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UNCLASSIFIED
A D
.r
t if*
w
D E F E N S E
O C U M E N T A I I O N E N T E R
F O R
S C I E N T I F I C
N D E C H N I C A L
N F O R M A T I O N
C A M E R O N
T A T I O N , L E X A N D R I A , I R G I N I A
ÜFCLASSIFIED
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N O T I C E :
hen
g o v e r n m e n t
or
other
d r a w i n g s , s p e c i -
f i c a t i o n s
or
other
d a t a
a r e used f o r any purpose
other
than
i n
connection
with
a definitely related
g o v e r n m e n t p r o c u r e m e n t o p e r a t i o n , t h e U . S .
G o v e r n m e n t
thereby I n c u r s
n o r e s p o n s i b i l i t y , no r any
obligation w h a t s o e v e r ;
and t h e
f a c t
t h a t
the Govern-
m e n t ma y
h a v e
f o n n u l a t e d ,
f u r n i s h e d ,
or in
any w a y
supplied
t h e
said
d r a w i n g s , s p e c i f i c a t i o n s ,
or
other
d a t a
i s
n o t
to
be
regarded
b y
implication
or
other-
w i s e
a s
i n
any manner licensing t h e holder or any
other
person
or c o r p o r a t i o n ,
o r
conveying
«my rights
o r
permission
t o m a n u f a c t u r e ,
use
o r s e l l any
patented
invention t h a t
may
i n
any
way
be
related
t h e r e t o .
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THIS DOCUMENT IS
BEST
QUALITY
AVAILABLE
THE
COPY
FURNISHED TO DTIC
CONTAINED
A SIGNIFICANT
NUMBER OF
PAGES WHICH DO
NOT
REPRODUCE LEGIBLY
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PRINCETON UNIV
ER
S
I
T Y
DEPARTMENT
OF AERONAUTICAL ENGINEERING
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DEPARTMENT
OF
THE
AIR FORCE
AIR FORCE
OFFICE
OF
SCIENTIFIC
RESEARCH
PROPULSION
RESEARCH
DIVISION
Grant
AF-AFOSR-92-63
SOLID
PROPELLANT IGNITION
STUDIES
;
IGNITION
OF TH
E
REACTION
FIELD
ADJACENT
TO THE
SURFACE
OF A SOLID PROPELLANT
Final
Technical
Report
1
October
1962
to
30 September
1963
Aeronautical Engineering
Report
No. 67 4
Prepared
by : C&HMJfe****̂ *
Clarke
E, Hermance
Research
Associate
(Kx^UA
^t^v
ca t
Reuel
hinnar
Visiting esearch
ngineer
u Joseph
Wenograd
Research
/Qaff Member
Approved b
r
Martirr'Summerfi
Principal
Investi'
Reproduction,
translation,
publication,
use and disposal
in
whole or
in
part
by or
for
the United
States Government
is
permitted.
1 December 1963
Guggenheim
Laboratories
for
the
Aerospace Propulsion
Sciences
Department
of Aerospace and Mechanical Sciences
PRINCETON-UNIVERSITY
Princeton, New
Jersey
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The contents
of
this
report
have
been
submitted
by
Clarke
E .
Herraance
in
partial fulfillment of the requirements
for
the
degree
of Doctor
of
Philosophy
from
Princeton
University,
1963, under
the
title of
"Ignition
of
the
Reaction
Field
Adjacent to the Surface of
a
Solid
Propellant."
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ACKNOWLEDGEMENTS
This
dissertation
wa s completed with the
assistance
of
a
large
number
of
kind
persons to
whom
I am
very
grateful.
It
wa s
my great
privilege and
pleasure
to
carry
out
this research under
th e
direction of
Professor
Martin
Summerfield
who
suggested
the
research
program.
is continued support and encouragement
were
vital
for
the completion
of
this work,
an d are
deeply
appreciated.
Many
fruitful an d stimulating hours of discussion
concerning the theoretical developments
in
this
program
were
spent
with
Professor
Reuel
Shinnar,
Visiting
Professor
in
the Department
of
Aeronautical
Engineering.
he
completion
of this
program
is in a
large
measure
due to
his
steadfast interest,
for
which
I am
wholeheartedly
grateful.
Dr. Joseph
Wenograd's
technical
help
and
personal
interest is acknowledged
gratefully.
pecial
thanks ar e
due the Department
of
Mechanical
Engineering,
and
particularly
to Professors R .
M.
Drake an d J. B.
Fenn of that Department,
for
continued support and encouragement.
Mr. L. L.
Hoffman
deserves great credit for h is
unselfish
help in
the
digital
computation
part of this
work,
and
I
wish
to
thank
him
very
m u c h , ,
essrs.
G .
Barnock
an d
N. Carney
were
most
helpful in the experimental
part of
this
program
an d their efforts are gratefully
acknowledged.
The
final
manuscript
wa s
typed
by
Miss
Yolanda
Pastor;
her
skill an d
unswerving effort
are
truly
appreciated. any
other members of the technical
staff
of the
Guggenheim
Laboratories
for the
Aerospace Propulsion Sciences
contributed
their time an d
effort.
I
would
like to
thank all
of
them
at
this time.
Finally,
I
would
like
to
take
this
opportunity
to
thank
my
wife, for
he r love an d encouragement
were
essential
for the completion of this
work.
Financial
support wa s
provided
by
the
U.
S .
Air
Force Office of Scientific Research
on
Grant
AF-AFOSR
92-63.
This
work made
use of
computer
facilities
supported
in
part
by National Science
Foundation
Grant
NSF-GP579.
11
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ABSTRACT
Early
experimental an d theoretical investigations
o f s o l i d propellant ignition
seemed
to
indicate
that ignition
w a s
caused
by exothermic
solid
phase reactions stimulated
at
t h e
e x p o s e d
surface o f a propellant by applied heat. Later
experiments,
n which
nitrate ester
an d composite propellants
w e r e
exposed
to
various gases
at
controlled high
temperatures
a n d pressures, showed that the ignition
delay wa s influenced
no t
only
by the
nature
of
the
propellant,
but by the quantity
of oxidizer present
in the
external
gas
and
the
gas pressure.
