.088 0.044 0.066 0.0070

0.168 0.091 0.0015 0.070 0.032 0.050 0.0042

93
Table F.2.5 Gas Velocities, x/d : 100

r/x u/u u'v'/u 2 u'/u v'/u w'/u k/u 2

C C C C C C

0.000 I.000 O.0000 0.238 0.174 0.173 0.0584

0.016 0.958 0.0066 0.234 0.169 0.174 0.0568

0.032 0.841 0.0110 0.251 0.166 0.175 0.0606

0.048 0.715 0.0139 0.248 0.164 0.174 0.0590

0.064 0.575 0.0143 0.239 0.156 0.164 0.0540

0.080 0.471 0.0120 0.209 0.149 0.150 0.0442

0.096 0.372 0.0105 0.173 0.140 0.138 0.0343

0.112 0.295 0.0084 0.146 0.126 0.119 0.0257

0.128 0.213 0.0059 0.129 0.111 0.100 0.0195

0.144 0.161 0.0042 0.103 0.091 0.076 0.0123

0.160 0.125 0.0016 0.080 0.074 0.065 0.0081

0.176 0.092 0.0007 0.059 0.064 0.050 0.0050

94
Drop Velocities

Table F.3.1 Drop Velocities (m/s) Along the Axis, dpo = 105 _m

x/d x/d

P P P P P P

I 15.62 0.309 0.273 30 21.26 1.585 0.262

2 16.92 0.347 0.283 35 20.45 1.625 0.237

3 18.21 0.397 0.305 40 19.54 1.493 0.239

4 19.40 0.440 0.329 45 19.25 1.414 0.261

5 20.27 0.532 0.324 50 18.71 1.518 0.275

6 20.97 0.616 0.329 55 16.89 1.616 0.302

7 21.65 0.783 0.329 60 15.70 1.603 0.336

8 22.13 0.879 0.322 65 14.53 2.009 0.361

9 22.34 0.990 0.338 70 13.17 2.013 0.458

10 22.57 1.134 0.339 80 11.16 2.187 0.602

11 22.94 1.141 0.332 90 10.52 2.367 0.621

12 23.24 1.202 0.347 100 9.99 2.357 0.693

15 23.52 1.259 0.345 110 9.34 2.360 0.621

18 23.37 1.350 0.351 120 8.26 2.255 0.586

20 23.26 1.476 0.340 130 7.76 2.020 0.755

23 22.67 1.537 0.311 140 6.56 2.010 0.725

26 22.06 1.548 0.278 ........

