. . a...»
r J.

3.

.quMuvak.33
.Ewmumwwzh .
.4 an”? .

 

2......
v . 1......
a! 1....
3 I

m3

3.}? . .
41?! as“: 1!.
2...\ .43: \Itr

1. . ..
.
n A.
. . .. rt
.

“9%;

. 5:3...
3.39% .
MU n1

1
E... .
3...“.
1.. 1....
file.

:4

lung»
.3. q Lam-”Ira.

.fnnuuu
1.1.1.3.":

w.

 

“Mm“ H
= .
.Kmfiwg

. .41 -. .¢ ..
Haggai. $135.5»

.. .35.! .
19119:: :31

I: J.

.lv‘.
(17...:
r... a... a.
.. Jr... r?

u.

gm.

a“ $34.11....

at“.
.

.l w tumwmg

 

glove

LIBRARY
Michigan State
University

This is to certify that the
thesis entitled

POPULATION AND SAMPLE BURNED AREA ANALYSES
FOR NEAR LIMIT FLAMES IN A SIMULATED LOW GRAVITY
ENVIRONMENT OVER THIN CELLULOSIC FUELS

presented by

KARIN LAKSMI ADITJANDRA

has been accepted towards fulfillment
of the requirements for the

degree In Mechanical Engineering

 

QijM

Major Professor’ 5 Signature
M40" 15', 2.605
I 7

Date

 

MSU is an Affirmative Action/Equal Opportunity Institution

 

 

PLACE IN RETURN Box to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED wim earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05—c1/C__—| RC/DateDueindd-p. 1 5 ‘

 

POPULATION AND SAMPLE BURNED AREA ANALYSES
FOR NEAR LIMIT FLAMES IN A SIMULATED LOW
GRAVITY ENVIRONMENT OVER THIN CELLULOSIC
FUELS

By

Karin Laksmi Aditjandra

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

2005

ABSTRACT
POPULATION AND SAMPLE BURNED AREA ANALYSES
FOR NEAR LIMIT FLAMES IN A SIMULATED LOW GRAVITY
ENVIRONMENT OVER THIN CELLULOSIC FUELS

By
Karin Laksmi Aditjandra

The National Aeronautical and Space Administration (NASA) Glenn Research
Center in Cleveland, Ohio, has been conducting combustion research in a microgravity
environment in order to increase space mission fire safety. The research program ATHIN A
(Analysis of Thennodiffusive and Hydrodynamic Instabilities in Near-extinction
Atmospheres) was a flight definition project related to that mission. Before this research
program was to be sent to the International Space Station (188) for further work ATHINA
had to meet specific scientific requirements. To fulfill the requirements, many earth bound
experiments were conducted in the NASA microgravity facilities (Drop Towers) and the
MSU microgravity simulator called the SMFT. The results of these experiments were
studied in this thesis.

The experimental flamelet study conducted at MSU produced results similar to and
compatible with the NASA facility. Flamelet propagation on a cellulosic fuel sample is a
form of fuel rich combustion. F lamelets propagate at a nearly constant rate over the
sample. The flamelet spread rate is proportional to the velocity of the oxygen supply. To
reach a steady state (a condition when flamelet continues to propagate indefinitely) it is
required that at least half of the total flamelet population be “productive”. The flamelet
population study included the development of a computer program to simulate the
cumulative population of flamelets using biological population measures and the logistic

model.

T 0 Gabriel, Hyacintha,
Paulus, and Antonius

for their love.

iii

ACKNOWLEDGEMENT

I would like to thank my academic advisor Dr. Indrek Wichman, for all his insights,
guidance and support throughout my graduate years. I also thank him for giving me the
chance to work on this excellent opportunity with NASA.

I would also like to thank Dr. Sandra Olson and Dr. Fletcher Miller of NASA Glenn
Research Center at Lewis Field for all the advices and assistance in this project.

Lastly, I would like to thank my family and Bryan Burkhart for their love, support

and assistance. Thanks to all my fellow graduate students for their support and assistance.

iv

TABLE OF CONTENTS

LIST OF TABLES .............................................................................................................. viii
LIST OF FIGURES ............................................................................................................... ix
NOMENCLATURE ............................................................................................................ xiv
CHAPTER 1
INTRODUCTION .................................................................................................................. 1
1.1 Experiments in the MSU Microgravity Facility ..................................................... 3
1.2 Experimental Data .................................................................................................. 6
1.3 Flamelet Study ........................................................................................................ 8
CHAPTER 2
PREVIOUS WORK AND LITERATURE REVIEW .......................................................... 10
2.1 Overview .............................................................................................................. 10
2.2 MSU Flame Rig .................................................................................................... 10
2.3 Simulated Microgravity Flame Tunnel ................................................................. 13
2.4 Experimental Procedure ....................................................................................... 16
2.5 Literature Review ................................................................................................. 17
CHAPTER 3
F LAMELET POPULATION ANALYSIS .......................................................................... 21
3.1 Background ........................................................................................................... 21
3.2 Approach .............................................................................................................. 22
3.3 Flamelet Population .............................................................................................. 24
3.3.1 Experiments in the Normal Position ............................................................. 24
3.3.2 Experiments in the Inverted Position ............................................................ 28
3.3.3 Flamelet Population Summary ..................................................................... 30
3.4 Flamelet Lifetime ................................................................................................. 35
3.4.1 Experiments in the Normal Position ............................................................. 35
3.4.2 Experiments in the Inverted Position ............................................................ 37
3.4.3 Flamelet Lifetime Summary ......................................................................... 39
3.5 Flamelet Census .................................................................................................... 43
3.5.1 Experiments in the Normal and Inverted Positions ...................................... 43
3.5.2 Flamelet Census Summary ........................................................................... 46
CHAPTER 4
F LAMELET BIFURCATION ANGLE ANALYSIS .......................................................... 50
4.1 Background ........................................................................................................... 50
4.2 Approach .............................................................................................................. 51
4.3 Results and Discussion ......................................................................................... 52
4.3.1 Experiments in the Normal Position ............................................................. 53

4.3.2 Experiments in the Inverted Position ............................................................ 53

4.3.3 Summary of Bifiircation Angles ................................................................... 54
CHAPTER 5
FUEL SAMPLE BURN ED AREA ANALYSIS ................................................................. 56
5.1 Overview .............................................................................................................. 56
5.2 Fuel Sample Area Burned Fraction ...................................................................... 56
5.2.1 Approach ...................................................................................................... 56
5.2.2 Experiments in the Normal Position ............................................................. 57
5.2.3 Experiments in the Inverted Position ............................................................ 60
5.2.4 F larnelet Region in the Burned Fraction Curve ............................................ 63
5.3 Flamelet Spread Rate ............................................................................................ 64
5.3. 1 Approach ...................................................................................................... 64
5.3.2 Experiments in the Normal Position ............................................................. 65
5.3.3 Experiments in the Inverted Position ............................................................ 67
5.4 Per-Flamelet Heat Release Across Sample .......................................................... 68
5.4.1 Approach ...................................................................................................... 68
5.4.2 Experiments in the Normal Position ............................................................. 69
5.4.3 Experiments in the Inverted Position ............................................................ 70
5.5 Oxygen Consumption Rate ................................................................................... 71
5.5.1 Approach ............................ ' .......................................................................... 71
5.5.2 Experiments in the Normal Position ............................................................. 74
5.5.3 Experiments in the Inverted Position ............................................................ 75
5.5.4 Discussion ..................................................................................................... 76
5.6 Stoichiometric Ratio ............................................................................................. 78
5.6.1 Approach ...................................................................................................... 78
5.6.2 Results and Discussion ................................................................................. 79
5.7 Flamelet Power ..................................................................................................... 80
5.7.1 Approach ...................................................................................................... 80
5.7.2 Results and Discussion ................................................................................. 81
CHAPTER 6
FLAMELET ANALYSIS ..................................................................................................... 82
6.1 Background ........................................................................................................... 82
6.2 Approach .............................................................................................................. 83
6.3 Average Number of Flamelets .............................................................................. 85
6.4 F lamelet Diameters, Gap Between Flamelets, and Quench Distance .................. 87
CHAPTER 7
POPULATION MODEL ...................................................................................................... 88
7.1 Background ........................................................................................................... 88
7.2 MATLAB Code .................................................................................................... 90
7.3 Factors of Accuracy .............................................................................................. 90
7.4 Time Lag ............................................................................................................... 93
7.5 Vibration Analyses ............................................................................................... 96
7.6 Temporal Perturbation of the Population Equation .............................................. 98

vi

7.7 Comparison with Experimental Data ................................................................. 102

7.8 Carrying Capacity and Time Lag ....................................................................... 103
7.9 Intrinsic per Capita Growth Rate ........................................................................ 107
CHAPTER 8
F LAMMABILITY MAP AND MODIFICATION TO THE APPARATUS .................... 108
8.1 Flammability Map .............................................................................................. 108
8.2 Modification on the SMFT ................................................................................. 109
CHAPTER 9
CONCLUSION AND FUTURE WORK ........................................................................... 111
APPENDIX A ..................................................................................................................... 114
APPENDIX B ..................................................................................................................... 116
BIBLIOGRAPHY .............................................................................................................. 124

vii

LIST OF TABLES

Table 1. List of tests analyzed for various tunnel heights and final air velocities ................. 7
Table 2. Average flamelet population, bifurcation rate, and extinction rate ....................... 31
Table 3. Average flamelet lifetime for mothers, infants, spinsters, and survivors .............. 39
Table 4. Summary of flamelet census for both normal and inverted tests .......................... 47
Table 5. Summary of the average bifurcation angles for experiments in the normal and
inverted positions at various tunnel heights and final air velocities ...................... 55
Table 6. Input variables to predict the oxygen consumption rate ........................................ 74
Table 7. Summary of predicted unconsurned oxygen rate .................................................. 77
Table 8. Summary of the average global stoichiometn'c ratio ............................................. 80
Table 9. Summary of flamelet power .................................................................................. 81
Table 10. Summary of flamelet diameters, gap spacing, and quench distance ................... 87
Table 11. Error norm table .................................................................................................. 92
Table 12. Sample calculations of the population equation .................................................. 94
Table 13. Log decrement ..................................................................................................... 98
Table 14. Average carrying capacity ................................................................................. 105
Table 15. Average time lag ................................................................................................ 106

viii

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.

Figure 9.

Figure 10.
Figure 11.
Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

LIST OF FIGURES

Images in this thesis are presented in color

Side view sketch of the MSU microgravity facility test section tunnel. ................ 3
FIarne—fi'ont to flamelets transformation. ............................................................... 4
Example of flamelets finger-like patterns. ............................................................. 5
Terminology diagram of the new naming arrangement of the test. ....................... 8
MSU Flame Rig. .................................................................................................. 11
MSU Flame Rig airflow system diagram ............................................................. 11
MSU Flame Rig/SMFT test section setup. .......................................................... 13
Simulated Microgravity Flame Tunnel (SMFT). ................................................. 14
SMFT airflow system diagram... .......................................................................... 16
Flammability Map [4]. ....................................................................................... 18
Flamelet bifurcation, starting with one flamelet and ending with two. ............. 22
Flamelet extinction, starting with three flamelets and ending with two. ........... 22
Example of flamelet population plot with 3 mm ttmnel height in normal
position of the test facility. ................................................................................ 25
Example of flamelet population plot with 4 mm tunnel height in normal
position of the test facility. ................................................................................. 26
Example of flamelet population plot with 5 mm tunnel height in normal
position of test facility. ...................................................................................... 26
Example of flarnelet population plot with high extinction rate in the middle of
the experiment. .................................................................................................. 27
Fingering pattern of a test with high extinction rate in the middle of the
experiment. ........................................................................................................ 28
Example of flamelet population plot with 3 mm tunnel height in inverted
position of the test facility. ................................................................................ 29
Example of flamelet population plot with 4 mm tunnel height in inverted

position of the test facility. ................................................................................ 29

ix

Figure 20.

Figure 21.
Figure 22.

Figure 23.

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.
Figure 32.
Figure 33.
Figure 34.
Figure 35.
Figure 36.

Figure 37.

Figure 38.

Example of flamelet population plot with 5 mm tunnel height in inverted

position of the test facility. ................................................................................ 30
Average number of flamelet population versus final airflow test velocity. ....... 32
Bifurcation rate versus extinction rate. .............................................................. 32

Number of flamelets for various tunnel heights with the same final air velocity

(2.5 crn/s for normal position and 3.5 cm/s for inverted position). ................... 33
Plot of number of flamelets versus the product of tunnel height and air velocity.
........................................................................................................................... 34
Example of flamelet lifetime plot with 3 mm tunnel height in normal position of
the test facility. .................................................................................................. 35
Example of flamelet lifetime plot with 4 mm tunnel height in normal position of
the test facility. .................................................................................................. 36
Example of flamelet lifetime plot with 5 mm tunnel height in normal position of
the test facility. .................................................................................................. 36
Example of flamelet lifetime plot with 3 mm tunnel height in inverted position
of the test facility. .............................................................................................. 37
Example of flamclet lifetime plot with 4 mm tunnel height in inverted position
of the test facility. .............................................................................................. 38
Example of flamelet lifetime plot with 5 mm nmnel height in inverted position
of the test facility. .............................................................................................. 38
Average lifetime for flamelet mothers versus final air flow velocity. ............... 40
Average lifetime for flamelet infants versus final air flow velocity. ................. 40
Average lifetime for flamelet spinsters versus final air flow velocity. .............. 41
Average lifetime for flamelet survivors versus final air flow velocity. ............. 41
A fingering pattern of a test with higher lifetime of flamelet spinsters. ............ 42
A fingering pattern of a test with higher lifetime of flamelet survivors. ........... 43

Example pie charts for results of experiments in the normal position of test
facility with tunnel heights of 3, 4, and 5 mm ................................................... 44

Example pie charts for results of experiments in the inverted position of test
facility with tunnel heights of 3, 4, and 5 mm. .................................................. 45

Figure 39.
Figure 40.
Figure 41.

Figure 42.

Figure 43.

Figure 44.
Figure 45.
Figure 46.

Figure 47.

Figure 48

Figure 49.

Figure 50.

Figure 51.
Figure 52.

Figure 53.

Figure 54.

Figure 55.
Figure 56.

Figure 57.

Figure 58.

Percentage of flamelet mothers versus final air flow velocity. .......................... 47
Percentage of flamelet infants versus final air flow velocity. ............................ 48
Percentage of flamelet spinsters versus final air flow velocity. ......................... 49
Fingering pattern with tunnel height of 5 mm and final air velocity of 2.5 cm/s
in the normal position of the test facility. .......................................................... 50
Fingering pattern with tunnel height of 3 mm and final air velocity of 5.5 cm/s
in the normal position of the test facility. .......................................................... 50
Picture of fingers with different bifurcation angles. .......................................... 51
Measuring angle of bifurcation. ......................................................................... 52
Bifurcation angle versus tunnel height for normal position of test facility ........ 53
Bifurcation angle versus tunnel height for inverted position of test facility. ..... 54
. Average bifurcation angle versus tunnel height. ................................................. 55
Measuring fuel sample burned area. .................................................................. 57
Area fuel burned fraction plot that represents results in the normal position of
the test facility with tunnel heights 3, 4, and 5 mm and various final air
velocities. ........................................................................................................... 58
Three regions of test RampDown_5mm_26.7-2.5_8.07(6)c. ............................ 59
Burned fraction for experiments in the normal position. ................................... 60
Fuel area burned fraction that represents the results in the inverted position of
the test facility with tunnel heights 3, 4, and 5 mm and various final air
velocities ............................................................................................................ 61
Average fuel burned fraction for experiments in the inverted position with
tunnel heights 3, 4, and 5 mm and various final air velocities. ......................... 62
Burned fraction with its fingering pattern superposed on top. ........................... 64
Measuring flamelet spread rate. ......................................................................... 65

Flamelet spread rate for experiments in normal position of test facility with
various tunnel height and final air velocities ..................................................... 66

F larnelet spread rate for experiments in the inverted position of the test facility
for various tunnel heights and final air velocities. ............................................ 67

xi

Figure 59.

Figure 60.

Figure 61.

Figure 62.

Figure 63.

Figure 64.

Figure 65.
Figure 66.
Figure 67.
Figure 68.

Figure 69.

Figure 70.
Figure 71.
Figure 72.
Figure 73.
Figure 74.
Figure 75.
Figure 76.
Figure 77.

Figure 78.

Per-flamelet heat release per unit length across the sample that represents the
results in the normal position of the test facility for various tunnel heights final
air velocities.......................~ ................................................................ _ ............... 69
Per-flamelet heat release per unit length across the sample that represents the
results in the inverted position of the test facility for various tunnel heights
final air velocities. ............................................................................................ 70
Predicted oxygen consumption rate plot that represents the results in the normal
position of the test facility with various tunnel heights and final air velocities.
......................... 74
Predicted oxygen consumption rate plot that represents the results in the
inverted position of the test facility with various tunnel heights and final air
velocities. .......................................................................................................... 75
Predicted unconsumed oxygen rate with unusual occurrence. .......................... 78
Fingering pattern segment showing the quantities q, g, and r (N = 7 and W“ =
17.8 cm). ........................................................................................................... 84
Line following process. ..................................................................................... 84
Average number of flamelets for 3 mm tunnel height. ..................................... 85
Average number of flamelets for 4 mm tunnel height. ..................................... 86
Average number of flamelets for 5 mm tunnel height. ..................................... 86
Non-dimensional population with delta = 0.1, 0.01 and 0.001 using Euler,
Modified Euler and 4"1 Order Runge-Kutta methods. ...................................... 92
Population with time lag = 0.9 and 1.0 .............................................................. 95
Population with time lag = 1.2 and 2 ................................................................. 95
Settling time peak. .............................................................................................. 97
Population with a = 1.5 and 1.0. ........................................................................ 99
Population with s = 0.5 and 0.01. .................................................................... 100
Population with a) = HM and n/Z. .................................................................... 101
Population with a) = 1t and 31t/2. ..................................................................... 101
Population experimental data. ......................................................................... 102
Experimental data with its numerical solutions ............................................... 103

xii

Figure 79. Flammability Map. ........................................................................................... 108

Figure 80. Diagram of the new airflow system with dehumidifier. .................................. 109
Figure 81. New airflow system with dehumidifier. ............................................................ 110
Figure A1. Flame spread rate [9]. ...................................................................................... 114

xiii

Arabic

a(t)

b(t)

dA
dt

df

NOMENCLATURE

Bifurcation as function of time

Fuel burned area (m2)

Extinction as function of time
Constant-pressure specific heat (J/kg*K)

Diffusivity (mz/s)
Fuel burned area rate (mz/s)

Fractal dimension
Fraction burned or frequency (Hz)

Gap between flamelets (m)
Enthalpy of formation (J /kg)
Enthalpy (J/kg)

Oxygen consumed height (m)

Fuel burned segment (m)

Mass (kg)

Mass flow rate (kg/s)

Molecular weight (kg/kmol)

Number of particle in a cluster or number of flamelets

Oxygen consmnption rate (kg/s)

Quench distance (m)

Flamelet instantaneous heat release (J/s)

xiv

>1

~<

Greek

1::

m E g 00

7i

90)

F larnelet energy production (J)

Clutter’s radius or flamelet radius (m) or intrinsic per capita growth rate (3")

Ratio of the fuel burned area and the number of flamelet
Time (3)

Temperature (K)

Average flamelet spread rate (m/s)

Flamelet population as function of time

Velocity (m/s)

Sample width (m)

Oxygen consumed width (m)

Distance (m)

Mass fraction

Stoichiometric oxygen coefficient

Log decrement of two consecutive peaks
Enthalpy change (J fkg)

Increment (m)

Perturbation variable

Carrying capacity

Density (kg/m3 or kg/mz)

Non-dimensional population as function of time

Time lag (s)

XV

Subscripts

(I)

1

avg

C6H1005

in

02

Frequency (radiant)

Damping ratio

Ambient

At distance x = 0
Average value
Air

Cellulose

Flame

Fuel

Inward direction
Oxygen

Surface

Initial condition

At distance x

xvi

CHAPTER 1
INTRODUCTION

Spacecraft fire safety is a very important issue for the National Aeronautical and
Space Administration (NASA). To increase spacecraft fire safety, NASA Glenn Research
Center at Lewis Field in Cleveland, Ohio, has been developing a research program in
nricrogravity combustion. This research is important and challenging because fire does not
behave in the same manner when it is in a l-g (9.81 m/sz) as it does in a microgravity
environment. ATHINA, an abbreviation for Analysis of Thermodiffusive and
Hydrodynamic Instabilities in Near-extinction Atmospheres, is a project conducted by
NASA Glenn Research Center. This project is a study of the propagation of an unstable
flame over a fuel in a low oxygen microgravity environment. In a low oxygen
environment, an unstable flame breaks into small separate flames that are called flamelets.
F lamelets are near-extinction flames that propagate in a unique style resulting in finger-like
patterns. Flamelets are hard to detect and their presence is dangerous because when the
environment becomes favorable, (i.e. oxygen concentration increases, or airflow into the
region increases, etc.) flamelets can transform into flames again, resulting in a fire.