Log-log
plots
of
experimental
ignition
delay
versus the
gaseous
oxidizer concentration exhibited a range
of
slopes
from zero to minus two
or
more. These experiments indicated
that the
igniter
gas plays a specific role in the ignition
process,
and that propellant
ignition
could
be
due
either
to
a
reaction
of
propellant
fuel
molecules
with
the
gaseous
oxidant
in
a
gas
phase
reaction,
or to
a
heterogeneous
surface
reaction between oxygen and the solid phase
fuel.
The object of this research was to
further
elucidate
the
ignition
mechanism
of
solid
propellants,
to identify
the
component processes, an d to lay the basis for
a
theory
of
ignition.
Experiments
were performed
in which
composite
propellant samples and polymeric fuel samples
were
exposed
to
high
and
low speed flows of
oxygen
containing
gases at
high temperature and pressure in
a shock tunnel. Ignition
of either
propellant or
fuel could not be
obtained
in
high
speed
flows
( c a .
5000
ft/sec)
even
in
pure
oxygen;
in
addition,
no
charring
or
decomposition
of
the
fuel
was
observed.
At
low
flow
speeds, on the
other
hand,
gnition
of the
composite
propellant an d the
polymeric
fuel
did
occur, and
the
ignition
delay was found
to
depend on the gas phase oxygen concentration.
The non-ignition
at
high flow
speeds indicated
that
dilution
or
sweeping
away
of the
gaseous
reaction zone
inhibited
the
ignition.
An
ignition
limit
for the
fuel
samples
near
50 %
oxygen mole fractions was observed, suggesting that
boundary
layer
flame
establishment
required
a
longer
fuel
sample.
These results
indicate
that
a
pure
solid
phase
ignition
mechanism
is incorrect, and strongly suggest
that
the site
of
ignition
is
in
a
gaseous reaction boundary layer
adjacent
to
the
surface
of
the
propellant
and
not
on
the
fuel surface
itself.
A previous approximate theory
of
solid
propellant
ignition
by
gas phase reaction, developed by
McAlevy
and
Summerfield,
did
not
predict the correct dependence of
ignition
delay
on oxygen
concentration;
therefore, the theoretical
situation wa s in doubt.
A
special point
of
interest
for the
111
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theoretical
development
is
that
proportionality
of
the
ignition
delay
to
the
gaseous oxidizer
concentration
raised
to a
power
substantially
greater
than
minus
one
has
been
observed in solid
propellant ignition. Therefore, the theory
of
thermal, gas
phase ignition was
extended
to check whether
a
gas
phase
ignition mechanism
could admit a
dependence
on
oxidizer
concentration
raised t o a power
greater
than
minus
one.
A mathematical
model
was formulated for
the thermal,
gas
phase
ignition
of
a
reaction
field
adjacent
to a condensed
phase
fuel
suddenly exposed
to a
hot,
stagnant, oxidizing gas.
The
characteristic ignition
properties
of
this
model were
treated first
by similarity
theory
and then
by
numerical
methods.
Two
cases
were
treated: in
the first
case
the
concentration
of
fuel
vapors
at
the
condensed
phase
surface
was taken
constant;
in
the second
case
a
constant
mass flux
of fuel
vapors
from
the surface
wa s
assumed.
The
surface
temperature
of
the condensed phase was assumed constant
( a
restrictive assumption
to be
removed
in later
work),
and
the
chemical
reaction was
represented by a
second
order
reaction
with
an
Arrhenius
function
temperature
dependence.
It is
significant
that
the
system of
three, coupled,
nonlinear,
partial differential equations
of
this
mathematical
model could be integrated by digital
techniques.
The integrations
were
both
stable and
convergent,
howing that
the
solution
of
similar problems of nonlinear
nature should
be
possible.
An
important
conclusion
was
that
when
(RT/E)
>
/5,
a
classical
induction
period
does
not
exist; the
reaction
temperature
rises continuously
and the
definition of
the state
of
ignition
becomes
arbitrary.
Consequently,
two
experiments
could
show
differing
effects
of
oxidizer concentration
on
the
ignition
delay
unless identical ignition
detection methods
were
used.
Furthermore, at least to
a limited
degree, a theory of
ignition
can be
made
to
fit
experimental
results
by
deliberate
choice
of
an
ignition
criterion.
It wa s
shown
that
for
any ignition criterion,
the
sensitivity of
the
ignition delay
to
changes in the
concentration
of
gaseous
oxidizer
ca n
vary
strongly.
A
log-log plot
of these
quantities
ca n exhibit
a slope
between
zero an d minus infinity.
Therefore,
the
gas
phase
ignition delay of a
heterogeneous
system
can
depend
on the
gaseous oxidizer
concentration
raised
to
a
power
greater
than
one
over
some
range
of
oxidizer
concentration.
The
presence
of
diffusional
processes
was
found
to
result in
a falsification of
the
activation energy of
the
chemical
reaction. The
apparent
activation
energy
found from
a plot
of
log
( t .
versus (l/T
was lower
than
the
actual
activation
energy?
ctivation energies
reported
on
the
basis
of
such
experimental
data
are
thus invalid.
IV
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The
analysis indicated
that gas
pressure
increases
could
have an adverse effect
on
the
ignition delay under
certain
restrictions
on
the
physical
parameters
of
the
system.
This
is
contrary
to
the prediction of a heterogeneous
surface ignition
theory,
but
unfortunately
there
is
no
experimental data to
support it.
This work is
significant
in
that
it
points
out
th e
type
of
decisive
experiments
needed
to
test
the
validity of
either
th e gas phase or surface
reaction
ignition mechanism.
Conclusive
interpretation of
the results of
these
experiments,
however, require
that
the
gas
phase
theory
be extended
by
relaxing
the restriction of constant temperature
at the
surface of the
condensed
phase.