95
Table F.3.2 Drop Velocities (m/s) Along the Axis, dpo = 180 um

B

P P P P P P

I 11.96 0.477 0.440 30 17.82 I.1I0 0.I 96

2 13.17 0.541 0.501 35 17.79 1.140 0.186

3 14.30 0.623 0.488 40 17.72 1.090 0.143

4 15.50 0.906 0.497 44 17.62 1.030 0.139

5 16.05 0.952 0.420 50 17.52 1.055 0.117

6 16.54 I 140 0.417 54 17.37 0.990 0.104

7 16.83 I 240 0.441 60 17.07 1.055 0.112

8 17.05 I 273 0.434 70 16.46 1.105 0.116

9 17.24 I 440 0.411 80 15.78 1.145 0.153

10 17.36 I 300 0.336 90 14.39 1.150 0.168

11 17.62 I 410 0.402 100 13.62 1.260 0.202

12 17.48 1.440 0.328 110 12.60 1.390 0.226

15 17.64 1.390 0.281 120 11.32 1.617 0.290

18 17.74 1.350 0.271 135 9.19 1.930 0.440

20 17.77 1.340 0.240 150 7.18 2.090 0.636

23 17.79 1.280 0.191 170 5.98 1.960 0.715

26 17.78 1.210 0.219 190 4.93 1.470 0.527

96
Table F.3.3 Drop Velocities: dpo = 105 um, x/d = I

m

r/x u /u u'/u v'/u w'/u

p pc p pc p pc p pc

0.0 I.000 0.0198 0.0175 0.0172

0.1 I.001 0.0] 92 0.0177 0.0172

0.2 I.004 0.0189 0.0177 0.0174

0.3 I.008 0.0186 0.0184 0.0175

0.4 0.996 0.0252 0.0195 0.0177

-0.1 I.012 0.0186 0.0172 0.01 69

-0.2 1.014 0.0175 0.0169 0.0163

-0.3 I.015 0.0176 0.01 75 0.01 71

-0.4 I .007 0.0235 0.0190 0.0181

97
Table F.3.4 Drop Velocities: dpo = 105 um, x/d = 20

rlx u lu u'/u v'lu w'lu

p pc p pc p pc p pc

0.00 1.000 0.0597 0.015] 0.0151

0.01 0.993 0.0643 0.0145 0.0141

0.02 0.981 0.0656 0.0148 0.0138

0.03 0.963 0.0682 0.0148 0.0139

0.04 0.943 0.0730 0.0152 0.0139

0.05 0.921 0.0718 0.0155 0.0135

0.06 0.896 0.0715 0.0155 0.0136

0.07 0.876 0.0738 0.0157 0.0137

0.08 0.849 0.0749 0.0162 0.0133

0.09 0.815 0.0806 0.0152 0.0133

0.10 0.782 0.0837 0.0172 0.0131

0.11 0.770 O.1030 O.O188 O.O136

98
Table F.3.5 Drop Velocities: dpo = 105 _m, x/d = 50

r/x u /u _-l'/u v'/u w'/u

p pc p pc p pc p pc

0.000 1.000 0.0775 0.0117 0.0116

0.008 0.995 0.0771 0.0113 0.0114

0.016 0.995 0.0766 0.0117 0.0119

0.024 0.991 0.0738 0.0124 0.0130

0.032 0.973 0.0770 0.0129 0.0139

0.040 0.953 0.0794 0.0147 0.0159

0.048 0.901 0.0936 0.0146 0.0168

0.056 0.851 0.1014 0.0171 0.0178

0.064 0.808 0.1092 0.0188 0.0207

0.072 0.764 0.1199 0.0186 0.0201

0.080 0.720 0.1193 0.0228 0.0229

0.088 0.619 0.1520 0.0289 0.0309

99
Table F.3.6 Drop Velocities: dpo : 105 um, x/d _ 100

r/x u /u G'/u v'/u w'/u

p pc p pc p pc p pc

0.000 1.000 0.236 0.0716 0.0694

0.012 0.980 0.256 0.0714 0.0714

0.024 0.87] 0.353 0.0756 0.0736

0.036 0.839 0.319 0.0698 0.0705

0.048 0.785 0.313 0.0788 0.0757

0.060 0.656 0.302 0.0684 0.0785

i00
Table F.3.7 Drop Velocities: dpo = 180 um, x/d _ I

r/x u /u u'/u v'/u w'/u

p pc p pc p pc p pc

0.0 1.000 0.040 0.037 0.037

0.1 1.001 0.039 0.037 0.036

0.2 1.001 0.038 0.037 0.035

0.3 1.003 0.038 0.037 0.037

0.4 1.005 0.041 0.037 0.038

i01
Table F.3.8 Drop Velocities: dpo = 180 um, x/d = 20

r/x _J /u u'/u v'/u w'/u ..

p pc p pc p pc p pc

0.00 I.000 0.074 0.012 0.012

0.01 0.999 0.074 0.012 0.012

0.02 0.987 0.073 0.011 0.011

0.03 0.973 0.078 0.012 0.011

0.04 0.949 0.084 0.012 0.011

0.05 0.909 0.087 0.012 0.011

0.06 0.885 0.101 0.012 0.012

0.07 0.858 0.130 0.013 0.012

0.08 0.822 0.127 0.013 0.011

0.09 0.788 0.130 0.014 0.011

0.10 0.756 0.149 0.019 0.012

0.I I 0.706 O.177 0.024 0.012

102
Table F.3.9 Drop Velocities: dpo = 180 um, x/d = 50

rlx u lu u'/u v'lu w'lu

p pc p pc p pc p pc

0.000 1.000 0.071 0.009 0.010

0.012 0.996 0.069 0.009 0.0097

0.024 0.981 0.075 0.009 0.0096

0.036 0.959 0.075 0.010 0.010

0.048 0.927 0.092 0.0]0 0.0097

0.060 0.870 0.102 0.012 0.010

0.072 0.819 0.103 0.015 0.011

0.084 0.761 0.097 0.015 0.012

0.096 0.715 0.100 ....

i03
Table F.3.10 Drop Velocities: dpo = 180 um, x/d = 100

rlx u lu u'lu v'lu w'lu

p pc p pc p pc p pc

0.000 1.000 0.089 0.016 0.015

0.012 0.983 0.091 0.015 0.016

0.024 0.966 0.095 0.015 0.015

0.036 0.919 0.107 0.016 0.016

0.048 0.870 0.116 0.017 0.018

0.060 0.778 0.120 0.018 0.019

0.072 0.694 0.128 0.022 0.021

0.084 0.585 0.144 0.027 0.023

0.096 0.470 0.167 0.030 0.025

104
F.4 Drop Number Fluxes

" _! " I!