This thesis performs “behavioral” studies of flamelet, and experimental data
collection is thus required. To perform experimental research in microgravity combustion
on earth, NASA Glenn Research Center has two microgravity facilities that are known as
DrOp Towers. The first drop tower is capable of creating a 104—g environment for 2.2
seconds; and the second drop tower is capable of creating a lO'S-g environment for 5
seconds. Compared to the 10'6-g environment in the space, the 104-g and 10'5-g

environments created in drop towers are considered quite good. These facilities though,

require a group of experienced staff and engineers as well as heavy machines and hardware
to perform experiments in the drop towers. NASA staff can conduct three experiments on
average per day in the 2.2-second drop tower. Moreover, NASA staff can conduct one
experiment on average per day in the 5-second drop tower. Because of this limitation,
NASA, along with the Michigan State University combustion group has come up with a
new idea to build an apparatus that is able to simulate a microgravity environment that
doesn’t require a group of experienced staff and heavy machines every time performing an

experiment.

The MSU combustion group had designed and constructed an apparatus that is
capable of simulating a microgravity environment by suppressing the buoyant force in
narrow width of the low-speed wind tunnel. This technique is adopted fi'om an apparatus
that is known as the Hele—Shaw cell. The apparatus was reconstructed; therefore it is
capable of conducting experiments in the inverted position.

The apparatus was designed carefully so that the tunnel height is adjustable over a
small range of approximately 1 mm to 7 mm. As shown in Figure 1, the tunnel height is
the distance from the quartz top window to the sample and from the sample to the copper
backing. For this thesis, the tunnel heights above and below the sample were the same for
each experiment. In [10] it was estimated that within 1 mm to 7 mm range the effect of the
buoyant force may be neglected. The range of the tunnel height was estimated by
calculating the Raleigh number, Ra, which was calculated based on the Prandtl number, Pr,
and Grashof number, Gr, for a heated plate; even though the heating provided by the
flamelets in the experiments was localized. Nevertheless, as a start the heated-plate

calculation of Ra shall be used until a better estimate of the gravitational influence can be

devised (including upside-down tests). When the Rayleigh number is critical, the
atmosphere becomes thermo-diffusively and hydro-dynamically unstable.

A side view sketch of the MSU microgravity facility test section tunnel is shown in
Figure 1. The heights above and below the sample were always equal. For this thesis, the
heights for each side of the sample were either 3-3, 4-4 or 5-5 mm. The air flows in the
opposite direction of the flame. In addition, the MSU microgravity apparatus is equipped
with a controllable airflow system. This airflow system is capable of producing a low

airflow rate to establish a near extinction atmosphere.

 

 

 

 

Outlet Quartz Top Inlet
....._. , t ..._
2 -I[ / 1. lgniter \Mre
2. Sample

Copper Backing

Figure 1. Side view sketch of the MSU microgravity facility test section tunnel.

1.1 Experiments in the MSU Microgravity Facility

There are many experiments conducted in the MSU microgravity facility both in the
normal and in the inverted positions of the test facility. One example of the experimental
sequence from one of the tests conducted in the MSU microgravity apparatus can be seen
in the set of pictures in Figure 2. There are seven pictures that show the transformation of a
flame-front into flamelets until the end of the test. Picture A shows when the ignition took
place. Picture B shows that a linear flat flame-front occurred as a result of the ignition.
The flame-front would travel and consume the sample in the direction opposite to the

airflow, which came from the right toward the left in Figure 2. The flarne-fiont thus

propagated from left to right. As soon as a flat flame-front was obtained, the flow control
system was programmed to reduce the airflow rate. The result can be seen in picture C.
This picture shows that the intensity of the flame-front diminished due to the airflow
reduction. The lack of oxidizer forced the flame-front to become unstable and it would

start to bulge at some points along the flame-front while regressing at others. These

.5
,I
D

 

 

Figure 2. Flame-front to flamelets transformation.

bulges would eventually split into several small flamelets as shown in picture D. Picture B
shows the initial distinct and separate flamelets. In this case there were seven initial

flamelets. Picture F shows a sample of the flamelet propagation. As can be seen from

pictures E to F, the number of flamelets had increased from seven to nine and the spaces
between flamelets had changed. Essentially, the changes occurred because of the flamelet
bifurcations and extinctions. Notice in picture F, there are two slightly larger flamelets,
numbers two and four from the top. These are flamelets that were about to bifurcate.
Picture G shows the end of the experiment, when the flarnelets reached the end of sample.
In this picture the number of flamelets had increased substantially. This may happen
because of the flow change effect at the end of the sample. The f'mger-like patterns, results

of flamelet propagation, are shown for the bumed-out sample in Figure 3.

 

Figure 3. Example of flamelets finger-like patterns.

Since the main objective of this thesis is to study the behavior of flamelets, the
finger like patterns such as shown in Figure 3 are very valuable. A list of the total number

of experiments used for this thesis is given in the next section.

1.2 Experimental Data

All of the experiments that were conducted in the MSU microgravity facility were
recorded with a digital camera. From the camera, each video file was transferred,
compressed and saved as .avi file in a computer. For this thesis, the experiments employed
were those with flamelets both in the normal and inverted positions of the test facility. The
normal position is when the apparatus is right side up: that is, when the quartz top is at the
upper side. The inverted position is when the apparatus is rotated 180 degrees, so that the
quartz top is at the bottom side. Flamelets occur mostly in tunnel heights of 3, 4 and 5 mm
with different low final air velocity ranges for different tunnel height. These experimental
data were employed in the subsequent discussion in this thesis. Table 1 in the following
page outlines the total ntunber of tests for each tunnel height with different air velocities.
The total number of tests that were analyzed is 49. Each of these 49 tests was performed
by different laboratory personnel at different time, before, and after the reconstructions and
modifications.

Each of these tests is named and throughout this thesis, there are two types of
naming arrangements. The t-35-25c and t-40-25c are the only two tests use the old naming
arrangement, and the remaining tests use the new naming arrangement. The new naming
arrangement began when the MSU microgravity apparatus was modified. The old naming
arrangement is short and simple but it is difficult to understand the conditions of the
experiment. Conversely, the new naming arrangement is longer but it is very easy to
understand the conditions of the experiment. It mentions the type of the experiment, the

position of the apparatus, the tunnel height, the air velocity range, and the deceleration rate.

Table 1. List of tests analyzed for various tunnel heights and final air velocities

Tunnel Height Air Velocity Number of Tests
mm cm/s Anal
Normal 3 2.5
3.5
5.5
12.5
2.5
3.0
3.5
4.0
5.0
2.5
3.5
5.0
7.5
10.0
Inverted 3.5
4.5
5.1
8.5
2.5
3.0
3.5
4.0
5.0
7.5
2.5
3.5
4.5
5.0

Position

 

r—nu—Au—awu—bi—t—tNWu—Iu—tr—tNu—ir—du—bNr—NNu—aNQAu-tAudi—I

To better explain the terminology of the new naming arrangement, consider Figure 4 on the
following page. The terminology of the old naming system is as follows. The letter ‘t’ is
an abbreviation for the word ‘test’. The number in the middle following letter ‘t’ is the test
series number. The last two numbers are the fuel type and the tunnel height. The letter ‘c’
is to indicate that the video file has already been compressed. The fuel type that has been

used for all these experiments was WhatmanTM 44 research grade ash-less filter paper.

RampDown_Inv_5mm_26.7—2.5_8.07(2)c

I

Indicates that the airflow was being “ramped
down”. Some “ramp up” experiments had
been performed. However, they were not
included in this thesis.

 

 

 

 

 

 

Indicates whether it was an inverted or normal
experiment (right-side up or upside-down).

 

 

 

I Indicates the tunnel height setup. I

 

 

I Indicates the initial and final air velocities in cm/s. I

 

 

I Indicates the deceleration rate in cm/sz. I

 

 

I Indicates the experiment series number that had the same conditions. I

 

I Indicates that the experiments video file had already been compressed. I

 

Figure 4. Terminology diagram of the new naming arrangement of the test.

1.3 Flamelet Study

This thesis focuses on the flamelet “behavior”. This flamelet study includes
detailed examination of the flamelet population. It consists of: (1) evaluations of the
bifurcation and extinction rates of the flamelet, (2) flamelet number count or census data,
and (3) flamelet lifetime measurements. The flamelet population examination will be
discussed in Chapter 3. Chapter 4 discusses the flamelet bifurcation angle using the

fingering pattern.

Another study that employs the fingering patterns of the flamelet is the sample area
burned measurement. This measurement is important because the sample area burned
serves as an estimate for the amount of oxygen consumed by the flamelet during
combustion. This study can also estimate the flamelet energy production as well as the air-
to-fuel ratio of the reaction. In addition to the estimation of the oxygen consumption rate,
the flamelet spread rate was measured. The sample area burned measurement study is
presented in Chapter 5.

Chapter 6 discusses a study that accounts for the size of the flamelets as well as
other measurable properties. This analysis includes measurements of the gaps between
flamelets, and the quenching distance, as well as the flamelet diameter.

The flamelet population study continues by developing a computer program that
models the flamelet “population demographics”. The model uses biological measures and
the logistic model. The solutions are found quantitatively using the numerical solution for
a differential equation. Some of the results will be compared to the study that was done at
NASA. This topic will be covered in Chapter 7. Lastly, Chapter 8 discusses the
flammability map of the MSU microgravity apparatus as well as the addition of the

dehumidifier to the MSU microgravity apparatus.

CHAPTER 2
PREVIOUS WORK AND LITERATURE REVIEW

2.1 Overview

This chapter describes the previous research efforts by the MSU combustion group
on the NASA-funded ATHINA project. The first part of these efforts by the MSU
combustion group was to design and construct the apparatus that produces conditions
resembling those of a microgravity enviromnent. This apparatus was called the MSU
Flame Rig. The second part of the effort was to modify the apparatus such that it is able to
perform experiments up side down. The modified apparatus was called the SMFT
(Simulated Microgravity Flame Tunnel). The last section of this chapter discusses some
related research on the opposed flow effect, microgravity combustion and branching

mechanism.

2.2 MSU Flame Rig

The MSU Flame Rig was designed and constructed carefully with safety in mind.
The detail of the design and construction of the MSU Flame Rig can be found in [10]. The
MSU Flame Rig was constructed mostly by employing non-flammable materials such as
aluminum. A picture of the MSU Flame Rig can be found in Figure 5 (picture does not
show the airflow system).

The MSU Flame Rig airflow system consists of air filter, pressure regulator,
rotameter, orifice and needle valve. A diagram of the airflow system can be seen in Figure
6. The airflow system allowed controllable clean air to flow from the source to the test
section. Air flowed from the building air supply to a 5-micron air filter. The clean air then

flowed to a pressure regulator. From the pressure regulator, air flowed through the

10

 

Figure 5. MSU Flame Rig.

 

 

 

 

 

 

 

 

 

PRESSURE
F'LTER REGULATOR
ORIFICE
ROTAMETER PLENUM
NEEDLE
VALVE
CONTRACTION
CHAMBER

 

 

 

 

 

 

 

TEST SECTION
TUNNEL ‘_I POROUS PLATE J

 

Figure 6. MSU Flame Rig airflow system diagram.

rotameter, which allows control of the airflow rate. After the rotameter, the flow was
separated to the needle valve and the orifice. The separation was intended to allow
accurate control of the air mass flow rate. From the needle valve and orifice, air flowed
into the plenum chamber. In the plenum chamber was a 2-inch diameter pipe with holes
facing the back wall. The purpose was to produce a uniform flow. From the plenum
chamber, air flowed to the contraction chamber. In this section a ramp was placed for the
air to be compressed, smoothed and prepared to enter the test section. Just before air
entered the test section, a porous plate was located after the ramp so the air that flowed into
the test section tunnel was a uniform, slug flow.

The test section tunnel of the MSU Flame Rig was designed so that the height was
variable. Below the test section holder there was a set of aluminum bars and shims to
adjust the tunnel height. To produce different tunnel heights, different sets of aluminum
bars and shims were used. In the tunnel, attached to the bottom test section were mica
strip, copper backing, and terminals to hold the igniter wire. The mica strip acted as the
sample holder as well as an insulator. The copper backing acted as a heat sink to the flame.
The igniter wire was designed carefully so it laid flat on the sample paper and was able to
generate a flat flame front. This setup was the same setup as in the NASA’s microgravity
facility. A picture of the MSU Flame Rig test section setup is shown in Figure 7.

The camera stand of the MSU Flame Rig was a separate piece. It resembled a tall
table where the four legs were about twice the height of the test section. On the top of the
table was a bar with a screw to mount the camera. There was also a hole that is just enough
for a small portion of the camera to slot into. The four sides of the camera stand were

covered with a black cloth so there was no light entering during experiment. The covering

12

during experiments provided a maximum visual contrast of the flame. as it was difficult to
see the flame in the light. Also attached to the camera stand was a red light, which was
activated during experiments. The red light acted as an indicator when the airflow rate was
reduced at the beginning of the test, besides being a background to obtain a better contrast

of the flame.

 

Figure 7. MSU Flame Rig/SMFT test section setup.

2.3 Simulated Microgravity Flame Tunnel

The MSU Flame Rig was modified and called SMFT, short for Simulated
Microgravity Flame Tunnel [12]. SMFT was the invertible version of the MSU Flame Rig.
Most part of the SMFT was the same with the MSU Flame Rig. There were five major
modifications that were done to the apparatus. This first modification was the addition of a
long shaft or spine that stretched from the plenum chamber to the test section tunnel. A
steel frame held the body of this wind tunnel at both ends of the shaft. A picture of the
SMFT can be seen in Figure 8. At one of the ends of the shaft (the one near the plenum

end) was a large size bolt that locked the shaft from rotating.

13

 

Figure 8. Simulated Microgravity Flame Tunnel (SMFT).

The second modification to the MSU Flame Rig was the spacers system that adjusts
the tunnel height. The spacers system was not applicable to the invertible SMFT because
they would fall when running experiment up side down. The new design to adjust the
tunnel height was to replace the aluminum bars and shims using a screw system. The
ttmnel height can be adjusted by adjusting the screws connected to the test section holder.
This screw system was also employed to adjust the distance between the sample and the
copper backing.

The third modification was done on the camera stand. On the top of the camera
stand crossed a bar with a screw to mount the camera. The camera stand of the old design

was cut into at least half of the original length and put together in a more compact size.

The camera stand was locked with clamps on the test section holder. Therefore, when the

apparatus is turned up side down, the camera is too.

The fourth major modification to the MSU Flame Rig included the quartz glass
holder, the sealing system and the lighting system. In the old design, the quartz glass was
held with a thin metal holder that was glued with duct tape and putty to the test section
holder. To prevent the quartz glass from falling off the holder when the apparatus is turned
upside down, the new design of the quartz glass holder locked it safely to the body with
three clamps on each side against a strip of rubber that acts as a compression seal. The
sealing system of the new design was better than the old one. In the old design, a large
quantity of putty and duct tape were consumed to seal the test section. It required a long
time to place the putty and duct tape for each test. In place of the putty and the duct tape,
in the new design, weather strip and rubber seal were used to stop leakage. The red bulb on
the MSU Flame Rig was replaced with four red LEDs on every corner of the camera stand.
The red bulb in the MSU Flame Rig frequently glared on the quartz glass, which often
yielded a poor photographic image. The LED display prevented glare and yielded better

images.

The fifth modification was done to the airflow system. A mass flow controller was
added to the airflow system of the MSU microgravity facility. The new airflow system
started from the building air supply, flowed to a pressure regulator, then to a mass flow
controller through a pressure relief valve. From the mass flow controller, air flowed
through a series of rotameters, then to the plenum chamber. From the plenum, air flowed

to the contraction chamber. From there, air flowed through a porous plate to the test

15

section tunnel. The mass flow controller was connected to a power supply as well as a
voltmeter. The power supply was connected to a computer with a software program called
LabViewTM that gave commands to the power supply and voltmeter to control the airflow
rate. The desired initial and final air velocities were entered in the initial and final voltages
input boxes, and the desired ramp down times were entered in the times input boxes. As
LabViewTM works in volts, the conversion spreadsheets from volts to crn/s are available in
the laboratory. The diagram of the new airflow system can be seen in Figure 9.

The pressure relief valve and the mass flow controller replaced the orifice and
needle valve system. With this new airflow system, the air velocity can be automatically
controlled; therefore the percent accuracy of the airflow rate is higher. Note on Figure 9,
the black arrows indicate the airflow direction. The white arrows indicate the connection

between two components.

 

 

 

 

 

 

 

 

 

 

 

 

Computer I
I Air Supply I
g I Voltmeter Power Supply I I Plenum I
I Filter I ,
Pressure Pressure Mass Flow Rotameter
Regulator Relief Valve Controller

 

 

 

 

 

Figure 9. SMFT airflow system diagram.

2.4 Experimental Procedure

A complete experimental procedure to run the MSU microgravity apparatus can be

found in [12]. The experimental setup for the SMFT was the same as for the MSU Flame

16

Rig (Figure 7). The following is a brief experimental procedure. First, a thin cellulosic
fuel sample is glued to the mica insulator. An igniter wire is installed on one side of the
fuel sample (the downstream side). The airflow approaches from the other side (upstream),
so that the flame propagates in the opposite direction of the airflow. This opposed flow
configuration is important to prevent any combustion products such as smoke from
blocking the flames.

Before running the experiments, a camera is mounted on top of the test section
tunnel to record the experiments. The initial and final voltages as well as the ramp down
times are entered in the input boxes in the computer. When everything is ready, the
‘Record’ button on the camera is pressed and the igniter wire is turned on until a linear flat
flame-front occurs. The LED is turned on. Then simultaneously ‘Run’ the LabViewTM
computer program and turn off the LED. (The LED indicates when the process of ramping
down the air velocity starts.) The computer automatically reduces the airflow to the desired

rate, and this occurs three seconds after the LED is turned off.

2.5 Literature Review

Many studies have been made on microgravity combustion over thin cellulosic fuels
as well as the effect of opposed flow. One article by Olson [5] focuses on the testing of the
forced opposed flow effect in microgravity flames, including considerations of the
mechanisms of flame spread over opposed flow and the influence of oxygen concentration.
A thin solid fuel (5 cm x 15 cm) with composition 99% cellulose was used for testing. The
results showed that the opposed flow strongly affected the appearance of a microgravity
flame. When the oxidizer velocities were low, the affect appears as a dark zone between

the fuel and flame. This was an indication of fuel rich combustion. The oxygen

17

concentration was varied to determine in the flame spread behavior as well as the transition
temperatures at which the change from fuel preheating to pyrolysis temperature occurred.
The transition temperatures range from 600 K to 675 K. This temperature range was
higher when the oxygen concentration was reduced.

A similar study by Olson, Ferkul and T’ien [4] focused on the microgravity flame
behavior of a thin cellulosic fuel in a forced opposed flow environment. An examination of
the flame behavior was carried out over a wide range of oxidizer velocities. As a result, a
flammability map was obtained in the form of a bowl shape curve with three major regions,
as shown in Figure 10. The first or leftmost region is the quenching region, where
insufficient oxidizer caused the flame to extinguish. The second region is the flame region.

30 F" ‘
HICROGRAVITY DATA

QUIESCENT FLAME SPREAD
LOH SPEED FORCED CONVECTION
FLAME EXTINCTION

NORMAL GRAVITY DATA

HIGH SPEED FORCED CONVECTION.
NATURAL convrcriou

X00

X’O

[>0

. BLOHOFF
COMPILED IN [6) BRANCH

QUENCHING
BRANCH

MOLAR PERCENT OXYGEN
as
O

 

X X «0er

 

10 I rlrlllrI I 1I1Irlrl I r IiIrIrI I rlrIrLrI
.I I 10 100 1000
CHARACTERISTIC RELATIVE VELOCITY. CM/S

Figure 10. Flammability Map [4].

18

The third region is the blow-off branch. A simple way to describe blow-off is to consider a
candle flame. When the oxidizer flow is too strong it can extinguish the flame. This
flammability map predicted the conditions of experiments under which flamelets may
occur. It is anticipated that flamelet-like behavior occurred near the quenching branch.

A work by Olson, Miller and Wichman [9] summarizes the expectations of steady
state in flamelets propagation. Steady state is when the flamelets continue to propagate
infinitely on a constant rate. Steady state is when the cumulative number of flamelets is
constant and hence the average fraction of the sample burned is also constant. The
observation time of the flamelet propagation must be longer than the average lifetime of the
flamelets. Three generations sufficed although more would give better results.

Wichman studied the flame spread in a forced opposed flow environment [14].
This article includes reviews of microgravity flame spread, flame-to-smolder spread
transition, and the quenched triple flame problem. In this study, theoretical models of
flame spread over thin and thick fuels were described and principal references were
provided.

Olson and T’ien studied the structure of low stretch diffusion flames and their
extinction characteristics using PMMA samples [6]. The experiments were performed in
normal gravity environment, but the understanding that was acquired may apply directly to
the microgravity (or simulated microgravity) environment. Another flammability map was
obtained and the quenching extinction limit occurred at low stretch with high-induced heat
losses. A preliminary pre-extinction indicator is flame oscillation.

The flamelet fingering (or branching) mechanism is a phenomenon that has been

observed in nature. A study by Ball [1] presents numerous branching mechanisms. In The

19

Self-made Tapestry, Ball introduces natural patterns such as tree branches, snowflakes, and
branching patterns in the fluid-dynamical Hele-Shaw cell. The density of the branches can

relate to the cluster radius.