In
addition,
theoretical
extension to
include
the
case of a
flowing
igniter gas
should
be
carried out.
v
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TABLE OF CONTENTS
TITLE
PAGE
ACKNOWLEDGEMENTS
ABSTRACT
TABLE
OF
CONTENTS
LIST OF
FIGURES
Part
I
Part
I I
TABLE
OF
SYMBOLS
CHAPTER
1-1
DISCUSSION
OF PREVIOUS
IGNITION
STUDIES
PART
I
CHAPTER
1-2
CHAPTER
1-3
A . INTRODUCTION
B . REVIEW
OF
EARLY
THERMAL IGNITION THEORY
1 .
Stationary Theory of Thermal Ignition
2 .
Nonstationary
Theory of
Thermal
Ignition
C .
PAST
EXPERIMENTS
ON
THE
IGNITION
OF COMBUSTIBLE MIXTURES
1 .
Ignition
of Gaseous
Mixtures
(Homogeneous Ignition)
2 . Ignition of
Heterogeneous
Mixtures
of
Gases
and
Liquid
Fuels
D . DISCUSSION
THERMAL
THEORY
OF
IGNITION
FOR
HOMOGENEOUS
AND HETEROGENEOUS
SYSTEMS
SIMPLIFIED MODEL
FOR THE
THERMAL IGNITION
OF A DIFFUSION FLAME
NEAR
A
COOL
SURFACE
A .
SPECIFICATION
OF
THE
PHYSICAL
PROBLEM
B .
DISCUSSION
OF
VARIATIONS
IN
THE
CHARACTERISTIC
GROUPS
1 . Constant
Pressure,
Variable
2 . Constant
3 .
Constant
y '̂)
Variable
Pressure
Page
i
ii
iii
vi
x
xii
xv
1
2
3
3
8
8
11
14
A . EFFECT
OF
REACTANT
CONSUMPTION
5
B . EFFECT
OF
QUIESCENT OR UNSTIRRED
MIXTURES
8
C .
SUMMARY 0
D . INTRODUCTION TO THE
THERMAL THEORY
OF
IGNITION IN
HETEROGENEOUS
SYSTEMS
1
y£ %
, Variable Pressure
2 3
2 3
30
31
32
32
vi
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TABLE
OF
CONTENTS-contd.
Page
CHAPTER
1-3
SIMPLIFIED
MODEL FOR
TH E
THERMAL
IGNITION
OF
A DIFFUSION FLAME
NEAR
A
COOL
SURFACE-
contd.
C .
DIAGNOSIS
OF
LIMITING
CASES 3
1 .
Variation
of
the
Ignition Delay
for
Large Initial
Values
of
Oxidizer
Concentration
3
2 . The
Sensitivity
of Ignition
Delay to
Changes
in
Pressure
4
D .
IGNITION
LIMITS
IN
TH E THERMAL
IGNITION
OF A
DIFFUSION
FLAME
7
E.
SUMMARY
OF
RESULTS
OF
NON-NUMERICAL ANALYSIS 0
CHAPTER 1-4
CHAPTER
1-5
CHAPTER II-l
THERMAL
IGNITION
OF A DIFFUSION FLAME
NEAR
A
COOL
SURFACE:
PRESENTATION
AND
DISCUSSION
OF
RESULTS
OF
THE
NUMERICAL
SOLUTION
1
A. SIMPLIFYING ASSUMPTIONS AND
THEIR VALIDITY 2
B . BEHAVIOR
OF
TH E
DIMENSIONLESS
IGNITION
DELAY
6
1 . Changes in ( A )
and/or ( B ) ,
and the Ignition Criterion 6
2 . Equal Changes
in
B , and ^ 9
3 .
Changes in
S >
0
9
C .
BEHAVIOR
OF
TH E
REAL
IGNITION DELAY
IN
TH E THERMAL
IGNITION
OF A DIFFUSION FLAME
0
1 . Variable
0
®
,
Constant Pressure
0
2 .
Variable Pressure
3
3 . The
Effect
of Variations
in Initial Gas Temperature
5
SUMMARY
OF
RESULTS 7
PART II
REVIEW
OF RECENT
RESEARCH
ON TH E
MECHANISM
OF
SOLID PROPELLANT
IGNITION 60
A. INTRODUCTION
0
B . THEORIES OF
PROPELLANT IGNITION 1
1 .
Discussion
of
Ignition
Criterion
1
2 .
Solid
Phase
Ignition 2
3 . Gas Phase Ignition 4
4.
Ignition
Due
to Heterogeneous
Reactions
at
the
Gas-Solid
Interface
6
VI i
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TABLE OF CONTENTS-contd.
Page
CHAPTER II-l
REVIEW OF RECENT
RESEARCH ON THE MECHANISM
OF SOLID PROPELLENT
IGNITION-contd.
C . EXPERIMENTAL
STUDIES OF
SOLID
PROPELLANT
IGNITION
1 . General Considerations
2 .
Hot
Wire Ignition
of Composite
Solid Propellants
3 .
Explosion
Tube
Propellant
Ignition Experiments
4 . Ignition of Nitrate Ester
Propellants
by Forced
Convection
5 . Ignition of
Nitrate Ester
Propellant
i n a
Pressurized
Oven
6 .
Propellant
Ignition
by
High Convective
Heat
Fluxes
7 .
The Ignition of
Composite
Solid
Propellants
in
a
Shock Tube
8 .
Ignition of Composite
Propellants
by a
Radiant Energy
Flux
9 .
Composite Propellant Ignition
in
a
Small Rocket Motor
D . DISCUSSIONS
AND
CONCLUSIONS
68
68
70
71
72
7 3
7 3
74
75
7 7
78
CHAPTER II-2
EXPERIMENTS
ON
THE
IGNITION OF
COMPOSITE
SOLID PROPELLANTS
CONVECTIVELY
HEATED
IN A
SHOCK
TUNNEL
A .
EXPERIMENTAL
1 . Basic Equipment Selection
2 .
Shock
Tunnel Operating Conditions
3 .
Other Equipment
4 . Experimental
Results
5 . Conclusions Obtained
from
Supersonic
Flow
Ignition Tests
6 .