Table F.4.1 Drop Number Fluxes (nc/n_o)

Along Axis, dpo = 105 _m

x/d Uncorrected Corrected x/d Uncorrected Corrected

1.0 1.000 1.000 20 0.177 0.190

1.5 0.943 0.945 22 0.156 0.169

2 0.929 0.932 25 0.126 0.138

3 0.853 0.859 30 0.0882 0.0987

4 0.756 0.764 35 0.0645 0.0737

5 0.683 0.693 40 0.0489 0.0570

6 0.608 0.619 45 0.0377 0.0449

7 0.541 0.553 50 0.0305 0.0372

8 0.471 0.483 60 0.0224 0.0356

9 0.442 0.455 70 0.0139 0.0300

10 0.409 0.423 80 0.00636 0.0164

12 0.351 0.365 90 0.00206 0.00656

15 0.258 0.272 100 0.000963 0.00401

17 0.223 0.237 ......

*n_o = 3769 x 106 counts/m2s. Uncorrected values are

raw data while corrected values allow for area bias.

105
Table F.4.2 Drop Number Fluxes (nc/n_o)

Along Axis, dpo = 180 _m

x/d Uncorrected Corrected x/d Uncorrected Corrected

1.0 1.000 1.000 35 0.042 0.043

1.5 0.949 0.949 40 0.033 0.034

2 0.902 0.903 45 0.025 0.026

3 0.812 0.813 50 0.0224 0.0233

4 0.749 0.751 60 0.0159 0.0170

5 0.648 0.650 70 0.0121 0.0133

6 0.584 0.586 80 0.0097 0.0108

7 0.509 0.511 90 0.0079 0.0090

8 0.459 0.461 100 0.0053 0.0061

9 0.432 0.435 110 0.0042 0.0062

10 0.327 0.329 120 0.0033 0.0069

12 0.266 0.268 130 0.0024 0.0075

15 0.195 0.197 140 0.0017 0.0056

17 0.134 0.136 150 0.0012 0.0043

20 0.1i3 0.115 160 0.00095 0.0037

22 0.097 0.099 170 0.00084 0.0036

25 0.076 0.077 180 0.00072 0.0033

30 0.055 0.056 190 0.00055 0.0029

*n_o = 1826 x 106 counts/m2s. Uncorrected values are

raw data while corrected values allow for area bias.

106
Table F.4.3 Drop Number Fluxes (n"In_), dpo = 105 _m

x/d Uncorrected Corrected r/x Uncorrected Corrected

x/d = I

0.0 I.000 -- 0.3 0.223 --

0.1 0.871 -- 0.4 0.055 --

0.2 0.567 ........

xld = 20

0.00 I.000 -- 0.05 0.131 --

0.01 0.839 -- 0.06 0.059 --

0.02 0.614 -- 0.07 0.027 --

0.03 0.400 -- 0.08 0.011 --

0.04 0.236 -- 0.09 0.0034 --

x/d = 50

0.000 1.000 I.000 0.048 0.0848 0.115

0.008 0.884 0.934 0.056 0.0449 0.0658

0.016 0.687 0.770 0.064 0.0216 0.0344

0.024 0.470 0.560 0.072 0.0106 0.0181

0.032 0.287 0.357 0.080 0.0056 0.0101

0.040 0.164 0.213 ......

x/d = I00

0.000 1.000 I.000 0.040 0.107 0.265

0.016 0.620 0.793 0.048 0.044 0.156

0.024 0.432 0.652 0.056 0.0122 0.0766

0.032 0.220 0.413 .......

*Uncorrected values are raw data while corrected values

allow for area bias.

