Simulation of stability of ignition and combustion of energetic materials under

action of pulsed radiation

V.E. Zarko, L.K. GusachenkoInstitute of Chemical Kinetics and

Combustion, SB RAS, Novosibirsk 630090

EUCASS 2011

Melted and evaporated in the combustion wave EMs →→ classical explosives (RDX, HMX); recently synthesized HNF, ADN, and CL-20

Radiation driven transient combustion regimes →→→ practical applications / / source of information on chemical kinetics characteristics

Specific coupling between physical and chemical processes on the burning surface

INTRODUCTION

The goals of the research Developing theoretical model for describing radiation assisted transient combustion behavior of EM in order to study

• Stability limits of steady-state pyrolysis modes of semi-transparent EM in dependence on radiation absorption parameters and power level

• Ignition stability of semi-transparent EM under action of radiant fluxes of various time history

• Extinguishment of stationary burning EM upon action of single radiation energy pulse

Ignition transients

Initial compound

Final compound

YcY3

Ignition-combustion transients

Vaporization on the reacting surface is

described by the Clausius-Clapeyron law

  (M/M1) Уg1,s P = const*exp(-L/RTs)

M -- molecular mass of gas mixture

M1 -- molecular mass of vapor

Уg1,s -- mass fraction of vapor above the EM surface

L -- latent heat of evaporation.

Problem Formulation

a) solid state Rm xxtx )(

)exp()(2

2

xtqx

T

x

TV

t

TC c

сc

mc

cc

(1)

Rm xxtx )(

,,0

,),(,)0,( 0

dt

dxV

x

T

TtxTTxT

mm

Rx

c

mmcc

Problem Formulation

cc

cmm

cc

c x

y))VV(

x

xV(

t

y

(3)

)RTEexp(yA,Q ccccccccc

(4)

cmmxxc

mmccmc VLx

TTtxTTxTtxy

m

00 )(,),(,)0,(,1),(

)exp()())((2

2

xtqx

T

x

TVV

x

xV

t

TC c

cl

ccm

mc

ccl

b) liquid state mxx0

(2)

c) gas phase (xL < x < 0)

W)x

T(

xx

T)

x

yD

C

CVV(

t

TC 21

3

1i

ii

p

picp

(5)

11

11

c1 )

x

yD(

xx

y)VV(

t

y

(6)

122

22

c2 )

x

yD(

xx

y)VV(

t

y

(7)

c) gas phase (xL < x < 0)

),RTEexp()y(A 1N

1111

),RTEexp()y(A 2N

2222

qzconstW

at ,tzttz,0xx 21L

0W in other cases

Instability of self-sustaining combustion

k = (Ts – To) ( lnrb/To)p

r = (Ts /To)p

Qm = Qm/c(Ts – To)

= c / l

m = (Tm – To)/(Ts – To)

Stability of steady-state combustion regimes

Stability of steady-state combustion regimes

A → r = 2 (k*-1)/(k*+1); B → r = 2 (k-1)/(k+1);

(stability limits at =1, Qm = 0.3)

r = (Ts /To)p

k = (Ts – To) ( lnrb/To)p

k*=1/(1+Qm)

11 /||

)0(/)0(

/

/

qq

f

qq

uuS st

11 /||

)0(/)0(

/

/

qq

f

qq

uuS st

11 /||

)0(/)0(

/

/

qq

f

qq

uuS st

Black colour = 100000 m-1, Dark – grey = 11500 m-1, Light grey = 1500 m-1

= 11500 m-1

Stability of ignition transients

kW/m2kW/m2

tH, s

tH, s

Black colour = 100000 m-1, Dark grey = 11500 m-1, Light grey = 1500 m-1

Stability of ignition transients

kW/m2

te, s

Black colour = 100000 m-1, Dark grey = 11500 m-1, Light grey = 1500 m-1

Stability of ignition transients

Extinguishing via action of a single radiant flux pulse, q0(Dt)

a=1000 cm-1

a=115 cm-1

kW/m2 kW/m2

kW/m2

kJ/m2

Dt,s

Radiation driven combustion of evaporated EMs is a source of information about the combustion mechanism.

Self-sustaining combustion regime fails for the EMs with significant heat release in the condensed phase and evaporation on the burning surface due to formation of temperature maximum in subsurface layer.

CONCLUSIONS

CONCLUSIONS (cont’d)

Melting heat makes effect on the stability of self-sustaining combustion: the larger the values of Qm and ∆T = Ts-Tm, the narrower combustion stability domain.

Stability of transition from ignition to stationary self-sustaining combustion depends on the steepness of radiant flux cut-off and transparency of EM.

CONCLUSIONS (cont’d)

• Further development of theoretical knowledge on transient combustion regimes urgently needs experimental substantiation.

• This, in turn, takes essential improvement of experimental techniques for measuring instantaneous burning rate and structure of the combustion wave.

Благодарю за внимание!Thanks for your patience!

Stability of steady-state combustion regimes

A → r = (k*-1)2/(k*+1);

c) gas phase (xL < x < 0)

(8)

0x

)V(

xV

t c

MTRp

2221113

3

2

2

1

1 Q,Q,M

y

M

y

M

y

M

1

(9)

0

0)0,()0,(;)0,(

21

210

x

y

x

y

x

T

xyxyTxT

at Lxx

y1 + y2 + y3 = 1

Dyx

Dyx

Dyx1

12

23

3 0

On the burning surface:

Lvyqx

T

x

Tcccrx

ccx

00 || (10)

v v y Dy

xy vc c c c1 1

1(11)

v v y Dyx

y vc c c c2 22 1 (12)

v v vc c c

bs TTR

LM

M

My

11exp 11

1 (14)

(13)