Ignition of the Reaction Field Solid Propellant

8/20/2019 Ignition of the Reaction Field Solid Propellant

1/252

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


2/252

N O T I C E :

hen

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or

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f i c a t i o n s

or

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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

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f o n n u l a t e d ,

f u r n i s h e d ,

or in

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supplied

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or c o r p o r a t i o n ,

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any

way

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related

t h e r e t o .


3/252

THIS DOCUMENT IS

BEST

QUALITY

AVAILABLE

THE

COPY

FURNISHED TO DTIC

CONTAINED

A SIGNIFICANT

NUMBER OF

PAGES WHICH DO

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REPRODUCE LEGIBLY


4/252

PRINCETON UNIV

ER

S

I

T Y

DEPARTMENT

OF AERONAUTICAL ENGINEERING


5/252

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


6/252

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."


7/252

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


8/252

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


9/252

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


10/252

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


11/252

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


12/252

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


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


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


13/252

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


14/252

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


15/252

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


16/252

•:•} .

.

,

;

• ; • ' -

> .•

; -

> >

'

• .

' ', '.

•

•

'

* *•

,

,

.

. • • ^

,

f

- '

.'

• '

*

*

'

.

y

•

•

t

';

t

ä\-

' . *

\

y. 'V.

. •

. ••

*•

•

•

•

* \

1^

:

• y . •

/

'•

. i

t

•./Ufc.

* •

\'

t

'

1

* : » -

*'

»

./

'* .'i'

•

•.Vi-

* •

•

*

• •

/ •

r

.

: • • >

•.

,

•

••

.

•

, ,

» ,

, •

••

1.

« , • ,

t

,

, . •

• • .

..•o *.

;'

•

'.

0

<

t

•.

>

«

:'

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


17/252

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


18/252

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


19/252

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


20/252

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


21/252

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


22/252

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


23/252

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


24/252

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


25/252

• .

«

•

•

•

'

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


26/252

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 ,


27/252

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 ]


28/252

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

Ignition of the Reaction Field Solid Propellant

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