(1

Nocr’ (1)

where N is the number of particles in a cluster and df is the fractal dimension. Ball also
introduces the instability theory of Saffman-Taylor who studied instability in viscous fluids
using the Hele-Shaw cell. When the fluid-front develops bulges and the pressurized tip
moves faster, this causes a finger to appear. This phenomenon is very similar to the
occurrence of the flamelet fingering pattern. When the flame-front becomes instable, it

starts to bulge at some points along the line, and then form flamelets.

20

CHAPTER 3
F LAMELET POPULATION ANALYSIS

3.1 Background

In a near limit extinction environment where there is not much oxygen, flames
break apart into flamelets. Flamelets propagate in search of oxygen and leave unburned
material behind that will show the formation of finger-like patterns. Some flamelets
survive and produce more flamelets. Some flamelets die or extinguish because of oxygen
starvation. This phenomenon makes flamelets look almost like other living things, and
allows one to study flamelets using biological measures, for example, the carrying
capacity. In biological terms, the carrying capacity is a feature that constrains populations
based on environmental limitations, such as food supply or the presence of predators. In
the flamelet world, the carrying capacity is limited by the oxygen supply.

When a flamelet reproduces, it is called bifurcation. On the other hand, when a
flamelet extinguishes because of oxygen starvation it is called extinction. Since flamelets
reproduce and die analogous to living organisms, many flamelet population analyses can be
carried out. These analyses were done for both normal and inverted positions of the test
section tunnel, with tunnel heights of 3, 4 and 5 mm, and various final low air velocities.
These population analyses include lifetime measurement and “census data” for events such
as bifurcations and extinctions.

Figures 11 and 12 are snapshots of bifurcation and extinction, respectively. The
time difference between snapshots was approximately one-third of a second. As shown in
the bifurcation sequence, initially a flamelet expanded, and then it broke up. The initial
flamelet was considered as dead or extinguished but it produced two new flamelets. On the

other hand, as seen in the extinction sequence, initially there were three flamelets. The

21

middle flamelet contracted, then it extinguished. Using biological terms, flamelets that
bifurcate are called the mothers (productive flamelet), the new flamelets are called the
infants, and flarnelets that don’t bifurcate but extinguish after a long period of time are
called the spinsters (unproductive flamelet). A flamelet was considered to be an infant if
the flamelet lived for less than 5 seconds. On the average, the first bifurcation for an
experiment occurred 5 seconds after the formation of the flamelets. Additionally, survivors

are flamelets that survive to the end of a given test.

Figure 11. Flamelet bifirrcation, starting with one flamelet and ending with two.

Figure 12. Flamelet extinction, starting with three flamelets and ending with two.

 

3.2 Approach

To analyze the flamelet population, recorded experimental data in movie video files
was required. Additionally, computer software programs were used to collect data from the
experimental movie. The first thing to do in collecting data was to watch the video record
using Windows Media Player repeatedly and to become familiar with the flamelet
distribution and the fingering patterns of the experiment. Then the video was watched

repeatedly to track the propagation of the flamelets (one by one) from the beginning to the

22

end of the experiment, using Windows Media Player as well as TRACKER]. TRACKER
was used to track the experiment flame by flame. In one second there are about thirty
flames. Therefore, the precise time for every event that occurred in the progression of a
flamelet can be tracked. Each event that occurred and its frame number were stored in a

Microsoft® Excel spreadsheet.

After every event (along with its flame number) was stored in a spreadsheet, the
flame numbers were sorted flom the smallest to the biggest. Therefore, the events were in
chronological order. The cumulative count of the flamelet population started
approximately when the designated test air velocity was reached, and lasted until the
flamelets reached the end of the sample or until the record was terminated.

Every time there was a flamelet bifurcation, the cumulative population was
increased by one. Every time there was a flamelet extinction the cumulative population was
diminished by one. With these data, a plot of the cumulative population of flamelet versus
time was obtained along with the cumulative numbers of bifurcation and extinction. The
rates of the bifurcation and extinction can be evaluated by dividing the respective totals by
the elapsed time. Note that near the end of an experiment the bifurcation and extinction
counts often increase substantially. This may happen because of the flow change at end of
sample. However, the sudden increase was neglected when evaluating the bifurcation and
extinction rates.

To measure the flamelet lifetime, the previously collected data for the population

analysis was used. For each initial flamelet, all of the events that occurred were listed in

 

rTRACKER is a software image analysis package that was developed at NASA and is flee
for NASA contractors and grantees.

23

order. Just as before, the flame number was sorted in the order flom the smallest to the
biggest. Then the lifetime of a particular flamelet can be calculated. The lifetime of a
flamelet was counted flom when a flamelet was formed until it bifurcated or it
extinguished. In other words, the flamelet lifetime was exactly the time difference between
events for each flarnelet. For example, consider a flamelet that initially formed at flame tl
and bifurcated at flame t2. Say, one of the two new flamelets extinguished at flame t3.
Therefore the lifetime of the initial flamelet is t2't], and the new flamelet has a lifetime of
t3-t2. The flamelet lifetime was presented in bar graphs using a logarithmic scale. Each bar
represents a flamelet and the height represents the lifetime.

To categorize the flamelet for census data, the flamelet lifetime data flom the
previous lifetime measurement were used. Based on the lifespan flamelets were
categorized into mothers, infants, spinsters and survivors. For easy observation the census

data were presented in the form of pie charts. In the charts, the survivors were not shown.

3.3 Flamelet Population

In the population graphs presented in this section, the x-axis (abscissa) is the
approximate time flom when the designated final low air velocity was reached. The left y-
axis (ordinate) is the cumulative numbers of bifurcation and extinction. The right y-axis is
the cumulative flamelet population. Also shown in the plots are the rates for the

bifurcation and extinction as well as the average instantaneous population.

3.3.1 Experiments in the Normal Position

There are three population graphs that represent the results for tunnel heights of 3, 4
and 5 mm. These can be found in Figures 13, 14 and 15, respectively. Shown in these

figures are the trend lines for bifurcation and extinction. The slopes are linear with a

24

parallel correlation to each other. This is an indication that the flamelet population
achieved a steady state. As noted in the figures, the bifurcation and extinction flequencies
were very close, and the same for all the three cases shown here. The carrying capacity
approximately was the average population, as there was just enough oxygen supply for the
flamelets to survive. Since the cumulative population fluctuates around the average, it can
be said that the flarnelet population was at the carrying capacity state. These population
graphs also show that the cumulative number of population over time has an oscillatory
behavior. Later in this thesis 3 separate chapter discusses a population model that describes

the oscillation.

Ram pDown_3mm_35.8-5.5_5.05(1)c

 

 

 

 
 
 
  
   

 

 

 

  

 

 

 

40 15
Earth" *
' nc on -
A Population 0'1"; Hz -
30 _\ ALA
Avg=8 AA A AA 10 r:
Number I A AA... A g
of 20 I ”we 3
Events _ A 3'
A 5 n.
10 A
A
0 [fig ' 0
0 50 100 150 200
Tlme(s)

Figure 13. Example of flamelet population plot with 3 mm tunnel height in normal

position of the test facility.

25

Ram pDown_4m m_33. 3-3_1 5. 1 5(2)c

 

    
 

  
 
 
 
 

 

60 15

50 _ Avg = 11 A A [A -

:I AAAA AA AAJ‘AA-

' "IAN” ................. ANNA ..... & .....M.A........m....fl....flunnufi... :9 ....... ..
40 - AAA); Arm AAA A '7' gal-1 10 c
Number 4A A AVA A w. 1 .2
A Iii
of 30 A 0.199 H2 4 3
Events A I 6‘
20 A i 5 '1

2 O Bifurcation ,

10 ,1. E1 Extinction ‘

I ‘ A Population 4

 

 

  

 

 

 

1: mi i

l I I I I I I I .l I l L I I_I I I I o

0 50 100 1 50 200
Time (s)

0

Figure 14. Example of flamelet population plot with 4 mm tunnel height in normal
position of the test facility.

Ram pDown_5m m_26. 7-2. 5_8. 07(6)c

 

   

 

 

 

 

 

 

 

50
. m .
40 ' Avg = 8 A M - 10
Number 30 _ . ................. AWAA. ...... MA..A.AA .................. ‘ "A... 2: .............. .. E
f _ A A A _ : ‘ E
E 0 t A A - a
ven S - -
2o 1: 0.153 Hz ‘ 5 8
A ‘ o Bifurcation .
1° _ a Extinction
1: g 0 153 Hz A Population .
0 I 1 I . . 1 I 1 Pg] I 1 0
° 5° 100 150 200

Time (s)
Figure 15. Example of flamelet population plot with 5 mm tunnel height in normal

position of test facility.

26

A few tests that were analyzed showed a slightly different trend of bifurcation and
extinction. For example, consider the flamelet population for 3 mm tunnel height with
final air velocity of 5.5 cm/s, test RampDown_3mm_35.8-5.5_10.1(2)c, in Figure 16. The
graph shows that the extinction slope is steeper than the bifurcation slope. This means that
the extinction rate is higher. It happened because in the middle of the experiment, there
was a significant increase of flameiet extinction. This can be visually explained using the
corresponding fingering pattern of the test shown in Figure 17 (note the high extinction rate
in the middle). As can be seen in the pattern several flamelets in the middle of the sample
suddenly extinguished within a short period of time. Such occurrence motivates the need

for a longer sample, since the flamelets appeared to require a longer time to reach a steady

 

 

   

 

 

 

 

 

 

state.
RampDown_3mm_35.8-5.5_10.1(2)c
4o 15
oBifurcation ‘
A i
30 _ opu on ‘
. - 10 g
umber ‘ 15
of 20 - . '5
Events _ A i 3'
A Avg . 5 n.
10 - A ‘
A .
at a. o
0 50 100 150 200 250

Time (s)
Figure 16. Example of flameiet population plot with high extinction rate in the middle of

the experiment.

27

 

Figure 17. Fingering pattern of a test with high extinction rate in the middle of the
experiment.
3.3.2 Experiments in the Inverted Position

Three flamelet population graphs that represent the results of the experiments in the
inverted position for tunnel heights of 3, 4 and 5 m can be found in Figures 18, 19, and
20, respectively.

Generally the flamelet population in the inverted position shows a similar behavior
to the flamelet population in the normal position. The flamelet populations with tunnel
heights of 4 and 5 mm have linear trend lines of bifurcation and extinction. These lines are
parallel to each other, which means that the flamelet propagation achieved steady state.
The cumulative number of the population shows an oscillatory behavior about that steady
state. The flamelet population for the 3 mm tunnel height shows a slightly different result.
Figure 18 shows that the trend line for extinction is steeper than for bifurcation. The
frequency of bifurcation is lower than the frequency of extinction. This could mean that
the experiment has not yet reached steady state or will never do so. In fact, many
experiments in the inverted position of test facility with 3 mm tlmnel height and very low

final air velocities extinguished before the end of the sample.

28

Ram pDown_lnv_3m m_34. 9-4. 5_10. 1 c

 

   

 

 

 

 

 

 

20
15
Number
of 10
Events an
g A A -
5 _ .
. OBlfurcatlon .
. g Lo-oss ”2 El Extlnctlon .
- APopulatlon .
15 0:1 -
o 1_ L L n l P l n 1 n 1 l L
0 50 100 150
Tlme (s)

15

Populatlon

Figure 18. Example of flamelet population plot with 3 mm tunnel height in inverted

position of the test facility.

Ram pDown_lnv_4m m_33. 3-3_10. 1 (2)1:

 

 

  
 

 

25
O Blfurcatlon O .
U Extlnctlon

20 A Populatlon 0.085 H2 .

 

AMA

  

Number 15
of A A I
Events 10 A A

 

J

 

1

 

0 50 100 150 200 250
TI me (3)

Populatlon

Figure 19. Example of flamelet population plot with 4 mm tunnel height in inverted

position of the test facility.

29

Ram pDown_lnv_5mm_26. 7-2. 5_8. 07(2)::

 

 

 

 

 

 

 

 

40 1O
- MA ”A A A 0.194 H2 A 1
30 r I .6
A m. AA A AA ,, A g -
a . I:
Number A ”9:8 A , 0' I. g - 6 3%
0f 20 " A o ’- a :' ‘ '5
e‘ 6‘ 0.
Events _ A o .. a + 4 0
C59 I 'i n.
A -- 4 ! I , ‘
10 " . ' 5' " OBIfurcatlon 2
b g 9. o 194 HZ D EX‘tlI'ICflOI'I
g; g- ‘ ' A Populatlon .
0 3|. L . . . A . . . . . . L l 0
0 50 100 150
Tlme (s)

Figure 20. Example of flamelet population plot with 5 mm tunnel height in inverted

position of the test facility.

3.3.3 Flamelet Population Summary

Table 2 is a summary of the average population, bifurcation and extinction rates.
The average population was plotted for each tunnel height for both normal and inverted
positions of the test facility. This plot can be found in Figure 21. In the figure, the normal
position data are presented on the left side and the inverted position data are on the other
side. Generally, the average numbers of flamelet population in both normal and inverted
positions are proportional to the oxidizer flow level as well as the tunnel height. That is,
the flamelet population increases as the final air velocity and tunnel height increase. Also,
it can be seen that the average flamelet population for experiments in the normal position

generally is higher than that in the inverted position.

30

Table 2. Average flamelet population, bifurcation rate, and extinction rate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tunnel Air Average Average .
Position Height Velocity PAvelratge Bifurcation Extinction (Extbrateifiif. rate)
(mm) (cm/s) opu a ron Rate (Hz) Rate (Hz) opu a mu
Normal 3 2.5 4 0.053 0.073 5.0E-3
5.5 9 0.151 0.157 6.7E-4
4 2.5 7 0.236 0.220 -2.2E-3
3.0 9 0.224 0.196 -2.9E-3
3.5 8 0.334 0.298 -4.5E-3
4.0 11 0.219 0.197 -2.0E-3
5 2.5 8 0.174 0.173 -2.7E-5
5.0 12 0.163 0.140 -1.9E-3
Inverted 3 3.5 5 0.091 0.139 9.1E—3
4.5 6 0.061 0.075 2.2E-3
4 3 .0 6 0.090 0.084 -1.2E-3
3.5 9 0.147 0.142 5.6E-4
4.0 9 0.133 0.115 -2.0E-3
5.0 6 0.135 0.135 0
5 2.5 7 ' 0.155 0.161 8.8E-4
3.5 8 0.170 0.150 -2.5E-3

 

 

 

 

 

 

 

 

The bifurcation rate versus the extinction rate was plotted in Figure 22. The dotted
line is the x=y line. As shown in the plot, the agreement between the bifurcation and the
extinction rates is nearly unity. This verifies that flamelet propagation nearly achieve a
constant rate or are in steady state. The trend line leans toward the bifurcation side, which
means that the bifurcation rate is on average slightly higher than the extinction rate. This is
because the initial flamelet distribution was not uniform, although the spread becoming
more uniform throughout the sample. When the bifurcation rate is higher flamelets
presumably continue to propagate, i.e. the spread rate can continue as long as there are
more bifurcations than extinction. In addition, it is apparent that generally the experiments
in the normal position have slightly higher rates of bifurcation and extinction. The

equations for the slopes are shown in the plot, where y_n is for normal position data points

and y_i is for inverted position data points.

31

Average Cumulatlve Number of

 

 

 

 

 

 

 

 

6 Normal 3mm CI Normal 4mm
A N al5 X l rted3 .
1° _ .. ...:me22... . .23:....':.: ‘1 ‘9
r — —Unear(lnverted 5mm) - - - Uneartlnverted 4mm] .
15 P — - -Llnear (Inverted 3mm) - -IJnear (Normal 5mm) .1 15
_ - - Linear (Normal 4mm) — - ~LInear (Normal 3mm) .
8 - A ‘ .
g 12 - , - 12
3 L Q .5] / / .
O. " y- / / ‘ . ‘1
8 9 ” .47 l§ X X - 9
+- L f a [:1 / + ’ ... + _ ‘
E 6 " / I % _ J ' X X "1 6
2 I ' I f X ><r .
IJ. r 0' ’ 4
3 - f - 3
. Normal Inverted .
o l l 1 l 1 l I l l 1 l 1 l o
2 3 4 5 6 2 3 4 5 6
Alr Veloclty (cmls)

Figure 21. Average number of flamelet population versus final airflow test velocity.

 

   
     

 

y_n = 0.8357x + 0.0184

Normal 3mm
Normal 4mm
Normal 5mm
Inverted 3mm
Inverted 4mm
Inverted 5mm

_..x=y

P
a
T

OXXDIO.

- - -Normal Llnear Trend
- - -Inverted LInear Trend

 

 

Extinction Rate (Hz)
0
M

9
uh
I

 

y_l = 0.8944): + 0.0159

 

l 1 l 1 1 1

0 0.1 0.2 0.3 0.4
Blfurcatlon Rate (Hz)

Figure 22. Bifurcation rate versus extinction rate.

32

Two plots, Figures 23 and 24, were established to further study on the total number
of the flamelet population. Figure 23 shows the total number of flamelets versus the tunnel
height for the same final air velocity. For the normal position of the test facility, the final
air velocity was 2.5 cm/s and for the inverted position, the final air velocity was 3.5 cm/s.
The plot shows that for fixed final air velocity of 2.5 cm/s, the number of flamelets
increases as the tunnel height increases for experiments in the normal position. However,
experiments in the inverted position show that the number of flamelets increases from
tunnel heights 3 to 4 m, then decreases from tunnel heights 4 to 5 mm for fixed final air

velocity of 3.5 cm/s.

 

10

 

 

m
‘6
B 8 '
E
2
u. 6
“6
I—
3 I," 9 Normal, v_air=2.5ch
E 4 r e a Inverted, v_air=3.5ch
5 — — Poly. (Normal)
— Poly. (Inverted)

 

 

 

 

 

 

2 I I I I I
2.5 3 3.5 4 4.5 5 5.5

Tunnel Height (mm)

Figure 23. Number of flamelets for various tunnel heights with the same final air velocity

(2.5 cm/s for normal position and 3.5 cm/s for inverted position).

33

Figure 24 shows the number of flamelets versus the product of the tunnel heights
and the final air velocity plot. The second order polynomial trend lines were drawn for
experiments in the normal and inverted positions of the test facility. For experiments in the
normal position, the trend shows that the number of flamelets generally increases, as there
is more oxidizer flowed into the system. Experiments in the inverted position show a

parabolic trend.

13

 

   

 

 

 

 

 

m

‘a',’ 11 r

0

g 9 _ 0 w 0 Normal

i.- ...N D Inverted

.5 )3" —— Poly. (Normal)
3 7 r xx - - - Poly. (Inverted)
n ’1.

E El

3

Z

 

 

 

0.5 1.0 1.5 2.0 2.5 3.0
Tunnel Height x Air Velocity (cmzls)

Figure 24. Plot of number of flamelets versus the product of tunnel height and air velocity.

34

3.4 Flamelet Lifetime
Flamelet lifetime is presented in the form of bar graphs. The x-axis (abscissa) is the
flamelet category and the y-axis (ordinate) is the flamelet lifetime on a logarithmic scale

with unit of second.

3.4.1 Experiments in the Normal Position

Figures 25, 26 and 27 represent the results of flamelet lifetime for experiments in
the normal position with tunnel heights of 3, 4 and 5 mm, respectively. Flamelets generally
lived less than 100 seconds. There are only a small number of flamelets that lived slightly
more than 100 seconds. As can be seen in these graphs, generally the slopes are gradually
increasing for each flamelet category. However, there are a few tests where the slope for
category flamelet infants is flat then rapidly increases. The flat part implies that there are
as many infants born as those that die right away.

RampDown_3mm_35.8-5.5_5.05(1)c

 

 

 

 

 

 

1000.00
100.00
9— 10.00
0
E
g 1.00
-I Infants
0.10
Mothers
0.01

Figure 25. Example of flamelet lifetime plot with 3 mm tunnel height in normal position of

the test facility.

35

Ram pDown_4m m_33. 3-3_1 0. 1 c

 

1 00. 00

10. 00

Llfetlme (s)
3
O

0.10

 

 

0.01
Figure 26. Example of flamelet lifetime plot with 4 mm tunnel height in normal position of

 

 

the test facility.
t-40-25c
1 000.0
1 00. O

3’— 10. o
o
E
g 1.0 ’ 1‘ 3 . 'z,:va_..f
-‘ 1.311.111

0.1

0.0

 

Figure 27. Example of flamelet lifetime plot with 5 mm tunnel height in normal position of

the test facility.

36

3.4.2 Experiments in the Inverted Position

The three bar graphs that represent the results in the inverted position of the test
facility with ttmnel heights of 3, 4, and 5 m can be seen in Figures 28, 29, and 30,
respectively. As for the normal position, the slope for categories flamelet mothers,
spinsters and survivors are gradually increasing. However, the slope for the flamelet
infants in the inverted position shows flat then rapidly increasing trend more ofien than in
the normal position. In addition, it is noticeable that the number of flamelets in the

inverted position is less than the number of flamelest in the normal position.

