NASA Technical Reports Server (NTRS) 19960047111: Theoretical and Numerical Investigation of Radiative Extinction of Diffusion Flames

220 Pages·5.7 MB·English

by  NASA Technical Reports Server (NTRS)

NASA-TM-III643
/ _J
Theoretical and Numerical Investigation of
Radiative Extinction of Diffusion Flames
By
Anjan Ray
A DISSERTATION
Submitted to
_Xiichigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of _Iechanical Engineering
1996
ABSTRACT
Theoretical and Numerical Investigation of
Radiative Extinction of Diffusion Flames
By
Anjan Ray
The influence of soot radiation on diffusion flames was investigated using both
analytical and numerical techniques. Soot generated in diffusion flames dominate
the flame radiation over gaseous combustion products and can significantly lower the
temperature of the flame. In low gravity situations there can be significant accunlu-
lation of soot and combustion products in the vicinity of the primary reaction zone
owing to the absence of any convective buoyant flow. Such situations may result
in substantial suppression of chemical activities in a flame and the possibility of a
radiative extinction may also be anticipated. The purpose of this work was to not
only investigate the possibility of radiative extinction of a diffusion flame but also to
qualitatively and quantitatively analyze the influence of soot radiation on a diffusion
flame.
In this study, first a hypothetical radiative loss profile of the form of a sech 2 was
assumed to influence a pure diffusion flame. It was observed that the reaction zone
can, under certain circumstances, move through the radiative loss zone and locate
itselfonthe fuelsideof thelosszone.contrary toour initial postulate. Oil increasing
the iiltensitv and/or width of the loss zone it was possible to extinguish tile flame
and extinction plots were generated. Ill tile presence of a convective flow, however,
the movement of the temperature and reaction rate peaks indicated that the flame
behavior is more complicated compared to a pure diffusion flame.
A comprehensive model of soot formation, oxidation and radiation was used in a
more itlvolved analysis. Tile soot model of Syed. Stewart and Moss [1] was used for
soot nucleation and growth and the model of Nagle and Strickland-Constable [2] was
used for soot oxidation. The soot radiation was considered in the optically thin limit.
.-kn analysis of the flame structure revealed that tile radiative loss term is countered
both by the reaction term and tile diffusion term. Tile essential balance for the soot
volume fraction was found to be between the processes of soot convection and soot
growth. Such a balance yielded to analytical treatment and the soot volume fraction
could be expressed in the form of an integral. The integral was evaluated using two
approximate methods and the results agreed very well with the numerical solutions
for all cases examined.
In loving mcm, ory of rny mother
ACKNOWLEDGMENTS
[ wish to express mv very sincere gratitude to Dr. I. S. Wichman for his guidance.
He took active interest in my work and particil)ated in all stages of problem solving.
It was a great privilege to work with him.
I would also like to thank Dr. J. V. Beck, Dr.._I. Miklavcic and Dr.._1. Zhuang
for serving on mv thesis committee and for offering important suggestions fox" im-
provelneXlt.
This work was supported by the microgravity com[mstion research program of the
NASA Lewis iqesearch Center. In Spring, 1996 this work was supported bv a generous
fellowship award from the 5Iichigan State l.'niversity Graduate School.
I am grateful to my colleagues Zori Pavlova, Nandu Lakkaraju and Bukkv Oladipo
for creating and sustaining a friendly atmosl)here at work. I would like to thank
my friend Umashankar fox' his elaborate help on formatting mv thesis using DTEX.
Bipasha helI)ed me with some of the drawings in this thesis.
.Nly friends have been extremely supportive throughout. I would fondly remember
o
the long telephone conversations with Mayukh and Debabrata. \Ve exchanged ideas.
shared good humor and infused inspiration into one another. The team of friends
at East Lansing created an atmosphere of bonhomie which has been of paramount
iml)ortance to me. Rabi. Ajit, Nidhan, Ashim and Kuntal have been great friends
and have always been there for me.
The greatest inspiration for my Doctoral work came from my parents. I have
learned a lot from the courage and fortitude of my father through difficult times and
V
a great personal loss. fie taught me tile value of exploring lie',',"avenues and to remain
undaunted in tile worst of times. Even in the midst of great t)ain and suffering, my
mother lent her unrelenting support for me in the early stages of mv Doctoral work.
Her ecstasy would have known no bounds today. Her invisible presence continues to