107
Table F.4.4 Drop Number Fluxes (_"/_), dpo = 180 um

x/d Uncorrected Corrected r/x Uncorrected Corrected

x/d-- 1

0.0 1.000 -- 0.3 0.179 --

O. 1 O.790 -- O. 4 O.039 --

0.2 0.441 ........

x/d = 20

0.00 I.000 -- 0.05 O. 136 --

0.01 0.913 -- 0.06 0.069 --

0.02 0.685 -- 0.07 0.036 --

0.03 0.460 -- 0.08 0.017 --

0.04 0.263 -- 0.09 0.0078 --

x/d = 50

0.000 I.000 I.000 0.048 0.148 0.150

0.008 0.911 0.914 0.056 0.085 0.086

0.O1 6 0.796 O.801 0.064 0.043 0.043

0.024 0.611 0.617 0.072 0.021 0.021

0.032 0.414 0.418 0.080 0.0099 0.010

0.040 0.252 0.254 ......

x/d -- I00

0.000 I .000 I .000 0.040 0.180 0.337

0.008 0.879 0.912 0.048 0.088 0.200

0.016 0.683 0.776 0.056 0.049 0.120

0.024 0.484 0.607 0.064 0.018 0.048

0.032 0.304 0.457 0.072 0.008 0.023

*Uncorrected values are raw data while corrected values

allow for area bias.

108
F.5 Drop Size Distributions

Table F.5.1 Axial Variation of SMD (um)

x/d SMD x/d SMD

dno = 105 um

I 105.0 100 53.4

50 95.6 130 39.8

70 75.0 ....

dpo = 180 _m

I 180.0 100 113.5

50 161.9 130 70.1

70 138.0 ....

109
Table F.5.2 Radial Variation of SMD (pm)

dp_ = 105 um dpQ = 180 um

r/x SMD r/x SMD

x/d = 50

0.00 95.6 0.00 161.9

0.024 87.4 0.024 157.8

0.048 82.9 0.048 157.6

x/d = 100

0.00 53.4 0.00 113.5

0.024 44.3 0.024 101.8

0.048 34.6 0.048 77.7

Ii0
Table F.5.3 Drop-Size Distributions, dpo = 105 _m

Range (um) Fraction Range (um) Fraction Range (um) Fraction

x/d = 50, r/x = 0.000 x/d = 50, r/x = 0.024 x/d = 50, r/x = 0.048

66.6-74.9 0.0409 58.9-67.3 0.0962 51.5-60.1 0.0762

74.9-83.2 0.1170 67.3-75.7 0.1058 60.1-68.6 0.1333

83.2-91.5 0.1988 75.7-84.1 0.2212 68.6-77.2 0.2190

91.5-99.9 0.3216 84.1-92.5 0.2692 77.2-85.8 0.2667

99.9-108.2 0.3216 92.5-100.9 0.3079 85.8-94.4 0.1714

x/d = 100, r/x = 0.000 x/d = 100, r/x = 0.024 x/d = 100, r/x = 0.048

9.2-18.3 0.0069 9.2-18.4 0.1377 0.0-9.3 0.0769

18.3-27.5 0.1310 18.4-27.6 0.1957 9.3-18.6 0.1978

27.5-36.6 0.2897 27.1-36.8 0.2319 18.6-27.9 0.3516

36.6-45.8 0.2690 36.8-46.0 0.2391 27.9-37.2 0.1868

45.8-54.9 0.1172 46.0-55.3 0.1304 37.2-46.5 0.1538

54.9-64.1 0.0621 55.3-64.5 0.0435 46.5-55.8 0.0330

64.1-73.2 0.0621 64.5-73.7 0.0217 ....

73.2-82.4 0.0621 ........

x/d = 70, r/x = 0.000 x/d = 130, r/x = 0.000

26.5-35.3 0.0041 0-9.3 0.096

35.3-44.1 0.0617 9.3-18.6 0.144

44.1-52.9 0.1646 18.6-27.9 0.160

52.9-61.8 0.1523 27.9-37.2 0.232

61.8-70.6 0.1564 37.2-46.5 0.264

70.6-79.4 0.1687 46.5-55.8 0.104

79.4-88.2 0.1728 ....