RampDown_lnv_3mm_34.9-4.5_10.1c

 

1000.00

100.00

1’— 10.00
0
E

E 1.00
.l

0.10

0.01

 

 

Figure 28. Example of flamelet lifetime plot with 3 mm tunnel height in inverted position

of the test facility.

37

Ram pDown_l nv_4m m_33.3-3_10. 1 (2)0

 

 

 

1000. 00
100. 00
3 1 0.00
0
E
‘6
“j 1 . 00
0- 10 Infants
0. 01

Figure 29. Example of flamelet lifetime plot with 4 mm timnel height in inverted position
of the test facility.

Ram pDown_lnv_5m m_26. 7-2. 5_8. 07c

 

1000.00

100.00

3 10.00
0
E

E 1.00
_I

0.10

0.01

 

Figure 30. Example of flamelet lifetime plot with 5 mm tunnel height in inverted position

of the test facility.

38

3.4.3 Flamelet Lifetime Summary

A summary of the average lifetime of flamelets can be found in Table 3. These
numbers were plotted and shown in Figure 31 through Figure 34. As listed in Table 3 and
shown in Figures 31 to 34, the lifetimes of flamelets mothers and spinsters for experiments
in the inverted position of the test facility are slightly higher than those in the normal
position. This shows that experiments in the inverted position has less cumulative
population overall, because there is less bifurcation that occurred. In Figure 31, the
average lifetime for flamelet mothers ranges from 10 to 60 seconds. It is shown in Figure

32 that the average lifetime for flamelet infants ranges from 0 to 1.5 seconds, and more

than half of it is concentrated between 0 and 0.5.

Table 3. Average flamelet lifetime for mothers, infants, spinsters, and survivors

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . Flamelet Flamelet Flamelet Flamelet
Tunnel Final Arr . .

Position Height Velocity Mother Infant Sprnster Survivor
(mm) (cm/s) Lifetime Lifetrme Lifetime Lifetlme

(S) (S) (S) (8)

Normal 3 2.5 30.85 0.15 13.07 118.57
5.5 34.04 0.86 46.25 40.30

4 2.5 15.32 0.33 25.11 16.79

3.0 24.49 0.58 23.65 20.58

3.5 16.14 0.35 12.96 12.03

4.0 25.60 1.22 15.78 30.91

5 2.5 24.98 0.56 24.57 29.64

5.0 32.14 1.13 32.97 19.90

Inverted 3 3.5 32.05 0.23 32.71 31.00
4.5 45.50 0.29 76.37 68.99

4 3.0 34.05 0.18 22.09 32.49

3.5 34.22 0.38 33.42 53.89

4.0 28.13 0.30 22.30 58.92

5.0 20.17 1.31 14.33 25.67

5 2.5 26.59 0.56 26.91 26.58

3.5 25.55 0.31 17.44 20.57

 

 

 

 

 

 

 

39

 

 

 

 

 

 

 

 

60 , 60

g : O Nor 3mm I Nor 4mm :
5 50 -E ANor 5mm ><Inv 3mm >\ E- 50
.... : X Inv 4m + Inv 5mm 1
r" 0 ~5 ’ i- 40
E 3:4 : X X X z 2

a ' “it i
.5 330 -E f % x ‘4" 1* 30
*5 5'20 ‘3 ‘ El >+< -- 20
9 I E!
w $2 '
a : I-i 1
g 10 J: -L 10
<1 5

0 I I I LII I I I I : I I I I ILI I I I : I I I l ILI I 'Lj I I I 0
2 2 5 3 3.5 4 4.5 5 5.5 6
Air Veloclty (cmfs)

Figure 31. Average lifetime for flamelet mothers versus final air flow velocity.

 

 

 

 

 

 

 

*5 :— 9 Nor Sam: I Nor 4mm 4
3 - A Nor 5mm >< Inv 3mm -
a 1'5 f X Inv 4m + Inv 5mm .- 1'5
"' - >1: 0 -
E A F I I at
O a b 4
° 51 0 1- :3. . -- 1.0
is : :
a .5 - l 1
I E d
a}, 0.5 -- A X X 3 “ 0 5
is - n a X 1
5 ' 9 Q X
0.0 . P 0.0
2 2.5 3 3.5 4 4.5 5 5.5 6

Air Veloclty (cmfs)

Figure 32. Average lifetime for flamelet infants versus final air flow velocity.

40

 

 

 

 

% 100 O Nor 3mm I Nor 4mm X 100
a A Nor 5mm >< Inv 3mm
E 8" >K Inv 4m + Inv 5mm 80
In ’5‘ ‘
e :4 .
g E 60 X 60
o a X 0
5 '5. 40 X 0 40

m X z: 9
a» i x. ..
:5 20 E + g 20
3: e E >+<

0 0
2 2.5 3 3.5 4 4.5 5 5.5 6

Air Veloclty (cm/s)

Figure 33. Average lifetime for flamelet spinsters versus final air flow velocity.

 

 

 

 

120 e 120

‘5 O Nor 3mm I Nor 4mm
3 100 A Nor 5mm >< Inv 3mm 100
E X Inv 4m + Inv 5mm
1:- 3 so so
5 g Y 55 e

60 K 60
53 w ’
a), m 40 ,1. X >+< 40
g + X I X

20 ‘ ’ + 20
4 fi B ' .... 8

0 0
2 2.5 3 3.5 4 4.5 5 5.5 6
Air Velocity (cm/s)

Figure 34. Average lifetime for flamelet survivors versus final air flow velocity.

41

In Figure 33, it appears that there is one outlier. This outlier is of the inverted test with test
conditions of 3 mm tunnel height and final air velocity of 4.5 cm/s. This particular test has
a higher average lifetime for flamelet spinsters. This can be explained by observing the
fingering patterns of the tests. A fingering pattern of a test with the same conditions
(inverted, thnel height = 3 mm, air velocity = 4.5 cm/s) is shown in Figure 35. This
picture shows that there are not many fingering branches. From the pattern, it can be said

that many of the flamelets traveled for long period of time as spinsters.

 

Figure 35. A fingering pattern of a test with higher lifetime of flamelet spinsters.

In Figure 34, an outlier appears at an air velocity equals to 2.5 cm/s. This outlier is
from the experiment in the normal position with tunnel height equals 3 m. From Figure
34, the average lifetime of the flamelet survivors is about 120 s. This can be explained by
observing the fingering pattern of the test. Shown in Figure 36 is the fingering pattern of
the test. It can be seen that there are two flamelets that survived to the end of the
experiment. These two flamelets traveled long without bifurcating until one of them
reached the end of the sample paper. Flamelet spinsters or long life survivors appeared in
many of the 3 mm tunnel height experiments both in normal and inverted positions of the

test facility.

42

 

Figure 36. A fingering pattern of a test with higher lifetime of flamelet survivors.

3.5 Flamelet Census

The flamelet census is presented in the form of pie charts. In the pie charts the

flamelet survivors were not included because they have no meaning in the total population.

3.5.1 Experiments in the Normal and Inverted Positions

The pie charts in Figure 37 on page the next page represent the results of tunnel
heights 3, 4, and 5 mm for experiments in the normal position of the test facility. The
charts show the percentages of the flamelet mothers, infants and spinsters. The pie charts
show that the distribution of each category is virtually uniform. At least 50% of the total
population are productive flamelets (mothers), and the other 50% of the total population are
unproductive flamelets (infants and spinsters).

The pie charts that represent the results for tests in the inverted position for tunnel
heights of 3, 4, and 5mm are shown in Figure 38. The three pie charts show a good
agreement with the results in the normal position. At least 50% of the total population is
productive flamelets (mothers) and the remaining 50% are unproductive flamelets (infants
and spinsters). The distribution of categories flamelets infants and spinsters are not as

uniform as the results in the normal position.

43

u Spinsters RampDown_3mm_
22% ' 35.8-5.5_5.05(1)c

   
 
 

  
 
 
 
 
  
   
 

Mothers
51 %
I Infants
27%
I3 Spinsters RampDown_4mm_
1 7% -;-; ...... 33. 3-3_1 5. 15(1 )c
Mothers
53%
I Infants 7
30%
D Spinsters
22% t-35-25c
Mothers
50%

I Infants '
28% ...
Figure 37. Example pie charts for results of experiments in the normal position of test

facility with tunnel heights of 3, 4, and 5 mm.

El Spinsters
5% Ram pDown_lnv_

3mm_34.9-4.5_10.1(2)c

   
   
  

I Infants
40% E Mothers
55%
El Spinsters Ram pDown_lnv_
17% -

4mm_33.8-3.5_5.05c

E Mothers
51%
I Infants ’
32%
E Spinsters
13% ._ Ram pDown_Inv_

5m m_27-2. 5_4.90

I Infants
37%

Figure 38. Example pie charts for results of experiments in the inverted position of test

facility with tunnel heights of 3, 4, and 5 mm.

45

3.5.2 Flamelet Census Summary

A summary of the population percentages of flamelet mothers, infants and spinsters
can be found in Table 4. The summary plot of percentage population of flamelet mothers
can be found in Figure 39. Drawn in the graph are the i 3% limits from the 50% line. The
majority of the tests show that flamelet mothers are within the 50% :1: 3% range. There are
21 tests between 47%-53%, 5 tests are above 53%, and 4 tests are below 47% (3 of them
are far below the line). Ignoring the three outliers, this result generally shows a good
agreement with the results studied at NASA. The prediction done by Olson, Miller and
Wichman [9] states that 50% of survivorship is necessary for flamelets to continue to

propagate indefinitely (steady state).

The three outliers shown in Figure 39 are of 3 mm tunnel height tests. One of the
three tests was in the normal position with a final air velocity of 2.5 cm/s. The other two
tests were in the inverted position with final air velocities of 3.5 cm/s and 4.5 cm/s. These
three tests had a relatively low oxygen delivery rate level. In these conditions flamelets
hardly survive, but they continued to move slowly for a very long time. In addition, these
test correspond to the outliers shown previously in Figures 31 and 32. In Figure 39, the
three outliers show low numbers of flamelet mothers, while in Figures 33 and 34 these

three outliers show high numbers of spinsters and survivors.

46

Table 4. Summary of flamelet census for both normal and inverted tests

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Position Tunnel Velocity Mothers Infants Spinsters
Height (mm) (cm/s) (%) (%) (%)
Normal 3 2.5 42.1 1 42.11 15.79
. 5.5 48.44 30.92 20.64
4 2.5 51.73 39.61 8.68
3.0 52.67 33.05 14.28
3.5 51.47 38.24 10.29
4.0 52.63 31.58 15.79
5 2.5 49.96 34.95 15.09
5.0 50.32 31.78 17.91
Inverted 3 3.5 42.11 44.74 13.16
4.5 47.07 35.22 17.72
4 3.0 52.60 40.24 7.16
3.5 49.38 31.34 19.28
4.0 53.57 28.57 17.86
5.0 50.00 27.08 22.92
5 2.5 49.23 34.50 16.27
3.5 - 51.92 28.85 19.23
60 _
... 55 i 5 X
a? ‘ \K
E _ g i I ONormaISmm
2 50 _ z I > i : lNormal4mm
‘6 I ANormal 5mm
5. X o
’6 - . Xlnverted 3mm
3 45 E Xlnverted 4mm
5 . O X +lnverted 5mm
u. 40 : ><
,
I
35 n l n l 1 I 1
2 3 4 5 6
Alr Veloclty (cmls)

Figure 39. Percentage of flamelet mothers versus final air flow velocity.

47

The next two graphs in Figures 40 and 41 are the population percentages of
flamelets infants and spinsters. As shown, the population percentage of flamelet infants
mostly scattered between 20% and 45%. On the other hand, the flamelet spinsters scattered
between 0% and 30%. The data points for the infants show a slight decrease as the air
velocity increases. Conversely, the data points for the spinsters show a slight increase as

the air velocity increases.

50

 

h
0|

 

9 Normal 3mm
. o I Normal 4mm
A A Normal 5mm
x Inverted 3mm
x X Inverted 4mm
+ X 4 + Inverted 5mm

h
D

0°

0

IIEIaéI I >< x
o

 

 

 

M
(II

Flamelet Infants (%)
0°
OI
T1riri111IIII11fiI|1lrtlrttl

 

 

 

N
O
1.

Alr Veloclty (cmls)

Figure 40. Percentage of flamelet infants versus final air flow velocity.

48

40

60
O

Flamelet Splnsters (%)
3 8

 

 

 

 

0 Normal 3mm
I Normal 4mm
A Normal 5mm
x Inverted 3mm
>K Inverted 4mm
+ Inverted 5mm

 

 

 

- X
+ o
_ I ”x f ’
+
. )K .
5 X I o
t E X ‘
. I I
I I
X
* A l
2 3 4 5
Alr Veloclty (cmls)

Figure 41. Percentage of flarnelet spinsters versus final air flow velocity.

49

 

CHAPTER 4
FLAMELET BIFURCATION ANGLE ANALYSIS

4.1 Background

The fingering pattern that flarnelets produce in search of oxygen has different
characteristics. Depending on the test conditions, such as the ttmnel height and the air
velocity, the fingering patterns have different gap spaces and bifurcation angles. Two

samples of the fingering patterns of two different tests are shown in Figures 42 and 43.

 

 

Figure 42. Fingering pattern with tunnel height of 5 mm and final air velocity of 2.5 cm/s

in the normal position of the test facility.

 

Figure 43. Fingering pattern with tunnel height of 3 mm and final air velocity of 5.5 cm/s

in the normal position of the test facility.

50

The white portion is the unburned fuel sample and the black portion is char. Figure 42
shows the fingering result of a test with a 5 mm tunnel height and a final 2.5 cm/s air
velocity. Figure 43 shows the fingering result of a test with a 3 mm tunnel height and a
final air velocity of 5.5 cm/s. As can be seen in Figure 42, the fingering is more
distinguished compared to the fingering in Figure 43. In Figure 43, the fingers are closer to
one another.

The flamelet “infants” previously discussed are those with lifetimes less than 5
seconds after bifurcation. Many of them had lifetimes that are less then 1 second. This
rapid extinction causes the flamelet burn pattern to be wavy. For example, consider
flamelets A and B in Figure 44. The pathway of flamelet A does not have branches,
however is wavy. Flamelet A unsuccessfully bifurcated many times. On the other side, the
pathway of flamelet B has 5 obvious branches. The bifurcation angle measurement
accounted the wavy edges caused by the fast extinction as well as the more obvious

separation.

 

Figure 44. Picture of fingers with different bifurcation angles.

4.2 Approach

At the end of each experiment, a picture of the fingering pattern was taken. The
picture was taken with the room lighting and the copper background to receive excellent
contrast. Bifurcation angle measurements were done easily with the help of Adobe

Photoshop 7.0. First, ovals were drawn following every curve of the fingering pattern.

51

Using the protractor tool the angle was determined for each oval. The data were stored in
the Excel spreadsheet. The burnt material near the end of the sample was ignored since the
fingering pattern was not a result of the flamelets, but because surviving flamelets reached
the end of the sample and burned backwards to consume more of the sample. Figure 45
shows how the bifurcation angle measurement was done. As was expected, at several
points there were multiple bifurcations. When that occurred, the average of the bifurcation
angles at that point was taken instead. Figure 45 shows an example of the bifurcation angle

measurement.

 

Figure 45. Measuring angle of bifurcation.

4.3 Results and Discussion

The measurement ignored which direction the flamelets grew because it was more
important to record the angle and not its direction (i.e., positive or negative with respect to

the inflow direction).

52

4.3.1 Experiments in the Normal Position

The average angles of bifurcation in the normal position for tunnel heights of 3, 4
and 5 mm are shown in Figure 46. The air velocities for the each tunnel height are 3.5
cm/s, 3 cm/s and 2.5 cm/s, respectively. As can be observed from the plot, the average
bifurcation angle is proportional to the tunnel height. When the tunnel height increases the

bifiJrcation angle increases as well. The bifurcation angle ranges from 15° to 22°.

 

 

 

 

24
22 r ‘
_
Angle 20 _ A
d .-
( agree)18 _
16 -
. O
14 1 1 1 J I 1 1 1 1 I 1 1 1 1 l 1 1 1 1
2 3 4 5 6
Tunnel Height (mm)

Figure 46. Bifurcation angle versus tunnel height for normal position of test facility.

4.3.2 Experiments in the Inverted Position

The average angles of bifurcation can be found in Figure 47 for experiments in the
inverted position of the test facility, with tunnel heights of 3, 4, and 5 mm. The air
velocities for each tunnel height are 3.5 cm/s, 3 cm/s and 2.5 cm/s, respectively. The trend
is similar to the results in the normal position, the angle of bifurcation increases as the

tunnel height increases. The values fall between 14° and 19°.

53

 

 

 

 

19
A

_ A

17 -
Angle
(degree)
15 r .
13 1 I 1 I 1 L 1
2 3 4 5 6

Tunnel Height (mm)

Figure 47. Bifurcation angle versus tunnel height for inverted position of test facility.

4.3.3 Summary of Bifurcation Angles

Table 5 lists the average bifurcation angle for tunnel heights 3, 4, and 5 mm with air
velocities of 3.5, 3, and 2.5 cm/s, respectively, for both normal and inverted positions of the
test facility. These numbers were plotted in Figure 48 for easy observation. The general
trend is very clear that when the tunnel height increases the bifurcation angle increases as
well. The bifurcation angle for experiments in the normal position, though, is higher than
the bifurcation angle for experiments in the inverted position. The second-order
polynomial trend lines were drawn, and they show significant increase from 3 mm to 4 mm
for both positions of the test facility, although the normal position appears to be more
major. From 4 mm to 5 mm the increase is more moderate for both positions of the test
facility. This may happen because the 3 mm tunnel height experiments produced more

flamelets initially; therefore there was little room for the flamelets to bifurcate laterally.

54

Overall the average lateral bifurcation angle ranges between 14° and 21°. This range is

close to the lateral growth angle in [9], which value ranges from 15° to 23°.

Table 5. Summary of the average bifurcation angles for experiments in the normal and

inverted positions at various tunnel heights and final air velocities

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Position Tunnel Height Velocity Bifurcation
(mm) (cm/s) Angle (0)
Normal 3 3.5 15.17°
4 3.0 19.30°
5 2.5 20.70°
Inverted 3 3.5 14.51°
4 3.0 17.02°
5 2.5 18.16°
21
. 5"".
20 -
19 _ ”U
Angle 18 - ...w-'"""
de ree ' ‘ __,.w'
( g )17 h A El Normal
. A Inverted
1e - ,
- ,r' - - - Poly. (Inverted)
15 - Poly. (Normal)
14 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1

Tunnel Height (mm)

Figure 48. Average bifurcation angle versus tunnel height.

55

CHAPTER 5
FUEL SAMPLE BURNED AREA ANALYSIS

5.1 Overview

In further study of the flamelet, the fuel sample burned area analysis plays a major
role. With this analysis, evaluation such as flamelet energy production can be done; and
more prominently the oxygen consumption rate during combustion can be predicted. The
prediction of the oxygen consumption rate along with the measurement of the flamelet
spread rate are very useful to evaluate other studies such as the fuel-to-air ratio, flamelet
power, and a few parameters for the population study using logistic model that will be
discussed later in this thesis (Chapter 8). All of these topics will be discussed separately in
sections 5.2 through 5.7, both for the normal and inverted positions of the test facility.
Additionally, all necessary measurements were done utilizing the experimental video file as

well as sophisticated computational software.
5.2 Fuel Sample Area Burned Fraction

5.2.1 Approach

The area burned measurement was done utilizing a software image analysis package
TRACKER. The first task was to set the image scale from the image to user units in order
to obtain results in the desired physical units. In TRACKER a suitable “threshold tracking”
area of interest (AOI) was used to distinguish the burned area from the un-burned area by
amplifying the color difference. Various image processing tools provided in the software
can be deposited into the “image processing sequence.” Then TRACKER recorded
continuously, by small increments, the distance across the length of the sample. Figure 49

shows how the area burned measurement was done along with a list of the necessary image

56

processing tools that must be stored in the sequence. “Extract Plane-luminance” set the
image in the A01 to a grayscale; “Threshold-Simple” set the bright color scale as white and
the dark color scale as black; “Measurement-Area” measured the white and the black areas
continuously; and “Threshold-Simple” was set by default. Afier measuring continuously
with TRACKER, the fuel burned fraction was calculated using a reference point at the

location of the ignition or at a point where the fuel was consumed uniformly.

 

‘ 1 ‘ :4” 1: u 2‘ 1“”14'
‘ If? r, '1’. {ELEV-A)?"

1
-‘42:

ple
Measurement - Area
Threshold - Simple

 

 

 

 

Figure 49. Measuring fuel sample burned area.

5.2.2 Experiments in the Normal Position

The burned area fraction ranges fiom 0 to 1. Where 0 is when the sample was not
consumed at all, and 1 is when the sample was entirely consumed. In the plot, x-axis is the
distance measured approximately fiom where the ignition was said to occur (this is an

arbitrary location). The typical area burned fraction curve for experiments in the normal

57

position of the test facility can be found in Figure 50. This figure also represents the fuel
burned fraction for tunnel heights 3, 4, and 5 mm with various final air velocities. The
general shape of the burned fraction curve can be divided into three regions. The first
region is the flat part, then the drop part, and the oscillatory part. These three regions
correspond to the flame-front region, flame-front to flamelet transformation region, and the
flamelet region, respectively. As appears in Figure 50, the flame-front region is flat
because the flame-front unifome consumed the fuel sample. Depending on the ignition,
in some tests the flame-front was not linear and uniform, therefore the curve would not
appear as flat as shown in Figure 50. The burned fraction in the flamelet region fluctuates

depending on the propagation of the flamelet.

