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i

OXIDES OF NITROGEN EMISSIONS FROM THE WMBUSTION OF

MONODISPERSE LIQUID FUEL SPRAYS

by

w; Ham id Sary

Submitted in partial fulfillment of the requirements for

the degree of

Doctor of 'Philosophy

Approved by il 

Dr. Nicholas P. Cernansky

ldll^o f. ! "=^

Principal Investigator

Flu

Research Sponsored by the NASA Lewis Research Centar

through research grant NAG 3-1

Department of Mechanical Engineering and Mechanics

Drexel University, Philadelphia, PA 19104

June 1985
7

4 ABSTRACT

L, '

A study of NOX formation in a one dimensional monodisperse spray

combustion system, which alloG► id independent droplet size variation, was

conducted. Temperature, NO and NOx concentrations were measured in the

transition region, encompassing a 26-74 micron droplet size range. Emission

measurements of hydrocarbons, carbon monoxide, carbon dioxide and oxygen were

also made. The equivalence ratio was varied between 0.8 and 1.2 for the fuels

used in this study, including methanol, isopropanaol, n-heptane and n-octane.

Pyridine and pyrrole were added to n-heptane as nitrogen-containing additives

in order to simulate ^hynthetic fuels.

Results obtained tram the postflame regions using the pure fuels indicate

an optimum droplet size in the range of 43-58 microns for minimizing NOx

production. For the fuels examined, the maximum NO X reductions relative to

the small droplet size limit were about 10-20% for lean and 20-30% for

stoichiometric and rich mixtures. This behavior is attributed to droplet

interactions and the transition from diffusive to premixed type of burning.

Preflame vaporization controls the gas phase stoichiometry which has a

significant effect on the volume of the hot gases surrounding a fuel droplet,

where NOX is formed. On the other hand, the release cif fuel vapor from the

droplet to the reaction zone is influenced by droplet interactions which

reduce the volume of the hot gases and NO x production by bringing the flame

closer to the droplet surface.

For small droplets, gas phase combustion and droplet ignition are

intensified by the high preflame extent of vaporization. Much of the NOx is

formed in the hot gases surrounding the burning fuel droplets, where premixed

type of burning appears to dominate. Large droplets burn in a diffusive

fashion, due to lower droplet vaporization before the flame front and the slow

propagation of the fuel vapor emerging from the surface of the burning

droplets. However, NO x production for large droplets increases as they

achieve elevated flame temperatures due to their higher Damkohler number. At

some intermediate size, where minimum NO x is predicted, the flame temperature
and the fuel vapor concentration in the gas phase fall in between the values

observed for the small and large droplets. Under this situation, droplet

Interactions reduct the burning rate And lower NOx formation by confining its

production to a thin reaction zone. These interaction effects are also

believed to be responsible for higher CO and 02, and lower CO2 emissions.

The occurrence of the minimum NO X point at different droplet diameters

for the various fuels appears to be governed by the fuel vaporization

characteristics. This point was verified by air preheating and synthetic

oxidizer experiments.

Experiments with nitrogen-bearing additives revealed that under

stoichiometric and rich conditions, reducing the droplet size increases the

efficiency of fuel-N conversion to NO X . This observation is associated with

improved oxidation of the pyrolysis fragments of the additive by better oxygen

penetration through the droplet flame zone.

Preflame spray vaporization and NO X formation from spray combustion are

also studied analytically. Temperature and fuel, oxidizer and NO mass

fractions around the burning droplets were determined from the numerical

solution of the governing energy and species equations. A qualitative

agreement between the predicted a'nd experimental results was found.
OXIDES OF NITROGEN EMISSIONS FROM THE COMBUSTION OF

MONODISPERSE LIQUID FUEL SPRAYS

A Thesis

Submitted to the Faculty

of

Drexel University

by

Hamid Sary

in partial fulfillment of the

requirements for the degree

of 

Doctor of Philosophy

June 1985
ACKNOWLEDGEMENTS

ii

Mechanics Department, Drexel University.

zc y

W F' It is with deep appreciation that I express gratitude to my

thesis advisor, Professor Nicholas P. Cernansky for his guidance

and continuous interest throughout this effort, His patient

supervision and enthusiasm have been necessary in making this work

possible.

I am also greatful to mv thesis committee members, Professors

Bakhtier Farouk, Chung W. Lau, Arthur M. Mellor, Izak Namer and

Charles B. Weinberger, for their suggestions acid recommendations

that were essential to the improvement of phis research. Many

thanks are due to Professors Richard S. Cohen and Ahtisham A.

Niaami„ and Dr. Surendra Singh for their thoughtful comments and

valuable conversations. Thanks are also given to many of my

fellow graduate students and collegues, in particular, to Richard

D. Wilk, for numerous informative and helpful discussions. The

assistance of the staff of the Mechanical Engineering Labs,

Altimus ' Seneca, Jake Stineman, Henry Mocarsky and Louis Haas, in

the design,, fabrication and trouble shooting of the experimental

setup is greatly appreciated.

This work was sponsored by the NASA Lewis Research Center

through research grant NAG 3 -1 to the Mechanical Engineering and
4: ^

Finally, I would like to thank my parents for theIr support,

encouragement and personal sacrifice, to whom I will always remain

indebted.
, iv

fi

t

^t

^i

TABLE OF CONTENTS

Paste

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

LIST OF TABLES . . . . . . . . . . . . . . . . xi

NOMENCLATURE : . . • . . . . . . . . . xii

ABSTRACT . . . . . . . . . . . . . . . . ., . xv

CHAPTEER 1 Introduction. . . . . . . . . 1

CHAPTER 2 Background and Literature Review. . . . . „ 4

2.1 Liquid Fuel. Spray Combustion. . . . . . 4

2.2 Transition Region Effects . . . . . . . 7

2.3 NN Formation in Spray Combustion Systems 8

CHAPTER 3 Experimental Set-Up acid Procedures. . . . . . . . 11

" 3.1 Introduction. . . . . . . . . . . . . . . . . 11

3.2 Spray Combustion Facility . . . . . . . . . . 11

- 3.2.1 Monodisperse Spray Generation System. . 11

3.2.2 Fuel and Air Flow System. . . . . . . . 12

3.2.3 Flame Holders . . . . . . . . . . . . . 14

3.2.4 Other Design Considerations . . . . . . 15

3.3 Sampling and Analytical Instrumentation . . . 15

3.3.1 NOX Measurement System. . 15

3.3.2 'Temperature Measurement System. . . 18

a

4=

CHAPTER 4 Experimental, Results and Discussion . . 20

4.1 Introduction. . . . . . . . . 20

4.2 System Verification . . . 20

4.2.1 Monodispersi, on Range. . 20

4.2.2 Radial Temperature and NOX Mapping. 21

s 
ing and Measurements of Exhaust

(UHC, CO, CO2 , and 02 ). . . . . . 9 . IL 10

A.2 Fuel 'Prevaporizing System . . . . . . . . . 109

V

' A. 3 Fuel. Type and Stoichiometry . . . . . . . 26

Air Preheating and Prevaporization. . . . . . 32

i Synthetic Oxidizers . . . . . . . . . . . . 38

i Fuel-Nitrogen Additives . , , . . . . . . . . 40

1 NOX Structure in Flame. . . . . . , . . . . 44

4.7.1 Pure (Nitrogen Free) Fuels.. . . . . 44

4.7.2 Nitrogen-Containing Fuels . . . . . . . 54

ilytical Studies. . . . . . . . . . . . . . . . 161

Introduct^in . . . . . . . . . . . . . . . 61

Spray Vaporization. . , . . . . . . . . . 62

I Spray Combustion. . . . . . . . . 68

► Droplet Interactions. . . . 72

i Array Geometry. . . . . . . . 74

i NO Kinetics . . . . . . . . . . . . . 77

' Representative Results. . . . . . . . . 0 . . 77

5.7.1 Preflame Spray Vaporization . . . . . 77

5.7.2 Burning Rate Correction Factor. . . . . 85

5.7.3 Spray Combustion and NO formation . . . 87

CHAPTER 6 Conclusions and Recommendations . . . . . . . . . 98

6.1 Conclusions . . . . . . . . . . . . . . . . . 98

6.2 Recommendations for future work . . . . . . . 100

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

. 102

APPENDIX A Supporting Experimental Facility. . . . . . . . 109

A.1 Introduction. . . . . . . . . . . . . 109
vi

Y

• w.rcJl.ir

APPENDIX B Complementary Results . . . . .

B.1 Introduction. . . . . . . . . . . . . . .

B.2 Axial N4, N0. , and Te.n.perature Profiles for,

Fuel-N .Addi , tyves.

. . . , . . . . 112

B.3 Exhaust Emission Measurements . . . . . 117

APPENDIX C Thermophysical Property Calculations. . . . . . 122

APPENDIX D Temperature Corrections . . . . . . . . . 124

APPENDIX E Computer Programs . . . . . . . . . . . 128

E.1 Droplet Interactions. . . . . . . . . . . . 128

E.2 Spray Vaporization. . . . . . . . . . . . 131

E.3 Spray CombuslJon. . . . . . . . . . 139

E.4 Sample Input Data . . . . . . . -150

VITA . . . . . 151
Vii

LIST OF FIGURES

Figure Page

3,1 One4imens onal spray combustion facility.. . . . . . 13

3.2 Temperature and gas s,%mpling combination probes.. . . 16

3. 3 {Dater cooled ges sampling probe. . . . . . . . . . 17

4,1 Monodispersion ranges o g single orifice aerosol

generation system.. . . . , 22

4.2 Microscopic photographs of droplet impactions on

glass slides . . . . . . . . . . . . . . . . . . . . . 23

4.3 Temperatures traverses across the burner.. . . . . . 24

4.4 NOx traverjes across the burner,. . . . . . . . . 25

4.5 Droplet size effect on post flame temperature, NO and

NO% , for isopropanol at various equivalence ratios.

o - NO; ! - %; p - Temperature. . . . . . . . . . . 27

4.6 Droplet size effect on post flame temperature, NO and

NOx, for methanol at various equivalence ratios.

o - NO; 0^ - NOx ; Q - Temperature. . . . . . . . . . . 28

4.7 Droplet size effect on post flame temperature, NO and

NOX , for n-heptane at various equivalence ratios.

o - NO; 9 - NOX ; 4 - Temperature,,, . . . . . .

. . „ . 29

4.8 Droplet size effect on post flame temperature, NO and

NO X , for n-octane at various equivalence ratios.

o - NO; • - NOx ; o - Temp rature. . . . . . . . , . 30

4.9 Air preheating and droplet size effects on post flame

temperature, NO and NO X , for methanol at ^i ?" 1.0.

o - NO; 0 - NOX ; p - Temperature. . . . . . . . . . . 33

4.10 Air preheating and droplet size effects on post flame

temperature, NO and: NO X , for isopropanoll at 1.0.

o - NO; 0 - NOX ; a - Temperature. . . „ . . . . . . 34

f
viii

,1' 

Se

4.11 Aix preheating and droplet size effecte on post flame

temperature, NO and NOX, for n-heptane at 1606

o - NO; - NOx; p - Temperature. . . . . . . . . . . 35

4.12 Air preheating and droplet size effects on post flame

tee, ;i3rature, NO and % v for n-octane at 1.0.

o - NO; ! - NN - Temperature. • . • . . . . . . . 36

4.13 Synthetic oxidizer and droplet size effects on post

flame NO, NOX and temperature for n-heptane at

• 1.0. Flame holder X.D. (mm); a - 14.3;

band c -12.7.. . . . . . . • . . . . . . . . . • . . 39

4.14 Effect of fuel-N content and droplet size on NO and

NOX for n-heptane doped with pyridine.

0-0- 0.85; o -(^ - 1.0; A-0- 1.2.. . . . . 41

4.15 Effect of droplet size on NO, NOX and temperature for

n-heptane doped with pyrrole (1%N by weight).

o - NO; 0 - NOX ; & - Temperature. . . . . . . . . • 42

4.16 Centerline NO, NOx and temperature profiles for

combustion of methanol. at 0 - 1.0. o 01 * - D -

37.0 pm;C3,M,x - D - 57.2 pm; p,A,+ D - 69.6 pm.. . 46

4.17 Centerline NO, NOX and temperature profiles for

combustion of isopropanol at b. 1.0' • o , •,* - D

37.0 pm; Cj M, x - D - 54.5 pm; Q,A,+ - 'D - 69.6 pm.. . 47

4.18 Centerline NO, NOX and temperature profiles for

combustion of n-heptane at 40. 1.0. o , •,* - D -

37.0 pm; Cl ,l► x - D - 49.5 pm; a ,♦,+ - D • 67.2 pm.. . 48

4.19 Centerline NO, NOX and temperature profiles for

combustion of n-octane at 4) . 1.0. o , •,* - D =

37.0 pm; 0,11,x - D . 43.3 pm; p n - 57.2 pm, . . 49

d

4.20 Sampling probe effects on centerline measurements of

NO and NOX for 37 pm n-octane droplets at - 0.85.

o , 0 - uncooled probe; O,• - water cooled probe. 50

4.21 Sampling probe effects on centerline measurements of

,. NO and NOX for 37 pm n-octane droplets at 0 - 1.0.

o , 0 - uncooled probe ;C3,11 - water cooled probe. . . 52

4.22 Sampling probe effects on centerline measurements of,

NO and NOX for 37 pm n-octane droplets at - 1.2.

o , • - uncooled probe; p ,n - water cooled probe. . . 52

° 4.23 Effect of synthetic oxidizers on centerline NO, NOX

and temperature for 37 pm n-heptane droplets 7? at 1.0. . . . . • . • • . . 55
ix

Page

Centerline NO, NOX and temperature profiles for

n-heptane doped with pyridine (1x N by weight).

o,•,*-D 37.0 pm; C7./jx-D a 49.5 pm;

A D 69.6 pm. . . . . . . . . 56

Centerline NO, NO X and temperature profiles for 37

pm n-heptane droplets doped with pyridine (1x N by

weight). (3,I ► x -4)- 0,85; a0At + - ;1.2. . . . . 57

Monodisperse droplet arrangement used in the

numerical calculations. . . . . . . . . . . . . . . • 6

5.2 Calculated evaporation characteristics of a 50 pm

diameter droplet in o.. monod sperse spray of methanol.

• - Droplet diameter; ♦ - Droplet temperature;

W Gas phase temperature; x - Mass transfer number;

+ - Extent of prevaporiration. Dotted lines

represent adiabatic vaporization. . . . . . . . . . . 79

5.3 Calculated evaporation characteristics of a 50 pm

diameter droplet in a monodi.sperse array of n-octane:

• - Droplet diameter; ♦ - Droplet temperature;

n - Gas phase temperature; x - Mass transfer number;

+ - Extent of prevaporzation. Dotted lines

represent adiabatic vaporization. .f. . . . . . . . . 80

5.4 Calculated temperatures for early stage vaporization

of monodisperse methanol and n-octane aerosols.

• - Droplet temperature; # - Droplet surface

temperature; n - Gas phase temperature.. . . . . . . . 81

5.5 Comparison of calculated and measured aerosol

temperatures. . . . . . . . . . . . . . . . . . . . . 84

5.6 Droplet configuration for a 55 droplet array. 88

5.7 Calculated burning rate correction factor as a

function of droplet spacing for various numbers of

interacting droplets. Data points represent the

calculated results based on droplet superposition

ptocedure. Solid lines are determined by the array

superposition method.. . . . . . . . . . . . . . . . 89

5.8 Evolution of temperature and mass fraction profiles

for a 27,.0 pm droplet in a monodisperse spray of

n-octane at 1.0 and Eo 0.61. . . . . . . . . . 91

5.9 Evolution of temperature and mass fraction profiles

for a 33.2 pm droplet in a monod' ., , „arse spray of

n,-octane at (0 = 1.0 and E6= 0.5b. , . . . . . . . . 92

4.24

4.25

5.1
5

k

Ij

^x

:^ f

fi>I «+

Rd

I

Palle

5.10 Evolution of temperature and mass fraction profiles

for a 47.7 pm droplet in a monodisperse spray of

n-octane at Ow 1.0 and Eo= 0.43. . . . . . . . . . 93

5.11 Comparison of measured and predicted NOX

concentrations at different droplet diameters and air

preheat temperatures for n-octane sprays at (^ = 1.0. 96

B.1 Centerline NO, NOX and temperature profiles for

n-heptaner doped with pyridine (0.1% N by weight).

o , 0,* - D 37.0 pun; C3 A, x - D = 49.5 pm;

p ,A,+ - D 69.6 pm., . . . . . . . . . . . . . . . 112

B.2 Centerline NO, NOX and temperature profiles for

n-heptane doped with pyridine (0.5% N by weight).

o ,•,* D=37.0 pm;pA,x-D=49.5 pm;

o,A,+ - D = '9.6 pm., . . . . . . . . . . . . . . . 113

B.3 Centerline NO, NOX and temperature profiles for 37pm

n-heptane droplets. 0,0,x -(0= 0.85; a „►,Y -O= 1.2. 114

B.4 ' Centerline 110, Nox and temperature profiles for 37 pm

n-heptane droplets doped with pyridine (0.1% N by

weight). 0 A,x -0= 0.85; A,A,+ - 1.2. . . . . . 115

B.5 Centerline NO, NOX and temperature profiles for 37 pm

n-heptane droplets doped with pyridine (0.5% N by

weight) . p ,/, x -4)- 0.85; p A, - rh = 1.2 . . . . . . 116

8.6 Effect of equivalence ratio on centerline CO, CO Z , OZ

and UHC profiles for 37 pm n-octane droplets.

0-- CO; n - CO2 ; 0- 02 ;A- UHC .. . . . . . . . . . . . 118

B.7 Effect of equivalence ratio on centerline Co, Cut , 02

and UHC profiles for 37 pm n-octane droplets.

O - CO ; n - COZ ; O - 0z; • - UHC. . 4 . . . . . . . . . 119

B.8 Droplet size effect on postflame CO, COI , OZ and UHC,

for n-octane at 0 = 1.0.

0 - CO ; 9 - COZ; O - Oz ♦ - UHC . . . . . . . . . . . . 121

D.1 Effect of gas sampling probe and thermocouple wire

diameter on flame temperature measurements.

o - With; 0 - Without the gas sampling probe. . . . . 126

e
LIST OF TABLES,

Table Page

4.1 Conversion efficiency of fuel-N to NO X from the

combustion of 37 pm n-heptane droplets doped with

pyridine . . . . . . . . . . . . . . . . . . . . . 45

4.2 Percent NOx consumed in the post flame gases of

37 pm n-heptane droplets doped with pyridine. . . . 59

5.1 Computed parameters for preflrme spray vaporization

of 50 μm droplets at various a:r preheat

temperatures. Droplet temperature is initially at

24"c . . . . . . . . . . . . . . . . . . . . . . . . 83

5.2 Computed burning rate correction factor for three

monodisperse arrays of droplets with X a 40.. 0 0 0 86

xi
xii

aF

NOMENCLATURE

A - pre-exponential collision frequency ,factor

D - mass transfer number

C 1

 - defined by equation (5-15)

CJAI = defined by equation (5-16)

C D

 = drag coefficient

Cp - Specific heat at, constant pressure

d = burner diameter in terms of droplet radius

D = droplet diameter

JO = mass diffusiv-ty

AH - heat of reaction

E = activation energy

f n• disturbance frequency

h = burner height in terms of droplet radius

i = radial index

j - species index

k = droplet index

K - thermal conductivity

R - droplet index

L = latent heat of vaporization

- center-to-center droplet spacing in terms of droplet radius

m - mass

m - vaporization/burning rate of fuel spray
xiii

M.

1[ • burning rate of a single fuel droplet

N - number of droplets

N r

number of radial meshes

N° = number of species

P = pressure

Q fuel flow rate

r = radial coordinate

rs = droplet radius

rr = normalized radial coordinate (r/r$)

Rep = Reynolds number„ (P U' D/ U)

n

R = Universal gas constant

S surface area of droplet

t time

T temperature

U droplet velocity

U' relative velocity between a droplet and gas phase

v radial velocity

w source term

W = molecular weight

X = mole fraction

Y = mass fracti^^n

Subscripts

b = boiling point

f = liquid

F = fuel vapor

g = gas phase

VV

^ s 
S

d

t xiv

is

i

Fp .'

Y

0 - oxidizer

o - initial

s surface

0o ambient

Greek Symbols bols

of - thermal diffusivity

d • droplet interaction matrix

- defined by equation (5-29)

X - defined by equation (5-30)

e . fraction of fusel droplet vaporized

- burning rate correction factor,

μ - absolute viscosity

= stoichiometrir molar coefficient

density

- equivalence ratio, (Fuel/Ox) /(Fuel/Ox)

actual staichiometric

IP - velocity potential defined by equation (5-51) i

G
XV

^1

Yt

ABSTRACT

OXIDES OF NITROGEN EMISSIONS FROM THE COMBUSTION OF

MONODISPERSE LIQUID FUEL SPRAYS

Hamid Sary

and

Nicholas P. Cernansky

A study of NO

x 

formation in a one dimensional mo,nodisperse

spray combustion system, which allowed independent droplet size

variation, was conducted!. Temperature, NO and NOx concentrations

were measured in the transition region, encompassing a 26-74

micron droplet size range. Emission measurements of hydrocarbons,

carbon monoxide, carbon dioxide and oxygen were also made. The

equivalence ratio was varied between 0.8 and 1.2 for the fuels

used in this study, including methanol, isopropanol, n-heptane and

n-octane. Pyridine and pyrrole were added to n-heptane as

nitrogen-containing additives in order to simulate synthetic

fuels.

Results obtained from the postflame regions using the pure

fuels indicate an optimum droplet size in the range of 43-58

microns for minimizing NO, production. For the fuels examined,

the maximum NO, reductions relative to the small droplet size
F

xv

limit were about 10-20% for lean and 20-30% for stoichiometric and

rich mixtures. This behavior is attributed to droplet

interactions and the transition from diffusive to premixed type of

burning. Preflame vaporization controls the gas-phase

stoichiometry which has a significant effect on the volume of the

'. hot gases surrounding a fuel droplet, where NQA is formed. On the

r

other hand, the release of fuel vapor from the droplet to the

reaction zone is influenced by droplet interactions which reduce

the volume of the hot gases and NO production by bringing the

X

flame closer to the droplet surface.

For small droplets, gas phase combustion and droplet ignition

are intensified by the high preflame extent of vaporization. Much

of the NOx is formed in the hot gases surrounding the burning fuel

droplets, where premixed type of burning appears to dominate.

Large droplets burn in a diffusive fashion, due to lower droplet

vaporization before the flame front and the slow propagation of

the fuel vapor emerging from the surface of the burning droplets.

However, NO production for large droplets increases as they

achieve elevated flame temperatures due to their higher Damkohler

number. At some intermediate size, where minimum NOx is

predicted, the flame temperature and the fuel vapor concentration

in the gas phase fall in between the values observed for the small

and large droplets. Under this situation, droplet interactions

lute the burning rate and lower NOX formation by confining its 

)duction to a thin reaction zone. These interaction effects are

=_o believed to be responsible for higher CO and 0 , and lower CO 2 2

Cssions.
Xvii

The occurrence of the minimum NO x point at different droplet

diameters for the various fuels appears to be governed by the fuel

vaporization characteristics. This point was verified by air

preheating and synthetic oxidizer experiments. ,

Experiments with nitrogen-bearing additives revealed that

u0 it stoichiometric and rich conditions, reducing the droplet

size increases the efficiency of fuel-N conversion to NO X . This

observation is associated with improved oxidation of the pyrolysis

fragments of the additive by better oxygen penetration through the

droplet flame zone.

Pr,eflame spray vaporization and NO X formation from spray

combustion were also studied analytically. Temperature and fuel

oxidizer and NO mass fractions around the burning droplets were

determined from the numerical solution of the governing energy and

species equations. A qualitative agreement between the predicted

and experimental results was found.

0

i
1

CHAPTER 1

V^ Introduction

Based on energy consumption figures published in 1982

(Gustaferro, 1982), combustion of liquid hydrocarbon fuels

constitutes 47% of the total energy usage in the United. States.

Despite the increasing contributions of other forms of energy such

as nuclear-, solar, and geothermal, our energy systems rely heavily

upon the supply of fossil fuels. The forecast predicts that the

combustion of liquid fuels will remain as the dominant source of

power generation for years to come. Another intriguing fact is

that about 42 percent of the liquid fuel is consumed in sprays.

The ease in storage, handling, and atomization of liquid fuel, has

made: spray combustion the driving force in large scale stationary

gas turbines and boilers, as well as in air and some ground

transportation vehicles.

Because of the wide use of fuel spray combustion, the

efficiency and pollutant formation from such applications have

become of major concern to both government and private industry.