Subsonic
Flow
Propellant
Ignition
Tes
7 . Results of Subsonic
Flow
Ignition Tes
8 .
Discussion
of Results of
Supersonic
and
Subsonic
Propellant
.Ignition
Test
9 .
Pure
Fuel
Ignition
Tests,
Technique and Results
1 0 .
Summary
of
the Pure
Fuel
Ignition
Test
Results
1 1 .
Discussion
of the Pure Fuel
Ignition Test
Results
1 2 .
Necessary
Considerations
in
the
Planning
of
Future Composite Solid
Propellant Ignition
Experiments
81
8 1
8 1
8 2
83
8 4
87
ts 8 8
ts
89
s
91
94
96
98
10 0
Vlll
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TABLE OF CONTENTS-contd.
REFERENCES
Part
I
Part II
APPENDICES
Page
A-l
A-2
A-3
A-4
A-5
A-6
A-7
A-8
A-9
A-10
TH E
BASIC
SHOCK TUBE -l
TH E
TAILORED INTERFACE CONDITION -2
INSTRUMENTATION
-4
1 . Shock
Sensors -4
2 . Amplifiers -5
OTHER EQUIPMENT
-6
1 . Supersonic Nozzle Design -6
2 .
Subsonic
Nozzle
-7
3 .
Ignition Model
Preparation
-9
SAMPLE SURFACE
CONDITIONS
-1 0
1 . Supersonic Flow:
Stagnation
Point
Heat Transfer,
Surface
Temperature
-10
2 , Subsonic Flow
Model
Surface Temperature
-1 1
ALUMINUM EVAPORATION
TECHNIQUE
FO R
FUEL
MODEL INHIBITION
-1 5
SIMILARITY ANALYSIS OF THE GAS PHASE IGNITION
MECHANISM
FORMULATED
BY
McALEVY ( 1 2 ) -1 7
SIMILARITY ANALYSIS
OF
A MODEL FOR HETEROGENEOUS
IGNITION B Y HYPERGOLIC SURFACE REACTION
-21
PROGRAMMING
METHODS FOR TH E NUMERICAL
INTEGRATION
OF TH E EQUATIONS
FO R
THERMAL
IGNITION
OF
A
DIFFUSION
FLAME
-27
A. SELECTION AND DISCUSSION
OF
FINITE-DIFFERENCE
TECHNIQUE
-29
B.
COMPUTATIONAL
DIFFICULTIES, PROCEDURES,
AND
OBSERVATIONS -35
TH E NEGLECT OF CONVECTIVE TRANSPORT
OF
MASS
AND ENERGY -37
F L O ' r t T
CHART
OF
COMPUTER
PROGRAM
A
GENERAL
PROGRAM FOR
TH E NUMERICAL
INTEGRATION
OF TH E
SE T
OF
PARTIAL DIFFERENTIAL EQUATIONS DESCRIBING TH E
THERMAL IGNITION OF
A DIFFUSION FLAME
NEAR A
COOL WALL,
FOR CASES
I
AND
II.
TABLE I
IGNITION
OF M2 PROPELLANT
FIGURES
IX
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LIST OF
FIGURES
FOR
PART I
FIGURE
1-1 Form
of
Numerical
Solutions
at
Successive
Intervals
of
Time
1-2
Dimensionless Ignition
Delay
versus (1/A),
case
I
1-3
Dimensionless
Ignition
Delay versus
(1/A),
case
I
1-4
Effect
of B Parameter
Variation
on Dimensionless
Ignition
Delay,
case
I
1-5
Effect of
B
Parameter Variation
on
Dimensionless
Ignition
Delay,
case
I
1-6
Effect
of
B Parameter Variation
on Dimensionless
Ignition
Delay, case I
1-7
Dimensionless
Ignition
Delay
versus
Ratio
B/A,
case
II
1-8
Dimensionless Ignition
Delay versus
Ratio
B/A,
case II
1-9
Dimensionless
Ignition
Delay
versus Ratio
B/A,
case
II
1-10 Effect of
Activation
Energy
on
the
Dimensionless
Ignition
Delay,
case
I
1-11
Effect of Activation
Energy
on
the
Dimensionless
Ignition
Delay,
case
II
1-12
Sensitivity
of Ignition Delay to
Initial
Gas
Temperature,
case
I
1-13
Sensitivity
of Real
Ignition
Delay
to
Initial
Oxidizer
Mole Fraction
at
Constant
Pressure,
case
I
1-14
Sensitivity
of
Real
Ignition
Delay
to
Initial
Oxidizer Mole
Fraction
at
Constant Pressure,
case
II
1-15
Sensitivity
of Real
Ignition Delay
to Initial
Oxidizer Mole Fraction
at Constant Pressure,
case
II
8/20/2019 Ignition of the Reaction Field Solid Propellant
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•
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ä\-
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. •
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•
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./
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•
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0
<
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:'
i
V.
'..•
•»■
fj
*. rf
t
.
•
LIST
OF
FIGURES
FOR
PART
I-contd.
FIGURE
1-16
Sensitivity of Real
Ignition Delay to
Initial
Oxidizer
Mole Fraction
at Constant
Pressure,
case
II
1-17
Sensitivity
of
Real
Ignition Delay
to
Pressure
Level,
Constant Initial
Oxidizer Mole Fraction,
case
I
1-18
Sensitivity
of
Real
Ignition
Delay
to
Pressure
Level;
Constant Initial
Oxidizer Concentration,
case
I
• 1-19
Sensitivity
of
Real Ignition Delay to Pressure
Level; Constant
Initial
Oxidizer
Concentration,
- .
case I
\I-20.
. . Sensitivity
of
Real Ignition
Delay to
Pressure
;
. Level;
Constant Initial
Oxidizer
Concentration,
. •
'• . .
ase
I
' . . • I . - i 2 1
' ' .
Sensitivity
of
Real Ignition
Delay
to Pressure
' • • . .
• •
. , . ' ; .
.Level;
Constant Initial
Oxidizer
Concentration,
' • • '
' / • .
;
:
° .case
I
:
1-22.'