Ram pDown_5m m_26. 7-2. 5_8. 07(6)c
1.2 ‘

 

1.0

0.8
Fuel Burned

Fractlon 0.6

 

 

 

 

0.4- ...........................................................................................
L.

0.2- ...........................................................................................

0.0 III-1.111111111111111111
0 5 10 15 20 25

Distance (cm)
Figure 50. Area fuel burned fraction plot that represents results in the normal position of

the test facility with tunnel heights 3, 4, and 5 mm and various final air velocities.

58

The fuel burned fraction shown in Figure 50 is from one of the tests with test
conditions of 5 mm trmnel height and 2.5 cm/s final air velocity. The fingering pattern of
this test (RampDown_Smm_ 26.7-2.5_8.07(6)c) can be found in Figure 51. Dotted lines
were drawn to divide the three regions discussed earlier. The flarnelet propagation was
almost uniform across the sample. The result is shown in Figure 50, where the burned

fiaction variation is close to steady.

 

 

Figure 51. Three regions of test RampDown_Smm_26.7-2.5_8.07(6)c.

For each tunnel height, the air velocity was varied to see the effect on the burned
fraction in the flamelet region. The result can be seen in Figure 52. As can be seen in
Figure 52, the fuel burned fraction is proportional to the final air velocity and the ttmnel
height. This result is consistent with the flarnelet population analysis. That is when the
final air velocity and trmnel height increase, the flamelet population increases as well (more
fuel consumption). In Figure 52, the average fuel burned fi'action for most of the tests fall
between 0.4 and 0.7, which means that most of the time flamelets consumed about 40% to

70% of the fuel sample. Roughly, the average burned fraction for all of the tests is about

59

58%. This number is comparable to the study performed at NASA [9], in which the
fraction of fuel consumed for opposed flamelets is about 62%.

Linear trend lines for each tunnel height were drawn in the plot. The equations for
these trend lines are y3=0.1248x+0.3095, y4=0.1630x+0.0599, and y5=0.1517x—0.2747, for
tunnel heights 3, 4 and 5 mm, respectively. As can be seen from the plot and the values of

the slopes, the trend lines are almost parallel to each other.

 

 

 

 

 

 

 

1.0
o 8 h ' ' D
' _ _ .A 'D’ ' ' '
Average 06 _ .D-

Fuel ' A ’ . ' El ’ , é
Burned ' ' [:1 ' , - ' '
Fraction 0-4 ' E ’ , - ' '

- . ' ’ ' . ONor 3mm
0.2 ' j . ' ' DNor 4mm
. Q' ' ANor 5mm
0.0 1 I 1 I 1 l 1
2 3 4 5 6
Air Velocity (cmls)

Figure 52. Burned fraction for experiments in the normal position.

5.2.3 Experiments in the Inverted Position

A fuel area burned fraction graph can be found in Figure 53. This graph represents
the results in the inverted position of the test facility for various tunnel heights and final air
velocities. The fuel burned fi'action curves for experiments in the inverted position

qualitatively agree with the results for the normal position of the test facility. The three

60

regions can be seen in Figure 53 like the three regions shown for the normal position. The
fuel burned fraction shown in Figure 53 had test conditions of 3 mm tunnel height and final
air velocity of 4.5 cm/s. It can be seen from the plot that there was not much fuel

consumption.

Ram pDown_lnv_3m m_34.9-4. 5_1 0.1c

 

1.2
1.0

0.8

Fuel Burned 0 6
Fractlon '

0.4

 

0.2

 

 

00 111111111l1’14111111l1111
I

 

Dlstance (cm)
Figure 53. Fuel area burned fraction that represents the results in the inverted position of

the test facility with tunnel heights 3, 4, and 5 mm and various final air velocities.

As before, the burned fraction for each tunnel height was compared for different
final air velocities. Figure 54 shows the average of fuel burned fraction for experiments in
the inverted position. As before, the results in the inverted position are similar to the
normal position. Generally the burned fraction is proportional to the tunnel height and final
air velocity. As the tunnel height and final air velocity increase, the burned fraction

increases as well. Again, this agrees with the population analysis. When there were more

61

flamelets there was more fuel consumption. The average fuel burned fraction shown in
Figure 54 mostly falls between 0.2 and 0.5. This means that in the inverted position,
flamelets consumed about 20% to 50% of the fuel sample. Approximately, the average
fuel burned fraction for all of the tests is 37%. This is about 21% lower than the average
fuel burned fraction for experiments in the normal position. This may occur because of the
difference in shape of the test section, such that the top portion was the heat sink where the
bottom plate was the quartz glass.

The linear trend lines for each tunnel height were drawn and the equations are
y3=0.3218x-0.4047, y4=0.2382x-0.3695, and y5=0.1623x-0.4290 for tunnel heights 3, 4,
and 5 mm, respectively. As can be seen from the plot that the lines are almost parallel to
each other, however the values of the slopes affirm that they are not as good as the other

results from the experiments in the normal position.

 

 

 

 

1.0
- 0an 3mm
Ellnv4mm
0.8 -
Alnv 5mm
. ,A
Avera e ,'
9 0.6 -
Fuel El
Burned v’ ,-

Fraction 0-4 '

 

 

 

0.2 r 9’ . '
0.0 1 1 1 1 1 1 1
2 3 4 5 6
Air Velocity (cmls)

Figure 54. Average fuel burned fraction for experiments in the inverted position with

tunnel heights 3, 4, and 5 mm and various final air velocities.

62

5.2.4 Flamelet Region in the Burned Fraction Curve

The burned fraction curve in the flamelet region shows a random fluctuating
behavior that can be casually related to observe the flamelet behavior. The fluctuation, as
described before, depends on the flamelet propagation. The peaks and the valleys of the
burned fraction curve correspond to the bifurcations and extinctions that occurred during
flamelet propagation. For example, Figure 55 that shows a fingering pattern of a test with a
semi transparent burned fraction curve of the same test (RampDown_Smm_26.7-2.5
__8.07(6)c) superposed on top. The test was done with a 5 mm tunnel height and a 2.5 cm/s

final air velocity.

Recall that in the burned fraction curve, 1 means that the fuel was entirely
consumed, while 0 means that the fuel was not consumed at all. Therefore the peaks
represent bifurcations while the valleys represent extinctions. In Figure 55 there were three
solid lines drawn between distances 5 and 10 cm. The lines were identified as a, b and C.
After the flame-front broke into five initial flamelets the burned fraction curve dropped
quickly because flamelet spread left unburned material in between. Then between lines a
and b the five initial flamelets spread and attempted to bifurcate. Thus, the burned fraction
curve increased in response to the increased fuel consumption. The slight bump at line b
was caused by two little flamelet extinctions indicated by the two crosses. Hence, the
curve leveled slightly. Then, between lines b and c the curve increased as more fuel
consumption occurred by flamelet bifurcation. Two bifirrcations occurred between lines b
and c, as indicated by the two red circles. Then at line c, the curve reached its highest point

and dropped again. This was clearly because there were two flamelet extinctions, denoted

63

by the two crosses at line c. The drop however, was minor because there was a bifurcation

(red circle past the line c) that counter balanced the extinctions.

 

 

 

Distance From Wire Icml

Figure 55. Burned fraction with its fingering pattern superposed on top.

5.3 Flamelet Spread Rate

5.3.1 Approach

The flamelet spread rate was measured using the image analysis software package
called SPOTLIGHT2 because of its capability to track the center of an object.
SPOTLIGHT was similar to TRACKER. However, SPOTLIGHT had certain image
processing tools that TRACKER did not provide such as “center tracking” AOI. It required

a few “image processing sequences” to track the flamelet spread rate continuously. As

 

2 SPOTLIGHT is a software image analysis package that was developed at NASA and is
free for NASA contractors and grantees.

shown in Figure 56, the sequence consisted of “ExtractPlane-intensity”, “Threshold-
simple-inverse”, “Filter-edge detect”, and “TL L ” simple "‘ which appeared by
default. The first threshold distinguished the bright and dark color scales of the image.
The edge detect simply detected the edge of the object (flamelet). The average flamelet

spread rate was measured based on several different flamelets.

:MWW

 

marriage-m1,» .
Threshold- simple- Inverse [49]
Filter edge detect
Threshold - simple - standard [128]

 

 

 

 

 

 

Figure 56. Measuring flamelet spread rate.

5.3.2 Experiments in the Normal Position

Applying the approach described above, the flamelet spread rate was plotted for the
three different tunnel heights and for various final air velocities. The distribution can be
observed in Figure 57. From the plot, it is shown that flamelet spread rate increases as the
air velocity increases. Moreover, the flamelet spread rate increases as the tunnel height
increases. At 2.5 curls and 3 cm/s final air velocities, the flamelet spread rate for different

nmnel heights are within the same scale, as they appear to be very close to each other. The

65

flamelet spread rate plot in Figure 57 shows similarity with the flamelet spread rate plot [9]

obtained at NASA (the plot can be found in appendix A, Figure A1).

As can be seen in Figure 57, the flamelet spread rate increases as the final air
velocity increases. A few spread rate measurement for uniform or corrugated flame (higher
final air velocity) was performed. The results show that the uniform or corrugated flame
spread rate is about three times higher than the flamelet spread rate particularly for the 5
mm tunnel height. This result is consistent with the study performed at NASA. Where

flamelet spread rate is said to be ‘/3 of the uniform flame spread rate [9] (Appendix A,

 

 

 

 

 

 

 

FigureAl).
4.0 -
9 3mm .
- :1 4mm
a. 5mm
3-0 ' — —3mm trend line .
Flamelet — - -4mm trend line ”.323,
Spread ’ - - - 5mm trend line A .~ '
Rate 2.0 - ...-"... JJJ"
(mmls) a ’5'
' C1 C1 3". ’Jz"
El. 4"
./' ,d
1 O ‘ .d'vv/ ”ii?”
E‘E'TD..-$r” ’
0.0 I l ' ' ' I I 1 1 1
2 4 6 8 10 12
Alr Veloclty (cmls)

Figure 57. Flamelet spread rate for experiments in normal position of test facility with

various tunnel height and final air velocities.

66

5.3.3 Experiments in the Inverted Position

Figure 58 shows the average flamelet spread rate for experiments in the inverted
position. Generally the flamelet spread rate is proportional to the trmnel height and the
final air velocity. Due to the low number of tests performed and the difficulty to track the
flamelet in the inverted position (because they pulsed most of the time), there was only one
test for the 4 mm tunnel height with a higher final air velocity. Comparing to the results in
the normal position, the results in the inverted position show a slightly different pattern.
For example, the 5 mm tunnel height shows a more significant increase from 3.5 chs to
4.5 cm/s final air velocities. While the 3 mm tunnel height shows a more moderate
increase from 5 cm/s to 8.5 cm/s final air velocities. Again this occurred because of the

difference in the test section tunnel geometry.

 

3.0

 

O Inv 3mm
. El Inv 4mm
.4. Inv 5mm
20 _ - - - 3mm trend
Flamelet 4 — - '4mm trend
Spread _ - - - 5mm trend
Rate ....
(mmls)

 

 

 

 

 

0'0 1 l 1 l 1 l

 

Air Veloclty (cmls)

Figure 58. Flamelet spread rate for experiments in the inverted position of the test facility

for various tunnel heights and final air velocities.

67

5.4 Per-Flamelet Heat Release Across Sample

The calculation of the per-flamelet heat release per unit length across the sample
was initially based on many assumptions. The first assumption made was that the
combustion reaction was stoichiometric. By definition, stoichiometric is when the amount
of oxidizer is exactly the amount needed to burn completely a quantity of fuel. For
cellulose (filter paper) and air (with a composition of 21% oxygen and 79% nitrogen, by

volume), the reaction can be written as:
C6H1005 + 6(02 + 3.76 N2) ——) 6COz + 51120 + 22.56N2. (R1)

For the above reaction, the mass ratio of air to fuel is shown in Equation (2). Here, MW,“r
(28.85 kg/kmol) and MWC6H1005 (162 kg/kmol) were the air and cellulose molecular
weights, respectively. The 4.76 was the number of moles of air (3.76 moles of N2 plus 1

mole of Oz), and 6 was the oxidizer coefficient.

_”1_=[ "fie-4.76.6]:508 (2)
m,r MWF

 

5.4.1 Approach

The evaluation of the per-flamelet heat release per unit length across the sample
was done using the burned fuel fraction and the flamelet spread rate data. The average per-
flamelet heat release per unit length across the sample was according to Equation (3).
Here, Yoz was the oxygen mass fraction (0.233), and p8 was the cellulose area density (74

g/mz). N and L were the number of flamelets and burned section, respectively.

Q(x) =13.1MJ/kg02 -5.08-Y02 - p, -(Ll /N,)- Imam, (3)
0

68

where
N L
SR =-—‘-- ". 4
(x) 1 N ()

 

I

Then the instantaneous average heat release rate per-flamelet was according to Equation
(5), where Navg was the average number of flamelet, and Vf was the flamelet spread rate.
The instantaneous heat release rate is expected to be proportional to the heat release per

unit length because, except for the value of Q(x), everything else in the formula is constant.

. _Q(x)'Navg'vf
q... - Ax (5)

 

5.4.2 Experiments in the Normal Position

An example of the per-flamelet heat release per unit length across the sample plot

can be found in Figure 59. This plot represents the results of the experiments in the normal

Ram pDown_4m m_33.3-3_15. 1 5(3)c

 

1.2

1.1
Heat Release

per Flamelet
per Unlt 1-0
Length (MJ)

0.9

 

 

 

 

o 8 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I
I

Dlstance (cm)
Figure 59. Per-flamelet heat release per unit length across the sample that represents the
results in the normal position of the test facility for various tunnel heights final air

velocities.

69

position for tunnel heights 3, 4, and 5 mm and various final air velocities. The heat release
linearly increases. The results confirm the speculated plot in [15]. In [15], the straight line

slope indicates that the overall per-flamelet heat release had reached steady state.

5.4.3 Experiments in the Inverted Position

The results of per-flamelet heat release per unit length across the sample for
experiments in the inverted position are similar to the results shown for the normal
position. Figure 60 represents the results of the experiments in the inverted position for
tunnel heights 3, 4, and 5 mm and various final air velocities. As can be seen, the per-
flamelet heat release linearly increases toward the end. Again, as it was speculated, this

behavior suggests that a steady condition had been reached.

Ram pDown_'l nv_3m m_34. 9-4. 5_10. 1 (2)c
0.80

 

Heat Release 0'78

per Flamelet
per Unlt 0.76
Length (MJ)

 

0.74

 

 

o. 72 1 1 1 I L 1 1 I 1 1 L I 1 1 1 I
10 12 14 16 18 20
Dlstance (cm)

 

Figure 60. Per-flamelet heat release per unit length across the sample that represents the
results in the inverted position of the test facility for various tunnel heights final air

velocities.

70

5.5 Oxygen Consumption Rate

At the NASA Glenn Research Center the oxygen consumption rate was measured
utilizing a special device. Unfortunately, the MSU Combustion Laboratory lacks
appropriate equipment to measure the oxygen consumption rate. Since it was impossible to
measure the oxygen consumption rate, some equations to predict the rate based on the
known conditions were established. The oxygen consumption rate was predicted (not

measured) using the area bumed rate data as well as the flamelet spread rate data.

5.5.1 Approach
There were five equations established to predict the oxygen consumption rate.

These five equations, though, assumed that the reaction was stoichiometric. The

stoichiometric Reaction (R1) was described previously in Section 5.4.

The first equation to predict the oxygen consumption rate is expressed in Equation
(6) below. Where dA/dt was the area burned rate, p; was the cellulose area density and
6(32/162) was the stoichiometric oxygen-fuel molecular weight ratio.

°..dA 23

0___. .. 6
2 dtp” 162 U

The second equation that predicts the oxygen consumption rate can be seen in
Equation (7) below. This equation assumed that the oxygen heat of combustion was 13.1

' : %'PF "Jr

02 (7)
902

71

The third equation that predicts the oxygen consmnption rate can be found in
Equation (8). This equation assumed that the fuel heat of combustion was 17.5 MJ/kg
(36111005 (the value was obtained from the first law of thermodynamics, and will be discussed
later in this section). The fuel surface temperature during the combustion was estimated as

700 K.

62 :%'pF 'CPF '(Ts —T0)-6-—32-
qF 162

 

(8)

The fth equation that predicts the oxygen consumption rate is stated in Equation
(9). This equation was established assuming that the oxygen heat of combustion was 13.1

MJ/kgoz, and the fuel surface temperature was 700 K.

° ___%’PF 'CPF '(Ts “To)

()2 (9)

 

902

Lastly, the fifth equation that was established to predict the oxygen consumption
rate is expressed in Equation (10) below. This equation assumed that the cellulose (fuel)
heat of combustion was 17.5 MJ/kg “”1005. As can be seen in this equation, there are two
common factors, qp, which would cancel each other out. This causes Equation (10) to
become exactly the same to Equation (6). Since this equation give the exact same results,

this equation will not be discussed in the result and discussion section.

. zm.6._3l

0 10
2 q, 162 ( )

72

Notice in all five equations, Equations (6) to (10), that the variables that appear are
all constants except “dA/dt”. Consequently, the oxygen consumption rate is proportional to

the area burned rate.

The value of 17.5 MJ/kgC6H1005 was obtained from the first law of thermodynamics.
Since the energy of the reactants was equal to the fuel enthalpy of formation, the energy of
the products was calculated according to Equation (11) with the assumption that the

reaction was stoichiometric:

Hpmm=51 ° +AhH20)+6-(h° +Ahc02)+22.56-(h;N2+AhN2)(11)

f H20 f C02
All the values of the hf and Ah were selected at the ambient temperature (298 K). At 298 k,

the values of the Ah terms were zero. By definition, the value of hm was also zero. Once

Hpmduct, was found, the fuel heat of combustion can be calculated.

Once the oxygen consumption rate was predicted, the unconsumed oxygen rate can
be predicted. The unconsumed oxygen rate was the difference between the constant inflow
oxygen rate and the oxygen consumption rate. With this relationship, the unconsumed
oxygen rate would be inversely proportional to the area burned rate. To evaluate the inflow
oxygen rate, first the air mass inflow rate was determined using continuity. The property of
air was taken at 298 K, the inlet area depended on the tunnel height, and the velocity was
the final air velocity. Then, the inflow oxygen rate was the product of the air mass flow
rate and the oxygen mass fraction. Table 6 lists all the constants involved to predict the
oxygen consumption rate. In addition, unit verification to check the validity of the oxygen

consumption rate equations can be found in Appendix A.

73

Table 6. Input variables to predict the oxygen consumption rate

 

 

 

 

 

 

 

 

 

 

 

 

 

Constants Values Units
p, 0.074 kg/mz
pg, 1.172 kg/m3

MWF 162 @110]
MW02 32 g/gmol
Cpp 1 1,704 J/kg*K
Ts 700 K
Tco 298 K
g; l 7.5 MJ/kgp
(102 I 3 . I MJ/kgoz
Yo; 0.233
w l 7.8 cm

 

 

 

 

 

5.5.2 Experiments in the Normal Position

The results of the predicted oxygen consumption rate from the four equations can
be seen in Figure 61. This plot represents the results of the predicted oxygen consumption
rate for experiments in the normal position of the test facility with various tunnel heights

RampDown_3mm_35.86.5_2.16(1 )c

 

1 E-05

8E-06
613-06 W

4E-06 r

 

 

25'06 ' W

Oxygen Consumption Rate
(kgISI

 

 

 

o E+oo 1 1 1 1 I 1 .1 1 1 I 1 1 L 1

Distance (cm)
Figure 61. Predicted oxygen consumption rate plot that represents the results in the normal

position of the test facility with various tunnel heights and final air velocities.

74

and final air velocities. The x-axis is the approximate distance from where ignition was
said to occur. The oxygen consumption rate in the flame-front region was insignificant.
Therefore the plot only included the oxygen consumption rate in the flarnelet region. As
can be seen in plot, the results using Equations (6) and (7) are close together, and the
results using Equations (8) and (9) are close together but much lower compare to the results

of Equations (6) and (7).
5.5.3 Experiments in the Inverted Position

The predicted oxygen consumption rate plot that represents the results in the
inverted position of the test facility for three tunnel heights and various final air velocities

can be found in Figure 62. Again, the results obtained using Equations (6) and (7) are close

Ram pDown_lnv_4m m_34-3. 5_5. 1 c

 

 

 

 

 

 

 

1.5-05
o h
if
c 8.E-06 -
g .
‘5.
E 1;? 6.E-06 -
3 a.
U) U) '
5 5 4E-oe -
U .
c .
3! 2E-06 -
5‘ ' _
o

o.E+oo L J J J 1 I l l l l 1 l 1

 

12 14 16 18 20 22 24 26

Dlstance (cm)
Figure 62. Predicted oxygen consumption rate plot that represents the results in the

inverted position of the test facility with various tunnel heights and final air velocities.