Although there have been many analytical studies to characterize

the combustion of fuel sprays, in most cases our knowledge is

t

based on empirical relationships (obtained from experimental

r ^?

results), which are often scale dependent. As a consequence,

9- .
i

^

y.

r

2

w

there is still, a lack of understanding of the most fundamental

processes tha', : occur during the combustion of fuel sprays. Most

of the difficulty is associated with simultaneous occurrence of

complex physical and chemical processes which snake the ,formulation

of a dec-riptive model of spray burning a strenuous task.

Recently, a number of extensive reviews (Williams, 1973; Faeth,

1979; Gh gier, 1983; Sirigoano, 1983) have discussed the state of

the art in the area of liquid fuel spray combustion and have also

suggested future directions for experimental and analytical

developments.

Oxides of nitrogen are among the major pollutants emitted from

combustion sources. Ire spray combustion, NO (NO+NO 2 ) emission

levels have been found to be influenced by the fuel spray

characteristics. While some researchers believe in a droplet size

effect, others have attributed their observations to aerodynamic

and mixing effects. Unfortunately, due to the operational

inflexibilities in their experimental systems, the importance of

the individual factors could not be distinguished. For instance,

change of droplet size often required substantial variations in

fuel and air flow rates which may have influenced the combustion

processes. Also, the related analytical studies have deviated

from modeling the physical, system by limiting their attention to

the combustion of single droplets. This study was undertaken to

resolve some of the contradictions by isolating the important

parameters that could lead to lower NO formation.

A well-characterized spray combustion facility was used to

simulate some of the basic processes that occur in practical
3

combustors such as diesel enginca or gas turbines. The

experimental variables include droplet size, sto chiometry, fuel

type, oxidizer composition, etc. Oxideo of nitrogen and

temperature constitute the major portion of the experimental

measurements made in this study.

Experimental results that are presented for a range of

operating conditions indicate an optimum droplet size for

minimizing NO production. Droplet interactions and transition

from diffusive to premixed, type of burning are considered to be

responsible for the observed behavior. This point has also been

examined through additional measurements and analytical

calculations. Numerical predictions are compared with the

experimental results and possible refinements to the model are

discussed.

Chapter 2 includes a review of some of the previous work in

the area of spray combustion and pollutant formation. The

experimental facility and measurements are reported in Chapters 3

and 4, respectively. The analytical calculations and predictions

are presented in Chapter S. Finally, the conclusions of the study

and recommendation for future work are given in Chapter 6.
H

CHAPTER 2

Background and. Literature Review

As noted, a number of extensive reviews dealing with fuel

spray combustion have appeared in the literature (Williams, 1973;

Faeth, 1979; Chi.ger, 1983; Sirignano, 1983). No attempt is made

to duplicate or summarize these landmark efforts here. Instead,

only the previous work particularly germane to the present study

is reviewed in this chapter. The three major areas covered are

liquid fuel spray combustion, trauAtion region phenomena and NOx

formation. Some of the specific topics such as droplet

interactions and NO formation mechanisms for fuels with

chemically bound nitrogen are examined more closely along with the

relevant findings of this study, in later chapters.

2.1 Liquid Fuel Spray Combustion

The most fundamental aspect of spray combustion inv, lves the

burning of single fuel droplets. Experiments with droplets

suspended from filaments (codsave, 1953), porous spheres fed by

liquid fuel (Spalding, 1953), freely falling droplets (Kumagai and

Isoda, 1956), and dilute sprays (Bolt and Boyle. 1956) have shown

>= that the surface regression rate of a fuel droplet during

;^' evaporation or combustion varies linearly with time and is
governed by the "D2 law". For isolated droplets, theoretical.

calculations relate this rate to the droplet size, fuel/ambient

gas composition, local temperature, pressure, and the relative

velocity between the fuel droplet and the gas phase. Excellent

agreemeit has been found between the physical model and the

experimental results.

Development of a chemical model for predicting the

concentration of the combustion products requires consideration of

heat, mass, and momentum transfer in addition to a knowledge of

the major chemical reactions. Certain assumptions, including

single fuel droplet, spherical symmetry, equal thermal and

molecular diffusivities, and a one step fuel oxidation reaction,

are commonly made to simplify the analysis. In spite of the

simplifications, the problem remains complex and numerical

treatment becomes necessary. One of the first analyses of this

type was done by Lorell et al. (1956) who determined the flame

structure around a single ethanol droplet under steady state

conditions. In their analysis, the flame temperature and its

thickness were found to be sensitive to the chemical, reaction

rates. When the reactions become infinitely fast, the reaction

zone reduces to a flame ,shell of infiitA.tesmal thickness. In this

situation, temperature and concentration profiles as well as flame

location can be determined explicitly (Williams, 1965). Unsteady

combustion of a single fuel droplet placed in a hot and reactive

environment was numerically investigated by Botros et al. (1980).

Their study showed that diffusional or premixed type of burning.

fir` depends on the fuel concentration in the droplet environment. In
6

contrast with the p2 law predictions, they demonstrated an

unsteady flame :front relative to the receding droplet radius.

New complications arise when one attempts to characterize the

behavior of fuel sprays. For instance, droplet size distribution

and air flow patterns require special consider; ;ions due to their

F,* effects on spray combustion (Beer and Chigier, 1983). Spray

vaporization results in fuel enrichment and cooling of the gas

phase (Law, 1977; Rao and Lefebvre, 1981) which can have

reign{ficant effects on ignition and burning of the droplets.

An individual droplet in a spray has to compete with its

neighbors for the available oxygen. This competition becomes

stronger for smaller droplet spacings and leads to an increase in

the droplet lifetime compared to that of an isolated droplet with

the same diameter.

Kanevsky (1956) showed that for a stationary array of nine

droplets, the burning rate for the center droplet reduced when the

droplet flame boundaries merged at decreased droplet spacings.

Similar results have also been obtained by others (Muruzzaman et

p11., 1971; Miyasaka aPA Law; 1981; Sangiovanni and Labowsky, 1982;

Xiong et al., 1985) using linear arrays of monodisperse fuel

droplets.

The theoretical work of Labowsky (1976-1980), Umemura et al.

(1981a,1981b), and Marberry gt al. (1984), assuming a quasi-steady

mass flux transport model, show that the evaporation rates,of

interacting droplets decrease when the droplet spacing is reduced.

Their calculations indicate that the spray evaporation rate can hi

determined by applying a correction factor to the single droplet
7

model which is only dependent of the array geometry.

Chiu 21 gl. (1977,1983) have identified four classes of sprays

that exhibit external sheeth, external group, internal group, and

single droplet modes of combustion. These regimes are separated

by a group combustion number which is defined as.the ratio of the

heat transfer in the gas phase to the heal transfer between the

gas and the liquid phase. In a recent study, Bellan and Cuffel

(19"3) presented a spray evaporation model in which the

interacting droplets were separated by spheres of influence, and

each droplet in the spray evaporated inside a finite surroundings.

Their predicted results show that the evaporation of interacting

droplets cannot be described by the D2 law over the entire droplet

lifetime.

2.2 Transition Region Effects

Another point of interest in spray combustion is the behavior

of spray systems in the "transition r1 ;; lon". In this region,

which covers a range of 15-80 μm droplet: diameter, the local

conditions around the droplets are influenced by their size and

spacings. Fcr these ,sprays, the dominance of heterogeneous or

homogeneous type of Turning depends on the amount of

prevaporization before the flame and ''^, strength of droplet

interactions in the flame. Such factors have been determined to

be responsible for a number of interesting and important

observations including increased burning velocities

a

(Polymeropoulos and Das, 1975; Hayashi et al., 1976;

Polymeropoulos, 1984), broadened flammability limits (Burgoyne and

I

7

r y.^
8

Cohen, 1954; Hayashi et al., 1981), lower ignition energies (Chan

and Polymeropoulos, 1981), and reduced NO emissions (Nizami et

x

a1., 1978-82). These findings are of significant value for the

design and development of high efficiency and low emission spray

r

combustors.

2.3 NO Formation in Spray Combustion Systems

x

Prediction of NO emissions from spray combustion sources by

isolating the contributing factors has been the subject of many

investigations. Nitric oxide formation in the vicinity of a

` diffusion flame around a single droplet has been analytically

treated by Kesten (1972) and Bracco (1973). The former study

dealt with transient NO formation, assuming quasi-steady droplet

combustion and an infinitely fast fuel oxidation reaction, while

in the latter case, steady state droplet combustion at a finite

r.

5 reaction rate was considered. Both studies showed that the NO

4

production per mass of fuel (Emission Index) increases with,

increasing droplet diameter. Kesten also demonstrated that under 

certain constraints (residence time equal to the droplet lifetime

and near stoichiometric values), the NO emission index for

homogeneous, gas phase combustion can be more significant than that

from the droplet combustion.

Exit plane measurements from a variety of experimental and

practical combustion systems have also indicated the effects of

droplet size and spray characteristics on NO emissions. 

I t X 

Increased NO emissions with increasing Sauter Mean Diameter (SMD)

have been measured from a marine gas turbine engine (Opdyke,

AY
9

1983). Mellor and co-workers (1976, 1980) showed that the NO

X

emissions from a gas turbine combustor can be correlated to the

characteristic times for droplet evaporation, mixing, and chemical

reactions. In a different study using a research gas turbine

combustor, Nicolls et al. (1980) reported a decrease in the NO 

r levels when the droplet size was increased from 10 to 57 microns

at a constant residence time.

Murphy and Borman (1979) evaluated the contribution of droplet

bu r ning to the total NO formed in their laminar mist flame.

Their result indicated higher NO emissions for larger droplets.

With a monodisperse fuel spray burning in an aerodynamically

stabilized flame inside a combustion tunnel, Nizami and Cernansky

(1978-1982) showed the existence of an optimum droplet diameter

(around 50 μm) for minimum NOx production.

Combustion of fuels which contain chemically bound nitrogen

contributes to additional NO emissions over what is formed from

atmospheric nitrogen. Unfortunately, very little is known about

the effect of droplet diameter on fuel-N conversion to NO

Perhaps the only qualitative study in this area was done by

Appleton and Heywood (1973) who showed a strong influence of the

degree of atomization and fuel/air mixing on the conversion

efficiency. In a similar study, Foster and Keck (1980) reported

significant levels of hydrogen cyanide in fuel-rich turbulent

diffusion flames as far as five burner diameters downstream of a

fuel atomizer nozzle. Increasing atomization pressure led to

intense mixing and resulted in major reductions in HCN and a

moderate rise in NO concentrations. Crowhurst and Simmons (1985a)

0
10

utilized a hollow sintered cylinder burner for a structural

examination of methane-acetonitrile-argon diffusion flames burning

in a stream of oxygen and argon. They concluded that nitric oxide

forms primarily on the oxygen side of the main reaction zone, with

some of the NO diffusing back into the pyrolysis region of the

flame and reacting with the nitrogenous radicals to form molecular

nitrogen.

Most mechanistic studies have concentrated on prevaporized and

premixed fuel,/air mixtures doped with a nitrogen containing

L compound. Overall, the NOx formation reactions from fuel-N

`I involve the oxidation of the pyrolysis fragments of the nitrogen

•

LL<< additive. Such mechanisms are affected by the flame stoichiometry

and have been discussed by Fenimore (1976a, 1976b), Haynes

(1977a), Crowhurst and Simmons (1983, 1985a, 1985b), Dasch and

Blint (1984), and others. Previous work of Fenimore (1976a),

Foster and Keck (1980), Sapre and Quader (1983) and Chen and Malte

(1.984), have shown little or no effect of the type of doping

compound on NOx yield. 
11

CHAPTER 3

Experimental Set-Up and Procedures

3.1 Introduction

In this chapter the basic combustion facility and the NOx and

temperature measurement systems are described. The operating

conditions and the actual measurements are discussed in Chapter 4.

Other instrumentation including the exhaust analyzers and the fuel

vaporizing system are specified in Appendix A.

3.2 Spray Combustion Facility

3.2.1 Monodisperse Spray Generation System

x

A Berglund-Liu Vibrating Orifice Monodisperse Aerosol

Generator, Model 3050 ( Berglund and Liu, 1973), is used to supply

a monosized spray of droplets to the combustion facility. This

generator has been employed successfully in other monodisperse

i

spray combustion studies ( Nizami et al., 1978-1982; Koshland and

Bowman, 1933, 1985).

Monodisperse droplet generation is achieved by applyin

k periodic disturbances to a piezoelectric ceramic which exer

mechanics], vibrations to a liquid jet emerging from an orifice

plate. The oscillation frequency is applied from a function 

Ja generator (Hewlett Packard Model 3310A). The perturbed jet then

^ 
12

breaks up into discrete droplets with a standard deviation of

approximately 1% of the mean diameter. Since one droplet is

generated per cycle cI disturbance, the droplet diameter can, be

calculated iron the liquid feed rate ( Q) and the, frequency of

1

disturbance ( f) and is given by ; D-(6Q/nf)/3. Thus, droplet size

can be varied by changing the frequency or the fuel flow rate.

Although the actual orifice size is not used in the

calculation of droplet diameter, an orifice plate is only capable

of providing monosized droplets within a relatively narrow range.

However, the monodispersion range can be extended easily by using

a set of orifice plates with various orifice diameters.

3.2.2 Fuel and Air Flow Systems

A schematic of the experimental facility is shown in Figure

3.1. A high infusion syringe pump ( Harvard Apparatus Model 901)

supplies liquid fuel to the aerosol generator. Air is supplied at

a regulated pressure of 35 psig from the house air compressor.

The stream of uniform droplets emerging from the orifice plate

is subjected to a turbulent jet of dispersion air to prevent

coagulation. A secondary flow of dilution air is also added to

achieve the desired stoichiometr?. For minimum fluctuations in

the flow rates, the air flows are adjusted by electronic flow

controllers (Tylan Model FC-260), and monitored by Mass Flow

meters ( Hastings Model ALL-5R).

A tapered baffle plate with 3 cm I . D. is positioned at 2 cm

above the droplet generator to improve the mixing of the dilution

air with the dispersed aerosol. The air /fuel aerosol then passes
13

o Gas Analyzers

pyrex Chimney (26.7cm X

Screen 3.2 cm LD)

t

Dispersed Droplet

Cooling Jacket

Water in —"C

Adjustable

Upper Housing ^^

Lower

Housing

Baffle Plate

Droplet

Generator

Dilution '

AC Signal

Generator

Air Dispersion Drain

Plug Syringe Pump

(Liquid Feed)

Figure 3.1. One-Dimensional spray combustion facility.

F

23 cm.
14

through a transition piece with smooth curvatures designed to

minimize any recirculation. Above the transition piece are flow

reducing sections which direct the laminarized aerosol, to a flame

holder where the monodisperse fuel spray is burned inside a screen

stabilized one dimensional flame. The flame is surrounded by a

long Pyrex tube to avoid outside air entrainment.

3.2.3 Flame Holders

In order to maintain one dimensional and stable flames for all

equivalence ratios, a series of 40x40 mesh stainless steel screen

flame holders (0.25 mm wire diameter) with matching flow reducing

sections were designed and fabricated. The wire meshes block 50%

of the area. In the absence of a flame, the fraction of droplets

that survive the screen flame holder was determined using a dual

beam He-Ne laser operated in the back scatter mode. By traversing i

the focal volume across the burner, a count rate of the droplets

was determined both with and without the screen in place. The

measurements indicate that the percentage of droplets which

ii

survive impaction on the screen are 37 and 24% for the 37 and 70

pm droplets, respectively. In the presence of a flame, those

droplets which do not make it through the screen and agglomerate

on the screen wires will flash evaporate and add to the vapor

phase in the fuel aerosol entering the flame. The flame holders

have exit diameters of 9.5, 12.7, 14.3, and 17 mm and are used for

equivalence ratios between 0.8 and 1.2. Both the flame holder and

the flow reducing section are water cooled to prevent uncontrolled

droplet vaporization.
15

3.2.4 Other Design Considerations

The design of the spray burner facility allows for adjustment

in the burner height from 16-23 cm above the orifice plate. A

burner height of 17 . 8 cm was selected experimentally based on the

aerodynamics of the dispersed aerosol. Below this optimum burner

height, the fuel spray jet is not completely spread and diffused,

resulting in a nonuniform velocity and fuel/air concentration at

the screen, as indicated by the shape and luminosit y of the flame.

Above this optimum height, a significant number of droplets begin

to settle out and accumulate on the droplet generator, leaving

them unburnt. Thus, the burner height is fixed by these practical

considerations.

3.3 Sampling and Analytical Instrumentation

3.3.1 NOX Measurement System

Nitric oxide and total NO X are collected using an uncooled

aerodynamic stainless steel sampling probe with an orifice

diameter of 0.3 mm as shown in Figure 3.2. For comparative

studies of the effect of sampling probes on NO X measurements, a

water cooled probe having an orifice size of 0 . 25 mm ( Figure 3.3)

is used. The probe is cooled to 50 9C during all measurements.

The gases are sampled at a line pressure of 80 torr to prevent

water condensation in the sampling line. Initially, the probes

were designed to achieve aerodynamic quenching. However, Colket

et al. ( 1982) have argued that a single probe may not be capable

of aerodynamic quenching for all ambient conditions. But, as

y

n
x M

O N

LL. 7 W

Fm V Q ,W

J ^ a ^

c^zp

M

z 

W

zSO

2 FS

J_QHWO

0Na0

c^ae0u

aoa

cd

00

tddavH

cv

00 W

16

r,

Ix
tio iW

M

k7i

00

0

0

U

cr

W Ch

W

44

17
pointed out in section 4.7.1, the use of cooled or uncooled.

sampling probes did not have a noticeable effect on the measured

NOX values and only resulted in differences between the NO2

levels.

The concentrations of NO and NOX are measured by a

chemiluminescent NO analyzer (TECO Model 12A), equipped with a

Molybdenum NO2 to NO converter. This system had been modified for

low pressure sampling (Nizami, 1978). A high vacuum sampling pump

and a variable sample capillary are used to maintain the analyzer

reaction chamber pressure at 8 tore. For each steady state burner

operating condition, continuous NO X sampling and measurements are

carried out for a period of two minutes and the measurements are

plotted by a strip chart recorder for accurate NO X concentration

readings. Using this method, all NO X readings were accurate to

within 1 ppm, with a day to day reproducibility of 5 percent.

3.3.2 Temperature Measurement System

Temperature measurements are made with a Pt/Pt -13' Rh fine

wire thermocouple (0.075 mm diameter) with. a bead diameter of

approximately 0.11 mm. The wires are inserted into a two-hole

ceramic support which is attached to the side of the uncooled

sampling probe (see Figure 3.2). This arrangement allows

simultaneous NOX and temperature measurements. The thermocouple

is connected to a digital display Trendicator (Doric Type 400 A)

as well as to a strip chart recorder for accurate measurements of

the mean temperature at a particular location in the burner

system. Positioning of the combination gas sampling/thermocouple

13

^
19

as

probe is achieved 'by a 3-b traversing mechanism.

In order to determine the actual temperature at a sampling

position, the measured value must be corrected for conduction and

radiation losses. Such corrections are laborious and contain some

level of uncertainty as discussed tn Anpendix D. For this reason,

no corrections were applied and the temperature results reported

in Chapter 4 represent the raw measurements only. Uncorrected

temperature readings are accurate to within 20 0C, with a day to

day reproducibility of 5 percent. .

V
20

CHAPTER 4 '

Experimental Results and Discussion

4.1 Introduction

Selected results on the effects of fuel type, stoichiometry,

air preheating, oxidizer composition and fuel nitrogen additives

on temperature and NOX formation are presented and discussed in

this chapter. Additional experimental results are given in

Appendix B.

In some cases, slight modifications to the experimental

4 facility were necessary to attain the desired operating

p conditions. Those changes are described appropriately.

r

s

The burner was ::perated under atmospheric presnure and in the

monodisperse droplet size range at a constant fuel feed rate of

0.382 cc/min. to achieve the desired stoichiometry, the dilution

air flow rate was varied, keeping the dispersion air flow rate at

1300 cc/min.

4.2 System Verification

4.2.1 Monodispersion Range

Since a single orifice plate can only opera te in a narrow

monodisperse range of droplets, a set of 20, 25, and 35 }tin orifice

plates were selected to cover a combined range of 36 to 74 pm

r 

r
21

droplet diameter. figure 4.1 shows the monodisperse operating

range of the aerosol generator determined by the manufacturer's

suggested "Jet deflection" method (Thermo System Inc., 1977) and

further confirmed by a slide impaction technique'recoimnended by

Berglund and Liu (1973). All droplets in a collected sample must

have the same size in order to be considered monodisperse.

Typical slide impaction results of monodisperse droplets are shown

in Figure 4.2.

4.2.2 Radial Temperature and NO 

X Mapping

One dimensionality and radial symmetry of the flame for three

different droplet sizes were examined by temperature and NOX

traverses at a height of 4 mm across the 17 mm flame holder.

In general, the flames appeared as pale blue and, for small

droplets j it looked as if tiny streaks were burning in a 1 mm

thick envelope flame with a luminous region extented to about 3

mm. Large droplets seemed to have occasional merging individual

flamelets and ..ere luminous up to 6 mm above the flame holder.

The luminous region was relatively longer for lower volatility

f uels.

The radial temperature and NOX profiles shown in Figures 4.3

and 4.4 indicate some asymmetry for the 69.1 pm droplets, but for

most part they are flat, thus confirming the one dimensionality of

the burner system.

* A 15 pm orifice plate was used to produce the 26.7 pm droplets.
2.2 

80

70

E

w 60

Uj

a_

0 50

UiJ

CL

0 40 X

0

30

Y

® MONODISPERSION RANGE

VOLUMETRIC FUP.. FEED RATE •0.382 cc/min I I I

20 25 35

ORIFICE DIAMETER ()um)

Figure 4.1. Monodispersion ranges of single orifipe aerosol

generation system.

J
23

c

O

G.Ou

c^a6

.HuvaOwbG

G1, m

{r

00

OO

a

^n

u v

.H v

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00

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'

r

T wo'

r

ORIGINAL PAGE ;y

OF POOR QUALITY

a^a0

-Dc0LUEmWNda0LCOLUE

Lt7 M

W.
11081

24

S A

eA

C3 1 y

0

0

A

17 mm DIA.

C

ISOPROPANOL = 8.388 cc/min

EGIM. RATIO = 0.906

PROBE LOCATION = 4 mm ABOVE FLAME HOLDER

ALONG AB ALONG CD

DROPLET DIAMETER = 69.1 ;a p._.._..^

DROPLET DIAMETER = S5.8 ;A p

DROPLET DIAMETER = 26.1 A Q -- - - - -^

-9 -6 -3 0 3 6 9

THERMOCOUPLE POSITION ACROSS FLAME HOLDER (me)

Figure 4.3. Temperature traverses across the burner.

r lW,1

A

.t

r
25

va

0

ALONG'AB ALONG CD

DROPLET DIAMETER = 69.1^us p —.

DROPLET DIAMETER = SS.8 um p

DROPLET DIAMETER 26.7

20 C, / -i-- ,moo^ o

# n

15 ^' 0

a e

A -i- B

17mm 01 A.

10 C

0 0

5 ISOPROPANOL = 0.388 cclmin

EGO. RATIO = 0.906

PROBE LOCATION = 4 mm ABOVE FLAME HOLDER

-9 -6 -3 0 3 6 9

GAS PROBE POSITION ACROSS FLAME HOLDER (mm)

Figure 4.4. NOx traverses across the burner.
26

4.3 Fuel `lXpe and Stoichiometry

Post flame temperature, NO, and NOx were measured in the 36 to

70 pm droplet size range. Several hydrocarbon fuels were used

including isopropanol, methanol, n-heptane, find n -octane. All

fuels, except for n-octane were HPLC grade and had a purity of

greater than 99 percent ( n-octane had a purity of 957). A fixed

sampling location on the burner centerline at 5 cm above the

screen flame holder was selected to avoid regions of high

temperature and concentration gradients found in axial probing.

These results are shown in Figures 4.5-4.8. Where available,

prevaporized / premixed limit results are also shown as data points

at zero droplet diameter. For these premixed experiments, liquid

fuel was vaporized in an evaporator and the fuel vapor was mixed

with the dispersion air before entering the combustion facility.

In all casen, a general trend was observed in which both NO and NOX

decreased with reducing droplet diameter, reaching minima around

43-58 μm, and then increasing to fairly constant levels with any

further decrease in the droplet diameter. The equivalence ratio

and fuel type appeared to only affect the absolute levels of NO),

measured, without appreciably affecting the observed droplet

behavior. However, NOx reductions were larger for rich mixtures

with increased number densities and droplet interactions. For

these tests at an air temperature of 24'C, the NOx minima occurrec!

at 43, 49, 54, and 58 pm initial droplet diameters for n-octane,

n-heptane, isopropanol, and methanol, respectively.
4

2 7

6

40 1200

q

1100 u

°a 00 0

30 1000

` x e

900 w

Z FLAME HOLDER - 12,7 mm DIA,

w EOUIV, RATIO a 1,13

P

t.