/
Sensitivity
of
Real
Ignition
Delay
to
Pressure
' • . . •
•
• ' • ; .
• .
• •
L e v e l ; '
Constant
Initial
Oxidizer
Mole Fraction,
•
. . ' i/'base
-11
..
-
-.•
. . 1 - 2 3 .
:
•
•
t
Sensitivity
of Real
Ignition
Delay to Pressure
' < > • . • . ' • ' t . . . . . ' ;
Level; Constant Initial
Oxidizer
Concentration,
. • ' • • . . ' ' . ' . . • • „ • case I I .
' ;
:l~2\-\
Sensitivity
of
Real Ignition Delay to Initial
-
- ' _ . * • • ; :
<
Gas Temperature Level,
case
I
1-25./
Sensitivity
of Real Ignition
Delay to
Initial
• • • ; Gas
Temperature
Level,
case I
XI
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LIST OF FIGURES
FOR
PART
II
FIGURE
1
ot
Wire
Ignition
of
Composite Propellants
2
itrate
Ester
Propellant
Ignition
in
an
Explosion
Tube
3
onvective
Ignition
of
Nitrate
Ester
Propellants
4 2 Nitrate Ester Propellant Ignition
at
Atmospheric
Pressure
5
9
Nitrate
Ester
Propellant
Ignition
at
Atmospheric
Pressure
6
omposite Propellant
Ignition by
Convection
in a
Shock Tunnel
7 Composite Propellant Ignition'
in
a Radiation
•
Furnace
_•.
. .
■
8
omposite Propellant Ignition
by Convection
in
a Shock
T u n n e l - ' . - . * . ,
9
. '
Composite and Nitrate Ester Propellant
Ignition
Data
from
End.Wall
Shock Tube
Tests
10
omposite
a n d '
Nitrate . - E s t e r
Propellant
Ignition
Data,
End Wall
Shock
Tube Tests
11
gnition of-Composite
Propellants by
Means of
Radiant
Heat
Flux
12
Ignition of
Composite
Propellants by Means of
Radiant
Heat
Flux
1 3 gnition
of Composite Propellants
by Means of
Radiant
Energy
14
gnition of Composite Propellants by Means of
Radiant
Heat Flux
1 5
gnition
Rocket
Motor Experiments
on
Composite
Propellants
1 6
gnition Rocket
Motor
Experiments on
Composite
Propellants
Xll
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LIST
OF
FIGURES
FOR PART
II-contd.
FIGURE
1 7
gnition
Rocket Motor
Experiments
on
Composite
Propellants
1 8
ave
Diagram
1 9
. , versus
M
ctual and
Theoretical
41
s
2 0 ersus
X^
2 1
T
versus
X^
„ „
theo
.
2 2
. ,
versus
M
41
2 3
, - - . and T versus
X^
2 4
mplifiers, Schematic Diagram
2 5 nstrumentation
Schematic
2 6 upersonic Nozzle
2 7 upersonic
Nozzle
2 8
upersonic
Model Viewed Through Test Section
2 9
verall
View
of
Test
Section
3 0
upersonic
Flow,
100% 0 - ,
Hemisphere
Cylinder Model
3 1
5°
Wedge
in
100%
0 Supersonic
Flow
3 2
5
edge in
Air,
Supersonic
Flow
3 3
5 edge
in
N Supersonic
Flow
3 4
abulation
of
Propellant
and
Fuel
Formulations
3 5 ypical
Film Record
of
Subsonic Flow Ignition Tests
3 5
ubsonic
Flow
Ignition
Test Results
3 7
cale Schematic
of
Subsonic
Nozzle
3 8
ubsonic
Model Mold
xm
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LIST OF FIGURES
FOR
PART
II-contd.
FIGURE
39 ounted, Subsonic Flow Sample
40
hin
Film Instrumented
Model
for
Surface
Temperature Measurements
41 ypical Voltage
Trace
versus Time,
Surface
Temperature Measurements
42 emperature
Ratio
versus at the Interface
Between
Gas-Slab,
and
Semi-Infinite
Solid
43
emperature History of Gas-Solid Interface
44 oated Samples
Mounted in
Vacuum
Evaporator
xiv
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TABLE
O F SYMBOLS
A
dimensionless
constant
characteristic
of
. ,
oxidizer consumption;
n/fh*
i n
c a s e I , ( - ^ = ~ = r )
f b r C
B dimensionless
constant characteristic of
heat generation;
[VLj?) case
I ,
( 2 | - -
7
=~= )
f o r
Case
I I
c
pecific
heat
of
solid
c specific heat
of
g a s
. P
C
F
•
fuel'concentration
i n
gas
phase
;
.. •••
o ....•• *
. C _
' . - / . « f u e l concentration a t
surface
of
condensed
phase
C ^
, . • • • oxidizer «concentration i n
gas
phase
' •
•.'*•' .
..
: C '
• • initial-value
o f . ' . C
'
•
ox
: * : • . . /V . •
, • . .
.
0
^.:.
/
D -
• „ ' . - m a s s d i f f u s i o n , coefficient
E
' . •
4
a c t i v a t i o r i
-
-energy:or-voltage.
•
.
•..••.• .: •«
•
. ••.-;•
•..'
f ( C
) • • any s p e c i f i e d - f u n c t i o n ' o f - . C orbits spatial
, gradient
•'•'_;
• • . • •
'
h convectiye h e a t
transfer.-coefficient
H ,
c h a r a c t e r i s t i c . ' t i m e
of homogeneous
induction period
H« characteristic'time . o f
heat
exchange
i n
a
homogeneous system
.
L haracteristic length
Le
ewis n u m b e r ,
D / o c
L p functional representation of
ignition
criterion
m5 ass f l u x o f fuel from surface
of condensed phase
n toichiometric
ratio or
surface
reaction
order
q
eat
transfer
rate
or
heat
flux
q
R
eat
of reaction
q
eat
of reaction per mole of oxidizer
P
ressure
xv
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TABLE OF SYMBOLS-contd.