75

together, and the results obtained from Equations (8) and (9) are close together, however,
much lower than the results from Equations (6) and (7). Up to this point, it is still

undetermined which one (or two) of these equations predicted more reasonable results.

5.5.4 Discussion

To compare the results of the four equations that predict the oxygen consumption
rate, the average percentage of the unconsumed oxygen rate were outlined in Table 7.
From the table, it can be seen that the predicted unconsumed oxygen rate from Equations
(6) and (7) generally are lower than the results from Equations (8) and (9). For example
the average in the normal position, the overall average for tunnel heights 3, 4, and 5 mm
from Equations (6) then (8) are: 70%, 39%, 28% and 91%, 81%, 78%, respectively. The
results from Equation (6) suggest that there was more oxygen consumed by flamelets
during the combustion. Where the results from Equation (8) suggest that there was only
10% to 20% of the oxygen that flowed into the system was consumed. Therefore, it can be
determined that the results using Equations (6) and (7) are more reasonable compared to
the results from Equations (8) and (9).

Observing Table 7, it can be seen that the percentage of the unconsumed oxygen
rate decreases as the tunnel height increases. This means that the there was more oxygen
consumed by flamelets for larger tunnel heights. Between the normal and the inverted
positions of the test facility, it can be seen that there was less oxygen consumed by
flamelets in the inverted position. This result is consistent with the population analysis in
Chapter 3. When there was less flamelets, clearly there was less amount of oxygen

consumed.

76

 

Table 7. Summary of predicted unconsumed oxygen rate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unconsumed Unconsumed Unconsumed Unconsumed
Tunnel Air Oxygen Oxygen Oxygen Oxygen
Position Height Velocity from from from from
(m) (cm/s) Equation (6) Equation (7) Equation (8) Equation (9)

(%) (%) (%) (%)
Normal 3 2.5 85 83 95 96
5.5 65 61 89 91
10.0 74 71 92 93
average 70 66 91 92
4 2.5 40 32 82 84
3.0 39 32 82 84
3.5 35 29 78 80
4.0 49 43 85 86
5.0 38 31 8O 82
average 39 32 81 83
5 2.5 28 19 78 81
Inverted 3 3.5 88 86 96 97
4.5 82 80 95 95
5.1 74 71 92 93
average 81 79 94 95
4 2.5 90 89 97 97
3.0 82 8O 94 95
3.5 49 43 85 86
average 77 74 93 94
5 2.5 68 64 90 91

 

 

 

 

 

 

 

In predicting the oxygen consumption rate, there were some tests that showed

unusual results. For example test number RampDown_Smm_26.7-2.5_12.l(7)c, whose

unconsumed oxygen rate plot is shown in Figure 63. The unconsumed oxygen rate from

Equation (7) reached to some negative values. Physically, this is impossible. There are a

few reasons why this sometimes occurred in some tests. The first reason is the assumptions

that were made when establishing the equations maybe slightly incorrect. Another reason

that may cause this is that there were leaks in the system that allowed oxygen from the

surroundings to act as additional sources of oxygen.

77

 

Ram pDown_5m m_26. 7-2. 5_1 2.10(7)c

 

 

 

 

 

 

 

 

1.55-05 L
o 1-
fi 1-
m .-
r: tors-05 -
a 1-
5‘ ... .
o 22 ~
3 5.0E-06 f
E .
3 .-
g .
3 0.0E+00 ....
c .
3 C

-5.0E-06 '

 

 

Dlstance (cm)

Figure 63. Predicted unconsumed oxygen rate with unusual occurrence.

5.6 Stoichiometric Ratio

Once the oxygen consumption rates were predicted, the global stoichiometric ratio
can be estimated. Since there are four different equations that can be used to predict the
oxygen consumption rate there are four different results of the global stoichiometric ratio
that were obtained. However, for comparison purposes, only the results from Equation (6)

will be presented in the results and discussion section.

5.6.1 Approach

Two important factors in evaluating the stoichiometric ratio [9] were the fuel
burning rate and the oxygen consumption rate (which was predicted in section 5.5). The
fuel burning rate equation can be found in Equation (12). The units for the fuel burning
rate was gmolp/s. Here Vf was the flame spread rate, fbumed was the fuel burned fraction, or

was the fuel surface density, w was the sample width, and MWF was the fuel molecular

78

weight. The oxygen consumption rate then can be expressed as in Equation (13) with unit
of gmolozls. The predicted oxygen consumption rate from the previous section was used in

the Axoz term. The global stoichiometric ratio then can be calculated according to

 

 

 

Equation (14).
v o o -W
"1F: f fburned PT (12)
MW,
. A . ~U -h-w
m0,= 102 p ° (13)
R-T
6:6"? (14)
m0

5.6.2 Results and Discussion

The average global stoichiometric ratios for both experiments in normal and
inverted positions with various tunnel heights and final air velocities were tabulated in
Table 8. When evaluating the global stoichiometric ratio, the results from using the oxygen
consumption rate from Equation (9) are about three times higher than the values from the
Equation (6). This confirms that Equations (6) and (7) produce more reasonable results
than the results of Equations (8) and (9). Therefore the results using Equations (8) and (9)
were ignored and not presented in this discussion.

The definition of stoichiometric combustion is when the amount of oxidizer is just
the exact amount demanded to burn some amount of fuel completely. That is when the
ratio of fuel-to-air is equal to unity. When the fuel-air ratio is >1, this means that the

mixture is fuel-rich. And when the ratio is <1, it means that the mixture is fuel-lean. From

79

this definition, it can be said that the reaction of the burning sample paper is fuel-rich, since
the values are all greater than 1. This agrees with the study performed at NASA [9]. The

global stoichiometric ratio is 1.25, which is a fuel-rich.

Table 8. Summary of the average global stoichiometric ratio

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stoichiometric
Tunnel Air Ratio from oxygen
Position Height Velocity consumption rate
(mm) (cm/s) calculation using
E9- (6)

Normal 3 2.5 1.35
5.5 1.31
10.0 1.33
4 2.5 1.27
3.0 1.20
3.5 1.13
4.0 » 1.25
5.0 1.21
5 2.5 1.08
3.5 1.08
Inverted 3 3.5 1.55
4.5 1.51
5.1 1.65
4 3.0 2.05
3.5 1.23
5 2.5 1.37

 

 

 

 

 

5.7 Flamelet Power

5.7.1 Approach

There were four equations to predict the oxygen consumption rate. Therefore there
are four results of the flamelet power. However, only the oxygen consumption rate fi'om
Equation (6) will be used in this section, since this equation produced more reasonable
results. The flamelet power was evaluated by multiplying the oxygen consumption rate per

flamelet by the oxygen heat of combustion. The unit of flamelet power is J/s or Watts.

80

5.7.2 Results and Discussion

The results of the flamelet power can be found in Table 9. The flamelet power
calculations were done using the oxygen consumption rate results of Equation (6). The
flamelet power increases as the air velocity increases. Moreover, flamelet has more power
when the tunnel height is larger. Between the inverted and the normal positions of the test
facility, flamelets in the normal position generally were brighter than flamelets in the
inverted position. In fact, when running experiments in the inverted position it was
noticeable that the inverted position always produced dim flamelets. Dimmer flamelets
also occurred at low final air velocities.

Table 9. Summary of flamelet power

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tunnel Air , Flamelet power from
Position Height Velocity oxygen calculation
(mm) (cm/s) using Equation (6) (W)
Normal 3 2.5 8
5.5 11
10.0 31
4 2.5 16
3.0 14
3.5 23
4.0 l 8
5.0 35
5 2.5 18
Inverted 3 3.5 4
4.5 6
5.1 14
4 2.5 8
3.0 7
3.5 13
5 2.5 9
3.5 28

 

 

 

 

 

 

81

CHAPTER 6
FLAMELET ANALYSIS

6.1 Background
There are three possibilities of combustion reaction for the burning cellulosic fire]
sample. First the combustion could be a stoichiometric reaction. Then it is possible that

the combustion reaction is fuel rich or fuel lean. The reactions describing the latter two

reactions are shown in Reactions (R2) and (R3), respectively:

C6H1005 + (6+0) (02 + 3.76 N2) —> 6CO2 + 5H2O + [302 + (22.56+3.76B)N2, (R2)
C6H1005 + (6—B)(O2 + 3.76 N2) —)

(6—ZB)CO2 + 5H2O +2BCO + (22.56+3.76B)N2. (R3)
The first reaction contains excess oxygen. This is seen in the product side where the excess
oxygen is indicated by B moles of 02. The second reaction describes combustion with an
oxygen deficit. It is shown by the excess carbon in the product side, that is the 20 moles of
CO.

The challenge with these two reactions was to determine the value of [3. However it
was possible to determine the [3 value by looking at the physical behavior of the flamelets.
An equation had been derived [15] relating the physical behavior of the flamelets to the
determination of the value of [3. The first step to determine the value of [3 is shown in
Equation (15) below. N was the expected number of flamelets, r was the radius of the
flamelets (here, it was assumed that the flamelet has a spherical shape), pi, and vA were the
air density and velocity, respectively. H*-W* was the area of oxygen consumed, D]: was the

fuel diffusivity and Y1": was the fuel mass fraction.

82

 

. . ‘.W‘
N.r: 1 [pA VADH Y :I=€ (15)
27r-5.08-(1+€] (’4' F' F

Rearranging Equation (15), Equation (16) was obtained. Equation (16) investigates
the number of flamelets at a particular point by measuring the physical properties of the
flamelets such as the radius, the gap between the flamelets, and the quench distance from
the sample edge. Here, W‘ is the sample fixed width, g is the gap between flamelets, and q

is the quench distance.

_ W. +g—2q
g+2r

N (16)

6.2 Approach

All of the quantities shown in Equation (16) such as W*, g, q and r were measured
using SPOTLIGHT. The measurement was done at various points across the sample,
excluding the portion consumed entirely by the flame-front. In SPOTLIGHT, there was a
line following AOI that was very useful. This tracking tool gave point coordinates for each
pixel counted once a morphological outline was specified in the A01. Just like
TRACKER, SPOTLIGHT had various image processing tools that can be deposited in the
line following the process sequence. The necessary sequences were “filter-smooth” to even
out the pixels, “threshold-simple” was to distinguish the dark and bright color and
“morphological-outline” was to draw lines between the bright and dark colors. Figure 64
shows the measurable quantities in Equation (16) while Figure 65 lists the processes done

in SPOTLIGHT.

83

 

Figure 64. Fingering pattern segment showing the quantities q, g, and r (N = 7 and W“ =

17.8 cm).

 

. 1

L" - 1."; “hula“; "J "veg...-
Th shold - simple -
Morphological - outline

 

 

 

 

 

 

 

Figure 65. Line following process.

84

6.3 Average Number of Flamelets

The x—axis is the distance across the sample from approximately the location where
the ignition took place. The results of the normal and inverted experiments were plotted
together. In addition, the average number of flamelets were rounded up or down to the
nearest integer value, since the number of flamelets must be an integer quantity.

The results of the number of flamelets equation, Equation (16), for the 3, 4 and 5
mm tunnel heights can be found in Figures 66, 67 and 68, respectively. In Figure 66, it can
be seen, that generally the number of flamelets increases as the air velocity increases both
for the normal and inverted experiments. The results for the 4 mm trmnel height are
generally more bunched together. It still can be seen, however, that the average number of

flamelets in the normal position is higher than the average number of the experiments in the

 

 

 

 

 

 

 

 

inverted position.
14 I —o - Normal, v = 2.5cmls
: + Normal, v = 5.5cmls
12 -_ —o - Inverted, v = 3.5 cmls
" —9— Inverted, v = 4.51ch
10 3
Number 8 i
of :
Flamelets :
4 E
2 E
: b
o P ....... 1 1
8 13 18 23 28
Dlstance (cm)

Figure 66. Average number of flamelets for 3 mm tunnel height.

85

 

 

 

 

 

 

 

 

 

20 _
18 E + Normal, v = 2.5 cmls
E —»o—- Normal, v = 3.0 cmls
16 -E , 9 Normal, v = 3.5 cmls
E —0— Normal, v = 5.0 cmls
1‘ ‘E — e- Inverted, v = 2.5 cmls
12 .5 —0— Inverted, v = 3.0 cmls
Number E + Inverted, v = 3.5 cmls
of 10 ‘:
Flamelets 8 .5
o -E
4 «E
2 -E
o ’ . . . : . : . . . ' . A - .
8 13 18 23 28

Dlstance (cm)

Figure 67. Average number of flamelets for 4 mm tunnel height.

 

 

 

 

 

 

 

 

 

14 _
—o—Normal, v = 5.5 cmls
12 : - I - Inverted. v = 2.5 cmls
E --I-- Inverted, v = 3.5 cm]:
10 :
Number 3 I
of I
Flamelets 5 :
4 E .4
2 _- I I I
: I ----- I
o h I I A
8 13 18 23 28

Dlstance (cm)

Figure 68. Average number of flamelets for 5 mm tunnel height.

The average number of flamelets for the 5 mm tunnel height can be found in Figure 68.

Just like the previous two, Figure 68 shows that the number of flamelets in the normal

86

position is higher than the number of flamelets in the inverted position. These figures serve
merely to formally quantity visual observations, from which are immediately recognizes

this fact.

6.4 Flamelet Diameters, Gap Between Flamelets, and Quench Distance

Table 10 summarizes the measured quantities to evaluate the number of flamelets
such as the quench distance, gaps between flarnelets, and flamelet diameters. The numbers
shown are the average values. These measurable properties, such as flamelet diameter, are
useful to study the population analysis using the logistic model that will be discussed in the

next chapter.

Table 10. Summary of flarnelet diameters, gap spacing, and quench distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Average Average Average Number of
Tunnel Arr
Position Height Velocity dflamelet flamelet gap quench flamelet
(mm) (cm/s) lameter, spacmg, (g) distance, calculated
(0 (cm) (CH1) (C1) (0m)

Normal 3 2.5 1.22 4.81 4.96 2

5.5 1.50 1.09 1.10 7

4 2.5 1.63 1.93 2.55 5

3.0 1.52 0.80 1.74 7

3.5 1.93 1.21 1.57 5

5.0 1.44 0.70 1.74 7

5 2.5 1.75 0.71 1.32 7

Inverted 3 3.5 0.90 1.35 4.80 4

4.5 1.13 1.29 3.30 5

5.1 2.03 1.50 3.55 3

4 2.5 1.57 0.81 7.43 1

3.0 1.21 3.41 2.64 4

3.5 1.67 1.07 0.99 6

5 2.5 2.56 1.70 1.66 5

3.5 2.74 1.55 0.35 5

 

 

 

 

 

 

 

 

 

87

CHAPTER 7
POPULATION MODEL

7.1 Background

The flamelet population demographics methods discussed in Chapter 3 shows that
the cumulative population has an oscillatory behavior. This behavior happened in most of
the tests. Both the NASA and MSU combustion groups had started to develop a theory to
describe this behavior. A first-order non-linear differential equation that fits the
experimental results had been developed. This model equation was based on biological
animal population measures and had been used with some success [9] to describe various

population behaviors. The general equation of the flamelets population model is

5‘3:- = a(t) - a(t) —b(t)-u(t) - u(t — r). b (17)

The factors a(t) and b(t) may vary as functions of time. The last factor on the RHS has a
time lag 1:, indicating that the destruction of a population trails its creation. The simplest
case occurs when the time lag, t, is zero, hence factors a and b are constants, and a/b = K.
As t-—>oo, rearranging Equation (17) will produce Equation (18). Note that x is known as

the carrying capacity.

dt K
A more complicated result occurs when t is not equal to zero. In this case, the equation is

non-linear and time-lagged. Letting p = 1.1/K, Equation (18) becomes:

88

£2?- = p(t) -[l — p(t — 7)] , P(O)=Po- (19)

This equation is solved numerically using numerical solution algorithms. These algorithms
include the Euler method, the Modified Euler method (also known as the second order
Runge-Kutta method), and the fourth order Runge-Kutta method. A computer software
program was developed to yield an accurate graphical result. MATLAB student version
6.0 was used to operate the numerical solution of the equation using all the mentioned
numerical solution methods. The MATLAB code was programmed systematically so one

can enter inputs, and plot the output.

The Euler method is the easiest method, however, it is not very accurate compared
to the modified Euler method. The Euler method is much less accurate than the fourth order
Runge-Kutta method. Nevertheless for comparison purposes as well as to find more
accurate numerical solutions, all the three methods were used. The Euler equation can be
found in Equation (20). Here h is the time increment step size. The modified Euler and

fourth order Runge-Kutta methods are presented in Equations (21) and (22), respectively.

yn+1:yn+hf(xnayn)’ n=09192rn (20)
k1 :hf(xnayn)a
k2 =hf(xn+l’yn +kl)’ n=0,1,2,... (21)

yn+l =yn +%(k1+k2)’

89

k1 :hf(xn’yn)’

k2 =hf(xn+§h’yn +Tkl)’

k3 = hf(x,,+_;_h’yn +é-k2)’ n=0,1,2,... (22)
k4 =hf(xn+l’yn+k3)’

yn+l :yn +%(kl +2.k2 +2.k3 +k4)’

7.2 MATLAB Code

The MATLAB code can be found in Appendix B. The code is presented as it is in
the MATLAB command window. Based on how MATLAB works, the naming of the
variables such as the time lag, increment time step and so on are different than in the
equations described above. To avoid confusion, there are comments on each line. The
comments are located after the percent (%) signs. The MATLAB code was divided into
five major parts, for Euler method, Modified Euler method, fourth order Runge-Kutta

method, error calculations between the three methods and the plotting commands.

7 .3 Factors of Accuracy

There are numerous trials in developing the numerical solution programs. One of
the major factors for obtaining more accurate solutions is the use of higher order
differencing methods. Among the three methods used in this research, the simplest method
is the Euler method. A higher order method is the Modified Euler method, which is
accurate of 0012). The highest order is the fourth order Runge-Kutta method, which is
accurate to 0(h4). Another factor in obtaining a more accurate solution is if the increment
time step is small. The smaller the increment time step, the more accurate is the solution.
The increment time step is denoted by h in Equations (20), (21) and (22), and delta in the

MATLAB code of Appendix B.

90

In order to compare the three numerical solution methods, the MATLAB code of
Appendix B included error norm calculations between the three methods. The goal is to

produce an error magnitude that is as small as possible. The error norm is defined as

 

N
llErrorll = ZJUUJMM - y(t.-),,...;...12]2 . (23)
i=0

The following Figure 69 shows the three different results of the three numerical methods
for different values of the numerical step size, delta. For comparison purposes the values
of the time lag and final time were set to be 1.3 and 30 seconds, respectively. The first plot
in Figure 69 shows the non-dimensional population with delta = 0.1. As can be seen in the
graph, the modified Euler and the fourth order Runge-Kutta curves lay almost on top of
each other, whereas the curve using the Euler method is separated from the others. The
second plot in Figure 69 shows the non-dimensional population with delta = 0.01. As can
be seen in the middle plot, all of the three curves converge and it is harder to see the
difference. The curve using the Euler method appears also to agree with the others
although it can still be seen that the Euler method still slightly deviates. In the third plot in
Figure 69 shows the non-dimensional population with delta = 0.001. As shown, all of the
three curves lay on top of each other, and it is hard to see any difference. Table 11 shows
the summary of the norm error between the three methods for the three different delta
values. Since it is obvious that the higher order of the numerical solution gives more
accurate results, for the remaining study in this chapter, the scheme is of higher order is

always used as the “standar ”.

91

 

 

' Eder, ct=0.1
0 Modtled Euler. [i=0]
1* 4 RungeKttta, dt=0.1

 

 

 

 

 

 

 

 

° Euler. (1:0.01
' Modfied EUer. dt=0.01
1* 4 ngeKLtta. (1:001

 

 

 

 

 

 

 

 

- EUer. at=0.001
- Modified Eller, or=0.001
+ 4 ngeKutta. a=0.001

Non-Dimensional Population

 

 

 

 

 

 

 

D 5 10 15 2D 25 30

TIME (8)

Figure 69. Non-dimensional population with delta = 0.1, 0.01 and 0.001 using Euler,

Modified Euler and 4th Order Runge-Kutta methods.

Table 11. Error norm table

 

 

 

 

Euler Euler Modified Euler
Delta v. v. v.
Modified Euler 4th Runge-Kutta 4th Runge-Kutta
0.1 1.300 1.349 0.049
0.01 0.331 0.332 0.001
0.001 0.103 0.103 3.42e-005

 

 

 

 

 

 

As can be seen in the table, the error norm approaches zero as delta decreases.
However, the error norms between the Euler method and the other two methods are still
larger than the error norm between the Modified Euler and the fourth order Runge-Kutta

methods. Note also that when delta = 0.1, it required a short time (about 2 seconds) for the

92

program to generate the answers for the three methods. However, as the value of delta was
reduced to 0.01, the program took more time to generate the answers. For the graph
presented above, it required a longer time (about 5 seconds) to obtain the answers. Lastly,
when the value of delta was reduced more to 0.001, it required a longer time (about 4
minutes) than the two smaller delta values to generate the answers and obtain the graphs

that is shown above.