20 800

0 0

0 30 40 s0 80 70

40 1200

4 1 100

E Q ^

a 300 • 1000

v

0

^

0 D

zx 0

0

0

908

z

0 0 w

E

20 FLAME HOLDER - 14.3 men DIA. 800 

EQUIV. RATIO - 1.0

0

L 0

0 30 40 s0 60 70

30 1200

r.

°

° 0 1100

eP °

^

a 20

^

1000

a

x

°

0

900

= FLAME HOLDER - 17 mm DIA, w

= EOUIV, RATIO - 0,86

w 10 ~

0 0

0 30 40 s0 60 70

DROPLET DIAMETER Cum)

Figure 4.5. Droplet size effect on post flame temperature, NO and

+ NO., for isopropanol at various equivalence ratios.

r

o - N0; • - NOx ; p - Temperature.
f

28

r

10 -1 

100

a

° 000

n

n O

a

900 ^,

a

00 O O a

x 51 800 D

°z FLAME HOLDER a 0,5 m+n DIA,

o

EOUIV, RATIO - 1 .1 q 700 CL

Z w

600

0 61, V 0

0 30 40 50 80 70

10 1100

0

a ° °

n O 0 0 C^

E

V

v

5

0 0 O 800 W

x

FLAME HOLDER - 12,7 mm DIA, M

o

EOUIV, RATIO a 1,0

Z

0

Z =

800 a

w

r

8 0 30 40 50 60 70 0

5

^_" _*- 1100

1000 n

E

aO

------ ---- ` ° ° ° a OV

Vd

a 900 .

w

ax o

B00

z <

Z FLAME MOLDER + 14,3 mm DIA, 780 wa.

EOUIV. RATIO . 0,84 600

0

0 30 40 50 80 70

DROPLET DIAMETER (,mm)

Figure 4.6. Droplet size effect on post flame temperature, NO and

NOx, for methanol at various equivalence ratios.

o - NO; • - NOA ; 6 - Temperature.
29

70 1200

s o

n n

r ; 80 ^+ A a A A A A

I 100 U

a

v

A

w

t

50 O O 1000 f

O O O

e

^ ^ .

FLAME HOLDER - 12,7 DIA. w

40 EQUIV. RATIO • 1 , 2 901 ►'

0 0

0 30 40 50 60 70

s0 1200

`. A

^^ A A A A

A A

A a 0

1100

`

O •u

4e o lose

L

x

O O

x

FLAME HOLDER - 14,3 DIA, fl00

EOUIV. RATIO • 1,0 ^!

30 A00

0 0

0 30 40 50 Be 70

` 30 1200

AA A A A A A A A

- - 1100 - U

u

^1000 V

O 

0 0 0

w

^

G

20 900

O

W

x FLAME HOLDER • 17 mm DIA, 800

EOUIV, RATIO a 0,85 ww

' $ 700 ~

H

800

f

le

i

0

0

0 30 40 s0 Be 70

DROPLET DIAMETER

Figure 4.7. Droplet size effect on post flame temperature, NO and

F NOX, for n-heptane at various equivalence ratios. 

o - NO; • - NOx ; 0 - Temperature.

f

LL

... __. N 
^j

j

4

R

i

I

30

A A A A

AAA

6-*k

O

O

p

O

FLAME HOLDER - 12,7 nom DIA,

EQUIV. RATIO a 1,2

30 40 s0 80

n

\

^\ A AA[^

FLAME HOLDER . 14,3 TT DIA.

EOUIY, RATIO + 1,0

1400

n i v

1300 ^v

w

1200 CS

DG

1100 a

I

w

1000 ^

900

0

70

1400

1300 v

^v

1200 Ix

D

H

a

1100 w

^i

W

1000

J 0

70

1400

1300

1200

I t 00 .vv

1000 w

800

Q

800 Cr

700 w

600 ~

AA A A A

0

A

y 

I

I _.—j 0

0 30 40 s0 60 70

DROPLET DIAMETEr, Cf+m)

Figure 4.8. Droplet size effect on post flame temperature, NO and

NOX , for n-octane at various equivalence ratios.

o - NO; • - NOX ; 6- Temperature.
irr

31

Similar trends in the experimental data were also found by

Nzami et al. (1978-82) who hypothesized the following mechanism

'to explain the observed behavior. Decreasing the droplet diameter

at a constant fuel feed rate increases the droplet number density

and, hence, droplet interactions, leading to depletion of the

local oxygen concentration around the burning droplets and a

suppression of the local flame temperature and NOx formation.

This analysis is also consistent with the results of Nuruzzaman gj

al. (1971), Kesten (1972), and Bracco (1973). Continued reduction

in droplet size further increases number density, but enhanced

vaporization brings about increased droplet spacings, mitigates

droplet interactions, increases burning rates and flame

temperature, and eventually reverses the decreasing NOx trend as

the situation approaches the premixed case.

The variations in NOx minima appear to be governed by the

differences in the physical properties of the individual fuels.

Larger initial droplet diameters are needed for high volatility

fuels, such as methanol, to overcome rapid prevaporization and to

give some level of droplet interactions in the flame. By the same

argument, lower volatility fuels like n-octane, can achieve the

optimum conditions at smaller droplet diameters.

In the next two sections, additional experimental results on

the effect of extent of prevaporization and droplet interactions

are presented. These phenomena have been incorporated into an

analytical model that is described in Chapter S.

I'

k

t

i

^ 
32 

4.4 Air Preheating and Prevaporization

In the previous section the shifts in the NOX minimum paints

for the test fuels were found to be consistent with the

differences in their evaporation and combustion characteristics.

In this section, the importance of enhanced prevaporization in

addition to droplet size effects on NOX

formation were

investigated by air preheating experiments.

Air preheating was accomplished by wrapping heating tapes

around the upper and lower housing assemblies ( Figure 3.1) and

controlling the temperature by a variac. For a constant setting,

there were only small variations in temperature ( less than one

degree centigrade) throughout the combustor. The water flow rate

in the cooling jacket was also adjusted to keep the exit watei`

temperature from the jacket equal to that of the preheated air..

For this study, measurements were made at a height of 10 cm above

the screen flame holder (the adjustment in sampling location was

made to reduce potential catalytic NO2 -4 NO conversion reactions

in the uncooled sampling probe).

The effect of air preheating and initial droplet diameter on

temperature, NO, and NO X for the various fuels are shown in

Figures 4 . 9-4.12. Air preheating results in enhanced vaporization

of droplets, shifting the minimum NOX point towards larger initial

droplet sizes and mitigating the reduction in NOX levels at the NOX

minimum point. These effects are believed to result from a

balancing of two phenomena: ( 1) a requirement for larger initial

droplet sizes to maintain some optimum extent of prevaporization,

since air preheating increases prevaporization and local fuel
AIR TEMPERATURE - 24 O C 10e ~

0

30 40 50 00 70 80 0

DROPLET DIAMETER Crm)

Figure 4.9, Air preheating and droplet size effects on post flame

temperature, NO o nd NOx, for m<A thanol at = 1.0.

o - NO; •- NOx ; 6-- Temperature.

^t

10

n

E

a

a

v

x 5 0

z

0

Z

e00

A AAA o A n A o e o A o 0 0

-see

n

• 

U

400 v

W

O O 300

ot

0 000 0 0 0 0 00 0 O

200 (L

W

R TEMPERATURE 44 'C t00

^- 0

40 50 00 70 60

--r

neon A An o e A e A '6A

000

see

n

u

400 v

W

a

0 000 0 O O 0

0 0 0 300 0 0 0 0 D

a

200 CLL

W

R TEMPERATURE 34 'C 100

0

40 FA C0 70 so

600

A AAA AA A eAo eA

see

n

U

O O^ 400 v

W

0 0 0 o

0 0 0

0 0 300 h^-

1280 d

t

W

33
34

i

A

0 X30

_

40 60

30

A A A^

LL

O

o

e0 70

eee

0

A

A e A n

age

v

v 

20 O O O O W

K O 400

Z

0

OIL

W

0 a

Z 200 w

0 AIR TEMPERATURE 24 *C

A _ 0

0 V 30 - 40 50 70

DROPLET DIAMETER Crm)

Figure 4.1r Air preheating and droplet size effects on post flame

temperature, NO and NO X , for isopropanol at = 1.Q.

o — NO; • — NOX ; B — Temperature.

e o

eee 0 0

o u

0

0 0 C 400

0

O

Wa

20O F

»r

ac

• a

w

H

36(

0 o o0

p 20

v

x

AIR TEMPERATURE 44 'C

0 30 40 Se O0 70

30 r— .. 7 A A00

A 0 0 A A d A

O

age eN

•

4

v

O

O

O O 400 w

O O

200 w

(L

W

0 ^"

O 000

n 20

v

x

0

Z

0

Z

10 ^ AIR TEMPERATURE a 34 °C
s0 

r

35

A AAA AO 0 A AA A A A 1 00e

see

n

Q

`p 40 0 000 see j

K ^

400 w

CL

T

30 AIR TEMPERATURE 44 ^C ' 200 w

0 i0 40 50 60 70 0

50

A AAA AA. A A A A

f 000

A

see

n

P

n

o 0 0

CL 40 0 w

o0 e

s00

x

o O

z

400 ^

0Z

a

T

30 ASR TEMPERATURE 34 °C 200

W

~

0 70 0

30 40 50 60

50

A A AI AA A A

o e

.1000

n

o

O O

O a00

n

E

OL

v

v

40 0 0 0 W

see

o•

Ox S i

400

a

Z T

W

30 AIR TEMPERATURE - 24 *C 200 ~

T- 0 ^r 70 0

30 40 50 B0

DROPLET DIAMETER Cpm)

Figure 4.11. Air preheating and droplet size effects on post flame

temperature, NO and NOx, for n-heptane at 1.0.

o - NO; • - NOx; 6 - Temperature.

7
ILP'111

{

36

60 1000

A A A0 0 eo A 0 4

see n

n 60 O f1 0 0 O

i

a

O

O

00

O 000 W

v a

K h0

2

40 400 W

o a

Z z

AIR TEMPERATURE 44 OC 200 w

30

0 30 40 50 60 70 0

60 1000

A e 00 a

AA 0 0 0

sae n

n so i

0 v

v

0 

O O

O 0 600

x

0

4® C 0 Oo ^.

400

oz as^

AIR TEMPERATURE - 34 *C 200 ►W- 30

® 30 Q 40 50 80 70

60 1000

800 n

n so i t

CL 0 0 0

p0 0 

0 O 500

v

ix

X

Z

40 O

f

400 a

o

W

a

Z s

AIR TEMPERATURE 24 ^C 2.00

30

0 40 50 60 70 0

30

DROPLET DIAMETER Crm3

Figure 4.12. Air preheating and droplet size effects on post flame

temperature, NO and NOx, for n-octane at 1.0.

o - NO; • - NOX ; a - Temperature.

^ 

E^

i

w
37

7

vapor concentrations as well as droplet spacings; and (2) fewer

droplets and reduced droplet interactions as the size is

increased. This tradeoff is particularly pronounced in the case

of methanol (Figure 4.9), where the NO X reduction phenomena almost

disappears with preheating.

In order to interpret these results, it is

important to realize that the effectiveness of air preheating on

fuel vaporization relies upon the droplet travel time as well as

the specific fuel properties. At a constant equivalence ratio and

fuel feed raze, the air flow requirement increases with increasing

fuel molecular weight, which consequently reduces the droplet

travel time. For instance, NOx minima for methanol, having the

:.< highest volatility and droplet travel time among the test fuels,

quickly moved towards larger initial droplet diameters and the NO,

levels began to reach a constant value at elevated air

temperatures. These effects were somewhat re l:arded for

t,

isopropanol due to its lower volatility and shorter droplet

residence time.

For n-heptaneg there is a relatively shorter droplet residence

time. Thus, preheat temperature increases primarily affected the

small droplet sizes and their, associated NO )( values, with some

smoothing in the large droplet region. N-octane, with the lowest

volatility and shortest droplet travel time, seemed relatively

unaffected by the increases in temperature. Air preheating

temperatures above 44°C are required to cause a significant shift

in NOX minima for n-octane. These factors are discussed in more

detail as part of the analytical studies in Chapter 5.

s

O
38

4.5 Synthetic Oxidizers

Results of the parametric fuel studies and air preheating

experiments indicated the importance of parameters such as fuel

properties and temperature on droplet diameter and interactions.

In spray combustion, changes in flame: temperature affect the

droplet lifetime, interactions with neighboring droplets, and the

formation of NOX . These effects were studied by a series of

experiments in which air was partly replaced by a mixture of

oxygen and argon, keeping all other operating conditions the same.

Air, oxygen, and argon were individually metered, then mixed

in a cross, and later divided into the usual dispersion/dilution

proportions before entering the combustion facility. In all cases

the volumetric ratio of oxygen to the inert gas (nitrogen plus

argon) was kept at 21/79.

The experimental results shown in Figure 4.13 demonstrate the

effect of droplet size and fraction of synthetic oxidizer on NO,

NO., and temperature at a sampling height of 10 cm above the flame

holder. Since argon is a monatomic gas with a lower heat capacity

than nitrogen, its substitution for nitrogen increases the flame

temperature and flame speed. For this reason, different size

flame holders had to be used (as indicated on the Figure) to

stabilize the flame.

Compared to air, the NOX minimum point moves towards larger

initial droplet diameters as the fraction of the synthetic

oxidizer increases in the gas phase. Lesser NOX reductions and

higher NOX levels (relative to air) can also be observed from the
39

s0 V---

E 0 0

a o

a

v

X

40 O 00•

Z O

S

0Z

30 AIR

0 30 40 S0 s0 70

70 --AV

n '

E

a

a e

s0

o O 000 0

0

Z ® 00 °

Z o

0

50 AIR + 'SX'CO2+Ark

0 30 4^ti so s0 70

70

n

E

a

60 ^ 0 X 0

0 0 Z

0

Z

so AIR + 30%(OZ+Ar,,

0 30 40 S@ 80 70

DROPLET DIAMETER Crm)

Figure 4.13. Synthetic oxidizer and droplet size effects on post

flare NO, NOX and temperature for n-heptane at

Ow. 1.0. Flame holdex- T.D. (mm): a -x.4.3;

b and c --12.7.
v

40

data.

All of the above observations are due to changes in flame

temperature. An increase in temperature reduces the droplet

lifetime and diminishes the droplet interactions , in flame. As a

consequence, the minimum NOX point occurs with larger droplets

which burn for a longer time. However, shifts towards larger

droplet diameters are accompanied by a lower droplet number

density and reduced interactions. Therefore, at very high

temperatures, the effect of droplet interactions on NOX production

is minimal.

4.6 Fuel-Nitrogen Additives

A series of experiments with simulated synthetic fuels were

conducted in order to investigate the effect of droplet size on }

the conversion of fuel-nitrogen to NOX . In general, synthetic

fuels contain traces of nitrogen-containing organic compounds

including pyridines, nitriles, quinolines, pyrroles, indoles and B

carbazoles (Chan et al., 1984). These compounds undergo thermal

decomposition in the reaction zone, producing radicals such as

HCN, N, CN, and NH which can either oxidize to NO X or recombine to

form molecular nitrogen.

N-heptane was doped with pyridine (C5H5N) and pyrrole (C4 H4 NH)

to give a 0.1-1.0 % nitrogen content by weight in the fuel

(typically found in synthetic fuels from shale oil).

The experimental data collected at a sampling position of 10

cm above the burner (Figures 4.14 and 4.15), indicate that the

optimum droplet diameter for minimizing NO, 4 (which was observed
900

8130 0 0

n U

a ee0

7130

x

Z 700 ° °p ° o

0 650 .

Z

800

N- HEPTANE+ 1.0 WT.9 N AS PYRIDINE

550

0 30 40 50 80

500

E 450

O

00

a

a

OX 400 Q • • ^.-^---^

Z

0 350 A

Z

300 L N-HEPTANE+ 0.5 WT.% N AS PYRIDINE

0

140

30 40 50 80

130 O 0000

n

E

a 120

p

v

ox 110

Z ° o

100

Z 90

O 1300 

7WT.9.

DO Col O O D O O O

80 N-HEPTANE+ 0.1N AS PYRIDINE

0v 30 40 50 60 70

DROPLET DIAMETER Cpm)

Figure 4.14. Effect of fuel-N content and droplet size on NO and

NOX for n-heptane doped with pyridine.

p-^= 0.85; o -0= 1.0; -t = 1.2.

h.

O

41
850

see

n

CL 750

CL

v 700

x

Z 650

0 60e

Z

sse

see

95E

^ 90Q

E

a

v esE

x

Z 80C

Z 75C

70F

806

n

E

n 7s6

v

0x

Z 706

0

Z

1000

800 U

800 v

W

Ix 400

H

a

200 W

0.

0 LW

H

1000

800

see v

W

400 0

H

Q

200 W

(L

0 E

H

1000

800

see v

W

H

200 W

a

0 ^W

42

r 

656

DROPLET DIAMETER Cp,)

Figure 4.15. Effect of droplet size on NO, NN and temperature

for n-heptane doped with pyrrole (17.N by weight), 

o - NO; • - NOx ; 6 - Temperature.
43

Ift a

previously with pure n-heptane) disappears with increases in the

fuel-N concentration. Also, it was noticed that more fuel,-N is

converted to NOX at small droplet diameters.

Appleton and Heywood (1973) suggested that the degree of

air/fuel mixing and the availability of oxygen atoms control the

oxidation of the nitrogenous species. In their investigation,

maximum conversion efficienci'..-- s were found for fuel-lean and well

atomized cases. The present results show that under

stoichiometric and rich conditions, reducing the droplet size

improves the oxidation of the pyrolysis fragments of the additives

to NOX by better oxygen penetration through the droplet flame

zones. The abundance of oxygen for lean mixtures made this

process less dependent on the size of droplets as shown in Figures

4.14• and 4.15. Changing the dopant from pyridine to pyrrole with

a different molecular structure did not change the results. The

fact that the type of nitrogen-bearing additive does not change

the NOX yield has also been addressed in a number of other studies

(Fenimore, 1976a; Foster and Keck, 1980; Sapre and Quader, 1983).

It should be pointed out that the presented results include

the thermal NOX contribution. However, for fuel-N, the dependence

of nitric oxide yield on flame temperature is not as strong as it

is for the oxidation of molecular nitrogen (De Soete, 1974;

Fenimore, 1976a). Therefore, temperature changes resulting from

droplet interactions become unimportant as the concentration of

the nitrogen-containing compounds in the fuel increases.

The conversion efficiency of the fuel nitrogen to NOX

(determined from a nitrogen balance and subtracting the thermal NOX

I
44

contribution) for the 37 pm dropletn are given in Table 4.1. The

fraction of fuel-N that was not recovered as NOX presumably

appeared mostly as NZ in the products. Foster and Keck (1980)

measured high HCN concentrations in fuel-rich turbulent diffusion

flames as far as five burner diameters downstream of the fuel

nozzle, constituting a large portion of the nitrogenous species

(HCN+NO+NH3).

In the following section, inflame and post .flame measurements

of NO, NOX , and temperature are presented.

4.7 NO Structure in Flame

4.7.1 Pure (Nitrogen Free) Fuels

Axial temperature, NO and NO X concentrations were measured for

various fuels and droplet sizes by traversing the gas sampling/

thermocouple probe along the burner centerline inside a 27 cm long

Pyrex tube. Figure 4.16-4.19 represent the measurements for

stoichiometric combustion of methanol,, isopropanol, n-heptane, and

n-octane aerosols, respectively. In general, temperature, NO and

NOX concentrations increase rapidly in the flame zone, with NO and

NOX reaching their maximum values slightly above the temperature

peak and then, decreasing gradually to relatively constant levels.

The effect of sampling probe on the me^;sured NO and NO X values

was also studied using the water cooled probe. The probe was

cooled to 50°C during all measurements. Figures 4.20-4.22,show

the concentration profiles of NO and NOX sampled by both cooled

and uncooled probes. The results indicate minor differences

between the NO% values for each condition while a higher NO Z yield

Y
t y

1 ry

45

Table 4.1. Conversion efficiency of fuel-N to NOx from

the combustion of 37 μm n-heptane droplets

doped with pyridine.

% N By Weight of Fuel 0-0.85 -1.0 ^ -1.2

0.1 73 74 69

(70 ) (64) (55)

0.5 70 80 59

(67) (70) (48)

1.0 70 76 59

(67) (66) (48)

Calculations are based on the maximum NOx concentration measured

along the burner centerline. Values inside the parentheses are

calculated based on the steady state NO X concentration at 10 cm

above the burner.

^
n

a

a

t 6

O

Z

r

n

E

Q

V

S

x

O

Z

V

46

6 .

14 00

-P 1200

v

W 1000

D!

F

400

Q

W60

n.

W 400

t200

0

0 2 4 6 6 10 12 14

el i

0 2 4 6 8 10 12 14

0 2 4 6 8 10 12 14

AXIAL POSITION OF PROBES (cm)

Figure 4.16. Centerline NO, NOx and temperature profiles for

combustion of methanol at 0 = 1.0. o , •,* - D =

37.0 pm; 0,0,x - D - 57.2 pm; 6,A,+ - D =t 69.6 pm.

'r
47

^dee

n

.v i X300

v 1200

w

1000

e00

a 600

f

w 400

200

0

0 2 4 6 6 10 i2 14

3S

30

r^ 2S

E

CL 20

U

0 1 '' z

10

S

0

0 2 4 6 8 10 12 114

35

30

E 2S

a

C 20

0 15

z

10

S

0

0 2 4 6 8 10 12 114

AXIAL POSITION OF PROBES (cm)

Figure 4.17. Centerline NO, NOX and temperature profiles for

combustion of isopopanol, at 0 = 1.0. o , •,* - D

37.0 pm; C1,0,x - D = 54.5 pm; p,A,+ - D = 69.6 pm.
48

1600

1400

V 1200

w

1000

Soo

a

w 600

w 400

200

0

A

M ^

0 2 4 8 8 10 12 14

70

60 Art-^4 '_7

s0

a 40

0 30

z

20

10

0

^

1- _ -

, I

0 2 4 6 a 10 12 14

+0

E s0

CL

a 40

0 30

z

20

10

0

0 2 4 6 8 10 12 14

AXIAL POSITION OF PROBES (cm)

Figure 4.18. Centerline NO3 NO X and temperature profiles for

combustion of .).-heptane at ^. 1.0. o , •, * - D =

37.0 μm; p,n,, k - D - 49.5 Lim; p,p,+ - D a 67.2 μm.

w
1600

1,400

1200 W

1000

d 800

a 600

w 400

r

200

0

0 2 4 6 8 10 12 14

70

60

n so

E

4

4 ^3

0 30

z

10

0 0 2 - 4 6 8 10 12 14

70 r

60F

E 50

a

40

0 30

z

20

10

0

0 2 4 6 8 10 12 1 4

AXIAL POSITION OF PROBES (cm)

Figure 4.19. Centerline NO, NUX and temperature profiles for

combustion of n-octane at ^= 1.0. o , *,* - D =

37.0 pm; 0,0,x - D = 43.3 pm; p,A,+ -- D = 57.2 pm.
50

40

30

rN

E

CL

20

O

2

0 0 0 0

O O O

+4 +t

0 D 0 0 0 0 0 0 0 0

0

D 0 0 0 D D 0 D O O

0

0

1400

1200

1000 C

830 W

o3'

600 a

400

CL

x

200

10 0

0

2 4 6 8 10 12 14

40

30

E

Q.

CL

20

Y^

O

Z

10

1a M

0 2 4 6 8 10 12 14

AXIAL POSITION OF PROBES (cm)

Figure 4.20. Sampling probe effects on centerline measurements of

NO and NOK for 37 pm n-octane droplets at 4)= 0.85.

o , • - uncooled probe; [3 , 0 - water cooled probe.

n
51

r

70

60

50

E

40

v

z 30

20

10

0

0 2 4 6 8 10 12 14

70

60

50

n

E

a 40

v

X

Z 30

20

10

M

0 2 4 6 8 10 12 14

AXIAL POSITION OF PROBES Ccm)

Figure 4.21. Sampling probe effects on centerline measurements of

NO and NOX for 37 pm n-octane droplets at ^ = 1.0.

o , • - uncooled, probe; p , g - water cooled probe.
52

t i

70

60

n so

0- 40

0

z 30

0 13 8 0

0 0

CP 8 0 8 6 j3'

1600

U

1400 •

1200

1000

800

600

400

200

0

20

10

0

0 2 4 6 8 10 12 14

(4

70

60

so

CL

%-, nx

0

z 30

20

10

0

0 2 4 6 8 to 12 14

AXIAL POSITION OF PROBES (cm)

Figure 4.22. Sampling probe effects on centerline measurements of

NO and NO X for 37 pm n-octane droplets at ^= 1.2.

o • uncooled probe; [3 , a- water cooled probe.
53

f,

L"

is observed when gases were sampled with the cooled probe„ This

occurs as a result of the oxidation of NO by HOZ which is formed

under rapid quenching in the sampling probe (Cernansky, 1977;

Hori, 1980; Duterque et al., 1981).