R
niversal
gas
constant
S
urface
area
T
emperature
V
olume
t
ime
t .
gnition
delay time
y ole
fraction
of reactant
in gas phase
y „
ole
fraction
of fuel
at
surface of
condensed
phase
y
00
nitial
mole
fraction of oxidizef' in gas phase
o <
hermal
diffusivity,
dimensionless
number,
temperature
coefficient
of resistivity
0 <
L
alue
of
empirical ratio,
:
from
B .
L .
H i c l c s
1 9 ) : . _
/S imensionless
number
. ' . : . /
'
• _
ö imensionless.
number,
ratio
of gas speci-fic heats
v imensionless
number'-
.
_ •
■
' . *
% imensionless fuel concentration''
. '
.
^QX
imensionless oxidizer
concentration
P
imensionless temperature,'
^ - ^ '
:
Wf
or-
'
T-7üoii)/%
r
hermal
conductivity
/* iscosity
/
imensionless
distance
f
e n s i t y
w
imensionless
number
t
imensionless
time
L
imensionless ignition
delay
Y^ imensionless function,
xvi
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TABLE
OF
SYMBOLS-contd.
Subscripts
I
or
II
reference
to
case
I
or
case II
0
initial state
F
fuel, solid or
gas
G
g a s
P
propelIant
s
solid or surface
i g n
ignition
XVI1
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CHAPTER
1-1
DISCUSSION
OF PREVIOUS
IGNITION STUDIES
A ,
INTRODUCTION
The
ignition
of
energetic
chemical
reactants
i s
a
critical part
of
any system in which combustion
i s
a
necessary
part of its operation. In such a
system,
the reactants to
be
ignited
may
be present
as
either a homogeneous mixture of
identical phases, or
a heterogeneous mixture
of
unlike phases.
From
the
standpoint of technological application,
i t i s
clearly
desirable
to understand
the
properties
of
ignition
in
both
types
of
reactant
mixtures.
In
the past,
the
ignition of combustible mixtures
has
been
quite
intensively studied
by
a large number of
investigators.
wo
general classes
of
combustible mixtures
were
studied
and in each case
a
variety
of
experimental
methods
were
used. hese two classes were those in
which
both reactants were
gaseous,
and
those
in which
one of
the
reactants was a
liquid,
hydrocarbon
fuel. brief review
of
typical experiments
and
results
for
each
of these
cases
i s given
in a
later
section of
this
chapter.
Now
in each
class
of
mixture,
the
common manifestation
of ignition
was
a
rapid acceleration
of
the
chemical reaction
rate
which
caused
a
sudden
temperature
increase
in the
system.
Two
alternative
explanations
for
this
accelerating
chemical
reaction
rate
exist.
The
first alternative i s
the
control
of
the
reaction rate
through
a predominance
of
chain
branching
over
chain breaking
chemical reactions and subsequent
acceleration
of
heat
release. he other
alternative
i s that
the reaction rate i s governed purely by the relative thermal
processes of heat
generation
and
heat
loss,
regardless of
the
detailed
form
of
the
chemical
reaction. The former
alternative may
be
termed
"chain
branching"
explosion or
ignition;
in
the
latter alternative ignition i s
considered
as
being purely thermal in
nature,
and arising out of a
favorable thermal unbalance
in
the
system.
Having certain experimental results, then, one is
faced
with
the
problem
discerning
which
of these alternatives
i s
best supported
by
the
data.
In
the case
of
"chain
branching"
ignition, the data persuades one to conclude
that
the previous
history of the
reaction
rate
i s
important
in
the
total
ignition
process. Consequently,
the
experimental
data
i s used
in
the
development
of
a
detailed
description
of
the chemical reactions
including
the formation and propagation of
free
radicals
and
8/20/2019 Ignition of the Reaction Field Solid Propellant
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activated
complexes. It is
only
recently,
however,
that
adequate
treatment
of
such
formulations
has been made possible
through
the
advent
of
high speed computing
devices.
On
the
other hand, the experimental data ma y indicate that
the
ignition was
purely
thermal in
nature.
It
should be
noted
that
the
latter
interpretation
of
experimental
data is based
on
the
previous theoretical
developments
of the properties
of thermal
ignitions. n
essential
feature of
thermal
ignition
theory is
the
assumption
of
a
chemical
reaction
rate
represented
by an
instantaneous
function of reactant
concentration
and temperature.
Consequently,
the
chemical reaction rate is
assumed
to
be
independent
of
its
previous
history.
Clearly, our
present
understanding
of
ignition
processes has
been
profoundly
influenced
by early theoretical
^nd
experimental
studies.
•
•
Actually,
the
"ignition
.of
most,
homogeneous-rand
heterogeneous^-mixtures
probably.involves
a.combination
of
chain
branching
an d
breaking
processes,
an d thermal
effects.
•
Even
so,
the assumption o f *
simple,
-one-step/chemical .'reaction
often
constitutes an
adequate-dfescription
o f .
the.
chemical
' •
' .
processes
during
ignition. Consequently, the
theoretical,
description
of the
properties
infierent-'in« thermal -ignition.
''
of combustible mixtures
is
<
a
fundamental area
of present, ; . , ' •
an d past, investigations.
*
•
• ' * . . '''.'•
.'•
B.
REVIEW
OF
EARLY
THERMAL'IGNITION'.THEORY;,
. . ' • _ .
.
The
basic, concept: o . f thermal.^ignition was
developed
•
by
van
t
Hof
f
(1.
1 ' ) • ,
. - w h o
.defined«
this,
type'ldf'ignition-as;.
v
'
the impossibility-of
thermal
equilibrium, being
established . ' • ' • ' •
between
a reacting
system and-its
1
s
urroundings.•
Le
Chatelier
' •
(1.2)
qualitatively
formulated t h i s , conditiori/'as; a - contact-•
between
the
curve'of heat
generation an d
the
;
-str
aight line
•
of heat
I ' o s s . -
• ; •
• * '
. • . • ' .
. • '
• •
' • •
' .
Quantitative
formulation
of
.thermal-;
ignition was
first done
for
a homogeneous
.mixture confined
in a
reaction'
vessel
in order
to
determine
the
characteristic
behavior
of
such
a system.