7.4 Time Lag

One of the major challenges encountered when developing the program was to
include the ‘time lag’ term, t, in the equation, Equation (19). The equation is already non-
linear without the lag, and because of this ‘lag" term the equation was much more difficult
to solve numerically. Here, the MATLAB code was built with two loops in the program.
The first loop was the linear loop; the second was the non-linear loop. Refer to Equation
(19) and with a fixed ‘lag’ value, 1:. First MATLAB would run within the linear loop. It is
linear since the argument (t-r) of the term p(t-T)1S negative and this term is therefore
neglected. In fact, the p(t)-p(t-1:) is set to zero when t < 1. When t = 1: this term takes the
value p(1:)-p(0) and when t = t+At it is p(t+At)-p(At), etc. When t _>_ 1' the MATLAB code
would jump to the second loop, the non-linear loop where the term p(t-1.') would be
included in the computation. Consider the simple sample calculations shown in Table 12.
Using the Euler method with the increment time step, delta = 0.5, initial condition p(0) =
1/ 10, and time lag 1: = 1. The calculations are fi'om the difference formulas given by

Equations (24) and (25) for the linear and non-linear portions, respectively. Note that

93

Equations (24) and (25) are the rearranged first order (Euler) finite-difference version of

Equation (19):
p(t+delta) = p(t) + delta - p(t) - [1], (24)
p(t+delta) = p(t) + delta - p(t) - [l- p(t-r)]. (25)

Table 12. Sample calculations of the population equation

 

 

 

 

 

 

 

t £04) Equation p(t+delta)
0 p(0 — 1) = p(-l) (24) p(0.5) = p(0) + delta - p(O) . [1]
(p(—1)—+0) =01 +0.5.0.1 ~ [1]
= 0.15
0.5 p(O.5 — 1) = p(-0.5) (24) p(l) = p(0.5) + delta - p(0.5) - [1]
(p(-O.5)—->0) =0.15+0.5-0.15.[1]
= 0.225
1 130—” = 9(0) (25) 13(15): 9(1) + delta ' 9(1) ' [1' 904)]
(p(O) = 0.1) = 0.225 + 0.5 ~ 0.225 - [10.1]
= 0.326
1.5 p(1.5 — 1) = p(0.5) (25) p(2) = p(1.5) + delta - p(l.5) - [1- p(l.5-l)]
(p(0.5) = 0.15) = 0.326 + 0.5 - 0.326 - [10.15]
= 0.465
2 9(2 — 1) = 9(1) (25) 13(25): 9(2) + delta ' 9(2) ' [1" 13(2'1)]
(p(l) = 0.225) = 0.465 + 0.5 ° 0.465 ' [1-0.225]
= 0.645

 

 

 

 

 

MATLAB works according to the same basic technique shown in Table 12 though with

much finer time steps, delta.

To see the effect of the time lag, the value of delta was set to 0.001. The value of 1:
was given the values 0.9, 1, 1.2, and 2. The results can be seen in Figures 70 (for 12 = 0.9

and 1) and 71 (for t = 1.2 and 2). As can be seen in all of the plots, the time lag influences

the oscillation pattern. The larger the time lag, the more extreme the oscillation becomes.

94

.5
0'1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C
0 1
:p
E
a 0.5
O
D.
E 00 5 10 15 20 25 30
.9
g 1.5 I l T I I
0)
.§ 1 ~
‘3
o 0.5 P
2

0 l l l l L

0 5 1D 15 20 25 30

TIME (8)
Figure 70. Population with time lag = 0.9 and 1.0.
1.5

1; 1-
3 0.5 Tau-1.2 ..1
g 00 0 1'0 1'5 210 1:5 30
.2 3 l I I I I
g
I 2 I.
d
s 1-
Z

00 :15 10 l 210 25 30

15
TIME (3)

Figure 71. Population with time lag = 1.2 and 2.

95

7.5 Vibration Analyses

This first order differential equation has a non-linear term that produces an
oscillating curve that resembles the basic oscillation that occurs in free excitation vibration
with an under damped response. Therefore it is possible to analyze the problem from the
vibration point of view. Some computations that can be made using ideas from vibrations
include evaluating the period, fi'equency and the settling time of the oscillation. Another

analysis that can be done using the observable peaks is to compute the damping ratio of the

oscillation.

Refer to the MATLAB code laid out previously. In the non-linear loop there are
loops that evaluate the peaks and the valleys of the oscillation with their corresponding
occurrence times. In the peak loop, there are loops that evaluate the period, the frequency,
as well as the log decrement. The period can be evaluated by taking the difference between
the times of two successive peaks. For example, peak A occurs at time t1, and peak B

occurs at time t2. The period is then tz-tl. Once the period is evaluated, the frequency can

be found according to the following correlation.

1
_ period

 

(26)

Clearly, this fi'equency may vary with the duration of oscillation. As t—mo it can be

determined that f—ioo, for example it is shown in the top plot in Figure 71.

The settling time is useful to predict when the oscillation will reach a steady state.
The settling time occurs at the 2% mark from the center of the oscillation. The last peak

that touches this 2% limit is defined as to be the settling time. For example, consider

96

Figure 72. Shown are the population curves for the three methods, where delta = 0.001, a
time lag r = 1.2 and an expended time range of to 50 seconds. Shown in the figure is the
2% limit line, which is defrned as the line 1.02 fiom the center of the oscillation at 1.00.
The settling time peak occm‘s at the peak value indicated in the figure. The settling time
for this case occurs at t = 25.805 seconds for the modified Euler, and fourth order Runge-
Kutta methods, and t = 25.806 seconds for the Euler method. As can be seen in the figure,

after t = 25.805 the curve starts to reach the steady state and it no longer crosses the 2%

limit line.

—..b
01
'

 

+ Euler
0 Modified Euler
‘ 4 RungeKutta

 

 

 

—L

 

 

 

 

 

 

Non-Dimensional Population

 

Settling Tlme
0.5 -
00 5 10 15 20 25 30 35 40 45 50
TIME (8)

Figure 72. Settling time peak.

97

The damping ratio can be evaluated using the following relations; where 5 is the log
decrement of two consecutive peaks, x is the peak value, and C is the damping ratio. Since

there are several peaks, an average value of 8 is used when evaluating the damping ratio, Q.

 

(27)

C = 5avg / (27:) (28)

As an example of the evaluation of the damping ratio, consider the non-dimensional
population shown in Figure 72. Using the results of the fourth order Runge-Kutta method,
the damping ratio evaluation can be found as in Table 13. Then using Equations (27) and
(28), the average of 8 = 0.074; therefore, Q = 0.012.

Table 13. Log decrement

 

 

 

 

 

 

 

 

 

s=0 s=1 =2 s=3 s=4
x“. 1.47 1.19 1.08 1.04 1.02
ln(x1/x1+s) 0 21 0.10 0.04 0.02

 

 

7.6 Temporal Perturbation of the Population Equation

Recall Equation (18), and where the carrying capacity factor it simply had a(t) and
b(t) equal to constants. It may be important to involve other factors that affect the
population of the flamelets, such that a(t) and b(t) are not constants. Now consider a(t) and

b(t) are equal to some function, say, a(t) = b(t) = 1+e-sin(00-t), in addition to the variable 1:.

Then Equation (18) becomes:

(29)
t a t

gl- = a(t)-u(t)[1—b—Et-;- -u(t — 1)].

98

Since a(t) = b(t), Equation (29) becomes:

% = (1+e-sin(wt))-u(t)'[1—u(’—T)]-

(30)
Notice that as e—>0 the equation essentially will become Equation (19). Additionally, the
value of a) is about the value of the period of the curve using Equation (19).

To observe the affect of the additional sinusoidal function in the equation, the
following Figures 73 and 74 were obtained using delta = 0.001, and time lag 1: = 1.2. to =
5.24 (or about 311/2) and s was assigned to 1.5, 1, 0.5 and 0.01. Note that in these figures
only the fourth order Runge—Kutta methods was used. As can be seen from this set of
figures, the influence of the factor a on the population is that the curve is undergoing

transition from rough to smooth, as the value of e approaches zero.

1.5

 

  
  

 

 

l l l l

10 15 20 25 30
° 4th Order Runge—Kutta without perturbation
*"— 4th Order Runge—Kutta with perturbation

 

 

 

 

 

Non Dimensional Population

 

 

 

l

l

Epsilon = 1.0

 

5 10

15
TIME (s)

20

25

Figure 73. Population with s = 1.5 and 1.0.

99

 

 

 
     

 

 

Epsilon = 0.5
I l I I

5 10 15 2D 25 31]

° 4th Order Runge-Kutta without perturbation

”*— 4th Order Runge-Kutta with perturbation
1.5 - I l l I

 

 

 

 

 

 

Non Dimensional Population

0.5 .
EpSIlon = 0.01

D I I I I I

[J 5 1D 15 2D 25 30
TIME (s)

Figure 74. Population with e = 0.5 and 0.01.

 

 

 

In addition, to observe the affect of 0) on the modified population model, Figures 75
and 76 were obtained. Only the fourth order Runge—Kutta method was used for this
comparison. One of the curves had the value of e = 0 (unperturbed curve). The time lag
and delta were set to 1.2 and 0.001. The value of 0) was varied while a was set to 0.5 in the
Euler method using the equation containing the sinusoidal function. Apparent in these
figures is that the curve becomes more stable as the value of (0 approaches 21:. This is

expected because sinusoidal fimctions repeat themselves every 271: radians.

100

LI.)

 

_.L

 

M
I

    

1

Omega = pil4

 

l l

 

D
C3

01

I
5 1D

15

2D 25 3D

 

° 4th Order Runge—Kutta without perturbation

 

 

 

_x

Ngn Dimer§ional Population

 

D

     
   

—°— 4th Order Runge—Kutta with perturbation

Omega = pit?

 

 

5 10

15
TIME (s)

20 25 3]

Figure 75. Population with 0) = n/4 and 1t/2.

 

 

 

 

1

 

2U 25 30

 

‘ 4th Order Runge-Kutta without perturbation
—*— 41h Order Runge-Kutta with perturbation

 

 

 

Non Dimensional Population

 

I l

 

J

r

Omega = 3’piQ j

I I

 

 

5 10

15
TIME (s)

20 25 30

Figure 76. Population with to = 1: and 311/2.

101

7.7 Comparison with Experimental Data

The population model so far had been developed as shown in Equation (30). The
next step in the further study of this population model was to compare the numerical results
with the experimental data. The experimental data shown in Figure 77 test
RampDown_3mm_35.8-5.5_2.16(l)c has obvious an oscillation pattern in the cumulative
flamelet population. The numerical solutions will be constructed upon the experimental
data, such that the numerical solutions with upper and lower limits appear to fit the

experimental data.

RampDown_3mm_35.86.5_2.18(1)c

O

Q
-I
01

 

 
  
   
 

 

 

 

Average=1o 0
5° A AA an 4099'
A m .21 a A 2313. 21:1. - «Am .13
*3 40 A A , ' 10
5 AA 2.3 AA 21mm 2%,.8 As cm s
.5 30 A A .1113. [A an - ..é’z: .-§° m 3
a A AA 4.33 A i g.
E A 0175“! 4?" °° «‘58 0.224 Hz 1 ‘
£20 A -8‘ _,§'6° 45
A 9°“. “fidj °Blfurcatlon
10 A 0:," ”gun“ a Exflnctlon
é" a 9.. ”' APo ulatlon
o g £‘5 . . I . . . . n . . . . n . - o
11 so me 150 zoo
Tlme(s)

Figure 77. Population experimental data.

The experimental population data was generated in the .exl format, these data were
transferred to the .m format and then plotted together with the numerical solution. One

example of the combined plots can be found in Figure 78. As can be seen the numerical

102

solution data curve follows the curve of the experimental data. For the preliminary attempt

to fit the numerical solution with the experimental data curve, Figure 78 shows a good

result.

experimental data such as 1:, to, and e, are 0.5, 1.5 and 1.7, respectively.

dd-L—L
MhmIIDM

d

Non Dimesionalized Population

0

Figure 78. Experimental data with its numerical solutions.

7.8

The values of the parameters that improve the numerical solution to fit with the

 

 

 

 

 

 

 

 

 

80 100
TIME (8)

Carrying Capacity and Time Lag

‘ 4th Order Runge-Kutta ‘
~ 0 Experlmental data 1
I _
‘ o o o o o «a ‘
O m (m r m 9’ .. ‘ Itch, I
-. O O (In) 0 0 mt‘. O I'I .-
0 O In 0 o O M) M O m
_ O O I}! 00 (ID 0 O {m
o o 0 o - o o
o
r O -
o
. o _
o
I— o .1
0
0 20 40 50 120 140 160 1. 200

In this section the two parameters that affect the population model were studied by

taking into account the physics of the flamelet. In [9], this study was done utilizing the

results from the NASA microgravity facility. The results were compared with the results

obtained from the MSU microgravity facility. The two parameters were carrying capacity,

1c, and time lag, 1?. Earlier in this chapter, the carrying capacity and time lag were estimated

103

 

to fit the population model with the experimental data. However, in this section the two
parameters were studied further in terms of the oxygen supply, and flamelet lifetime for the
carrying capacity, and time lag, respectively.

The carrying capacity, k, was defined in terms of the oxygen supply and the oxygen
consumed per flamelet. Using the mass conservation equation, the oxygen mass flow rate
was determined involving the inlet area, density at ambient temperature and the final air
velocity. Whereas the mass flow rate of oxygen consumed per flamelet was determined
using Equation (13) stated in Chapter 5. With these two properties, the carrying capacity

can be expressed as:

m 02

K=——-—. , (31)

m 02 flame/er

In Chapter 5, there were four ways to predict the oxygen consumption rate.
However, only two of the equations gave reasonable results. These are Equations (6) and
(7). Equations (8) and (9) on the other hand did not give reasonable results, therefore they
were ignored. Since the results of Equation (7) always gave about the same with the results
of Equation (6), therefore in the following Table 14 only the carrying capacity using the
oxygen consumption rate of Equation (6) will be presented. Table 14 lists the average
carrying capacity for various final air velocities for normal and inverted positions of the

test facility with tunnel heights of 3, 4, and 5 mm

The values of the carrying capacity for the experiments in the normal position of the
test facility are ranging from 8 to 19. This range is reasonable compared to the value of

carrying capacity that was evaluated at NASA, which is 12. The values of the carrying

104

capacity in the inverted position, though, are arbitrary. There is a possibility that the
gravitational effect plays a role in the inverted position experiments, therefore the methods

to calculate oxygen consumption rate and the carrying capacity may not be accurate.

Table 14. Average carrying capacity

Position Tunnel Hei (mm) AirV ' (cm/s

Normal 3 2.5
5.5
10.0
2.5
3.0
3.5
4.0
5.0
2.5
3.5
4.5
5.1
2.5
3.0
3.5
2.5
3.5

 

The time lag, 1:, was evaluated in terms of the flamelet lifetime, spread rate and the
lateral angle of bifiircation. The time lag, r, then can be expressed as in Equation (32).
Here 2r is the flamelet diameter, Vf is the flamelet spread rate and y is the lateral angle of
bifurcation. The results that were presented earlier in this thesis such as the flamelet lateral

2-r

= 32
T V, 42142) ( )

bifurcation angle, flamelet spread rate and the flamelet diameter can be found in Chapters

4, 5 and 6, respectively. With these measurable properties, the time lag can be calculated

105

and the results can be found in Table 15, that shows the average time lag of experiments in
the normal and inverted positions of the test facility for tunnel heights of 3, 4, and 5 mm

with various final air velocities.

Table 15. Average time lag

Position Tunnel Hei (mm) Air V ' (cm/s) Time

Normal 3 2.5. 64
5.5 83
10.0 87
2.5 56
3.0 58
3.5 71
4.0 74
5.0 49
2.5 58
3.5 29

Inverted , 3.5 59
4.5 77
5.1 107
2.5 77
3.0 63
3.5 65
2.5 122
3.5 80

 

The average time lag, for the experiments in the normal position is ranges from 295
to 87s. The average time lag generally increases as the final air velocity increases.
However, the experiments in the inverted position show a reverse characteristic. Generally
the time lag decreases as the final air velocity increases. The values are ranging from 593
to 1223. Compared to the results in [9], the time lag that was studied ranges from 243 to
37s for an experiment with 5 mm tunnel height in the normal position. The time lag values

presented in Table 15 are about 2 to 3 times longer.

106

7.9 Intrinsic per Capita Growth Rate

The intrinsic per capita grth rate, to, for steady population growth with limiting
resources (in this case oxygen) can be found by taking the difference between the
bifurcation rate and the extinction rate divided by the total number of population [9]. For
example, consider the bifurcation and extinction rates, and the average population of test t-
40-25c, which values are 0.136 bifurcation/s and 0.124 extinction/s, and 10, respectively.
The intrinsic per capita growth rate is then (0.136 bifurcatiorr/s-0.124 extinction/s)+10
flamelets = 0.00119/s. This small number (~0) suggests that when the population
approaches steady state, the growth becomes slower because of the competition for the
resources.

The intrinsic per capita growth rate, r0, without limiting resources, can be
determined based on the fractal number, flamelet spread rate, and the average flamelet
lifetime [9]. The three properties were composed into the power law equation. Thus it can

be expressed into Equation (33):

U, -V -t "
r. cc (no-[717‘] . (33)
In [9], the fractal numbers, f, were measured using the box-counting method and the values
are typically 1.7 :t 0.1 for fingering patterns. For a uniform flame-front, the fractal number
is 2, and for a no-branch fingering pattern, the fi'actal number is typically 1. The term
UGO/2D is the characteristic length scale of the diffusive gas-phase Stokes flow. The value
of D is 1.6 cmz/s. The exponent, n, of the power law relation is 0.6, which was obtained

from the fingering smolder study.

107

CHAPTER 8
FLAMMABILITY MAP AND MODIFICATION TO THE APPARATUS

8.1 Flammability Map

The flammability map for the MSU microgravity facility (SMF T) was established
by running numerous experiments with various test conditions. The results fiorn the SMFT
were combined with the results from NASA’s microgravity facility. The following Figure
79 (was generated at NASA) shows the agreement between the two sources. Overall, the

results fiom MSU and NASA agree well. In the middle of the plot, there are four data

Flame Characteristics Map
Zero Gravity Facility (open) and MSU data (dotted)

 

.

   

(spaclngl'1, mm 1

 

 

 

0.1 ~
3 Corrugated]
Uniform
65 O 'V 21%02,1atm
Whatman44
0.01 . 4
0.1 1 10 100
Opposed Flow Velocity, cmls

Figure 79. Flammability Map.

108

points (of the Corrugated/Uniform) that fall in the flamelet region. These peculiar data
were carefully checked and a few more experiments were performed to ensure that they

were not supposed to be in the flamelet region.

8.2 Modification on the SMFI‘

When bunting sample paper, humidity is a factor that may have affects on the final
results. To reduce this variable factor, NASA dries off the sample paper prior to the
experiments. As a preliminary step to reduce this factor fi'om the system, a dehumidifier
was added into the airflow system. The dehumidifier was located after the filter before the
pressure regulator. A diagram of the new airflow system can be found in Figure 80, and a

picture of the dehumidifier can be found in Figure 81.

 

 

 

I Fm" I‘_I Air Supply I Computer I

I Dehumidifier I

I Voltmeter Power Supply] I Plenum I
I Plenum I 7

I

Pressure Pressure Mass Flow 5 Rotameteri
Regulator Relief Valve Controller

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 80. Diagram of the new airflow system with dehumidifier.

The dehumidifier has two filters on one side, and two desiccant tanks on the
topside. When the pressurized wet air comes in from the filter to one of the tanks, the
desiccant materials (consist of molecular sieve, alumina, and silica gel) in the tank absorbs

the water vapor. Then some portion of the dry air flows through a purge orifice to the

109

 

Figure 81. New airflow system with dehumidifier.

plenum, and the remaining portion flow to the other tank at near atmospheric pressure to
reabsorb the water vapor and then exit to the atmosphere. Afler 30 seconds of one cycle,
the first tank will regenerate itself. Then the pressurized wet air flows into the other tank.
The second tank does the same process for 30 seconds then the wet air will flow back to the
first cycle. The dry air that comes out of the tanks has pressure change caused by the
different cycle. Therefore, to avoid unsteady pressure that goes into the test section tunnel

a plenum is located after the dehumidifier before the pressure regulator.

110

CHAPTER 9
CONCLUSION AND FUTURE WORK

Overall this flamelet study went well. Most of the results studied in this thesis
show similarity with the results studied at NASA. In addition, the results for the
experiments in the normal and inverted positions are close but not the same. This can
happen because of the different geometrical shape of the test section and the different
conditions of the top and bottom plates. Also, this may happen because gravity plays a role
in the behavior of the flamelets in the inverted position. When running an experiment, it
can be visually observed that the flamelets in the inverted position are dimmer, weaker and
always pulsing.

The flamelet population study using the experimental data from the MSU
microgravity facility shows good agreement with the study that was performed at NASA.
This study verifies that 50% i 3% of the flamelet must be productive (mothers) for flamelet
to reach steady state. In an evenly spaced experiment, flamelets propagate with a nearly
constant rate. This corresponds with the 1:1 agreement between the bifurcation and the
extinction rates. Between the results in the normal and inverted positions of the apparatus,
the average cumulative number of flamelet population is higher when the apparatus is right
side up than it is on the other side. The average cumulative number of flamelet population
shows an increasing when there is more oxygen that flows into the system (i.e. by
increasing the tunnel height or the air velocity).