In these flames, nitric oxide originates from the molecular

nitrogen in air accorP ag to the Zeldovich mechanism (described

elsewhere; e.g., Bowman, 1972). Some "prompt" NO formation is

observed near the flame front at a few millimeters above the flame

holder (considered as the main reaction zone). This is

particularly noticed in fuel-rich cases where the Zeldovich

mechanism cannot account for the measured NO, levels. Several

plausible reaction schemes for the prompt NO formation in rich

flames involving the attach of hydrocarbon fragments on N Z and the

conversion of the products to NO have been suggested, (Fenimore,

1971; Bachmaier et al., 1973; Haynes; 1977b; Hayhurst and Vince,

1983). In spray combustion, the presence of liquid droplets

increases hydrocarbon cracking and thus intensifies the prompt NO

production.

The consumption of NOX in the Post flame regions appears to be

independent of the fuel type or stoich;iometry. Equivalence ratio

seemed to only affect the NO X reduction rates. For 37 }im n-octan(

droplets, this accounted for a drop of 22, 27, and 317 at 0 =0.85,

1.0, and 1.2, respectively. Duterque et al. (1981) reported

similar behavior, in a stirred reactor.

Changes in flame temperature were also found, to affect the

removal rate of NOX in the ,post flame regions. Experiments with

synthetic oxidizers were carried out at an equivalence ratio of

l

i
t

t

54

1.0 (see section 4.5 for the experimental details). Figure 4.23

compares the axial NOX and temperature profiles obtained for 37 pm

n-heptane droplet combustion with various oxidizers. The data

show that raising the flame temperature increases the NOx

formation: markedly, but also augments its downstream decay to

constant levels.

A possible explanation for the axial NOX reduction is the

removal of NO by nitrogen atoms which are generated from the

molecular nitrogen at high temperatures. Other reactions that can

>r

also contribute to the consumption of NOS are discussed in the

following section.

4.7.2 Nitrogen-Containing Fuels

Several operating conditions were selected to study the NO,

formation in spray combustion from fuel-N. Centerline NO, NO X and

temperature measurements for stoichiometric combustion of

n-heptane doped with 1% nitrogen by weight as pyridine, are shown

in Figure 4.24. Effect of equivalence ratio for a fixed droplet 

diameter of 37 pm is demonstrated in Figure 4.25. Again, in the

flame zone, NO and NO, rise quickly with temperature to their

maximum values, and then fall slowly to a plateau in the post

flame regions. Both NO and NO, peak faster at higher fuel,-N

contents and stoichiometries, indicating a strong dependence on 02

concentration but a weak dependence on flame temperature for

fuel-N transformation. Similar results fo7- different fuel-N

concentrations are shown in Appendix B.

Surprisingly, in each case, a lower percentage of the measured 

f

i
55 

C^,^ 321f11`db3dW31

m m m^ m m m m m m

omD ^ ^ N W ^ t^0 4 N

Cwdd) XON

x

0

z

^ Oz

a .^

N N O

^ a H

JJ b C

a a

u m o a,

a

ui

m N

a

m

b

ar, a.

LL 0 cn 0 u H

o '4

H

O

^ p

tIa ca

n. ti o 4-4 a ri

Q W .b

'+4

N

N

cn

Cl!

a

CD

co

.H

fL4

i

. 

^r
AXIAL POSITION OF PROBES (cm)

Figure 4.24. Centerline NO, NOK and temperature profiles for

n-heptane doped with pyridine (1% N by weight).

o , •,* -D= 37.0 put; C},M,x-D-49.5 pm;

p ,A,+ - D 69.6 pm. 1

1100

1000

900

800

! 700 CL

600

V

o S00

z 400

300

200

100

0

I

f

n

E

a

CL

0

z

0 2 4 6 8 10 12 14

16

,; 14

V 12

10

e

a e

t

►W- 4

2

on -

M M

^0

+

aa

T

P

y

T

j0

30

00 2 4 6 6 10 12 1.4

56
57

1600

t 400

U

v 1 200

W

O^ 1000

D

800

Uj

0. 800

430

x< 

*----X-

"*-* '-- -, "

+

^W

11

8 a

7

x

z S

4 0

z 3

2

1

1100-

1000-

E

a

n 70700

0 800

z Soo

C; 400

z 300

200

100

00

2 4 a 8 to 12

AXIAL POSITION OF PROBES Ccm)

Figure 4.25. Centerline NO, NO-A and temperature profiles for 37

pm n-heptane droplets doped with pyridine (1% N by

weight). ON, X 4= 0.85; 6,A,+ 1.2.
58

peak NO was consumed far from the burner, as compared to the

X

results with nitrogen-free fuels. Table 4.2 summarizes the

reduction percentages for the conditions studied. One may reason

that the NO generated from the fuel-N is far greater than the

X

thermal NO and therefore its removal by the flame radicals is

x

less efficient.

At this point a closer look at some of the processes that

control the NO formation from fuel-nitrogen may help the

X

interpretation of the results. It is generally believed that, in

fuel rich flames, the overall reaction mechanism for fuel-N

conversion to NO

x 

occurs according to the following path

(Fenimore, 1976b; Haynes 1977a; Chen and Malte, 1984):

NO

0

Fuel-N > HCN --► NH

i0

Na N

2

Among different reactions that can lead to the oxidation of the

NHi species (N,NH,NH 2 ,NH 3) and NO formation, the reaction:

N+OH -> NO+H

is considered to be the most important (Haynes, 1977a). The

unoxidized NH

i 

species can react with NO as it forms to generate NZ

by any of the following reactions:

N+NO --* N 2+0

NH+NO 2 +OH

NH +NO N +H 0

2 2 2

For lean mixtures, due to the abundance of 0

2 

and the presence

of 0 atoms, the fuel-N transformation to NO is much easier. The

X

I^

Li

,O
59

IV -

Table 4 . 2. Percent NO* consumed in the post flame gases of

37 pm n-heptane droplets doped with pyridine.

N By Weight of Fuel -0.85 0.1.0 0-1.2

0.0 19 28 20

0.1 9 18 20

0.5 5 15 20

1.0 4 15 20

J

7
likely reactions are perhaps those suggested by Appleton and

Heywood (1973), by which radicals such as NH and CN oxidize to NO

according to:

NH+O NO+H

NH+O OH+N

N+O NO+O

2

and,

CN+O NO+C

CN+O —+ CO+N

N+02 --! NO+O ,

In ammonia oxidative systems, NO can also form when nitroxyl

hydride (HNO) which is a product of amine species oxidation, is

stripped from its hydrogen (Dasch and Blint,1984). This can

happen as a consequence of radical termination reactions:

HNO+NH 2 -^ NO+NH3

HNO+O NO+HO

or, the radical branching reaction:

HNO+M NO+H+M.

Other routes for NO formation and destruction in these flames 

involve OCN radicals ( Crowhurst and Simmons, 1983, 1985x, 1985b)

OCN+O mh CO+NO

OCN+NO -;m N +C 2 2 ,

as well as

CN+NO xis N +CO.

2

V O
4

Y

7

61

CHAPTER 5

Analytical Studies

5.1 Introduction

So far, it has been shown that, in spray combustion,

variations in fuel properties, air preheating temperature and

oxidizer constituents affect the NO, production. These parameters

are examined by an analytical model which Is described in this

chapter.

The model is in two parts rind consists of spray vaporization

and spray combustion. First, droplet diameter and extent of

vaporization before the flame are evaluated by the fuel spray

vaporization model. Then, the calculated results are used as

initial conditions in the spray combustion model that also

considers droplet interactions and the 7eldovich mechanism of NO

,formation. Temperature and fuel, oxidizer and NO mass fractions

around the burning droplets are determined from this analysis.

Single component nitrogen free fuels are studied; therefore,

atmospheric nitrogen is the only source of NO X formation.

Details of the assumptions and the governing equations as well

as the comparison between the experimental and computed results

are discussed in the following sections. Calculations of the

tbermophysical properties are given in Appendix C.
5.2 Spray Vaporization

Given the initial state of a monodisperse fuel spray at the

aerosol generator, this model predicts the final-droplet diameter

and the extent of vaporization of the spray prior to the flame.

Various equations describing the motion of droplets in the gas

flow field, as well as energy and mass conservation equations,

were considered. A stepwise droplet tracking technique was used

to estimate the local vaporization parameters within the spray and

to solve the coupled equations.

Starting with the equation of motion (Beer and Chigier, 1983),

the forces acting on a droplet travelling in a gas flow .field are

balanced according to

2.r2

.1413 )1 

rs3 dt y/ins s39- H/3119 N39}Co n 5 9 2 (5-1)

The droplet acceleration term on the left side of equation (5-1),

which is determined from the rate of change of spray velocity due

to divergence, is balanced by the gravity, buoyancy, and drag

force terms on the right side. Considering a drag coefficient of

C u = 24/Rep (Re o<1), U', the relative velocity between the droplet

and the surrounding gas can be determined from equation (5-1)

62

u^. yr2 [9( )tat f^

181

or

(5-2)

o^ 8 0,2.

(5-3)

^

[[tt 

FY
ool

^z

mf 't mF =mf +mF

0 0

(5-4)

63

I 'l

Since equation ( 5-1) is one dimensional, its use in the model

requires some justification. From visual observations of the

spray pattern in the experimental setup ( Figure 3.1), it was found

that the droplets are contained within an inverted cone createl by

the dispersion jet. The spray cone is diluted by rapid dilution

air entrainment near the baffle plRte and diverges gradually to a

maximum spread of about 1.5 cm along the 17 . 8 cm path to the flame

holder. Because of the smnll cone angle, the radial variation of

droplet size is expected to be negligible. Therefore, a one

dimensional model should adequately describe the droplet motion in

the preflame regions. Furthermore, the entrainment effect was

determined experimentally ( Cernansky and Sarv, 1983) and used to

calculate the drople t_ travel time. This was'done by integrating

the ratio of the unit volume of the spray cone to the volumetric

flow rate of the combined dispersion and dilution air flows

(described empiricala, v as a function of axial distance). Also,

the gas phase temperature in the model was adjusted based on the

dilution air entrainment results.

At any given time, the total mass of fuel is constant. This

can be expres3ed as

Assuming that the heat and mass transfer rates around the

droplets are suffici3ntly fast to rapidly modify the local

properties of the gas phase, the mass fraction of fuel vapor; Y F ,

is given by (Law, 1977) '

slit

i Q
M

^`

64

p YF + E f

YF

(5-5)

+EYED

where, YF° and Yf

° are the initial mass fractiovi E of vapor and

r A

liquid fuel, in the combined vapor/gas system, and G is the

w

fraction of liquid vaporized defined as

mf-mf

or

. 3

F. a 1-(rs /rs ) • ( 5-7)

0

For a control volume of aerosol containing both liquid and

a vapor, the energy balance is given by

'» cP t cpT+(m _m L +(m _m )CP T (m -m cp (7 f 9 9 0 ,f fa jC f .f -fo .f ,^ 9

= mfo cP o + C irr90 + r"F cP (5-8) 9 0

Solving for T3 from the above equation, the gas temperature can be

expressed as

^

9=

YfocP^T-^'-E)T^ +cp9 ?^o-Y}o^^+(c}- ^9)T] , (5-9)

cp9 (I+eyYO

The evaporation rate for a droplet influenced by the relative

gas phase motion is given by (Rao and Lefebvre, 1981)

.N k o.S 

a

m 4 t! s ^^ ► (^+8) Q +o, zs- Re , (5-10)

9

E.
4 

k

w

r

i 

.w

65

r.

where, k9 and C R are the conductivity and specific heat of the

gas surrounding a droplet of radius rs , and B is the vaporization

mass transfer number given by the following expressions

B- YF - YFS (5-11)

YFa -

Assuming that the fuel mass fraction at the droplet surface is

that corresponding to the saturated vapor pressure, one can

integrate the Clausius -Clapeyron equation and use Dalton's law to

obtain

YS = j1 ( 1-exp[ 

R (

1 /T S -1/T6)]

1111 C

(5-12)

m can also be expressed as 0

z

It1 =- y 71 r< fir . (5-13)

Substituting equation ( 5-3) into equation (5-10), and using the

equality between equations ( 5-10) and ( 5-13) , we get

rs 3/i

d-6

 - C2 ^ i ^. ^^ rs )

where

$C f 

^ o.sC^= 0.25!( dt +9 ^ 9 - ^^^ 9

2 l I$

and

C - Kg Qn ^1^-8^.

2 P9 CP9

The parameters in the equations given for C i and Cz are

( 5-14)

(5-15)

(5-16)

^. 
66

temperature dependent. However, the gas phase and the droplet

surface temperature are also related by

B — 

c p9 ( T -T

(s-17)

l._+ CP ( T '-T)

4

and TS is solved using the equality between, equations (5-11* land

(5-17) (Lewis dumber - 1).

The droplet temperature must be determined prior to the gas

phase temperature calculations. Since the temperature inside a

droplet varies both radially and with time, the heat conduction

equation takes the form

aT _ 

djc Z ( r2 . ( 5-18)

at r2- a ►-

a r

with initial conditions

T (r, o, = T (r) (5-19)

t.. O

and boundary conditions

aT

( f = p ( 5-20)

r r_o

7- (5-21)

which has to be solved to get the temperature distribution within

the droplet. A dimensionless radial coordinate, r=r/rs is used to

include changes of droplet size during heating or cooling.

Substitution of Y into equations (5-18) to (5-21) yields

a Z

a— ,f a ( r a 1 (5-22)

at _ rZ r2 ar fir" l
67

with T, (r,o)= Tf00) (5-23)

(

ar ) _ o (5-24)

Pr^^ ^.o

} and Tf.y = T • (5-25)

^=1

The above differential equation can be easily replaced by a

finite difference equation. In the explicit form as described by

Law and Sirignano (1977), droplet temperature can be determined by

simple marching. This technique requires small time steps to

avoid instability. On the . other hand, the implicit procedure is

unconditionally stable and, therefore, is a more appropriate

choicA Using &r and Qt to denote the radial and time intervals,

the implicit finite difference approximation of equation ( 5-22)

becomes

T,^ (^-I)+T01

(l+ 2*6 )+ T _Ti

t-1 c «I

(5-26)

with Tf = T f , (5-27)

0 0

T

f$ = T

t2, , (5-28)

where,

d^ pt

(5-29)

• s

and

f - (5-30) rSz (°r)2•

The superscript prime specifies the new value of temperature

determined at the end of a time step and the subscript i

zi

O 
68

designates the radial index for Nr meshes. Equation (5-26)

represents a system of linear equations wich can be written in

matrix form with (6-1), (1+2Y) and becoming the

coefficients of a tridiagonal matrix. Knowing the initial and

boundary conditions as given by equations (5-27) and (5-28), the

simultaneous system of equations is solved for Nr -1 unknowns, T' .

c

Once the radial temperature distribution has been determined, the

average droplet temperature can be evaluated by spatial

integration.

J0,

u I

z

T.^ (err rr )d r

.^ (5-31)

14/3 7T (^ ) •

Substituting for Tt from equat;.on (5t-al) into equation (5-9) gives

the gas phase temperature, T9.

Equation (5-14) can now be integrated as a function of time,

subject t— r, (t-0) - rso . Dividing the total dreplet travel time

into time steps, the local terupetatures, mass fractions, gas

properties and droplet diameter can be evaluated at the end of

each time step. The calculated values are then used as the

initial conditions for the next step. This procedure is continued

until the total travel time, is reached.

5.3 Spray Combustion

It was noted that, in the present experimental setup, the fuel

spray enters a self-supporting, one dimensional flame, stabilized

on a screen flame holder. Due to vaporization along the spray

path and droplet impactions on the screen wires, part of the fuel ^ 
69

is prevaporized and premixed with the oxidizer. The

prevaporization due to simple evaporation is calculated by the

vaporization model just described, while the screen impaction

contribution to prevaporization most be determined experimentally

and entered manually.

After the fuel spray enters the combustion zone, solution

involves a transient-diffusive-convective problem. The basic

formulation is similar to that of Botros et al. (1.980) in their

numerical treatment of a single fuel droplet burning in a reactive

gaseous system.

With assumption of uniform pressure, zero relative velocity,

and one-step reaction kinetics for fuel oxidation, the governing

equations in a spherically symmetric system reduce to

continuity

P z

a + r2'r (9 

y r ) o (5`-32)

fuel :

P ^ a YF

PIS + v. -21 Y ( P o^ rZ ^YF v W c^ (5-33 ) ZL a r r1 a r 3

r=- F F

oxidizer :

p 

^aY°

+ tr6Y°)-! (P ^r2 ^Y° ^.-yW w (5-34) g a t ar rt

)r 9 ar 0 0

energy

P ^P ( a--^ + tr ^T9 ^ - i 'a ( K r 2 ,) _ VW D H w

F

(5-35) 9 9 ^t ar r 2 ar r F

state

NI

P= P R T 7 9 9

Y^ (5-36) j=1 W.

where a2s^,SW = A e x^ _ E ^ \ Xo P 1 

Ro 1 (5-37)

R T3 R 9 J

3

0 is the mass diffusivity, u is the convective velocity due to
70

r, I

droplet vaporization and temperature variations in the gas phase,

} is the stoichiometric coefficient, A is the pre-exponential

term and E is the activation energy (for n-octane, A=4.6x10 

r1,

E=30,000 and for methanc, l, A-3.2x10 

12

, E-30000 cal /mole; Westbrook

and Dryer, 1984).

Boundary conditions at the droplet surface (r-rs ) are

C1 31T S 3 J) _ - y rl rs2 

95 

(tPS ---t) (5-38)

S 

5J rF\ 

+ 9 s^

drs )

(1-YF )=0 (5-39) l ^r is s d t J s

(p 

3 3 ^D ' _ P9 ( zrs _I t ) YO = 0 (5-40)

^

T)

r s

- P^s ( sdry 

)^ =0 (5-41)

T( r= os) = T5 . (5-42)

At the midpoint between the droplet centers, the ambience boundary

conditions are

(^YF ) = C_ YL = C T ar ^ ar co

)^=0. (5-43)

The initial conditions at t=0 are given as radial profiles

T9 (r,0) - T90 r) (5-44)

YF (r,0) = YFo (r) ('5-45)

Yo(r,0) = YO0 (r) (5-46)

v(r,0) vo (r) (5-47)

with rs (0) - 

rsc .

(5-48)

4 
71

J,

Wy^^

C

Applying the dimensionless coordinate, r, the governing

equations (5-32) to (5-35) as well as the boundary and initial

conditions ( Eqs. 5-38 to 5-48) can be represented as

n a._._P, .+ (p yr z) = o at r rs a r

y

(5-32)1

p (aYF ate

2 ^r 

^P9^rZ 

2 

rF

F W^60 (5-33)1

9 a t rs ,- r rs a

P CYO

Y°^-rl aN (p ^rZ aYO ^ ^ _ a ow

9

(5-34)1

^r r rs ar ar

P CP ( + 9) . (K r 

z ^T9 W dNw(5-35 )1

2 9 F F 9 9 a^ rs a r r rs ar ar

(3 Ns3 ^ _ - yrrZP9s ( s- (5-38)^

^ dt CI-6

Pg a YF P

_ d rs s N -^-

9 ( r s (I - YF

- 0 s

(5-39 ) ,

.

r$ r r=^ s d^

,F P

(^Y^ - ( swdr )YD — 0 (5-40)1

Jr-1 9s rs zr

d.6

s

a Kys aT9 P( s_ d r L o

^

(5-41) f

/fit N

rs r r, l 9s d t

7^^ _ Ts

(5-42)'

( aYF ( aY° = 1-

^ T9)

>r

(5-43)r

a r "_ a v r_ ,00 -C)r r= 00

9 `r o) = 19 0 (r) (5-44)'

Y4 _ YF ( r, o) = YF r) (5-45)

'I

9

t

O

e ^. ... ....... ,.. vm mom .... -..
f

V

M 72

Yo (r, o) = Yoo +-, o) (5-46)'

zr(r,o) = o(r,d) (5-47)'

0 r'5( o) rso (5-48)'

A finite difference approximation scheme was used to solve

these governing partial differential equations. For better

resolution In the high gradient regions around the droplet

surface, the radial spacing was ramped according to

xi = r,-r +0.2+0.06(1-2), 1)2. (5-49)

Also, in order to apply this model to sprays, the burning rate was

corrected to account for droplet interactions. Since the droplet

surface regression rate, s- `

rs

 is directly proportional to the

mass burning rate, such correction was accommodated by adjusting

the velocity term in the model. Calculations of the correction

factor are discussed in the next section.

5.4 Droplet Interactions

A mathematical procedure hai been developed to transform the

quasi-steady transport equations describing the Stephan flow field

around the interacting droplets to the 'Laplace equation. Details

of the analysis as well as the underlying assumptions have been

given by Labowsky ( 1976-1980) and therefore, will not be repeated

here. However, the following discussion should provide some

insight to the development of the model.

The combined fuel /oxidizer conservation equation can be

written as

O. Cp9^(YF-Yo'' wl_9^v(YF-Yo 

yFF}^- o. (5-50)

0 0 O W

0
73

Defining the velocity potential,,as

^(1^ YF +` ( 

';y'OWO (1+Yo,^ v w

k , (5-51)

(1+13)

the mass averaged gas velocity, v, can be expressed according to

I

V jon (1+B) V (5-5-2)

where 'B is the combustion transfer number given by

V, wF

B 

M FS+

o'wo°.

1-YFs

(5-53)

Equation (5-52) together with the mass conservation equation

(V.P U =0) yields the Laplace equation

2

b Y =0. (5-54)

From the definition of Y (Eq. 5-51), the boundary conditions

become

i

l on the surface of droplets

0 far away from the droplets.

The above equation is solved using a superposition technique

called the method of images. Briefly, in order to solve for the

fields, a series of point sources and sinks are placed inside

every droplet in the array which satisfy the boundary conditions.

r

The burning rate of the droplet k in an array is determined

by integrating the mass flux over its surface area

m^ =

j5

P^ AS. (5-55)
properties and only depend on array configuration.

74

SuLatitution for v from equation (5-52), gives

m k - 0 rPQ In (1+B) I f pw .dS.

4)l rs

(5-56)

The right hand side of equation ( 5-56) can be rewritten as

(5-57)

where Mk is the burning rate of droplet k if it were burning as

an isolated droplet and 

7k 

is the burning rate correction factor

for droplet interactions defined as

I

k y ^ rs

.dS. (5-58)

For an array of N interacting droplets, can also be shown

as (Labowsky, 1980b)

N ,

XM 7 °^ Q ^'^

^ Q^I

(5-59)

I

where c^ designates elements of an NO matrix representing the

transfer rates of droplet k, when it is in the field of a unity

potential droplet, 9 , with the rest of the array being at zero

potential. Using the method of images, these elements can be

determined by sodding the images source strengths inside; the k-th

particle that are associated with the Q field.

As it appears, the calculations of the combustion rate,

cup-section factor are independent of the fuel or oxidizer
75

55 Array Geometry

In this work, the correction factor is computed for an evenly

t

dispersed configuration inside the flame holder. The droplets are

` divided i nto geometrically similar pLinar arrays ' separated by the

interdroplet spacing , as shown in Figure 5.1. Except for the

`xdroplets near the burner wall, every droplet is encircled by six

immediate neighbors placed at the corners of a hexagon. For a

burner diameter, d, and center-to-center droplet spacing,/., the

number of droplets that can be placed on a layer is equal to

d?

number of droplets per Layer

2 

^y (5-60)

Sin

The total number of droplets per unit volume or number density

is given by

h

n cl ^-

droplet number density = '' (5-61

71 h d Z/y

Since the burner dimensions are large compared to the droplet

spacings ( i.e. h/t» y ), the above expression simplifies to

2

droplet number density = 3

Stin 60

(5-62)

Usually, droplet number density is measured by optical,

counters or determined from the operating; conditions (as in

well-chara - t-Arized sprays). Thus, droplet spacing in a uniformly

distributed monodisperse spray, can be calculated from equation

t r 
` 7 6

i

ti^Q 0 Q 0^^

- - — 0 O O Q O ---

IoO 

O 0 0`'`.

^0 0 0

d

0

so

---104 0

0 0

Figure 5.1. Monodisperse droplet arrangement used in the

numerical calculations.

^^ 

ii

Ii
It

77 

(5-61).