Thus, : i t is-.°informative' to determine critical
explosion
conditions
in
terms
of vessel ' s i z e , pressure, an d
initial
temperature.
In
this
case,'one"wishes
to
know
what
steady, or
stationary,
states
can be
tolerated
by
the
mixture.
Secondly, one may wish
to
determine
the induction
period
of
the
explosion
an d
its
dependence
on
the
mixture's
initial
conditions. The
theoretical
description
of
this
case requires
formulation
and
solution of the
transient,
or
nonstationary,
behavior
of
the
confined
mixture.
The
following two
sections
provide
a
brief
review
of the
early
theoretical developments
describing these
two
8/20/2019 Ignition of the Reaction Field Solid Propellant
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• .
«
•
•
•
'
cases.
These developments
provide
the
basic
understanding
of thermal ignition
which
i s essential
for
the developments
in
thermal
ignition
theory
which
follow
in the next
chapter.
1 .
Stationary Theory of Thermal Ignition
The theoretical
development
for
determination
of the
limiting
or
critical stationary
state
for a
confined
homogeneous
mixture
has
been
done
by
Semenov
(1.3
)
and
others. Recently, limitations and
extension of the early
developments
of
this
case were
discussed
in
references
( 1 . 4 )
and
( 1 . 5 ) .
In the stationary
theory of thermal
explosion,
one
assumes
that
the heat generated
by
chemical reaction i s
continuously
distributed
throughout
the
reactant
mixture.
Heat
loss
i s
assumed
to take
place
by
conduction
t o
the
vessel walls which are maintained
at
a
constant•temperature.
Because
all
possible
states of
the
reactant mixture up
to
the
conditions
of
explosion
are
assumed
to
be
stationary,
the time
derivative of
the
temperature'
i s
equal
to zero.
It i s further
assumed
that
the
temperature
rise
a t -
the
.
critical
conditions
for
explosion
i s
'small'compared
to
the
. ' •
. • '
•
initial
temperature of the
mixture;
This assumption
allows- '
[ _ • . ' "approximation
o f .
the exponential term
. i n the"-chemical
reaction
• . * ; ' . ' ' .
- •
rate,
term/ simplifying
the final
' d i f f e r ' e n t ' i a l ^ e q u a t i o n . The'
j . '
• •
_
. m o s t important
. . c o n s e q u e n c e
of
this apprpximation
. i s .
that
all
1
\
•
. '
«the
physical
parameters
of
the-system
can
be
grouped,
into
. . • . . '
• _
one
c o n s t a n t ,
•
', '
appearing
only
in'the
differential
•
equation.
. • ,
'.•..■
'.'•'
.
•
. v-
"-.
'•'
'.
The constant," ) characterizes
t h e ' solution;of
the
different
equation
in
that
for
some
critical value'of
< S
stationary
state
cannot exist and explosion will occur.
This method i s
quite accurate
in its
prediction
of
the
critical
conditions
for
explosion as
a function of
vessel wall
temperature,
pressur
and vessel
size,
see
reference
(1.6). The effect
of
free
convection
in the
mixture
have
been
ignored,
but
under
normal
experimental
situations
this
effect
can be
neglected
justifiab
2 .
Nonstationary
Theory
of
Thermal
Ignition
In
the nonstationary
theory developed
by
Todes
(1,7), Rice
(1 . 8) and Frank-Kamenetskii (1.6), one deals
with the reaction
vessel a s a whole,
assuming
that
the
temperature i s uniform
over
all points
in
the vessel.
Under
conditions
in
which explosion i s imminent,
heat
conduction
8/20/2019 Ignition of the Reaction Field Solid Propellant
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within
the
mixture
is ignored, an
assumption
which is
equivalent
to
replacing
all
temperature
dependent quantities
by
their
value
at
some
mean
temperature.
It
is
tacitly
assumed, then, that the reactant mixture remains
well
mixed,
an d
always homogeneous.
Errors introduced
by these assumptions, however,
are
relatively
minor
compared
to the assumptions
that density
is independent
of
temperature an d
that
the
chemical
reaction
can
be approximated by an Arrhenius rate term. Pragmatically,
however, the two assumptions
just
mentioned
are justifiable
in the sense that their
use in theoretical developments of
steady
state
gaseous flames
ha s
produced
reasonably
correct
results.
Under
all
the
above
assumptions, one
then
considers
the
time
rate
of
change
of
temperature inside
a
vessel
containing
a
homogeneous
reactant
mixture. he competing
processes
in
this
case
are
chemical heat
generation,
reactant
consumption,
an d heat transfer
to
the
walls of the vessel. It has been
normally assumed the chemical reaction does no t deplete the
concentration
of either/any reactant
during the induction
period
because the
total
temperature
rise during
the induction
period is taken
to
be small compared
to
the initial temperature.
Consequently,
the Semenov approximation of
the
temperature
dependent exponential term of the Arrhenius
function ha s
been
made.
Heat loss
to
the vessel walls is assumed
to take
place
through
Newtonian
cooling.
After suitable
nondimensionalization
of
the
temperature,
the
nonstationary
behavior
of
the
reaction
vessel
is
characterized
by
the
two
dimensionless groups contained
in
the
following differential equation. On e should note that
the reaction
vessel
is
assumed
to have
a surface
area
and
volume of
an
d
/
respectively,
an d
that
the
heat
transfer
coefficient between the mixture an d the vessel
walls
is
defined as
>
.
Other symbols are standard,
and their
definitions ma y be found in the Table of Symbols.
where aP
V .
c
Y
0
?
&
£
/Z
r
°> -
H ,
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The group, i
,
may be termed the
characteristic
time of
the chemical induction
period;
£
s the
characteristic
time
of
heat exchange
in
the
system.
The
form
of
the
solution
of [ 1 ]
above,
i s
*~f(i'%)
[2 ]
where
n may
be
chosen to be either
t or Hg). It
i s
clear
from this
formulation that
the
ratio
(H1/H5,
)
completely determines
the
form of
the
solution
[ 2 ] .