nourish my inner self and this work is a tribute to how much she has always meant
to nle.
vi
TABLE OF CONTENTS
LIST OF TABLES
X
LIST OF FIGURES xi
1 Introduction 1
Literature Review 4
2.1 Introduction ................................ -I
2.2 Background ................................ 4
2.3 Soot .................................... 5
2.:3.1 ttow Does Soot Affect Us? .................... 5
2.3.2 Appearance ............................ 6
2.3.3 Morphology and Ctlemical Structure .............. 6
2.3.-I Characterization of the Soot Distribution ............ 7
2.:3.5 Soot Evolution .......................... 7
2.:?,.6 Soot Oxidation .......................... 9
2.3.7 The Influence of Fuel Structure ................. 10
2.3.S Effect of Pressure ......................... l0
2.3.9 Influence of Additives ....................... 10
2.3.10 Influence of Oxygen Addition .................. 11
2.4 Soot ._lodels ................................. ll
2.5 Soot Radiation .............................. 14
2.6 Diffusion Flames in Microgravity . ................... 15
3 Influence of a Simple Heat Loss Profile on a Pure Diffusion Flame 19
3.1 Introduction ................................ 19
3.2 Review of Pure Diffusion Flame Results ................ 20
3.3 Problem Geometry . . . . ........................ 21
:_1.4 Choice of Parameter values ........................ "2"2
3.5 Formulation ................................ 26
vii
:3..5.1 Infinite Reaction Rate (IRR) Solutions as Initial Conditions 2$
3..5.2 Simple Heat Loss Profile ..................... "29
3.6 Numerical Solution ............................ :31.
3.7
Relation Between Temperature and Density . ............. :3)'-
3.8
Evaluation of g0 .............................. :312
3.9 Reslllts and Discussion .......................... :3:3
:3.9.1 Comparison with the top-hat profile ............... .5:2
3.10 Conclusions ................................ .54
4
Influence of a Simple Heat Loss Profile on a Diffusion Flame with
Fuel Blowing 56
4.l Introduction ................................ 56
4.2 Problem Definition ............................ 56
4.3 Fornmlation ................................ .58
4A Boundary Condition for the Fuel Equation ............... .59
4..5 Solution for Infinite Reaction Rate ................... 60
4.6 Parameter Values ............................. 63
4.7 Results and Discussion .......................... 63
4.8 Conclusions ................................ 89
5 Estimation of Soot Layer Profile and Thickness 91
•5.1 Introduction ................................ 91
.5.2 Soot 3lodel ................................ 92
5.3 Examination of the Soot .Model ..................... 93
.5.3.1 Rapid equilibration of q ..................... 9.5
5.4 Formulation of the Full Problem ..................... 98
5.5 Numerical Solution ............................ 102
.5.6 Analytical Approximation ........................ 104
5.7 Integral Evaluation Using Laplace's Method .............. 106
.5.8 Comparison of Results .......................... 107 ,
•5.9 Influence of soot radiation ........................ 109
5.9.t Background ............................ 109
.5.9.2 Formulation of the Radiation term ............... 110
.5.9.3 Results ............................... 119.
.5.10 Conclusions ................................ 1I4
6 Investigation of the Comprehensive Soot Radiation Problem 116
6.1 Formulation ................................ 117
viii
6.I.L The InfluenceofThermophoresis ................ 121
6.2 Parameter\:alues ............................. 122
6.:1 NmnericalSolution ............................ 12:1
6.4 ResuLtsandDiscussion.......................... 12:1
6.5 Estimation ofthe Soot\'oIume FractionProfile ............ 155
6.6 Conclusions ................................ L59
7 Conclusions and Recommendations for Future "Work 161
A Asymptotic Calculations for a Simplified Model of the Interaction
of a Diffusion Flame with a Heat-Loss Zone 165
A.1 Abstract ................................... 165
A.2 Introduction ................................ 165
A.3 Formulation ................................ 167
A.3.1 Physical Discussion ........................ 167
A.3.2 The Mathematical Problem ................... 168
A.3.3 The ForlnofH(Z) ........................ 171
A.3.4 The Radiation Term ....................... 175
A.4 Results ................................... 176
A.4.L Influence of If on Oxidizer, Fuel and Temperature Profiles 176
A.4.2 Influence of .Negative 1t on Flame Shift ............. 185
A.4.3 Reaction-Zone Analysis using Activation-Energy Asyml)totics 191
A.4.4 Influence of Heat-Loss Zone on Flame Displacement ...... 197
A.5 Discussion and Conchlsions ....................... 198
BIBLIOGRAPHY 201
ix
LIST OF TABLES
3.1 Flame Temperature versus }oo data .................. "_)3
3.2 Parameter values ............................. 25
4.1 uoL/ao for different values of Uo..................... 63
X