5.6 NO Kinetics

Nitric oxide formation reactions involving the oxidation of

atmospheric nitrogen ( Zeldovich mechanism) are considered. These

reactions and their rate data are listed below (Bracco, 1973;

Bowman, 1975; Peterson and Laurendeau, 1,982; Dasch and Blint,

1984).

Forward rate constant Backward rate constant

0 +N ^ NO+N 1.36x10e.y %p(-75,400/RT) 3.1x103exp(-334/RT)

2

N +0 ^ NO+0 6.4x10 T exp(­6260/RT) 1.5x1U T exp(-38,640,/RT)

13 19

OZ+ 

2

O +O+N2 6.Ox1O (118,000/ITT) 1.0x10

x exp(-118,000/RT)

The rate constants for the bimolecular and termolecular reactions

are in units of cm /mole sec and cm /mole sec, respectively. In

view of the fact that NO transformation to NO is not considered,

these reactions account for the total NO production.

x

Assuming steady-state N atom concentration and equilibrium

concentration for 0 atom with respect to 0 , concentrations of N2

and NO are determined as their species conservation equations are

s: solved simultaneously with the energy, fuel and oxidizer

equations. The initial and boundary conditions are similar to

those for oxygen as discussed in section 5.3

5.7 Representative Results

5.7.1 Preflame Spray Vaporization

Calculated results for stoichiometric sprays of methanol and 

_

,
78

n-octane are presented in Figures 5.2 and 5.3 for an initial

E

droplet diameter of 50 pm and droplet and gas temperatures of 24

`C. These plots show changes in droplet diameter, gas phase and 

u droplel ^ temperatures, extent of prevaporization and the mass

transfer number during vaporization. The last point on each curve

corresponds to conditions at the end of the droplet travel time in

the preflame regions of the combustor.

After vaporization is initiated, the droplet surface

temperature drops to its lowest value. Then, as illustrated in

Figure 5.4, it increases gradually and approaches the falling gas

and droplet temperatures. The reduced ga g temperature and

increased fuel vapor concentration decrease the rate of

vaporization substantially, inhibiting further droplet size

reduction. This is also demonstrated in the plots of the mass -

transfer number versus droplet travel time, where B number

decreases continuously and nears zero as the fuel vapor

concentration reaches its saturated value.

When vaporization occurs adiabatically, heat is extracted from

the liquid fuel as well as the gas phase to vaporize the droplets.

Among the fuels used in this study, methanol and isopropanol

require higher heat of vaporization than n-heptane and n-octane.

At the same time, the air to fuel mass ratio for a fixed

stoichiometry is less for the alcohols as compared to the alkanes,

leading to a more effective cooling and enrichment of the gas

phase by droplet vaporization. Under such conditions, the vapor

pressure at the surface of the fuel droplets decreases and thus

i ' hinders further changes in the evaporation characteristics of the
79

e.q

20

is

12

8

4

0

-4

-8

10.14

w

w

O

Z 0.0

M

Z

0

O

0-

ViO

E

55 ki

LLJ

4S 0

Ld

40

-j

0.

0

35

14 M

19'

Z

0.8

0

0.

0.6 <

w

a0.4 LL- 0

Z

0.2

Li

0.0 

Id U. f4b rd. I e (d. its 14 . Z-q 0.30 0.360

DRPLET TRAVEL TIME (sec)

Figure 5.2. Calculated evaporation characteristics of a 50 pm

diameter droplet in a monodisperse spray of methanol.

Droplet diameter;A - Droplet temperature;

n - Gas phase temperature; x - Mass transfer number;

+ - Extent of prevaporization. Dotted lines

represent adiabatic vaporization.
w

m

Z 0,02

m

Z

0

H

Fa

0,01

0

ci

a

0.03 1.0

Z

0

HF--

0.8 N

H

o!

0

0.6

w

o:

a

0.4

0

Z

0.2 LJ

x

w

80

24 - - _ 60

n

E

20 55 v

16 ^-''---- --- s0 w

cY

w ---------------------- a

H

^- 12 --_

45

o; w

w

a.

w

8 40 0

a.

^

a

0

4

35

0 0

0.03 0.06 0.09 0.12 0.15 0.138

0.00 0 0.03 0.06 0.09 0.12 0.15 0.f8

DROPLET TRAVEL TIME (sec)

Figure 5.3. Calculated evaporation characteristics of a 50 pm

diameter droplet in a monodisperse spray of n-octane.

• - Droplet diameter; ♦ - Droplet temperature;

• - Gas phase temperature; x - Mass transfer number;

- Extent of prevaporization. Dotted lines

,i represent adiabatic vaporization.

i

1
10.ddb 4,010 0.015 0.020 0.025 0.030

0.005 0.010 0.015 0.020 0.025 0.030

DROPLET TRAVEL TIME (sac)

o!

w

a.

w

-0

4

0

6

2

R

4

0

-4

-8 0

Figure 5.4. Calculated temperatures for early stage vaporization

of monodisperse methanol and n-octane aerosols.

♦ - Droplet temperature; ♦ - Droplet surface 

temperature; n - Gas phase temperature.

N-OCTANE

81
82

fuel spray, even for long droplet residence times.

In these calculations, the spray is considered to vaporize

adiabatically while travelling inside the upper and lower housing

assemblies. But, as the fuel aerosol enters the flow reducing

sections, additional heat is transferred to the cold spray from

the combustor walls which are kept at the air preheat temperature,.

Heating of the aerosol by constant temperature walls is treated as

a thermal-entry length problem. This results in an increase in

the gas and dro p let temperatures and a decrease in droplet size as

shown in Figures 5.2 and 5.3. In the absence of the wall heating,

adiabatic spray vaporization continues for the entire droplet

travel time as shown by the dotted lines.

Table 5.1 .summarizes the calculated vaporization parameters

for the fuel, spro°ys tested in this study, based on an initial

droplet diameter of 50 pm and different air preheating

temperatures. As expected, the final droplet size and the extent

of prevaporization are strongly influenced by fuel volatility and

ambient temperature. These predictions are used later as initial

conditions in the spray combustion model.

Figure 5.5 compares the predicted results of the aerosol

temperature with the actual measurements made along the spray

centerline. Since droplet impaction and agglomeration on the

thermocouple tip was unavoidable, it is assumed that the

measurements represent the average of the droplet, gas phase and

droplet surface (wet bulb) temperatures. Both measured and

calculated values correspond to initial droplet diameters equal to

the NO, minima, air temperature at 22 0C and overall stoichiometr,y .
e,

i

a

^f

83

Y`

P

^G 

Tabu 5.1. Computed parameters for pr.eflame spray vaporization. of

50 μm droplets at various air preheat temperatures.

Droplet temperature is initially at 24*C,.

f` Air

Tewperature

CIO

fi 24

34

44

Droplet Diameter at the Flame Bolder (pm)

Methanol Isopropanol N-heptane N-octane

35.0 40.0 33.4 40 .0

25.6 34.1 24.6 33.3

0.0 25.2 3.2 22.4

4 ^ 

Y
8,4 

2 5 1.

n

oU - N-OCTANE

v

20 Q N-HEPTANE c^ 0 0 0 G 0 0 0 o no

0 0 0 0 0 0 0

^ 1s Q

W

0.

°

LJ

n

to

c°n 0

w

00 2 4 6 8 10 12^ 14 16 18

n

2 5

r- -^

° O - ISOPROPANOL

v

20 0 — METHANOL wa

Q15 0 0 0 0 0 0 0

W

p ^

W10 O O O O

f O O

J 5 0

0

0- 0

r UJ 0

x ^a

C3 0 O 0 q 0 0

^0 2 4 6 8 10- -•'12 14 16 18

HEIGHT ABOVE ORIFICE PLATE- (cm)

r, Figure 5.5. Comparison of calculated and measured aerosol

temperatures. Solid lines represent the Calculated

values.
85

of 1.0. In spite of the uncertainties in the measorements and, the

model predictions, the trends are similar.

5.7.2 Burnipg Rate Correction Factor.

Effects of droplet number density and into-rdroplet spacings on

spray burning rate are examined for evenly dispersed arrays of

monosized droplets (similar to the one shown in Figure 5.1). In

such cc.-figuration, droplets that are located around the array

center experience a stronger interaction than those located close

to the outer edge.

Computed burning rate correction factors for three arrays of

interacting droplets are listed in Table 5.2. The calculations

were done for a fixed interdroplet distance of 20 droplet

diameters (4-40). In all cases, the burning rate correction

factor, 7, for any given droplet is less than unity, indicating

slower burning compared to that of an isolated droplet of the same

size. ^ increases as one moves away from the center of the array

and decreases with increasing number of droplets.

For closely packed arrays or those that contain large number

of droplets (>37), the accurate determination of 7 by Labowsky's

droplet superposition procedure becomes exceedingly tedious.

Thus, A second superposition method was used to extend his

technique to cases that involve a great number of droplets. This

development is based on the fact that any monodisperse array can

be constructed by superimposing arrays of six droplets around a

Fprimary array of seven. For instance, a 55 droplet array can be I J.

WV

1W composed of eight consecutive arrays spaced about the center of
86

TABLE 5.2 Computed burning rate correction factors for three

monodisperse arrays of droplets with Z =40.

Number of Droplets

Center Edge

Per .Array Droplet Droplet Array Average

7 0.865 0.897 0.892

13 0.813 0.872 0.847

19 0.772 0.835 0.815
17

the primary array, as demonstrated in Figure 5.6. With every

addition, the burning rate of the entire configuration reduces by

a factor which is equivalent to the burning rate correction factor

of the superimposed array. Figure 5.7 shows the calculated

average burning rate correction factor as a function of droplet

spacing for variot:;, monodisperse arrays. The data points and the

solid lines represent the results obtained from the droplet and

array superposition techniques, respectively. The ^.esults are in

good agreement with a maximum difference of 1.0% f>r the studied

cases.

When droplet interactions are considered in a spray combustion

,h

model, the burning rate correction fa-.tor has to be reevaluated as

the interdroplet spacing changes. However, successive application

of the droplet interaction model could add up co a considerable

increase in the computation time. To overcome this problem, the

dependence of the, burning rate correction factor on X, is expressed

as a functi.ona.1 relationship. Computed values of 7 are used to

determine the 'best fit' in the form of four degree polynomials.

These expressions are utilized in the spray combustion model to 

facilitate the evaluation of l.

5.7.3 Spray combustion and NO formation

Computations were performer: for stoichiometric sprays of

n-octane and methanol. In all cases, the initial conditions at

t=0 were determined by the spray vaporization model.. The time

U 

domain was set equal to the duration, after which, the calculated

results were at their steady state values. ;`
H$

e ^ o

Q ® e 0 ® e

® U • 0 • 8

e e u 0 0 u o 0

® • 0 0 0 •

0 o a 0 0 a e e

e ® 0 4 ® 0

Q e e

Figure 5.6. Droplet configuration for a 55 droplet array.
m

D 00 C.0

CD m CD m m

w

o d ^4

4) 0

0

t4 0

o u

o w 4) ,o

"mwC4

uuav'da

W .^ H

H ^s

P.

.0 a C!

uN•,^ou

_U auiw° *db

L Noosdcsa

U ou• od ° c~d

Q u

a) cC a to

CL 0

^ f ^H ^ "'o

J gooO'le bb N O N c

mo

b44 bOb

•u

0 u to O

u u d u u 0

41

N o u a0

r

vi

v

00

^^ w

=

r M M Ln rn Ln N

89
90

To initiate combustion, the gas phase temperature was raised

to 1100 0K by reacting a part of the fuel vapor and the oxidizer.

Further fuel and oxidizer consumption as well as the temperature

rise due to the heat release are determined by the spray

combustion model. The continous increase in the gas phase

temperature eventually leads to droplet ignition which is seen as

a bulge in the temperature profiles. Figure 5.8 to 5.10 show the

development of temperature and species profiles for 27.0, 33.2 and

47.7 pm n-octane droplets, corresponding to initial droplet

diameters of 37.0, 43.3 and 57.5 gm, respectively. The time

dependence of the profiles are noted on the plots. Followed by a

rapid reduction in the fuel vapor concentration, the flame

temperature reaghes its maximum value close to the droplet

surface. The location of the maximum temperature coincides with

r

the crossing of the fuel and oxidizer profiles and moves with

changes in droplet vaporization rate and oxygen concentration

during combustion. For small droplets, gas phase combustion, and

droplet ignition are intensified by the high preflame extent of

vaporization. Much of the NO is .firmed in the hot gases

5 surrounding the burning fuel droplets, where premixed type of

Y

burning appears to dominate. In the case of large droplets,

temperature rises slowly as the reactions occur in a relatively

narrow zone. This is .attributed to a lower droplet vaporization

before the flame front and the slow propagation of the fuel vapor

emerging from the surface of the burning droplets. 8 g g Plets. After the

initial temperature rise, diffusional burning is also observed

^' near the droplet surface, as indicated by the peak in temperature
.. { ,

3 t o 0,0011 sec

10

10 ®^

E 10

n -1

to

0 -2

z

10

-3

10 r

10 i 0 M9 10 5S 40

2400

n

V 2100

0

v

1800

w (^

1500

1200

a 900

E

600

300

0,8

0.8

> 0,4

0,2

0,0

y

.. .. ...

5

p

5 4

0.20

0.16

r

0.12

N w

0.08 }

Q

0.04

2.00

F

w 91

I - t- 0,0 sec; 4 - in 0,0015 sec

2 - to 0 0009 sec 5 in 0 Alen sec

RADIAL DISTANCE x r-1

So

Figure 5.8. Evolution of temperature and mass fraction profiles

for a 27.0 pm droplet in a monodisperse spray of

n-octane at q)= 1.0 and Eo = 0.61. '

lx

i
5

0,20

0.16

1 - t- 0,0 sac; 4 - t- 0,0018 sec

2 - t- 0,0012 sec; 5 - t- 0,0021 sac

3 - t- 0,0013 sac; 6 t- 0,0160 sec

1 0 1

}

1 0

.^

92

E 10

CL

va ^^1

Z -2

10

-3

10

10

n

2400

0 2100

v

W 1800

1600

5200

w

a. 

s00

F- 600

300

0

1,0

0.8

0,6

Ur G. Q

0.2

0.0

0,12

N

O}

0.08

0,04

10,00

RADIAL DISTANCE x s1

n

Figure 5 . 9. Evolution of temperature and mass fraction profiles

for a 33.2 pm droplet in a monodisperse spray of

n-octane at 4). 1.0 and Eo = 0.55.
93

1 - !- '3,0 sac; 4 - !- 0.0034 sec

2 - !- 0,0019 sac; 5 !- 0,0039 sec

3 - It- 0,0024 sac; 6 E- 0,0180 sec

t0

1

10

n 0

E 10

Q.

v -1t0

to

-3

to

-410

2400

0 2100

V

j 1500 _

1200

a 900

f

600

300

1.0

0,8

0.6

}4' 0,4

0.2

0.0

RADIAL DISTANCE x r

s

0

6

2

N

}

8

4

0

Figure 5.10. Evolution of temperature and mass fraction profiles

for a 47.7 pm droplet in a monodisperse spray of

^tane at %F= 1.0 and =0 = 0.43.

I

f

I

I
n

t

s 94

profiles. However, NO production for large droplets increases as

they achieve elevated flame temperatures due to their higher

Damkohler number. At some intermediate size, where minimum NO X is

predicted, the flame temperature and the fuel vapor concentration

6w

in the gas phase fall in between the values observed for the small

and large droplets. Under this situation, droplet interactions

reduce the burning rate and lower NO formation by confining its

production to a thin reaction zone.

In these plots, there is little change in the nitrogen

b: μ

' profiles as a very small amount of it reacts to form nitric oxide.

A slight but gradual decline in the NZ levels is noticed as the

product gases move out radially and change the nitrogen mass

fractions. Since, nitrogen is always in abundance, nitric oxide

formation is primarily influenced by the gas phase temperature and

oxygen concentration. The location of maximum NO formation is in

the vicinity of the peak temperature, but it moves outward to

regions of higher oxygen concentration as the temperature peak

begins to diminish.

Similar profiles were also obtained for methanol sprays. The

main difference between the methanol and n-octane results is in

the relative location and the magnitude of the flame temperature.

For methanol, the flame front stays very close to the drople

surface due to its high heat of vaporization. This phenomenon has

also been recognized by Resten (1972). Relative to n-octane,

methanol has a lower heat of combustion which gives a lower flame

temperature. These two events result in a lower NO formation for

i
f

95

methanol. In addition, inclusion of the prompt NO formation

mechanism can ke expected to increase the difference, by

predicting a higher contribution for n-octane.

Predicted and experimental results for n-octane, showing the

effects of droplet size and air preheating temperature on NOy

formation, are compared in Figures 5.11. Although the calculated

results are higher than the measured values, the general trends

are in reasonable agreement. As the air preheat temperature

increases, more fuel is vaporized before the flame front, leading

to a rapid increase in the flame temperature and the weakening of

the droplet interactions. The model also predicts the shifts of

the NOx minimum point towards larger droplet diameters with

increased air preheating temperatures. In these analyses, the

contribution to the total extent of preflame vaporization due to

screen impaction was not considered. Such consideration requires

experimental measurements of fuel droplet losses. Inclusion of

this effect is expected to reduce the skewness of the predicted NO,

trends on both sides of the minimum NO point, thereby improving

the agreement between the model and experiment.

In summary, the computed results indicate the importance of

the extent of prevaporization and droplet interactions on NO,4

production. Gas phase stoichiometry has a significant effect on

the volume of the hot gases surrounding a fuel droplet, where NO

is formed. On the other hand, the release of fuel vapor from the

droplet to the reaction zone is controlled by droplet interactions

which reduce the volume of the hot gases and NO production by

bringing the flame closer to the droplet surface.
e

96

90

80

^ 70 E

Q. a

60 x

0

z

50

40

303 3

90

80 MODEL

E 70

CLa

%.10 60 Tair- 24 C X

0

z

_- 50

40

EXPERIMENT

3030 35 40 45 50 55 60

DROPLET DIAMETER (pm)

Figure 5.11. Comparison of measured and predicted NOx

concentrations at different droplet diameters and air

preheat temperatures for n-octane sprays at = 1.0.
97

While a qualitative agreement exists between the measurements

and the predictions, the model overestimates the NO eml ,,s on

levels. Higher NO predictions are directly related to the greater

flame temperatures computed in the model, using a single step fuel

oxidation rate. The discrepancies can be remedied by the

following considerations. Use of detailed kinetic mechanisms for

the fuc;'. oxidation and NOh formation can improve the predictions

`. significantly. An accurate determination of the actual droplet

travel time in the preflame regions of the combustor is also

desirable due to its importance in the evaluation of the initial

conditions for this model. Also, the applicability of the

spherico-symmetric governing equations is restricted to zero

gravity or convection free situations. Convective effects distort

r

the spherical flame shape which can bring about different droplet

interactions and NOX formation. A detailed analysis of the flow

field around the burning droplets would be necessary in order to

r- relax the restrictions imposed upon spherical flames.

These refinements should alleviate the differences and make 

the model a useful tool for defining the operating conditions at 

which NO X formation is minimum.

i

^
98

CHAPTER 6

Conclusions and Recommendations

6.1 Conclusions

A one dimensional monodisperse fuel spray combustion facility

was developed and used to study the formation of oxides of

nitrogen under various operating conditions. Inflame and

postflame measurements of temperature, NO and NOV and other

emissions were made over a 26-74 pm droplet size range and

different stoichiometries. Single component fuels including

methanol, isopropanol, n-heptane and n-octane, as well as

nitrogen-containing fuels were tested.

Postflame measurements of the exhaust gases from the

combustion of nitrogen-free fuels indicated the existance of an

optimum droplet diameter for lower NOx production in the 43-58 μm

droplet size range. Up to 30% reduction in the NOX emissions,

relative to the small droplet limit, was detected. The observed

behavior was attributed to the effects of droplet size, gas phase

stoichiometry and droplet interactions in the flame.

Extent of prevaporization determines the gas phase

stoichiometry and affects the temperature and the volume of the

hot gases surrounding the fuel droplets. The thickness of the

reaction zone, however, is influenced further by droplet
99

interactions which control the s,yiray burning rate. All of these

factors depend on the initial droplet diameter and the fuel

evaporation characteristics. For small, droplets, rapid

vaporization before the ,flame front Intensifies gas phase

reactions, leading to a fast increase of temperature and NO x

production,. Laege droplets evaporate Less, but form more NO as

X

they attain higher flame temperatures during their lifetime.

Droplet interactions are weak for both small and large

droplets. This is caused by rapid prefame vaporization and

increased droplet spacings in the former case, and fewer

-` interacting droplets in the case of large droplets, T,Ae optimum

droplet diameter for minimum NO, formation occurs at some

intermediate size with relatively stronger interactions.

A mathematical model for the analysis of preflPme droplet

vaporization and O formation in the combustion of nitrogen-free

x

fuel sprays, was developed. The predicted results indicated a

qualitative agreement with the measurements and demonstrated the

importance of the evaporation and combustion characteristics on NO

emissions.

s 'r

With nitrogen-containing additives, the nitrogen

transformation process to NO

x

 was less dependent on flame

temperature and was influenced primarily by oxygen concentration.

At high fuel-N contents, NO

x 

decreased continuously with

increasing droplet size. For small droplets, oxidation of the

pyrolysis fragments of the nitrogen additive improved as a result

of higher prevaporization and better oxygen penetration through

the droplet flame zone.

i

i
100 

6.2 Recommendations for Future Work

While this study points out the potential for minimizing NO

x

emissions f rom fuel spray combustors, further experimental and

theoretical advancements are still needed befoxe'the acquired

knowledge can be applied to such systems.

Suggested experimental studies and their objectives are listed

below.

(a) In situ droplet sizing and number density measurements in

the flame and prior to the flame is required to obtain

valuable information on vaporization and burning rates of

interacting fuel droplets. The number of interacting

droplets that survive the screen impaction and the total

extent of preflame vaporization can be determined from

such measurements.

(b) Detailed analysis of combustion products and probe

reactions are necessary to explain the observed NO

X

consumption in the post flame regions.

(c) Polydispersed sprays and the effect of Sauter Mean 

Diameter on NO formation should be considered for their

X

i

applicability to practical spray combustors.

(d) Inflame and postflame analyses of the nitrogenous species

must be carried out to get a better understanding of

nitrogen transformation and NO yield in fuel sprays that

X

contain chemically bound nitrogen.

As far as the modeling aspect of spray combustion and NO

X

formation is concerned, improvements can be achieved in several

ways.
101

(e) A more detailed chemical model for fuel oxidation is

needed to improve prediction of NO production.

(,f) Flame shape distortion due to convective affects and its

impact on droplet vaporization, droplet interactions and

NO formation requires some consideration. An in-depth

x

analysis of the ,flow field around the burning fuel

droplets is needed to account for such phenomena.

(g) Fuel-N conversion to NO should be studied by implementing

x

a comprehensive species transformation mechanism into the

spray combustion model.
10^

1

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1983, "Group Combustion Models and Laser 'Diagnostic Methods in

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u, 1985a, "A Structural Study of Methane -Acei:onitrile-Oxygen

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a

W 

. _ _ _ F ,^ .r-,-,-

a

tom?

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11 1.04

Crowhurst, D. and R.F. Simmons,

1985b, " A Structural Study of Acetonitrile -Oxygen Diffusion Flames

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Dasch, C.J. and R.J. Blint,

1984, "A Mechanistic and Experimental Study of Ammonia Flames,"

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1974, "Overall Reaction Rates of NO and N 2 Formation from Fuel

Nitrogen," Fifteenth Symposium ( International) on

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Faeth, G.M.,

1979, "Spray Combustion Models-A

AIAA Seventeenth Aerospace

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Review," AIAA Paper No. 79-0293,

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1971, " Formation of Nitric Oxide in Premixed Hydrocarbon Flames,"

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r 1953, "Studies of the Combustion of Drops in a Fuel Spray- The

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T

f

3

S

1

h

Z y.:.x -
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Gustaferro, J.F.,

1982, "U.S. Energy for the Rest of the Century," Office of

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1976, "Propagation Velocity and Structure of Flames in DropletVapor-Air Mixtures," Combustion Science and Technology 15,

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1983, "The Origin and Nature of "Prompt" Nitric Oxide in Flames,"

Combustion and Flame 50, 41-57.

Haynes, B.S.,

1977a, "Reactions of Ammonia and Nitric Oxide in the Burnt Gases

of the Fuel-Rich Hydrocarbon-Air Flames," Combustion and

Flame 28, 81-91.

Haynes, B.S.,

1977b, "Production of Nitrogen Compounds from Molecular Nitrogen

in Fuel-Rich Hydrocarbon-Air Flames," Fuel 56, 199-203.