The cumulative number of flamelet population shows an oscillating behavior. A
first-order deferential equation was developed to simulate this oscillating behavior. The

major factors that influence the equation in order to fit the experimental results are the

111

value of the time lag (t), the initial condition, and the two perturbation features of 00 and 8.
Overall the preliminary step to study the flamelet population shows good progress and
some of the factors studied show similar results with the study performed at NASA.

The results of the flamelet lateral angle of bifurcation study show that generally
when the tunnel height increases the bifurcation angle also increases. The flamelet
bifurcation angle of experiments in the normal position generally is higher than that in the
inverted position.

With the help of TRACKER and SPOTLIGHT, the burned area measurement was
done. The burned are study shows that when the apparatus is right side up, flarnelets
consumed about 40% to 70% of the fuel whereas when the apparatus is up side down,
flamelet consumed about 20% to 50% of the fuel sample. The flame spread rate is
proportional to the air velocity. The flamelet spread rate increases as the air velocity
increases. This agrees with the results that were performed by NASA. The oxygen
consumption rates were predicted and the results were used to calculate the global
stoichiometric ratio. The global stoichiometric ratio shows that the combustion reaction for
the burning cellulosic paper is fiiel rich combustion.

For future work, it is desired for a longer as well as wider test section area for a
larger sample paper for better statistical analysis. Therefore a modification to the apparatus
is necessary. The current test section and the heat sink should be replaced with a more flat
surface of test section and heat sink to obtain better experiments and fingering pattern.

In this thesis, the oxygen consumption rate was predicted. For more accurate
oxygen consumption rate, it is desired to install a device that can capture the product gases

and measure the oxygen level. Another study that can be done in the future is to measure

112

the sample surface temperature, and the development of the population analysis using the

logistic model.

113

APPENDIX A

Hele—Shaw Spread Rate data
Whatman 44, 5 mm gaps
Comparison with RITSI flight data

 

 

 

 

 

   

 

 

 

 

 

 

 

 

0.30
D opposed
0 concurrent Cl
1 A RITSI 30 /
0.25 ~ v RITSI 20 I:
j —transient name-1, 11) A U D
g . ——-1ransientmt(164:r2
o . I
q; 0'20 -l Uniform Flame
1'6 1 I
m j A
B 0.15 4
9 ‘ '
O- I
w ‘ I
03 -
E 0'10 a Plateau l
u. l
. O I
0.05 1 I O
I
Z I
0.00 , ' - T
Air F low Velocity, cm/s
Figure A1. Flame spread rate [9].
From Equation (6):
° dA 32
02 = — 0 p17 . 6 . —_
dt 162
2 k802
kgoz =m ng.#.km_oI
s s m2 g,-
From Equation (7):
dA 4 P
a. = dt ” "‘
‘10,
m2 [c] kg F
kgoz : S kg F "12
s k]
kg 02

114

From Equation (8):

(IA
0 —.CPF.pF.(Ts-To) 32

02= dt '
qF 132
2

m k] ng K kgo
. 2 . 2
kgo2 _ S ng'K m #10710]

S U kg F
kg F kmol

 

 

 

From Equation (9):

(1A
_'CPF ’pF '(Ts -To)

(3.: d.

 

 

 

 

 

kgo2
From Equation (10):
£4. .
62 = dt qr pp. 2-
qF 162

m2 . k] .kgr kgo2
kg_o.__ s kgp m2 ,#,kmol
s — k1 lie;
kg). kmol

 

 

 

 

115

APPENDIX B

clear
clc

%Inputs for all 3 methods:
lag=1.2; %Time lag 'tau'
finalt=50; %Final time

 

94. %

 

% EULER METHOD %

%Inputs for Euler Method:

delta=0.001; %Increment time step. When finalt/delta=# of data points
y(1)=1/10; %Initial condition for population

ti(1)=0; %Initial condition for time

k=l; %Time counter for the equation

w=0; %Frequency 'omega'

eps=0; %Perturbation 'epsilon'

%Begin LINEAR loop

for t=[delta:delta:lag]; %Time interval for the linear loop
y(k+1)=y(k)+(delta*((1+eps*sin(delta*w*(k+l)))*y(k)*(l-y(k)))); %The equation
ti(k+l )fi; %Time counter
k=k+l; %Data point counter

end %End of LINEAR loop

%This loop runs the non-linear part of the equation

%Also calculations for peaks, valleys and their corresponding time in the oscillation
p=1; %Initial time counter for peak

v=1; %lnitial time counter for valley

c=1; %Initial time counter for settling time 'ts'

ts=0; %Initial condition for settling time

startts=0; %Initial condition for a helper counter

period=0; %Initial condition for period

ln(1)=0; %Initial condition for log decrement

sumln=0; %Initial condition for average log decrement

%Begin NON-LIN EAR loop
for t=[lag+delta:delta:finalt]; %Time interval for the non-linear loop

y(k+1 )=y(k)+(delta*((1+eps*sin(delta*w*(l(+l )))*y(k)*(1 -y(k-lag/de1ta)))); %The
equation

ti(k+l )=t; %Time counter

k=k+l; %Data point counter

116

%Begin SETTLING TIME 100p
if startts==l; %Counter
if y(k)<(0.02*(peak(1)-l)+l); %Define settling time boundary 1. Value after '>' sign
is variable
ify(k-1)>(0.02*(peak(l)-1)+1); %Define settling time boundary 2. Value after '>'
sign is variable
tspossible(c)=k*delta; %All possible settling time value. Point at curve that
crosses with the boundary
=c+1; %Counter
end
end
end %End of SETTLING TIME loop

%Begin PEAK loop
if y(k)<y(k-l); %Define peak boundary 1
if y(k-1)>y(k-2); %Define peak boundary 2
peak(p)=y(k-1); %Peak
peakt(p)=(k-1); %Peak corresponding time
startts=l; %Counter

%Begin period, frequency, and log decrement loop calculations.

if p>l; %Define a boundary I
period(p-1)=(peakt(p)-peakt(p-l))*delta; %Period
freq(p-1)=l/period(p-l); %Frequency
ln(p)=log(peak(p-l)/peak(p)); %Log decrement
sumln=1n(p)+sumln; %Sum log decrement to calculate factor 'd' for damping

ratio
end %End of period, frequency, and log decrement loop
p=p+1; %Counter
end
end %End of PEAK loop

%Begin VALLEY loop
if y(k)>y(k-l); %Define valley boundary 1
if y(k-1)<y(k-2); %Define valley boundary 2
valley(v)=y(k-1 ); %Valley
valleyt(v)=(k-1 ); %Valley corresponding time
v=v+1; %Counter
end
end %End of VALLEY loop
end %End of NON-LINEAR loop

peak %Display the value of peak
peakt=peakt*delta %Display the corresponding peak time
valley %Display the value of valley
valleyt=valleyt*delta %Display the corresponding valley time

117

period %Display all period values

freq %Display the corresponding frequency of the period

ts=max(tspossible) %Display settling time

tspossible %Display all the time when the curve crosses the settling time (2%) line
In %Display log decrement for all two consecutive peaks

d=(sumln/(p-1)) %Display the average value of factor 'd' in calculating the damping
ratio 'zeta'
zeta=d/(2*pi) %Display damping ratio 'zeta'

 

94-. -%

 

% MODIFIED EULER METHOD %

%Inputs for Modified Euler Method:

delta2=0.001; %Increment time step. When finalt/delta=# of data points
y2(l)=1/10; %Initial condition for population

ti2(l)=0; %Initial condition for time

k2=l; %Time counter for the equation

%Begin LINEAR loop

for t2=[delta2:delta2:lag]; %Time interval for the linear loop
n1=de1ta2*(y2(k2)*(1-y2(k2))); %Define first root of the equation
n2=delta2*((y2(k2)*(l -y2(k2)))+n1); %Define second root of the equation
y2(k2+1)=y2(k2)+(0.5*(n1+n2)); %The equation
ti2(k2+l)=t2; %Time counter
k2=k2+l; %Data point counter

end %End of LINEAR loop

%This loop runs the non-linear part of the equation

%Also calculations for peaks, valleys and their corresponding time in the oscillation
p2=1; %Initial time counter for peak

v2=1; %Initial time counter for valley

02=1; %Initial time counter for settling time ’ts'

t82=0; %Initial condition for settling time

startt82=0; %Initial condition for a helper counter

period2=0; %Initial condition for period

ln2(l)=0; %Initial condition for log decrement

sumln2=0; %Initial condition for average log decrement

%Begin NON-LINEAR loop

for t2=[lag+delta2:delta2:finalt]; %Time interval for the non-linear loop
n1=delta2*(y2(k2)*(l-y2(k2-1ag/delta2))); %Define first root of the equation
n2=delta2*((y2(k2)*(1-y2(k2-lag/delta2)))+n1); %Define second root of the equation
y2(k2+1)=y2(k2)+(0.5*(n1+n2)); %The equation
ti2(k2+1)=t2; %Time counter

118

k2=k2+1; %Data point counter

%Begin SETTLING TIME loop
if startt82==1; %Counter
if y2(k2)<(0.02*(peak2(1)-1)+1); %Define settling time boundary 1. Value after '>'
sign is variable
if y2(k2-l)>(0.02*(peak2(1 )-1)+l); %Define settling time boundary 2. Value after
'>' Sign is variable
tspossible2(c2)=k2*delta2; %All possible settling time value. Point at curve that
crosses with the boundary
02=c2+1; %Counter
end
end
end %End of SETTLING TIME loop

%Begin PEAK loop
if y2(k2)<y2(k2-1); %Define peak boundary 1
if y2(k2-1 )>y2(k2-2); %Define peak boundary 2
peak2(p2)=y2(k2-1); %Peak
peakt2(p2)=(k2-1); %Peak corresponding time
startt52=1; %Counter

%Begin period, frequency, and log decrement loop calculations

if p2>1; %Define a boundary
period2(p2-1)=(peakt2(p2)-peakt2(p2-1))*delta2; %Period
freq2(p2-1 )=1/period2(p2-l ); %Frequency
ln2(p2)=log(peak2(p2-l )/peak2(p2)); %Log decrement
sumln2=ln2(p2)+sumln2; %Sum log decrement to calculate factor 'd' for

damping ratio
end %End of period, frequency, and log decrement loop
p2fi2+1; %Counter
end
end %End of PEAK loop

%Begin VALLEY loop
if y2(k2)>y2(k2-1); %Define valley boundary 1
if y20<2-l )<y2(k2-2); %Define valley boundary 2
valley2(v2)=y2(k2-1); %Valley
valleyt2(v2)=(k2-1); %Valley corresponding time
v2=v2+1; %Counter
end
end %End of VALLEY loop
end %End of NON-LINEAR equation loop

peak2 %Display the value of peak
peaktZ=peakt2*delta2 %Display the corresponding peak time

119

valley2 %Display the value of valley
valley12=valleyt2*delta2 %Display the corresponding valley time

period2 %Display all period values

freq2 %Display the corresponding frequency of the period
t32=max(tspossible2) %Display settling time

tspossible2 %Display all the time when the curve crosses the settling time (2%)
line

1n2 %Display log decrement for all two consecutive peaks

d2=(sumln2/(p2-l)) %Display the average value of factor 'd' in calculating the
damping ratio 'zeta'
zeta2=d2/(2*pi) %Display damping ratio 'zeta'

 

 

% %
% FOURTH ORDER RUNGE-KUTTA METHOD %

%Inputs for Fourth Order Runge-Kutta Method:

delta3=0.001; %Increment time step. When finalt/delta=# of data points
y3(1)=1/ 10; %Initial condition for population

ti3(1)=0; %Initial condition for time

k3=l; %Time counter for the equation

w3=0; %Frequency ‘omega’

eps3=0; %Epsilon ‘perturbation’

%Begin LINEAR loop
for t3=[delta3 :delta311ag]; %Time interval for the linear loop

r1=delta3*(((1+eps3*sin(delta3 *w3 *(k3+1)))*y3(k3)*(1-y3 (k3)))); %Define first root of
the equation

r2=delta3*(((1+eps3*sin(delta3 *w3*(k3+1 )))*y3(k3)*(1 -y3(k3)))+(0.5*r1)); %Define
second root of the equation

r3=delta3*(((1+eps3*sin(delta3 *w3*(k3+1)))*y3(k3)*(1-y3 (k3)))+(0.5*r2)); %Define
third root of the equation

r4=delta3 *(((1+eps3 *sin(delta3 *w3 *(k3+ l )))*y3 (k3)*(1 -y3 (k3 )))+r3); %Define fourth
root of the equation

y3(k3+1)=y3(k3)+(1/6*(r1+2*r2+2*r3+r4)); %The equation

ti3 (k3+1)=t3; %Time counter

k3=k3+l; %Data point counter
end %End of LINEAR loop

%This loop runs the non-linear part of the equation

%Also calculations for peaks, valleys and their corresponding time in the oscillation
p3=l; %lnitial time counter for peak

v3=l; %Initial time counter for valley

c3=1; %lnitial time counter for settling time 'ts'

ts3=0; %Initial condition for settling time

startts3=0; %Initial condition for a helper counter

120

period3=0; %Initial condition for period
1n3(1)=0; %Initial condition for log decrement
sumln3=0; %Initial condition for average log decrement

%Begin NON-LINEAR loop
for t3=[lag+delta3 :delta3 :finalt]; %Time interval for the non-linear loop

r1=delta3 *((1+eps3 *sin(delta3 *w3 *(k3+1)))*y3(k3)*(l-y3(k3-lag3/delta3))); %Define
first root of the equation

r2=delta3*(((1+eps3*sin(delta3*w3*(k3+l)))*y3(k3)*(1-y3(k3-lag3/delta3)))+(0.5*r1));
%Define second root of the equation

r3=delta3*(((l+eps3*sin(delta3*w3*(k3+l)))*y3(k3)*(l-y3(k3~1ag3/delta3)))+(0.5*r2));
%Define third root of the equation

r4=delta3 *(((l+eps3*sin(delta3 *w3*(k3+1 )))*y3(k3)*(1-y3(k3-lag3/delta3)))+r3);
%Define fourth root of the equation

y3(k3 +1 )=y3 (k3)+(1/6*(r1 +2 *r2+2*r3 +r4)); %The equation

ti3(k3+1)=t3; %Time counter

k3=k3+l; %Data point counter

%Begin SETTLING TIME 100p
if startts3m1; %Counter
if y3(k3)<(0.02*(peak3(1)-1 )+l); %Define settling time boundary 1. Value after '>'
sign is variable '
ify3(k3-1)>(0.02*(peak3(1)-1)+1); %Define settling time boundary 2. Value after
'>' sign is variable
tspossible3 (c3)=k3*delta3; %All possible settling time value. Point at curve that
crosses with the boundary
c3=c3+1; %Counter
end
end
end %End of SETTLING TIME loop

%Begin PEAK loop
if y3(k3)<y3(k3-1); %Define peak boundary 1
if y3(k3-l)>y3(k3-2); %Define peak boundary 2
peak3(p3)=y3(k3-1); %Peak
peakt3 (p3)=(k3-l); %Peak corresponding time
startts3=1; %Counter

%Begin period, frequency, and log decrement loop calculations

if p3>1; %Define a boundary
period3(p3-1)=(peakt3(p3)-peakt3(p3-l))*delta3; %Period
freq3(p3-l)=l/period3(p3-l); %Frequency
ln3(p3)=log(peak3(p3-l)/peak3(p3)); %Log decrement
sumln3=ln3 (p3)+sumln3; %Sum log decrement to calculate factor 'd' for

damping ratio
end %End of period, frequency, and log decrement loop

121

p3=p3+1; %Counter
end
end %End of PEAK loop

%Begin VALLEY loop
if y3(k3)>y3(k3-1); %Define valley boundary 1
if y3 (k3-1)<y3(k3-2); %Define valley boundary 2
valley3(v3)=y3(k3-1); %Valley
valleyt3 (v3)=(k3-1); %Valley corresponding time
v3=v3+1; %Counter

end

end %End of VALLEY loop
end
peak3 %Display the value of peak
peakt3=peakt3*delta3 %Display the corresponding peak time
valley3 %Display the value of valley
valleyt3 =valleyt3 *delta3 %Display the corresponding valley time
period3 %Display all period values
fi'eq3 %Display the corresponding frequency of the period
ts3=max(tspossible3) %Display settling time
tspossible3 %Display all the time when the curve crosses the settling time (2%)
line
ln3 %Display log decrement for all two consecutive peaks

d3=(sumln3/(p3-1)) %Display the average value of factor 'd' in calculating the
damping ratio 'zeta'
zeta3=d3/(2 *pi) %Display damping ratio 'zeta'

._..__.__. n I
94-. 7°

 

 

% ERROR CALCULATION %
%note: y(k)--Euler, y2(k2)--Modified Euler, y3(k3)-—4th Runge-Kutta

errorsum=0; %Counter
for j=[1:k2-1]; %Interval
pterror=(y(j)-y2(j))"2; %Squared term
errorsum=errorsum+pterror; %Norm error, summation term
end
error=errorsum"0.5 %Error between euler and modified euler

errorsum2=0; %Counter
for j2=[1 :k3-1]; %Interval
pterror2=(y2(jZ)-y3(jZ))"2; %Squared term
errorsum2=errorsum2+pterror2; %Norm error, summation term
end

122

error2=errorsum2"0.5 %Error between modified euler and 4th RK

errorsum3=0; %Counter
for j3=[1 :k3-l]; %Interval
pterror3#y(j3)-y3(i3))"2; %Squared term
errorsum3=errorsum3 +pterror3; %Norm error, summation term
end
error3 =errorsurn3"0.5 %Error between euler and 4th RK

94-. ——%

 

 

 

% PLOTTING and DOWNLOAD EXCEL EXPERIMENTAL DATA %

t4=[0:finalt];
y4=1 .02;

hold on

subplot(2,l ,2); plot(ti,y,'b+',ti2,y2,'ro',ti3,y3,'g.',t4,y4,'.-k') %Graph
xlabel('TIME (S)','fontsize',18)

ylabel('Non-Dimensional Population','fontsize',18) %Plot and axes' labels
axis([0 20 0 1.7]) %Axis range

legend('Euler','Modified Euler','4 RungeKutta') %Show legend

123

BIBLIOGRAPHY

. Ball, P., 1999, “The Self-Made Tapestry: Pattern Formation in Nature,” Oxford
University Press.

. Greenberg, Michael D., 1998, “Advanced Engineering Mathematics,” Second ed.,
Prentice Hall Inc., New Jersey.

. O’Keefe Controls Co. Form OK-253.

. Olson, Sandra L., Ferkul P., and T’ien, J .S., 1988, “Near-Limit Flame Spread Over
a This Solid Fuel in Microgravity,” T wenty-Second Symposium (International) on
Combustion/The Combustion Institute, pp. 1213-1222.

. Olson, Sandra L., 1991, “Mechanisms of Microgravity Flame Spread Over a Thin
Solid Fuel: Oxygen and Opposed Flow Effects,” Combustion Science and
Technology, Vol. 76, pp. 233-249.

. Olson, Sandra L., T’ien IS, 2000, “Buoyant Low Stretch Diffusion Flames
Beneath Cylindrical PMMA Samples,” Combustion and Flame, Vol. 121, pp. 439-
452.

. Olson, Sandra L., Kashiwagi, T., Fujita, O., Kikuchi, M., Ito, K., 2001,
“Experimental Observations of Spot Radiative Ignition and Subsequent Three-
Dimensional Flame Spread Over Thin Cellulose Fuels,” Combustion and Flame,
Vol. 125, pp. 852-864.

. Olson, Sandra L, April 2005, “Sub-Critical Rayleigh Number (<Rac) Apparatus for
Materials Flammability Screening,” draft.

. Olson, Sandra L., Miller, F .J ., and Wichman, 1.8., 2005, “Characterizing Fingering
Flamelets Using the Logistic Model,” draft.

10. Oravecz, Lisa M., 2001, “Instabilities of Spreading Diffusion Flames in

Microgravity and the Design and Construction of a Hele-Shaw Apparatus that
Produces Flames in the Near Extinction Limit Regime Under Simulated Low
Gravity Conditions,” MS. Thesis, Michigan State University.

11. Palm, William J. III, 2001, “Introduction to MATLAB 6 for Engineers,” First ed.,

McGraw-Hill Higher Education, New York.

12. Tanaya, Stefanus A., 2004, “Examination of a Simulated Micro-Gravity Device for

Evaluating Flame Instability Transitions and Flame Spread Over Thins Cellulosic
Fuels,” MS. Thesis, Michigan State University.

124

13. Turns, Stephen R, 2000, “An Introduction to Combustion Concepts and
Applications”, 2nd edition, McGraw-Hill.

14. Wichman, LS, 1992, “Theory of Opposed-Flow Flame Spread,” Prog. Energy
Combustion Science, Vol. 18, pp.553-593.

15. Wichman, IS, 2003, “Notes on Theory of Flamelet Formation,” Department of
Mechanical Engineering, Michigan State University, draft.

125

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

IIIIIIIIgillIIIIIIIIIIIIIIIIIIII