88.2-97.1 0.1193 ....

iii
Table F.5.4 Drop Size Distributions, dpo = 180 um

Range (um) Fraction Range (_m) Fraction Range (_m) Fraction

x/d = 50, r/x = 0.000 x/d = 50, r/x = 0.024 x/d = 50, r/x = 0.048

135.0-143.2 0.0413 126.6-135.0 0.0155 128.1-136.6 0.0579

143.4-151.9 0.1157 135.0-143.4 0.1395 136.6-145.1 0.1405

151.9-160.3 0.2149 143.4-151.9 0.1938 145.1-153.7 0.2149

160.3-168.7 0.4793 151.9-160.3 0.2481 153.7-162.2 0.2397

168.7-177.2 0.1488 160.3-168.7 0.2636 162.2-170.7 0.2645

.... 168.7-177.2 0.1395 170.7-179.3 0.0826

×/d = 100, r/x = 0.000 x/d = 100, r/x = 0.024 x/d = 100, r/x = 0.048

78.9-87.7 0.0504 44.0-52.8 0.0494 17.9-26.8 0.0505

87.7-96.4 0.1513 52.6-61.6 0.0617 26.8-35.8 0.0707

96.4-105-2 0.1849 61.6-70.4 0.0247 35.8-44.7 0.0606

105.2-114.0 0.2101 70.4-79.2 0.0988 44.7-53.6 0.0707

114.0-122.7 0.2269 79.2-87.9 0.1358 53.6-62.6 0.1414

122.7-131.5 0.1092 87.9-96.7 0.2346 62.6-71.5 0.2020

131.5-140.3 0.0504 96.7-105.5 0.1235 71.5-80.4 0.1818

140.3-149.0 0.0168 105-5-114.3 0.1235 80.4-89.4 0.0909

.... 114.3-123.1 0.0494 89.4-98.3 0.0707

.... 123.1-131.9 0.0741 98.3-107.3 0.0404

.... 131.9-140.7 0.0247 107.3-116.2 0.0202

x/d = 70, r/x = 0.000 x/d = 130, r/x = 0.000

94.4-103.0 0.0081 9.1-18.3 0.0316

103.0-111.5 0.0484 18.3-27.5 0.0526

111.5-120.1 0.0645 27.5-36.6 0.0737

120.1-128.7 O.1210 36.6-45.8 0.0842

128.7-137.3 0.2500 45.8-54.9 0.1684

137.3-145.9 0.3145 54.9-64.1 0.1263

145.9-154.4 0.1452 64.1-73.2 0.2316

154.4-163.0 0.0484 73.2-84.2 0.1474

.... 84.2-91.5 0.0316

.... 91.5-100.7 0.0526

112
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117
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

NASACR-174838

4. Title and Subtitle 5. Report Date

The Structure of Dilute Combusting Sprays January 1985

6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

J-S. Shuen, A.S.P. Solomon, and G.M. Faeth None

10. Work Unit No.

9. Performing Organization Name and Address

11. Contract orGrant No.

The Pennsylvania State University NAG3-190

Mechanical Engineering Building

Uni versi ty Park, Pennsyl vani a 16802 13 Type of Report andPerioCod vered

12. Sponsoring Agency Name and Address Contractor Report

NationalAeronauticsand Space Administration 14S.ponsoringAgency Code

Washington,D.C. 20546

505-31-42

15. Supplementa_ Notes

Final report. Project Manager, Robert R. Tacina, Altitude Wind Tunnel Project

Office, NASALewis Research Center, Cleveland, Ohio 44135.

16. Abstract

An experimental and theoretical study of drop processes in a turbulent flame is

described. The experiments involved a monodisperse (105 and 180 _m initial

diameter) stream of methanol drops injected at the base of a turbulent methanefueled diffusion flame burning in still air. The following measurements were

made: mean and fluctuating phase velocities, mean drop number flux, drop-size

distributions and mean gas-phase temperatures. Measurements were compared with

predictions of two separated flow models: (I) deterministic separated flow, where

drop-turbulence interactions are ignored; and (2) stochastic separated flow,

where drop-turbulence interactions are considered using random-walk computations.

The stochastic separated flow analysis yielded best agreement with measurements,

since it provides for turbulent dispersion of drops which was important for present test conditions (and probably for most combusting sprays as well). Distinguishing the presence or absence of envelope flames around the drops, however,

was relatively unimportant for present test conditions, since the drops spent

most of their lifetime in fuel-rich regions of the flow where this distinction

is irrelevant.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Spray modeling Unclassified - unlimited

Turbulence interactions STARCategory 07

Combustor

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Penalty for Private Use, $300

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