Hori, M.,

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Kanevsky, J.,

1956, "Interference During Burning in Air for Nine Stationary Fuel

Droplets Arranged in a Body-Centered Cubic Lattice,"

Jet Propulsion 26, 788.

Kent, J.A.,

1970, "A Noncatalytic Coating for Platinum-Rhodium Thermocouples,"

Combustion and Flame 14, 279-282.

Kesten, A.S.,

1972, "Analysis of NO Formation in Sing?.e Droplet Combustion,"

Combustion Science and Technology 6, 115-123.

Koshland, C.P. and C.T. Bowman,

1983, "Combustion of Monodisperse Droplet Clouds in a Reactive

Environment," Paper No, 83-43, Western States Section/

The Combustion Institute, October 17-18.

Koshland, C.P. and C.T. Bowman,

1985, "Combustion of Monodisperse Droplet Clouds in a Reactive

Environment," Twentieth Symposium (International) on

Combustion, The Combustion Institute, Pittsburgh, PA.

Kumagai, S. and H. Isoda,

1956, "Combustion of Fuel Droplets in a Falling Chamber," Sixth

Symposium (International) on Combustion, P.726, Chapman

and Hall, London.
106

Labowsky, M.,

1976, "The Effects of Nearest Neighbor Interactions on the

Evaporation Rates of Cloud Particles," Chemical Engineering

Science 31, 003-813.

Labowsky, M.,

1978, "A Formalism for Claculating the Evaporation Rates of

Rapidly Evaporating Interacting Particles," Combustion

Science and Technology 18, 145-151.

Labowsky, M.,

1980a, "Calculation of the Burning Rates of Interacting Fuel

Droplets," Combustion Science and Technology 22, 217-226..

Labowsky, M.,

1980b, "Transfer Rate Calculations for Compositionally Dissimilar

Interacting Particles," Chemical Engineering Science 35,

1041-1048.

Law, C.K.

1977, "Adiabatic Spray Vaporization with Droplet Temperature

Transient," Combustion Science and Technology 15, 65-74.

Law, C.R. and W.A. Srignano,

1977, "Unsteady Droplet Combustion with Droplet Heating-II;

Conduction Limit," Combustion and Flame 28, 175-186.

Lorell, J., H. Wise and R.E. Carr,

1956, "Stead-State Burning of a Liquid Droplet. II. Bipropellant

Flame,' J. of Chemical Physics 25, 2, 325-331.

Marberry, M., A.R. Ray and K. Leung,

1984, "Effect of Multiple Particle Interactions on Burning

Droplets," Combustion and Flame 57, 237-245.

— s 

Mellor, A.M.,

1980, "Semi-Empirical Correlations for Gas Turbine Emissions,

Ignition, and Flame Stabilization," Prog. Energy Combust

Sci. 6, 347-358.

Miyasaka, K. and C.R. Law,

1981, "Combustion of Strongly-Interactive Linefir Droplet Arrays,"

Eighteenth Symposium (International) on Combustion. p.283,

The Combustion Institute, Pittsburgh, PA.

Murphy, M.J. and G.L. Borman,

1979, "Oxides of Nitrogen Emission from a Burning Fuel Mist,"

` Combustion Science and Technology 21, 53-63. 

Nicholls, J.A., C.W. Kauffman, D.G. Pellaccio, D.R. Glass and

1980, J.F. Driscoll, "The Effect of Fuel Sprays on Emissions From

= r a Research Gas Turbine Combustor," Combustion Science and

j Technology 23, 203-213. 

"

h
1,07

Nizami, A.A. and N.P. Cernansky,

1978, "A Monodisperse Spray Combustion System and the Measurement

of Oxides of Nitrogen," Paper No. 78-37, Western States

Section, The Combustion Institute.

Nizami, A.A. and N.P. Cernansky,

1979 ? "NO% Formation in Monodisperse Fuel Spray Combustion,"

Seventeenth Symposium (International) on Combustion, p.475,

The Combustion Institute, Pittsburgh, PA.

Nizami, A.A., S. Singh and N.P. Cernansky,

1982, "Formation of Oxides of Nitrogen in Monodisperse Spray

Combustion of Hydrocarbon Fuels," Combustion Science and

Technology 28, 97-106.

Nuruzzaman, A.S.M., A.B. Hedley and J.M. Beer,

1971, "Combustion of Monosized Droplet Streams In Stationary SelfSupporting Flames," Thirteenth Symposium (International) on

Combustion, p.787, The Combustion Institute, Pittsburgh, PA.

Opdyke, G. Jr.,

1983, "Private Communication," AVCO, Lycoming Division, Stratford,

CT.

Perry, R.H. and C.H. Chilton (ed.),

1973, Chemical Engineer's Handbook, McGraw-Hill, New York, NY.

Peterson, R.C. and N.M. Laurendeau,

1982, "A Kinetic Mechanism for Fuel-Nitrogen Conversion in Lean to

Rich Flames," Paper No. 82-15, Central States Secti ,)n/ The

Combustion Institute, March.

Polymeropoulos, C.E. and S. Das,

1975, "The Effect of Droplet Size on the Burning Velocity of

Kerosene-Air Sprays," Combustion and Flame 25, 247-257.

Rao, K.V.L. and A.H. Lefebvre,

1981, "Spontaneous Ignition Delay Times of Hydrocarbon Fuel/Air

Mixtures," Paper No. 81-03, Central States Section/ The

Combustion Institute, March 23-24.

Sangiovanni, J.J. and M. Labowsky,

1982, "Burning Time of Linear Droplet Arrays: A Comparison of

Experiment and Theory," Combustion and Flame 47, 15-30.

Sapre, A.R. and A.A. Quader,

1983, "Conversion of Fuel Nitrogen to NO in Automotive Engines,"

SAE Paper No.831675.

Sirignano, W.A.,

1983, "Fuel Droplet Vaporization and Spray Combustion Theory,"

Prog. Energy Combust. Sci. 9, 291-322.

s

r
M

x

{ Spalding, D.B.,

1953, "The Combustion of Liquid Fuels," Fourth Symposium

(International) on Combustion, p . 847, The Williams & Wilkins

Co., Baltimore, MD.

Thermo Systems Inc.,

1977, Instruction Manual for Model 3050 Berglund-Liu Vibrating

Orifice Monodisperse Aerosol Generator, St. Paul, MN.

Tuttle, J.H., M.B. Colket, R.W. Bilger and A.M. Mellor,

1976, " Characteristic Times for Combustion and Pollutant Formation

in Spray Combustion," Sixteenth Symposium (;International) on

Combustion, p.209, The Combustion Institute, Pittsburgh, PA.

Umemura, A., S. Ogawa and N. Oshima,

1981a, "Analysis of the Interaction Between Two Burning Droplets,^^

Combustion and Flame 41, 45-55.

Umemura, A., S. Ogawa and N. Oshima,

1981b, "Analysis of the Interaction Between two Burning Droplets

with Different Sizes," Combustion and Flame 43, 111-119.

Westbrook, C. K. and F. L. Dryer,

1984, "Chemical Kinetic Modeling of Hydrocarbon Combustion,"

Prog. Energy Combust. Sci 10, 1-57.

Williams, A.,

1973, "Combustion of Droplets of Liquid Fuels: A Review,"

Combustion and Flame 21, 1, 1-31.

Williams, F.A.,

1965, Combustion Theory, Addison-Wesley, Reading, MA.

P

Y

Xiong, T.Y., C.K. Law and K. Miyasaka,

1985, Interactive Vaporization and Combustion of Binary Droplet

Systems," Twentieth Symposium (International) on Combustion,

The Combustion Institute, Pittsburgh, PA.

1;08
109

APPENDIX A

Supporting Experimental Facility

A.1 Introduction

The major components of the experimental setup, i.e., the

monodisperse aerosol generator and the temperature and NO,

measurement systems, were described in Chapter 3, This appendix

provides a description of additional facilities including a fuel

prevaporizer and other exhaust gas analyzers.

A.2 Fuel Prevaporizing System

In order to determine the small droplet size limit, a fuel/air

heating arrangement was added to the experimental facility. This

set up provided prevaporized/premixed fuel/air mixtures by

combining the liquid fuel and air in a tee and heating the mixture

in a stainless steel tube. The tube was formed into a vertical

three-loop helix and wrapped with heating tape. The fuel vapor

was heated to abort 65°C before entering the burner through the

normal dispersion air path. This heating was sufficient to keep

the mixture above the dew point of the fuel and to avoid

condensation of the fuel vapor on the combustor walls. Normal

cooling of the fuel vapor in the combustor resulted in a mixture

temperature of about 26°C at the flame holder exit.

V. _ __........ ,., .. ,...,... i^,^r,^n svMr2zxu+yrrr^-rre.x iv.^. .,..^.. _ ♦ ^71!N N,^^^.(r^' _ ^ rQ
11,0

A.3 Sampling and Measurements of Exhaust Gases (UHC, CO, CO 2 and OZ)

Inflame and postflame combustion gases were sampled and

analyzed for hydrocarbons, carbon monoxide, carbon dioxide and

oxygen concentrations. Hydrocarbons were measured as propane

using a heated flame ionization detector (Beckman Model 402). CO

and CO2 were measured using nondispersive infrared analyzers

(Horiba Models AIA--21-AS and AIA-21, respectively). 02

concentration was measured using a polarographic analyzer

(Teledyne Model 326AL). Due to the high flow requirements by the

analyzers, the combustion gases were sampled under atmospheric

pressure using a 3.17 mm (O.D.) stainless steel tube with a 2 mm

opening at its tip.

4
APPENDIX B

Complementary Results

B.1 Introduction

This appendix reporLg expeI°iuntal, resul tts taken in addition

to those presented in Chapter 4. In particular, the effects of

fuel nitrogen content and droplet size on tho NO, flame structure

are demonstrated in section B.2, while the results of the exhaust

emission measurements for a number of operating conditions are

given in section B.3.

B„2 Axial NO, NOX and Temperature Profiles for Fuel-N Additives

Representative results for the axial variations of

temperature, NO and NOX concentrations for n-heptane droplets

doped with f% nitrogen by weight as pyridine, were shown in

Figures 4.24 and 4.25. Additional results at different fuel-N

contents are shown in Figures B.1-B.5. After a rapid increase

with temperature in the flame zone, NO and NO X reduce gradually in

the post flame regions to their steady state levels. Results for

different size droplets indicate that more fuel-N converts to NO%

at smaller diameters. These general trends are similar to those

discussed previously in sections 4.6 and 4.7.2.

W 

ill

F
160 

f

11 T.—

1200'

Ia 00a

W p 800-

400-

200

0 2 4 6 a 10 12

16

12

0

z

1 1

160

120

CL

Be

40

01

AXIAL POSITION OF PROBES (cm)

Figure B.1. Centerline NO, NOX and temperature profiles for

n-heptane doped with pyridine (0.1% N by weight).

0 D -- 37.0 pm; [3 ,g,x - D = 49.5 pm;

a ► v+ D = 69.6 pm.
113

i

1600

JU

^ 1400. t+ '^^ '

1200

a 1000 x X % ^

a

800-

JAR

a see

T

ham- 400

200

002

4 8

8 10 12

14

600

see

400 E '

a

a

000

0

z

200

100

0e

2 ^^ 6 8 10 12 14

600

see -

400

CL

a

300

0

Z 200

100

00 2 4 8 8 10 12 14

AXIAL POSITION OF PROBES <cm)

Figure 'B.2. Centerline NO, NO x and temperature profiles for

n-heptane doped with pyridine (0.5% N by weight).

o , •,* - D = 37.0 yam; q ,0,x D = 49.5 pm;

A A,+ D = 69,6 }gym.

i
AXIAL POSITION OF PROBES Ccm)

Figure 13.3. Centerline NO, NOX and temperature profiles for 37 pm

n-heptane droplets. q ,go x -4)= 0.85; 6,A,+ 1.2.

6

n

F

ff

C,

4

0

3

z 2

1

O^

0 2 4 6 a 10 12 14

a

CL

V

X

0

z

7?

U

0, t

W

IU

114
1600

U

1400+

5000-.'du 200L I

a 1000.

Q800

a

CL 800

E

►W- 400

200

00 

2

160

rze

a

CL v

r.^ O 80

r

z

0z

r

/^

1

a

a

v

K

O

z

O

z

x

10 12 1

AXIAL POSITION OF PROBES (cm)

Figure B.4. Centerline N0, NOK and temperature profiles for 37 pm

n-heptane droplets doped with pyridine (0.17 N by

weight) . 0 ,M, x -^ = 0.85; p ,A,+ - (P = 1.2.
n ^

u

V

w 1

Q

W

Q

F

W

H

6

S

n

t

v

4

w

t7 3

z

0 2

z

1

60

50

n

E

°a 40

v

k

O 30

Z

O 20

z

10

11,6

AXAIL POSITION OF PROBES (cm)

Figure B.5. Centerline NO, NOX and temperature profiles for 37 }gym

n-heptane droplets doped with pyridine (0.57 N by

weight) . O ,M,x 0.85; 6,A,+ 1.2.

It
117

B.3 Exhaust Emission Measurements

Exhaust gas analyses along the burner centerline were carried

out in order to determine the local equivalence ratios and 

combustion efficiencies. Concentrations of major products and

reactants including unburned hydrocarbons, CO, C( and were

determined from the combustion products of n-octane aerosols for fi

different stoichometres and droplet sizee. The hydrocarbon

sampling line was heated and therefore, the measurements are on a

wet basis. The CO, CO -ana 0 measurements, however,, are on dry

2 2

basis, since water was condense d and removed from the sampled

gases before they were analyzed.

Figure B.6 and B.7 show the effect of equivalence ratio on the

a ial variations of UHC, CO, CO and 00 concentrations in a 37 pm

2

aerosol of n-octane. The results demonstrate a rapid increase in

CO and CO with a substantial reduction in 0 and UHC

2 2

concentrations in the flame zone. Further consumption of 0 2 , UHC

and CO occurred in the post flame regions with CQZ values reaching

steady levels at about 5 cm above the flame holder. For lean and

stoichiometric mixtures, the exit plane CO measurements were very

low (order of ppm's), but increased for rich mixtures. On the

other hand, the hydrocarbon emissions were consistently low for

i

different equivalence ratios, indicating complete combustion for

all cases.

The UHC emission measurements are shown only for the post flame

regions. Large fluctuations in the UHC readings were observed

near the flame zone where fuel droplets were drawn into the

sampling probe, due to the high sampling flow requirements by the

hydrocarbon analyzer.

r^ 
118

16

0 12

CrIj

0Z 8

N

0

L)

Ck

0 2 4 6 8 10 12 14

16 2

A A

0 12-

C\j

0 E

z

CL

0.

0.

U

0

U

0

0 2 4 6 8 to 12 14'

AXIAL POSITION OF' PROBE (cm)

Figure B.6. Effect of equivalence ratio on centerline CO, CO2 , 02

and UHC profiles for 37 pm n-octane droplets.

q - CO; n - CO2 o 02 ; ♦ - UHC.

.........

CL

CL
lly 

I'

r

r

n 

16

a^

0 12 E

u

N

0

o g

z

a

0

U 4

0

U

0

S

4

3 ^

E

a

a

v

2 U

i

0

16 2

0

12

S,

a

c^

av m

U

4

,

0

U

0 0 2 4 6 8 10 12 14

or 2 4 6 8 10 12 14

AXIAL POSITION OF PROBE (cm)

Figure B.7. Effect of equivalence ratio on centerline CO, CO 2 , 02

and UHC profiles for 37 μm n-octane droplets.

p - CO ; • - CO2 ; o - 02 ;,L - UHC .

Fr

30,
R

120 

The effect of droplet diameter on exhaust emissions was

examined at an equivalence ratio of 1.0. Figure B.8 shows the

UHC, CO, CO2 and 02 measurements at 10 cm above the flame holder.

The highest CO and 02 , and lowest CO 2 concentrations were

observed around 43 pm droplet diameter (i.e., the observed NOy

minimum point, for n-octane at ( =1.0). This behavior is caused as

a result of increased droplet interactions and suppressed flame

temperature which lead to reduced 02 consumption and higher CO

formaticn. Hydrocarbon concentrations appear to increase with

increasing droplet diameter.

Computed equivalence ratios, based on the exhaust gas

analysis, are about 12% leaner than the measured input values.

However, gas chromatographic analyses of the exhaust gases for CO2

and CO concentrations, revealed only a 3% difference in the

overall stoichiometry relative to the measured input values, which

is well within the accuracy of the measurments. The discrepancy

in the measurements by the exhaust analyzer is due to

instrumentation and calibration errors. However, this does not

bias the above discussion, since, it is based solely on the

relative changes of , concentrations rather than the absolute

values.

1

i
12

1Y 

32

28

24

20

CL E

16 U N

0

U

6'

12

8

3

A A AA A—'_-A^^

0 0

30 40 so 60

DROPLET DIAMETER Cpm)

Figure B.8. Droplet size effect on v-ostflame CO, CO2 02. and UHC,

for n-octane at 1.0.

0 - CO CO2; 0 02 ; ♦ - UHC.
122

APPENDIX C

Thermophysical Property_ Calculations

Certain properties of liquids, such as latent heat of

vaporization and vapor pressure, are influenced primarily by

temperature. For a mixture of ideal gases, transport properties

vary not only with temperature, but also with concentration of the

individual components of the mixture. These variations were

included in the analytical computations.

The temperature dependence of each property was established as

a polynomial expression which fit the tabulated data with best

accuracy. At any given temperature, for known species

concentrations, the multicomponent transport properties are

calculated based on the following formulae (Perry and Chilton,

1973)

density:

P

P 

M RT7- Yj/WJ ^_i

specific heat:

C- Y,C P J= J PJ

thermal conductivity:

13

K= i= J J

►4' 1/3

2- ^W

J=1
123

^z

absolute viscosity: N^

V2

I ' ^ N W 1/2

X. .

i

These values were updated during the computations to account for

changes in temperature and species concentrations.
1.24

APPENDIX D

Temperature Corrections

As pointed out in Chapter 3, a bare Pt /Pt-13% Rh thermocouple

was used for temperature measurements. The results presented in

y Chapter 4 indicate that all temperature readings and, in

particular, the maximum flame temperatures are lower than

expected. Several factors including convective heat losses to the

gas sampling probe, conductive heat losses along the thermocouple

wires, radiative heat losses from the thermocouple ,junction and

catalytic reactiono on the surface of the , junction are considered

to be responsible for the discrepancy. The latter case was found

to be important only with new thermocouples. Catalyt ic activity p'

on the thermocouple junction was tested in a manner similar to

Rent (1970). After inserting a thermocouple into a flame, the

flame was blown out, leaving the thermocouple exposed to the cold

fuel/air mixture. It was noticed that while aged thermocouples

cooled down quickly to the gas temperature, new ones continued to

glow at a temperature of about 800 `C, indicating surface reactions

on the junction. Reduced catalytic effects were observed after a

few hours of operation at high temperatures.

The actual temperature is often calculated from an energy

balance on the thermocouple junction (F'ristrom and Westenberg,

1^ 

ti 

t[

l:

F 
k

k a

1

1,25

1965). This requires a knowledge of the local gas properties as

well as the emissivity of the junction, which are generally

difficult to evaluate. As a result, any correction determined by

this method is subject to a high level of uncertainty.

Instead, a more direct approach was taken to estimate the true

temperature. Four Pt/Pt-13% Rh thermocouple wires with different

wire diameters (0.05 to 0.25 mm), but equal lengths (30 cm), were

used to measure the flame temperature of a Bunsen burner at a

fixed location. The bead diameter of each thermocouple was

approximately 50% larger than the wire diameter. Figure 'D.1 shows

the variations of the flame temperature with the wire diameter.

As expected, the losses are lower with smaller wires. In fact,

the small heat dissipation resulted in the melting of the 0.05 mm

a

thermocouple wires shortly after a maximum temperature of 1781'C

was measured. From these results, the actual flame temperature

can be estimated by extrapolating the experimental trend to a

thermocouple bead of zero diameter. With the 0.075 mm

thermocouple, the combined conductive and radiative corrections

are estimated to be about 72°C at a measured flame temperature of

1772°C.

Another source of error in the reported data is related to the

interference of the stainless steel gas sampling probe. The

probe, as shown previously in Figure 3.2, was adjacent to the

thermocouple and is believed to have acted as a heat sink,.

reducing the convective heat transfer to the thermocouple bead.

Without the probe, the Bunsen burner flame temperature was about

222'C higher than that measured in its presence.
C9

M

CD

a^

N

N

E u+ o

C9

v

°u u a

o v

^ e o0

I.v aHiN

C9 H

3

45 m a

N

°

W

^ e N

m

O^ aH^

Ln U

oo 04

I

LL

C9 0 00 c •

W° 4)

1— u a^i

LLJ IV

4-4 CO

Q W b o

m 'o .

^ A

a

00 ,H

4'

m

126

C Oa 7 38%V83dW31 3WdI3 a38nsV3W

R1
127

In summary, the total corrections for a measured temperature

of 1550°C could be as high as 294 00. This amounts to an absolute

f

temperature of about 2117 0K which is close to the maximum

adiabatic flame temperature. However, these Corrections are not

constant and require reevaluation at other temperatures. With

respect to the volume of the temperature data collected in this

study, determination of the actual temperature for all

measurements was found to 'be impractical and, therefore, was not

pursued.

r

1

P

p

t

Q
:12 8

APPENDIX E

Computer Programs '

E.1 Droplet Interactions

FORTRAN Variable Definition

A (N,N) Interaction matrix.

ALl Distance between source and particle I.

ETA Average array burning rate correction factor.

I Particle index.

IG Index for number of source generation.

IGEN Total number of source generation.

J Particle index.

JJ Particle index.

- K Index for total number of sources per generation.

Kl Source index in previous generation.

L Particle index.

N Number of particles.

R (N) Radius of particle I.

S (IG,K) Strength of source S.

X (IG,K) x-coordinate of source S.

XO (N) x-coordinate of particle I.

Y (IG,K) y-coordinate of source S.

YO (N) y-coordinate of particle I.

z (IG,K) z-coordinate of source S.

z0 (N) z-coordinate of particle I.

E
129

PROGRAM INTERACT

C

C hhhhhhhhhhhhAAAAA AAA* AAA AAA hhhhhhhhhh AAA hh AAA hhhhhAA AAA #h

C h PROGRAM TO ACCOUNT FOR DROPLET INTERACTIONS IN ARRAYS h

C h OF MONODISPERSE OR POLYDISPERSE DROPLETS h

C hhhhlthhhhhhhkr4^4r4r4hhhlthhhr4r4hhhhhhhhh,4,4hhhhhhhr4h4hhhh^ri4,4h,4r4

C

DIMENSION X(19,9000),Y(19,9000),Z(19,9000),XO(19),YO(19)

DIMENSION ZO(19),A(19,19),R(19),S(19,9000)

READ(7, h ) N

READ ( 7 , h ) .IGEN

DO 10 I=1,N

10 READ (7, h ) XO(I),YO(I),ZO(I),R(I)

DO 11 L=1,N

A(L,L)=R(L)

I =L+1

DO 12 J -1,N-1

X(1,J)=XO(L)

Y(1,J)=YO(L)

Z(1:,J)=ZO(L)

S(1,J) =R(L)

12 CONTINUE

DO 13 IG=2,IGEN

K1=(N-1)hh(IG-2)

DO 14 K=1,(N-1)hh(IG-1)

IF (I.LE.N) COTO 50

I=1

50 ALI=SQRT((X(IG-1,K1)-XO(I))hh2+(Y(IG-1,K1)-YO(I))Ah2

A +(Z(IG-1,K1)-ZO(I))hh2)

S(IG,K)=-R(I)hS(IG-1,K1)/AL1

IF (I.NE.L) COTO 60

A(I,I)=A(I,I)+S(IG,K)

GO TO 70

60 A(L,I)=A(L,I)+S(IG,K)

70 X(IG,K)=XO(I)-R(I)hR(I)h((XO(I)-X(IG-1,K1))/ALlhh2)

Y(IG,K)=YO(I)-R(I)hR(I)*((YO(I)-Y(IG-1,K1))/AL1hh2).