Often the vessel i s considered adiabatic, or
the
time of heat exchange i s long compared
to
the
induction period.
In either
case,
the right hand term of equation
[ 1 ]
can be
neglected, and
the
solution of the resulting equation i s
- 0 -
W
[ 3 ]
Well into the ignition
range,
equation
[ 3 ]
will be
valid;
however,
near
the ignition limit,
ft,
and
/ ^ sre equally
important.
It
should
be
noted
that
at
some
critical constant
value
of
the
ratio
Hi/^z) there
will
be
a
sharp change
in
the
form of
equation [ 2 ] .
When
iHi/Hz)
i s
much
greater than
its
critical value, the
real
induction delay which
i s
necessary
for ( 9 o reach some
value
*
depends upon the
pressure
or
initial concentration of either reactant in the
manner
shown
below.
1 Ö
^
INDUCTION
4
]
where
- pressure,
/ or
Y z . The dependence of
on
temperature
and
activation
energy
i s
[ 5 ]
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Note
that the criterion selected
to define explosion
or
ignition does not
affect
the
induction delay's dependence
on
the
physical
parameters
of
the
system
as
shown
in
equations
4 ]
and
[ 5 ]
above.
One
should
note
that
the
above
results
are
commonly accepted as defining thermal ignition or explosion.
Experimental
results
which follow
the predictions
of
equations 4 ] an d [ 5 ] are often used as
proof
that
the
reaction mechanism
was thermal. f the results of experiments
did
not
follow
these
patterns, t was
often concluded
that
the
ignition or explosion initiation was
not
governed by thermal
processes.
However, when
the
ratio of
characteristic times,
\H\/ni) is
not greatly
larger
than the
critical
value,
equations
4 ]
and
[ 5 ]
are
no
longer
true.
In
addition,
it
•
is entirely possible
that
one of the reactants is consumed as
the
ignition
or explosion
progresses.
Consequently, one
m u . s t
re-examine the formulation of
the
nonstationary
thermal
theory,
as
is done
in
Chapter
1-2.
'
Recently, the
thermal theory of' ignition
for_
-
quiescent,
gaseous
homogeneous systems
has
been
extended t o -
. ' '
ignition in
flowing
systems by
Khitrin
an d Goldiiberg (1. 9 )
V
They examined
the
critical
characteristics of flammability
including concentration
limits
and
their
dependence
on
pressure
an d initial temperature, limit burning velocities,
an d flame
front
stabilization criteria. Khitrin
(1.10)
discussed'the.
•
consequences of the thermal theory,of homogeneous mixture
ignition
in
a
fast,.laminar
or turbulent
flow
past
heated
wall
or
planar
body.
The
ignition
by
heated,
bluff
bodies
'\
.
could
not
be treated except in
the
case of an ellipse which
i
/..
approached
a
planar body. Ignition
delays,
as.functionally" ,
related to
temperature, pressure,
an d oxidizer'concentration . ' •
were
not
discussed because.stationary
state,
theory
was used.
. .
• .
Toong,
reference (1.11), has'presented
ä
'
theory'
fo r the steady
state
ignition
an d
combustion
of
a homogeneous
mixture flowing
over
a
heated flat
plate.
•
A
second
order,
thermally controlled chemical
'reaction
wa s
assumed.
The
necessary
wall
to
free stream
temperature
ratio
for
establishment
of a flame wa s
calculated
fo r
variations
in
pressure,
plate
length,
free
stream velocity, and
free
stream temperature.
Reasonable agreement between theory and experiment
was
obtained;
however,
th e
results
of
this
theory
ar e
difficult
to
compare
with those of
a
transient analysis of
homogenous mixture
ignition.
In 1955, reference (1.12), Marble an d Adamson
presented a
theoretical treatment of the steady, constant
pressure combustion of a
flowing, homogeneous mixture. They
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considered
two parallel
flows, one
of
high temperature
combustion
products an d
the
other
of
a
premixed
combustible,
and
the
development
of
ignition
as
the
separate
flows
mixed;
a perturbation analysis of the pertinent equations wa s
made.
Th e
dependence
of
ignidon
of the stream was
noticed
in
this
treatment,
but
the
effect
was
not
considered
important;
consequently no
investigation
of
this
point
wa s
undertaken.
Dooley, in
(1.13),
treated
the
case
of initially
unmixed, different temperature reactants in
parallel
flow;
after
mixing by diffusion,
ignition
and
steady
combustion
ensued. he analytical treatment of this case of
heterogeneou
combustion
was treated by a perturbation analysis similar to
that of (1.12).
gain,
the problem of
ignition definition
wa s noted, but remained
univestigated.
A nonstationary
treatment
of
thermal ignition
was treated recently
by
Thomas (1.4
including the
consumptio
of on e reactant by an
n
t
order
reaction
during the induction
period.
B y
employing
the
quadratic
approximation
to
the
exponential reaction
rate
term,
analytic
solutions were
obtained
for
several
interesting
cases.
he use
of
this
approximation,
however,
limits
the
applicability
of
his
treatment
to
cases in which
the
temperature
rise at explosion
is less than 10 0 .
Primary
emphasis wa s
placed
on the
behavior
of the system just above its critical condition,
and
the effect of
reactant consumption on this condition and
on
the
induction
period.
In
reference
(1.5
) , the ignition of
ammonium
perchlorate
an d
cuprous
oxide
by simple
self-heating
wa s
treated
by
nonstationary
thermal
theory.
hrough
the
use
of
an
effective
heat
transfer
coefficient characterizing
the
system's heat loss, reasonable agreement
between
theory
and
experiment
wa s
obtained.
The
work of Thomas,
above, was
used
to justify
the
assumption
of
uniform
temperature
in
the
reacting system,
during
the ignition
delay
necessary
to reach
a chosen
temperature.
A theoretical treatment of spark ignition has
been
presented by Jost (1.14) where the spark wa s represented
by a point
source
of
energy
in
a homogeneous, combustible
mixture.
Under
the assumptions of
a
threshold source energy
value,
quasi-steady
state after some specified time p up
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