Z(IG,K)=ZO(I)-R(I)hR(I)h((ZO(I)-Z(IG-1,K1))/ALlhh2)

IF (FLOAT(K)/(N-1).NE.INT(K/(N-1))) COTO 80

Kl=K1-1

80 I=I+1

14 CONTINUE

13 CONTINUE

11 CONTINUE

WRITE (5,350)

350 FORMAT (' THE INTERACTION MATRIX ,ALPHA :')

ETA=0.0

DO 19 1=1,N

WRITE (5,300) (A(I,JJ),JJ=1,N)

DO 19 J=1,N

ETA=ETA+A(I,J)

19 CONTINUE
130

300 FORMAT (19F7.3)

WRITE (5,400) E`rA/N

400 FORMAT (/,' ii.R2AY AVERAGE CORRECTION FACTOR =',F6.4)

STOP

END
A

Al

ADIAB

AIRFLO

AIRMIX

B

BETA

BHRAT

BNO

C

C1

C2

C3

CCONFG

CCPFG

CHT

CLAT

CON1

CON2

LONG

CONL

CONST2

CONST3

CPF

CPG

CVAP

CVISFG

D

D1

D2

DELU

DIFF

DISAIR

DR

DT

DTO

DTINC

EXTENT

F1

F2

FMW

FNAME

GAMMA

(N)

N

(3)

(N)

(N)

(N)

(2)

(2)

(5)

(3)

(5)

(2)

(N)

(N)

131

E.2 Spri_y Vaporization

FQRTRAN Variable Definition-

Locafly defined variable.

Adiabatic/non adiabatic vaporization flag.

Air flow rate at a given axial location.

Curv- fit constants for dilution air entrainment.

1+2 ^.

Vector of intermediate coefficients

Burner diameter to height ratio.

Evaporation mass transfer number.

Defined by equation 5-15.

Defined by equation 5-16.

Locally defined variable.

Curve fit constants for conductivity of fuel vapor

as f(T).

Curve fit constants for specif i^ heat of fuel vapor

as f(T).

Curve fit constants for distance above orifice

as f(TAU).

Curve fit constants for heat of vaporization as f(T)

Locally defined variable.

Locally defined variable.

Conductivity of gas phase.

Conductivity of liquid fuel.

Locally defined variable.

Locally defined variable.

Specific heat of liquid fuel.

Specific heat of gas phase.

Curve fit constants for vapor pressure as f(T).

Curve fit constants for fuel vapor viscosity as f(T).

Coefficient vector containing elements of TD.

Locally defined variable.

Locally defined variable.

U2-U1.

Diffusivtty.

Dispersion air flow rate.

Radial spacing.

Ramped time increment.

Initial time increment.

Time increment multiplier.

Extent of prevaporizaton.

Locally defined variable.

Locally defined variable.

Molecular weight of fuel.

Chemical name of fuel.

vector of intermediate coefficients y

t

r

f

k

aF
F` •

132

FORTRAN Variable Definition

HT Burner height.

HTVAP Heat of vaporization.

I Local index.

IFP1 Locally defined variable.

JTIME Time index.

L Local index.

N Igo. of radial meshes.

N2MW Molecular weight of N2.

NTIME No. of time steps.

02MW Molecular weight of 02.

P Total pressure.

PRNO Prandtl No.

PVAPOR Vapor pressure.

R Radial position.

REDHT Height of the reducing sect ^>i,

REYNO Reynolds No.

RHOG Gas phase density.

RHOL Liquid fuel density.

RS Droplet radius.

RSO Initial droplet radius.

RSP =RS.

RU Universal gas constant.

SYOW Inverse average molecular weight.

T Gas phase temperature.

TO Initial gas phase temperature.

TAU Cumulative evaporation time.

TBOIL Boiling temperature of fuel.

TD (N) Droplet temperature.

TDROPO Initial droplet temperature.

TDROP Average droplet temperature.

TEVAP Total evaporation time.

THETAM Non dimensional temperature evaluated by

interpolation.

TOTAIR Total air flow rate.

TSURF Droplet surface temperature.

U1 Gas phase velocity at time=TAU-DT.

U?. Gas phase velocity at time=TAU.

V (N) Vector containing the computed solution of TD.

VISCG Gas phase viscosity.

XF Fuel vapor mole fraction.

XN2 N2 mole fraction.

X02 02 mole fraction.

XPLUS Locally defined variable. 

YF Fuel mass fraction. 

YFLG Liquid fuel 'mass fraction.

YF"LG1 Initial mass fraction of liquid fuel.

YFS glass fraction of fuel at droplet surface.

YN2 N2 mass fraction.

Y02 02 mass fraction.
133

p

PROGRAM VAPOR

C

C AAAAAAAAAAAAAAA)t ,jAtAAAAt**A AAA AAAAAAtAAAtAAAAAAAtAtAAAA AAAAAAtAAAA

C *At SPRAY VAPORIZATION PROGRAM

C ** THIS PROGRAM USES A DROPLET TRACKING TECHNIQUE TO

C ** CALCULATE THE PREVAPORIZATION PARAMETERS ALONG THE AA

C *04 SPRAY PATH *ok

C ^r^k^k^t^kltfk^c^k^k^k^t^k^4^k^k^t^k^k^t^+4^k^4^k^4^t^t^td4^k^4^t^^k^4^4^^k^k^k^k^kr^fc^4^k^k^4^t^t^s^tkdt^t^s^t^t

C

REAL N2MW

COMMON FMW , N2MW , 02MW , CFG,CONG,DIFF , RHOG,VISCG

COMMON RU,P,XF,X02 , XN2,SYOW

COMMON CCPFG ( 2),000NFG ( 2),CVISFG(2)

DIMENSION TD(51) , A(51),B ( 51),C(51),D(51)

DIMENSION CVAP ( 5),CLAT ( 3),AIRMIX ( 3),CHT(5)

CHARACTER All FNAME

C

C ------------------ INITIAL CONDITIONS ---------------------

C

N=20

NTIME=60

TAU=0.0

PRINT A ,' ENTER DROPLET DIAMETER ( MICRONS)

READ (*, A ) RSO

RSO=RSO / 2.0A1.OE-6

RSP=RSO

RS=RSO

PRINT A ,' ENTER AIR TEMPERATURE (C)

READ ( *,jh) TO

TO =T0+273.1.5

PRINT A,' ADIABATIC VAPORIZATION ( 1=Y ,O=N)

READ ( A ,k) ADIAB

PRINT *,' ENTER THE HEIGHT OF THE REDUCING SECTIONS (CM)

READ () REDHT

READ ( 8,200) FNAME

RF."AD ( 8,210)FIOI,RHOL , TBOIL , CONL , CPF,YFLGI , TEVAP,BHRAT

READ ( 8,220) ( CVAP ( I),I=1,5)

READ ( 8,230) (CLAT ( I),I=1,3)

READ ( 8,240) TOTAIR,DISAIR,(AIRMIX ( I),I=1,3)

READ ( 8,250) ( CCPFG(I),I=1,2)

READ ( 8,260) ( CCONFG ( I),I-1,2)

READ ( 8,270) ( CVISFG ( I),I=1,2)

READ ( 8,280) ( CHT(I) , I=1,5)

200 FORMAT (All)

210 FORMAT ( 8F8.4)

220 FORMAT ( 5E10.4)

230 FORMAT ( F8.1,F9.5,F10.5)

240 FORMAT ( 2F7.1 , F10.1 , 2F7.1)

250 FORMAT ( 2F9.6)
c

17

20

134

FORMAT (2E10.3)

FORMAT ( 2010.4)

FORMAT (5F8.4)

02MW=32.0

N2MW=28.0

P=1.0

RU=0.08205

T=TO

TSURF=297.15

TDROP= 297.15

TDROPO=297.15

YF=0.0

Y02=0.231

YN2=0.769

DTO=2.0E-4

DTINC =( 2.0*TEVAP / NTIME-2.0*DTO) / (NTIME-1)

U1=27.59

DO 5 I.,-=1,N+1

TD(I)=TDROP

YFLG= YFLGIATOTAIR / DISAIR

WRITE, ( 5,101) FNAME

FORMAT ( 18X,All,/)

WRITE ( 5,102)

FORMAT (' 'IME ( SEC) HT(CM) D(MIC) Tg(C) Ts ( C) Td(C) B

E')

---------------------- BEGIN ITTERATION ----------------------

DO 16 JTIME= I,NTIME

DT=DTO+ ( JTIME- 1)*DTINC

TAU=TAU+DT

IF (TAU.GE . 2.7E-4) GOTO 7

AIRFLO=DISAIR+AIRMIX ( 1)*TAU

GO TO 9

AIRFLO =AIRMIX ( 2)+AIRMIX ( 3)*TAU

YFLG=YFLG*DISAIR / AIRFLO

YF-YF*DISAIR / AIRFLO

T=(DISAIR*T+(AIRFLO -DISAIR)*TO)/AIRFLO

DISAIR =AIRFLO

-----------------------" VELOCITY ---------------------------

260

270

280

5

101

102

*

C

C

C

7

9

C

C

C

HT=CHT(1)

DO 18 I=2,5

HT=HT+CHT ( I)*(ALOG ( TAU))**(I-1)

18 CONTINUE

U2=(AIRFLO / 6000.0)/(3.14159 / 4.0*(HT/ BHRAT)**2)

HT=HT/100.0

DELU=U2-U1

VAPOR PRESSURE CALCULATIONS -----------------

PVAPOR = CVAP(l)

DO 20 I=2,5

PVAPOR=PVAPOR+CVAP ( I)*(TSURF - 273.15 )**( I-)

CONTINUE I
135

--------------------- GAS PROPERTIES --------- --

CALL FRACT (T,YF,YN2,YC2)

CALL PROPTY (T,YF,YN2,YO2)

------------------ HEAT Of VAPORIZATION ---------------------

HTVAP=CLAT(1)

DO 22 I=2,3

HTVAP=HTVAP+CLAT(I)*TSURF**(I-1)

22 CONTINUE

YFS= 1.0/(1.0- (1.0-EXP(HTVAPAFMW /8315.0(1.0 /TSURF-1.0 /TBOIL)))

* /(SYOWAFMW))

IF (YFS.GT .YF) GOTO 40

YFS =YF

40 CONST2=CLAT(2)+2.OokCLP..T(3)*TSURF

CONST3-EXP(HTVAP*FMW/a3i5. OA(1.0 /TSURF-1.0/TBOIL))/(SYOWAFMW)A

* (HTVAPAFMW/8315.0)/(TSURFAtTSURF)AYFS*YFS

D2=-(CPG*(T-TSURF)*(YFS-1.0)-(HTVAP+CPFA(TSURF-TDROP)) ,k(YF-YFS))

A /(CPGA(-(YFS-1.0)+CONST3A(T-TSURF))+CONST3A(HTVAP+CPF*

A ( TSURF-TDROP))-(YF-YFS)A(CONST2+CPF))

TSURF=TSURF+D2

IF (ABS(D2).GE.0.005) GOTO 17

BNO= YF-YFS)/(YFS-1.0)

------------------ DROPLET SIZE CALCULATIONS ----------------μ

C1=0.25ASQRT(ABS( 8. 0A(9.81A(RHOG-RHOL)+DELU/DTARHOL)ARHOG

A /(18.OAVISCG*VISCG)))

C2=CONG/(CPGARHOL)AALOG(1.0+BNO)

C3=0.0

DO 24 I =1,35

C3=C3+(-1.0) *A( I+1)*(C1*RS**1.5)A*(I-1)ARS*RS/(1.5A(I-1)+2.0)

24 CONTINUE

38 F1=0.0

F2=0.0

DO 30 I=1,35

F1=F1+(-1.0)**(I+1)A(C1*RSAA1.5)AA(I-1)ARS*RS/(1.5A(I-1)+2.0)

F2=F2+(-1.0)AA(I+1)*(C1*RS*A1.5)A*(I-1)ARS

30 CONTINUE

F1=C3-Fl-C2ADT

F2=-F2-C2

D1=-F1/F2

RS=RS+D1

IF (ABS(Dl).GE.1.OE-8) GOTO 38

EXTENT=1.0-(RS/RSP)AA3

U1=U2

------------------ DROPLET TEMPERATURE -----------------

TDROPO=TDROP

TD(N+1)=TSURF {

C

C

C

C

C

C

C

C

C

C

C

C

C
i

1.36

DR= 1.0/N

A1=DTACONL/(RHOLACPFARSARSADR)

R=0.0

DO 55 I=2,N

R=R+DR

A(I)=A1/R-AJAR/UR

B(I)=1.0+2.0*AJAR/DR

C(I)=-Al/R-AJAR/DR

D(I)=TD(I)

55 CONTINUE

C(2)=-2.0AA1

D(N)=D( N)+(A1/(1.0-DR)+A1*(1.0-DR)/DR)ATD(N+1)

C

C SOLVE A SYSTEM OF LINEAR EQNS TO GET DROPLET TEMPERATURE PROI

C

CALL TRIDAG(2,N,A,B,C,D,TD)

TD(1)=TD(2)

TDROP=0.0

DO 52 I=1,N

CON1=(TD(I+1)-TD(I))/2.0

CON2=TD(I+1)-CON1A(FLOAT(I)*DR)

TDROP=TDROP+3.0*(CON1/4.OA((FLOAT(I)ADR)**4-(FLOAT(I-1)ADR)AA

+CON2/3.OA((FLOAT(I)*DR)AA3-(FLOAT(I-1)ADR)AA3))

52 CONTINUE

C

C ------------------ GAS PHASE TEMPERATURE --------------------

C

T=(YFLGA(CPFA(TDROPO-(1.0-EXTENT)ATDROP)--EXTENTA(HTVAP+TSURFA

A (CPF-CPG)))+CPGAT)/(CPGA(1.0+ExTENTAYFLG))

IF (T.LE.TO) GOTO 14

T=TO

14 YF=(YF+EXTENTAYFLG)/(1.0+EXTENTAYFLG)

YFLG=(1.0-EXTENT)AYFLG/(1.0+EXTENTAYFLG)

YN2=(1.0-YF)/(1+0.231/0.769)

Y02=1.0-(YF+YN2) 

RSP=RS

C

C ---------- THERMAL ENTRY LENGTH SOLN FOR WALL HEATING -------

C

IF (ADIAB.EQ.1.0) GOTO 11

IF (HT.LT.REDHTA I.OE-2) GOTO 11

PRNO=VISCGACPG/GONG

REYNO=RHOGAU2AHT/BHRAT/VISCG

XPLUS=(HT-REDHTAI.OE-2)/(1.43/200.0)/(REYNOAPRNO)

IF (XPLUS.GT.O.001) GO TO 62

THETAM=I.0-XPLUSA(1.0-0.962)/0.001

GO TO 69'

62 IF (XPLUS.GT.0.004) GO TO 63

THETAM=0.962+(0.001-XPLUS)A(0.962-0.9013)/(0.004-0.001)

GO TO 69

63 IF (XPLUS.GT.0.01) GO TO 64

THETAM=0.908+(0.004-XPLUS)A(0.908-0.837)/(0.01-0.004);

GO TO 69

64 IF (XPLUS.GT.0.04) GO TO 65 

i
` 137

' THETAM= 0.837+ ( 0.01-XPLUS ) *(0.837 - 0.628 )/( 0.04-0.01)

GO TO 69

65 IF ( XPLUS . GT.0.08) GO TO 66

THETAM= 0.628 +( 0.04-XPLUS ) A(0.628 - 0.459 )/( 0.08-0.04)

GO TO 69

66 IF ( XPLUS . GT.0.1) GO TO 67

THETAM= 0.459+ ( 0.08-XPLUS ) A(0.459 - 0.396 )/( 0.1-0.08)

GO TO 69

67 IF ( XPLUS.GT.0.2) GO TO 68

THETAM= 0.369+ ( 0.1-XPLUS ) A(0.396 - 0.190)/(0.2-0.1)

GO TO 69

68 THETAM=0.0

69 T=TO- ( TO-T)ATHETAM

C

11 WRITE ( 5,290) TAU,HT* 100.0,2 . OE6ARS , T-273 . 15,TSURF-273.150I

A TDROP- 273.15 , BNO,1 . 0-(RS/RSO)A*3

290 FORMAT ( F8.5,2X,F5.2 , F9.3,3 ( F6.2),F8 . 5,F7.4)

16 CONTINUE

_

y STOP

END

_ SUBROUTINE FRACT ( T,YF,YN2 , YO2)

REAL N2MW

COMMON FMW,N2MW,02MW , CPG,CONG , DIFF,RHOG , VISCG

COMMON RU,P,XF,X02,XN2,SYOW

C

C ^t^kk^trk^4^Cc^k^ti^cd4^krk^k^k*^kk^lrt^t^c^kkykykk*k^t^k^tkd4^k^kf^^t^4ikk^t^cft^kdk^k^ks^t^t^k^k^tdk^t^k^kr':i.::

C MASS TO MOLE FRACTION CONVERSION AND AVERAGE DENSITY CALL. ti

C

' C

***^:^

SYOW=YF/FMW+YO2/02MW+YN2/N2MW

XF=YF/(FMWASYOW)

X02=Y02/(02MWASYOW)

XN2=YN2 /( N2MWASYOW)

- RHOG=P/(SYOW*RU*T)

RETURN

END

SUBROUTINE PROPTY ( T,YF,YN2,YO2)

REAL N2MW

' COMMON FMW,N2MW,02MW , CPG,CONG , DIFF , RHOG,VISCG

COMMON RU , P,XF,X02 , XN2,SYOW

COMMON CCPFG ( 2),000NFG ( 2),CVISFG(2)

C^

C

C

*

GAS PROPERTY CALCULATIONS

^k*

- 0

C

***

' C ---------------------- CP MIXTURE -------------------------

C

CPG =( YF*(CCPFG ( 1)+CCPFG ( 2)*TA1.8)+YO2A ( 0.36-5.375 / SQRT ( TA1.8)

* +47.8/(1.8 AT)) +YN2 A 0.338-123.8 /( 1.8AT) +4.14E4 /( 1.8A1.8ATAT))) 1-

A A4186.9

i

L,

I

It•'y
?P

138

C -------------- THERMAL CONDUCTIVITY OF MIXTURE ---------------

C

CONG-(XFA(CCONFG(1)+CCONFG(2)*T+CCONFG(3)ATAT)^FMWAA(l.0/3.0)

A +X02A(0.0078491+6.784E-SAT-4.903E-9ATAT)AO2MWAA(l.0/3.0)

+XN2.*(0.0143906+4.545E-5AtT+1.515E-9AtTAtT)ArN2MWAt,4(1.0/3.0))/

At (XFAFMWAA(l.0/3.0)+XO2AO2MWAAt(l.0/3.0)+XN2AN2P.WAt.4(l.0/3.0))

C

C

C -------------- ABSOLUTE VISCOSITY OF MIXTURE ----------------

C

VISCG=(XFA(CVISFG(1)+CVISFG(2)AT)ASQRT(FMW)

A +X02A(l.697E-5+5.51E-8AT-1.OE-10ATAT)ASQRT(02MW)

A +XN2A(l.697E-5+5.51E-8AT-1.OE-10ATAT)ASQRT(N2MW))/

A (XFASQRT(FMN)+X02ASQRT(02MW)+XN2ASQRT(N2MW))

C

DIFF=CONG/(RHOGACPG)

RETURN

END

SUBROUTINE TRIDAG(IF,L,A,B,C,D,V)

DIMENSION A(l),B(l),C(l),D(l),V(1),BETA(51),GAMMA(51)

C

C

C LINEAR SIMULTANEOUS SYSTEM OF EQNS SOLVER

C REF: "APPLIED NUMERICAL METHODS," CARNAHAN ET AL.

C JOHN WILEY & SONS, 1976.

C

C

1

BETA(IF)=B(IF)

GAMMA(IF)=D(IF)/BETA(IF)

IFP1=IF+l

DO 1 I=IFP1,L

BETA(I)=B(I)-A(I)AC(I-1)/BETA(I-1)

GAMMA(I)=(D(I)-A(I)AGAMMA(I-1))/BETA(I)

V(L)=GAMMA(L)

LAST=L-IF

DO 2 K=1,LAST

I=L-K

V(I)=GAMMA(I)-C(I)AV(I+1)/BETA(I)

RETURN

END

2
K'

w

139

t

r

E.3 Spray Combustion

FORTRAN Variable Definition

AIRO Total oxidizer mass around a burning droplet.

AIRMAS Cumulative oxidizer mass.

B Preexponential constant for fuel oxidation reaction..

BRATEI Backward reaction rate constant for: 02+N2 = 20+N2.

BRATE2 Backward reaction rate constant for: O+N2 = NO+N.

BRATE3 Backward reaction rate constant for: N+02 = NO+O.

BURND Burner height.

CF Stoichiometric molar coefficient for fuel.

CO toichiometric molar coefficient for oxydizer.

CPDT 1Cp dT.

DIST Center-to-center droplet spacing,2Z

DR = DRI.

DRO First radial spacing.

DRI (N) Ramped radial spacing.

DRLST Last radial spacing.

E Activation energy for fuel oxidation reaction.

ELLAST Locally defined variable.

ELMAS Locally defined variable.

FRATEI Forward reaction rate constant for: 02+N2 = 20+N2.

FRATE2 Forward reaction rate constant for: O+N2 = N04-N.

FRATE3 Forward reaction rate constant for: N+02 = NOd-0.

FUO Total mass of fuel.

FUMAS Locally defined variable.

J Local index.

NBRACH Burning rate correction factor equation flag.

NDROP Number of droplets in a planar array.

NODEN Droplet number density.

NOMW Molecular weight of NO.

PHIO Overall equivalence ratio.

PI 3.14159

PORUT2 Locally defined variable.

Q Heat of reaction.

RO Universal gas constant.

REAM Rate of U formation from: 02+N2 = 20+N2.

REACT2 Rate of N formation from: O+N2 = NO+N.

REACT3 Rate of NO formation from: N+02 = NO+O.

RHO Gas phase density.

RHODIF P x V

RHOS Density at droplet surface.

RVDRDT Locally defined variable.

SDRLST Locally defined variable.

SOXF Stoichiometric oxygen to fuel mass ratio.

LYOWBK Previous inverse average molecular weight.

T (N) Flame temperature.

TAU Cumulative reaction time.

TENLOG Log base 10 of nondimensional particle spacing.
140

C^

9

FORTRAN Variable Definition

TGAS Initial reaction temperature.

TGASO Inlet gas phase temperature.

TLO Boiling temperature of fuel.

TNEW (N) Updated flame temperature.

TOTFUl, Sum of cumulative (reacted and unreacted) fuel ma:

TOTMEa Locally defined variable.

TOTMSO Combined mass of fuel and oxidizer.

" TOTOX Sum of cumulative (reacted and unreacted) oxidizer

mass.

V (N) Radial velocity.

X1 Local x-coordinate of a droplet.

XN Mole fraction of N.

XNO Mole fraction of NO.

XO Viola fraction of 0.

Y1 Local Y-coordinate of a droplet.

YFGAS Initial fuel vapor mass fraction in gas phase.

YFNEW (N) Updated fuel vapor mass fraction in gas phase.

YN2 (N) Mass fraction of N2 in gas phase.

YN2GAS Initial mass fraction of N2 in the gas phase.

YN2NEW (N) Updated N2 mass fraction in gas phase.

YNO (N) Mass fraction of NO in gas phase.

YNONEW (N) Updated NO mass fraction in gas phase.

Y02 (N) Mass fraction of 02 in gas phase.

Y02GAS Initial mass fraction of 02 in the gas phase.

Y02NEW (N) Updated 02 mass fraction in gas phase.

YPMINS Combined mass fraction of product (no N2)

at R+DR(I-1).

YPPLUS Combined mass fraction of product (no N2)

at R+DR(I).

YPROD Combined mass fraction of product (no N2)

at R+DR(N).
i 1.41.

PROGRAM COMB

C

C ** SPRAY COMBUSTION PROGRAM *ot

C WITH NO FORMATION KINETICS Aro;

C

REAL N2MW,NOMW

COMMON FMW,N2MW,02MW,NOMW,CPG,CONG,DIFF,RHO,RU,P

COMMON XF,X02,XN2,XN,XO,XNO,SYOW

DIMENSION T(301),TNEW(301),Y'(301),YFNEW(301)•,YO2(301)

DIMENSION Y02NEW(301),YN2(301),DRI(301)

DIMENSION YN2NEW(301),YNO(301),YNONEW(301),V(301)

C

C ------ ------------ INITIAL CONDITIONS ---------------------

C

351 FORMAT (F7.2,I5,F7.2,F5.2,F7.4)

352 FORMAT (F'7.2,F7.4,F6.1,F6.1,F6.2)

353 FORMAT (4E10.3)

READ (7,351) RSO,NODEN,TGASO,PHIO,EXTENT

READ (7,352) FMW,CONL,RHOL,TLO,CO

READ (7,353) HTVAP,Q,B,E

TAU=0.0

RSO=RSO/2.0A1.OE-4

TGASO=TGASO+273.15

DRO=0.2

CF=1.0

02MW=32.0

N2MW=28.0

NOMW=30.0

P=1.0

RO=8.315A1000.0

RU=0.08205

SOXF'=COA02MW/(FMW*PHIO)

C

C ---------------- DROPLET CONFIGURATION IN THE ARRAY ----------

C

CALL CONFIG(RSO,DIST,NODEN,NDROP)

C

RSO=RSOA1.OE-2

RS=RSO

N=INT(—DRO+0.03+OQRT((DRO-0.03)AA2-4.OA(I.0—DIST)A0.03)/0.06)-1

WRITE (5,35) DIST,2.OARSOAlE6,NODEN,NDROP,PHIO

35 FORMAT (' INIT DROP SPAC.=',F5.2,' DO =',F6.2,' NO. DENS

=',I4,' DROPS/ARRAY=',I3,' PHI=',F5.3/)

C

FUO=4.0/3.0A3.14159ARHOLARSOA 3/(1.0—EXTENT)

TOTMSO=FUOA(1.0 +SOXF/PHIO)

AIRO=FUOASOXF/PHIO

r

i

{ 

qP

if
142

TGAS=1100.0

18 YF'CAS=1.0 /( 1.0+4.29ASOXF/( EXTENT*PHIO))

Y02GAS-(1.0-YFGAS)/(4.29)

YN2GAS - 3.29AY02GAS

CPDT=( Y02GASA ( 0.36Al . 8k(TGAS -TGASO)-2.0*5.375 A( SQRT(TGASA1.8)- 

A SQRT ( TGASO*1.8))+47.8*(ALOG(1.8*TGAS)-ALOG(1.8ATGASO)))+

A YN2GAS *( 0.338A 'l.8*(TEAS -TGASO) - 123.8*(ALOG(I.8*TEAS),

A ALOG ( 1.8*TGASO))- ( 4.14E4)/1.8*(1.0 / TGAS'- 1.0/TGASO)) +YFGAS*

A (0.0694 * 1.8*(TGAS -TGASO)+(5.27E•-4)/2.0*1 . 8A1.8A ( TGAS*TGASA TGASOATGASO))),42326.0

YFGAS - YFGAS -CPDT/Q

Y02GAS=YO2GAS -CPDT/ QASOXF

IF (YFGAS.GT . 0.001) GOTO 23

TGAS-TGAS-50.0

GO TO 18

23 DO 10 I=1,N+1

T ( I) `TGAS

YF(I)=YFGAS

Y02(I) = YO2GAS

YN2(I) = YN2GAS

YNO(I)=0.0

V(I)=0.0

10 CONTINUE

T(1)=TLO

YF(1)=0.80

YG2(1)=0.0466

YN2(1)=0.1534

TNEW ( 1)=T(1)

YFNEW ( 1)-YF(1)

Y02NEW ( l) -YOV 1)

YN2NF,W ( 1)=YN2(1)

DT-R30A0.7E-3

DRLST=DRO+(FLOAT(N-1,))*0.06

SDRLST=DRLST

DO 20 I=2,301

DRI(I) =DR0+(FLOAT ( I-2))A0.06

20 CONTINUE

C

C ---------------------- BEGIN ITTERATION -----------------------o

C

DO 16 JTIME= 1,150000

IF (JTIME . LT .10) GO TO 43

DT=800.OARSARS

43 TAU=TAU+DT

CALL FRACT ( T,1,YF,YN2,YO2,YNO)

SYOWBK=SYOW

RHOS=RHO

C

C -------------------- DROPLET INTERACTIONS --------------------

C

CALL CONFAC ( DIST,RS4 , RS,NDROP,ETA) 

C

C BEGIN RADIAL MARCHING

C

Q
143 

IF (RS.GE.1.5E-6) GOTO 339

FUMAS=0.0

GO TO 354

339 FUMAS=4.0/3.0A3.14159*RHOLARSA*3

354 TOTMAS=FUMAS

AIRMAS=0.0

R=1.0

DO 12 I=21.N

DR=DRI(I)

R =R+DR

C

C--------------- ------ GAS PROPERTIES ------------------------- C

CALL FRACT (T,I,YF,YN2,Y02,VNO)

CALL PROPTY (T,I,YF,YN2,YO2,.YNO)

C

C -- CONSERVATION OF ENERGY

PORUT2=(P/(RUAT(I)))AA2

TNEW(I)=T(I)+DTA(-V(I)/(RSADR)A(T(I+1)-T(I-1))/2.0+LONG/(RHO*

A CPGARSARS)A((T(I+I)-T(I-1))/(RADR)+(T(I+1)-2.0*T(I)+T(I-1))

* /(DR*DR))+CFAFMW*PORUT2/(RHO*CPG)AXFAX02ABAEXP(-E/(RO*T(I)))AQ)

C ---

- ---- CONSERVATION OF FUEL --------------------

C

PORUT2=(P/(RUATNEW(I)))AA2

YFNEW(I)=YF(I)+DT*(-V(I)/(RSADR)*(YF(I+1)-YF(I-1))/2.04RHOADIF'F'/

A (RHO*RS*RS)*((YF(I+1)-YF(I-1))/(RADR)+(YF(I+1)-2.0*YF(I)+

F A YF(I-1))/(DRADR))-CFAFMW/RHOAPORUT2AXF*X02*

n BAEXP(-E/(ROATNEW(I))))

IF (YFNEW(I).GE.0.0) GOTO 300

YFNEW(I)=0.0 

C --------------- CONSERVATION OF OXIDIZER ------------------ C

300 Y02NEW(I)=YO2(I)+DTA(-V(I)/(RSADR)A(YO2(I+l)-YO2(I-1))/2.0+RHOA

A DIFF/(RHO*RSARS)*((YO2(I+1)-YO2(I-1))/(RADR)+('O2(I+1)

A -2.OAY02(I)+YO2(I-1))/(DRADR))-COA02MW/RHOAPORUT2*XFAtXO2A

. A HAEXP(-E/(ROATNEW(I))))

IF (Y02NEW(I).GE.O.0) GOTO 400

Y02NEW(I)=0.0

C

C +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

C + NO KINETICS +

C ++♦+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++..

C

C ------------ REACTION RATES FOR ZErnOVICH MECHANISM ------------- C

' 400 FRATEI=6.OE10A4.94E8/(ROATNEW(I))AEXP(-4.94E8/(ROATNEW(I)))

4 HRATE1=1.0E8

FRATE2=1.36EllAEXP(-3.1.5E8/(R0ATNEW(I)))

_ BRATE2=3.lElOAEXP(-1.4E6/(ROATNEW(I)))

r F'RATE3=6.4E6ATNEW(I)AEXP(-2.62E7/(ROATNEW(I))) !;

BRATE3=1.5E6 ATNEW(I) AFXP(-1.62E8/(RO ATNEW(I))) I
144

XO-SQRT(FRATEl/BRATElARUATNEW(I)/P*X02)

XN=XOA(BRATE3AXNO+FRATE2AXN2)/(FRATE3*X02+BRATE2*XNO)

C

C ---------- SOURCE AND SINX TERMS FOR ZELDOVICH MECHWiISM ----

C

REACTI=PORUT2*(2.OAFRATElAX02AXN2-2.OABRATElAXOAXOA'XN2A

A SQRT(PORUT2))

REACT2=PORUT2*(FRATE2AXOAXN2-BRATE2AXNOAXN)

REACT3=PORUT2A(FRATE3*XNAX02-,BRATE3AXNOAXO

C

' C ---------------_,__— N2 CONSERVATION

C

YN2NEW(I)=YN2(I)+DTA(—V(I)/ (RSADR) A(YN2(I'+1)—YN2(I-1))/2.0+Rii(

A DIFF/(RHOARSARS)A((YN2(I+1)-YN2(1-1))/(RATJR)+(YY2(I+1)

A —2.0AYN2 ( I)+YN2 ( I-1))/(DRADR)))

C

C --------------------- NO CONSERVATION -------------------------

C

YNONEW(I)-YNO(I)+DT*(—V(I)/(RSADR)A(Yr)O(I+1)—YNO(I-1))/2.0+RHC

A DIFF/(RkIOARSARS)A((YNO(I+1)—YNO(I-1^/)/(RADR)+(YNO(I+1)

A —2.OAYNO(I)+YNO(I-1))/(DRADR))+NOt*i/RHOA(REACT2+REACT3))

C

C -------------------- OVERALL 0/F RATIO ----------------------

C

ELMAS-4.0/3.OA3.14159A(RA*3—(R- IJR)AA'3)ARSAA3AP /(RUA

A (SYOW+SYOKBK) / 2.0A(THEW ( I)+TNDV (1-1))/2.0)

` YPMINS = 1.0—(YFNEW ( I-1)+YO2NEW( 1 -1)+YN2NEW(I-1))

YPPLUS=1.0-(YFNEW(I)+YO2NEW(I)+YN2NEW(I))

-AIRMAS=( ( YO2NEW ( I)+YO2NEW ( I-1))/2.0+ ( YPMINS+YPPLUS)/2.OA

A (1.0-114./514.0))AELMlkS+AJRMAS

FUMAS-((YFNEW(I)+YFNEW(I-1,))/2.0+(YPMINS+YPPLUS)/2.*114./514.)

A AELMAS+FUMAS

g TOTMAS=ELMAS+TOTMAS

-^ SYOWBK=SYOW

C ------------------------ CONTINUITY --------------------------

C

IF (RS.LT.1.5E-6) GOTO 64

RVDRDT=CONLA(T(2)—T(1)) /(RSADROAHTVAP)

4 C V(I)=((P/(RUATNEW(I)ASYOW)—RFO)/(3.ADT)ARSA(1,,—RAA3)+

C A RVDRDT)/(RHOARAR)

V(I)=RVDRDTA(RHOL-RHOS)/(RHOARHOL*R*R)

64 IF (JTIME.NE.I.AND.FLOAT(JTIME)/1000..NE.JTIME/1000) GOTO 12

IF (I.GT.2) GOTO 700

WRITE (5,. 444 )

444 FORMAT(' R T V YF Y02 YN2'

A ,' XN XO YNO' )

WRITE (5,123) R—DR,INT(T(1)),V(1),YF(1),

* Y02(l),YN2(l),0.0,0-0,YNO(l)

700 WHITE (5,123) R,INT(TNEW'^I)),V(I),YFNEW(I),

Y02NEW ( I),YN2NEW ( I),XN,X0,YNONEW(1)

123 FORMAT (lX,F7.1,1X,I5,F7.3,3F7.4,3E10.3)

12 CONTINUE 

^

R

t

E
^F

:145

C -------- ASSIGN THE NEW VALUES -------------------

C

DO 14 I=2,N

T(I)=TNEW(I)

YF(I)=YFNEW(I)

Y02(I)-YO2NEW(I)

YN2(I)-YN2NEW(I)

YNO(L)=YNONEW(I)

14 CONTINUE

IF (RS.LT.1.5E-6) GOTO 66 W.

C

C --------------------- 0/F RATIO CHECK -- ---- -----

C

ELLAST-TOTMSO—TOTMAS

YPROD=1.0—(YO2NEW(N)+YFNEW(N)+YN2NEW(N))

72 TOTOX=AIRMAS+ELLAST*(YO2NEW(N)+YPROD*(1.0-114./514.))

TOTFUL=FUMAS+ELLAST*(Yf'(N)+YPROD*114./514.)

IF (ABS(TOTOX/TOTFUL-SOXF).LT.0.01) GOTO 74

ELLAST=(SOXF*FUMAZ-^AIRMAS)/(YO2(N)+YPROD*(1. - 114/514.

* -S0 F*114./514.)—SOXFAYF(N))

GO TO 72

74 DRLST=((ELLAST)/

* ( 4./3.*3. 1 4159*RS**3*P /( RU*SYOW*TNEW(N)))^*R**3)**(1 . 0/3.0)—R

SDRLST=DRLST+SDRLST

IF (SDRLST.GE .DRI(N+1)) GOTO 45

N=N-1

SDRLST=SDRLST+DRI(N+1)

45 DRLST=SDRLST

IF (SDRLST.LE.DRI(N+2)) GOTO 41

SDRLST=SDRLST—DRI(11+1)

N=N+1

DRLST=$I)RLST

C

C ------------ BOUNDARY CONDITIONS AT SURFACE --------------

C

41 RVDRDT=CONL*(T(2)—T(1))/(RS*DRO*HTVAP)

RS=RS—DTARV.!)RDT/RHOL*ETA

IF (RS) 99,99,24

24 V(1) RVDRDT*(1.0/RHOS+,:, 0/RHOL)

RHODIF=CONL/((0.0694+5.27E-4*T'LO*1.8)*4186.9)

YF(1)=(RHODIF*YF(2)/(RS*DRO)+RVDRDT)/(RHODIF/(RS*DRO)4,RVDRDT)

Y02(1)=(RHODIF*Y02(2)/(RS*DRO))/(RHODIF/(RS*DRO)+RVDRDT)

YN2(1)=(RHODIF*YN2(2)/(RS*DRO))/(RHODIF/(RS*DRcO)+RVDRDT)

YNO(1 )=( RHODIF*YNO(2)/(RS*DRO ))/( RHODIF /( RS*DRO) +RVDRDT)

GO TO 68

66 DO 62 I=1 A

V(I)=0.0'

62 CONTINUE

YF (1) =YF (2 ,r

YN2(1)=YN2(2)

Y02(1) =YO2(2)

YNO(1)=YNO(2)

C T(1)=T(2)

h
C

C

C

C

C

C

c

146

C ------------ BOUNDARY CONDITIONS AT AMBIENCE -------------

C

68 T(N+1)=T(N)

'IF(N+],)=YF(N)

Y02(N+1)-YO2(N)

YN2(N+1)-YN2(N)

YNO(N+I)=YNO(N)

V(N+1)=V(N)

C

28 IF (JTIME.NE.l.AND.FT,,OAT(JTIt4E)/1000..NE.JTIME/1000) GOTO 16

WRITE (5,222) TAUo2.OARSA1.OE6e1.0—(RS/RSO)AA3,ETA,

JTIME,DR,N

222 FORMAT (' T(SEC)=',E10.3,';D(MIC)=',F6.3,';E=',F5.3,

;ETA=',F5.3,';ITER=',I6,';DEL=',F5.1,';N=',I3/)

16 CONTINUE

99 STOP

END

SUBROUTINE FRACT(T,I,YF,YN2,YO2,YNO)

REAL N2MW,NOMN I

COMMON FMW,N2MW,02MW,NOMW,CPG,CONG,DIFF,RHO,RU,P

COMMON XF,X02,XN2,XN,XO,XNO,SYOW

DIMENSION T(1),YF'(1),,YN2(1),YO2(1),YNO(1)

C

C

C MASS TO MOLE FRACTION CONVERSION AND AVERAGE DFI T SITY CALL.

C

C

SYOW=YF(I)/!Fr,W+YO2(I)/02MW+YN2(I)/N2MW+(1.0-YF(I)-YO2(I)-YN2(

A A((114./514.)/18.0+(l.-114.0/514.0)/44.0)

XF=YF(I)/(FMWASYOW)

X02oYO2(1)/(02MWASYOW)

XN2=YN2(I)/(N2MWASYOW)

XNO=YNO(I)/(NOMWASYOW)

RHO=P/(RUAT(I)ASYOW)

RETURN

END 0

SUBROUTINE PROPTY(T,I,YF,YN2,YO2,YNO)

REAL N2MW,NOMW

COMMON FMW,N2MW,02MW,NOMW,CPG,CONG,DIFF,RHO,RU,P

COMMON XF,X02,XN2,XN,XO,XNO,SYOW

DIMENSION T(1),YF(1),YN2(1),YO2(1),YNO(1)

GAS PROPERTY CALCULATIONS

------------------------- CP MIXTURE ---------------------------

CPG = (YF(I) A (0.0694+5.27E-4 AT(I) A 1.8)+YO2(I)A(0.36-5.375/ i

SQRT(T(I)A1.8)+47.8/(1.8AT(I)))+YN2(I)A(0.338-123.8/(1.8AT(II,

+4.14E4/(1.8A1.8AT(I)AT(I)))+(1.0-YF(I)-YO2(I)-YN2(I))A

(0.681A(0.368-148.4/(1.8AT(I))+3.2E4/(1.8A1.8AT(I)AT(I)))
1.4 7

s ..

A +0.319 A ( 1.102 - 33.1/SQRT ( 1.8AT ( I))+416 . 0/(1.BAT(I)))))A4186.9

C

C -------------- THERMAL CONDUCTIVITY OF MIXTURE --------------

C

CONG- ( XFA(•-0 . 026834 + 1.329E- 4AT(I) - 1.741E- 8AT (I ) AT(I)) A

A FMWAA ( 1.0/3.0)+XO2A ( 0.0078491+6.784E- 5AT(I) - 4.903E - 9ATk'I)A•

A T(I))A02MWAA ( 1.0/3.0) +XN2A ( 0.0143906+4.545- 5AT(I)+1.515E-9A

A T(I)AT ( I))AN2MWAA ( 1.0/3.0 )+( 1.0-)M,-X02-XN2)A(0.681A

A (-0.0009023 +6.915E-5AT(I) - 3.688E- 9AT(I ) AT(I))A44.OAA(1 . 0/3.0)

A +0.319A(' 0.0048332+1,.303E- 4AT(I) - 7.059E- 9AT(I ) AT(I))A

A 18.OAA(1.0/3.0)))/(XFAFMWAA(1.0/3.0)+XO2AO2MWAA(1.0/3.0)+XN2A

A N2MWAA(1.0/3.0)+(1.0-XF-XN2-X02)

A A(0.681A44.OAA(1.0/3.0)+0.319A18.OA*(1.0/3.0)))

C

DIFF=CONG/( RHOACPG)

RETURN

END

SUBROUTINE CONFIG ( RSO,DIST , NODEN , NDROP)

C

C AAAAAAAAAAAAAAAAAA/tAAAAAAkAAAAAAAAAAAAAAAAAAAAAAAAA^rA^kAAA^tA**

C A PROGRAM TO DETERMINE DROPLET SPACINGS FOR AN EVENLY

C A DISPERSED , MONOSIZED ARRAY A

C AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

C

NDROP=O

BURND=1.43

PI=3.1415927

DIST=( 2.0/(NODENASIN ( PI/3.0)) ) AA(1.0 / 3.0)/(2.OARSO)

BURND = BURND/( RSOA2.0)

DO 15 J - 1,INT ( BURND/( 2.0ADISTASIN ( PI/3.0)))+1

DO 20 I=1,INT ( BURND/( 2.0ADIST))+1

X1=(I-1)ADIST

IF (FLOAT(J)/2.0.NE . INT(J / 2)) GOTO 30

X1=Xl+DIST/ 2.0

30 Y1=(J - 1)ADISTASIN(PI/3.0)

IF (SQRT ( XlAXl +Yl AYI) . GT.BURND / 2.0) GOTO 20

NDROP =NDROP+1

IF (IAJ.EQ.1) GOTO 20

IF(Y1 . EQ.0.0) GOTO 40

NDROP=NDROP+I

IF (X1.EQ . 0.0) GOTO 20

NDROP=NDROP+2

GO TO 20

40 NDROP=NDROP+1

20 CONTINUE

15 CONTINUE

RETURN

END
1,48

SUBROUTINE CONFAC ( DIST,RSO,RS , NDROP,ETA)

A SUBROUTINE TO CALCULATE BURNING RATE CORRECTION FACTOR A

A FOR MONODISPERSE SPRAYS. STATEMENT NUMBERS CORRESPOND A

A TO THE NTkis'.ER OF INTERACTING DROPLETS IN A PLANAR ARRAY.A

AA*AAAAAAA ^<;,^;. ^AAAAAAAAAAAAAAAAAAAAAAA^kAAAAAAAAAAAAAAAA;4AAA

TENLOG=ALOG10(2.OADISTARSO/RS)

IF (TENLOG.LT.3.17) GOTO 25

ETA=1.0

GO TO 27

25 NBRACH =( NDROP-1)/6--8

GO TO (55,61,67,73,79,85091,97,103,109,115,121,127,133,139,

A 145,151,157),NBRACH

55 ETA=-1.2436435+TENLOGA(2.2164602-0.8041338ATENLOG+0.1235272A

A TENLOGATEliLOG- 0.00641 71ATENLOGAA3)

GO TO 27

61 ETA=-1.21.,8263+TENLOGA(2.1265647-0.7282704ATENLOG+0.098952A

A TENLOGATENLOG-0.0036453ATENLOGAA3)

GO TO 27

67 ETA ,1.2337979+2'ENLOG*(2.0958116-0.6898761ATENLOG+0.0856408,k

A TENLOGATENLOG-0.0021527*TENLOGAA3)

GO TO 27

73 ETA=-1.1997394+TENLOGA(1.9788084-0.5967735ATENLOG+0.0559048*

A TENLOGATENLOG+0.0012112ATENLOGAA3)

GO TO 27

79 ETA=-1.1988726+TENLOGA(1.9448054-0.5593372ATENLOG+0.0432551*

A TENLOGATENLOG+0.0026203ATENLOGAA3)

GO TO 27

85 ETA=-1.1423215+TENLOGA(1.8058571-0.4514555ATENLOG+0.0088748A

A TENLOGATFVLOG+0.0065384*TENLOGAA3)

GO TO 27

91 ETA=-1.1428598+TENLOGA(1.7650879-0.4115640ATENLOG-0.0042657A

A TE:NLOGATENLOG+0.0079962ATENLOGAA3)

GO TO 27

97 ETA=-1.0798480+TENLOGA(1.6162612-0.2968254ATENLOG-0.0409864*

A TENLOGATENLOG+0.0122215ATENLOGAA3)

GO TO 27

103 ETA=-1.0748937+TENLOGA(1.5'707712-0.2552938ATENLOG-0.0544528A

A TENLOGATENLOG+0.0137137ATF.NLOGAA3)

GO TO 27

109 ETA=-1.00304424,TENLOGA(1.41.62596-0.1363881ATENLOG-0.0927271A

A TENLOGATfsNLOG+0.0181601ATENLOGAA3)

GO TO 27

115 ETA=-0.9990754+TENLOGA(1.3675382--0.0938431AIENLOG-0.1063837A

A TENLOGATENLOG+0.0196740ATENLOGAA3)

GO TO 27

121 ETA=-0.9380671+TENLOGA(1.2264606+0.0151967*TENLOG-0.1417152A

A TENLOGATENLOG+0.0238125ATENLOGAA3)

GO TO 27

1
1.4 9

127 ETA=-0.9125118+TENLOGA(1.1476325+0.0791626*TENLOG-0.1622019*

A TENLOG*TENLOG+0.0261359*TENLOGAA 3)

GO TO 27

133 ETA=-0.8509631+TENLOG*(1.006496 +0.1864841ATENLOG-0.197862iA

A TENLOGATENLOG+0.0303513 ATENLOGA* 3)

GO TO 27

139 ETAS-0.8368802+TENLOG*(0.9543458+0.2317049*TENLOG-0.''1115844*

* TEIJLOGATENLOG+0.0318774ATENLOGA*3)

GO TO 27

145 ETA=-0.7636684+TENLOGA(0.7898749+0.3588799ATENLOG-0.2532952A

A TENLOG*TENLOG+0.0368515ATENLOGAA3)

GO TO 27 w 151 ETA=-0.7478763+TENLOGA(0.7367701+0.4021712ATENLOG-0.2670025A

A TENLOGATENLOG+0.0383796*TENLOGAA3)

GO TO 27

157 ETA=-0.6827373+TENLOGA(0.5896260+0.5165399*TENLO(;-0.3047329A

A TENLOGATENLOG+0.0429093*TENLOGAA3)

27 RETURN

END -

^
150

E.4 Sample Input Data

E.4.1 13roplet Interactions Program

7

6

0.000 0.000 0.000 1.0

20.000 0.000 0.000 1.0

20.000 0.000 0.000 1.0

10.000 17.321 0.000 1.0

10.000 -17.321 0.000 1.0

-10.000 -17.321 0.000 1.0

-10.000 17.321 0.000 1.0

E.4.2 Spray Vaporization Proqram

R

-{ N-OCTANE

114.2 707.0 398.15 0.132 2205.0 0.0663 0.1703 12.45

2.267E0 0.2138EO 8.594E-3 1.42E-4 1.28E-5

J 368370.0 421.2021 -1.4705

3400.0 1300.0 7253000.0 3272.0 498.0

0.0694 0.000527

F' -1.306E-1 7.997E-4

7.2029E-7 1.7494E-8

31.59 9.935 1.372 0.095 0.0026

E.4.3 Spray combustion Program

47.68 400 23.64 1.00 0.43

114.20 0.0199 707.0 380.0 12.50

3.027E5 4.460E7 1.150Ell 1.260E8
n

VITA

Hamid Sary was born in . He

Attended Drexel University where he received the B.S. degree in

Mechanical Engineering in 1979. During his undergraduate study,

he obtained cooperative work experience at the Franklin Institute

Research Laboratories, Ecolaire Inc., and Drexel University. He

continued his graduate study at Drexel and obtained the M.S. and

Ph.D. degrees in Mechanical Engineering in 1981 and 1985,

respectively. During this period, he served as a

research/teaching assistant in the ME department and co-authored

four papers.

Mr. Sary is a member of SAE, ASME, and Sigma Xi.

. F {r 

O