weapons and materials research burning-rate models and their successors martin s. miller muri...

Weapons and Materials Research

Burning-Rate Modelsand Their Successors

Martin S. Miller

MURI Kickoff Meeting

17 OCT 02


Goals of Briefing

• Convey complexity of phenomena

• Concepts - continuum-mechanics paradigm

• Recent modeling approaches

• Frozen ozone

• RDX

• Propellants

• The MURI challenges


PHENOMENA


98% NC (13.16%N)

2.8 mm/s @ 1 MPa


28.7% NC(12.68%N)22% Nitroglycerine

47.3% Nitroguanidine

2.3 mm/s @ 1 MPa


76% RDX (5 micron)12% CAB

4% NC(12.6%N)8% Energetic Plasticizer

0.8 mm/s @ 1 MPa


80% HMX (200/20 micron)20% Polydiethylene Glycol Adipate

0.5 mm/s @ 1 MPa


CONCEPTS


Propellant Combustion & Modeling Abstraction

RDX CompositePropellant M43

@ 15.5 atmD

ark

Zon

eV

isib

le f

lam

e

Caricature of Molecular Nature of 3-Phase Processes

GAS-PHASE FLAME elementary reactions thermal conduction convection molecular diffusion multi-component transport thermal diffusion

LIQUID/FOAM c-phase reactions thermal density changes mixture properties thermal conduction convection molecular diffusion bubble formation

UNREACTED SOLID thermal conduction convection thermal density changes

MULTI-COMPONENTEVAPORATION &GAS/SURFACE REACTIONS

{

MELTING{


Conservation Equations for 1-D, Steady-State Combustion at Constant Pressure

Chemical-Species Conservation in Each Phase:

)(,..,1 specieschemicalKk d

dxY V m

dY

dxWk k

kk k a f 0

Energy Conservation in Each Phase:

d

dx

dT

dxmc

dT

dxY V c h Wp k k p

k

k

K

k k kk

K FH IK

1 10

Mass Conservation:

0mdx

d

conduction convection diffusion reaction

diffusion convection reaction

constm

SOLID LIQUID GASx

x = 0x = -xliq

T(x)


0dx

dTliq

liqK

kkk hYm

1

00

liqK

kkkk hVY

1

000

0dx

dTgas

gasK

kkk hYm

1

00

gasK

kkkk hVY

1

000

SOLID LIQUID GASx

x = 0x = -xliq

solliqliq

K

k

xk

xk hYm

1

liq

liqliq

K

k

xk

xk hYm

1

liq

liqliqliq

K

k

xk

xk

xk hVY

1

liqx

liq dx

dT

liqx

sol dx

dT

Energy Fluxes at the Phase Boundaries

convection

convection

diffusion

diffusion

conduction

conduction

T(x)


An Example of a Surface Regression Mechanism:Single-Component Evaporation

EQUILIBRIUM

Equilibrium vapor pressure pLiquid

M W nvcondensing 14e j

M Mescaping condensing

npRT

E

s

v 8RTW

s

12

FH IKE

NON-EQUILIBRIUM

Liquid

M W X pRT vtotal

scondensing FH IK

1

40

M WpRT

RTW

E

s

sescaping FH IK

14

812e j

Surface Regression escaping condensing m M M= -

E

Vapor pressurereduced from p by reactions

totals pXTm ,, 0


The 3-Phase Mathematical Problem Posed

• Integration over solid phase for heat flux:

• Integration over liquid phase for heat flux :

• Integration over gas phase for heat flux :

• Surface regression mechanism: (p, Ts)m

Solution eigenvalues: xliq , Ts, } m

)()( liqliqliqsol xx

)0()0( gasliq

),( sTpmm

),,,( 0 mTxT sliqsol

),,,( 0 mTxT sliqliq

),,( mTp sgas


Iteration Scheme for 3-Phase Problem

Solve Conservation Eqns. in Liquid Layer

Liq./Solid BC Satisfied?

Solve Conservation Eqns. in Gas Phase

Surface Regression Mechanism Satisfied?


Gas/Liq. BC Satisfied?

Converged Eigenvalues

xliq, Ts, and m

Choose trial values of xliq, Ts, and m

totals pXTm ,, 0m

)()( liqliqliqsol xx

)0()0( gasliq


MODELS


Solid-Propellant Combustion-Modeling Timeline

1971Guirao & Williams

AP(14s,10r)

1986Hatch

NG(19s,60r)

1950Parr & Crawford

Rice & GinellDB

1990MeliusRDX

(38s,158r)

1996Miller

O3

(3s,3r)

RDX(45s,232r)

Liau & Yang1995

RDX(45s,232r)Davidson & BecksteadPrasad, Yetter, & Smooke1997

2000Miller & Anderson

O3, RDX, NG

Double Base(59s,365r)Miller & Anderson2002

2003Miller & AndersonRDX/BAMO-AMMOCL20/BAMO-AMMO(80s,550r)

MURIContribution?

1950's1940's 1960's 1970's 1980's 1990's 2000's 2010's

Single Overall Irreversible Rxn, Analytic Approx.Elementary Rxns, Decoupled Transport & Kinetics, Numerical Soln.Two Overall Rxns, Coupled Transport & Kinetics, Numerical Soln.Elementary Rxns, Coupled Transport & Kinetics, Numerical Soln.

Gas-Phase Treatment:

RDXBenReuven & Caveny

1977


FROZEN OZONE


• 3 Reversible Gas-Phase Reactions

• Heterogeneous Reaction Considered

Ozone Chemistry

I: O M O O M H 25.65 kcal / mole3 2 298.15K0

II: O + O O + O H = - 93.41 kcal / mole3 2 2 298.15 K0

III O O M O M H kcal moleK: . /. 2 298 150 119 06

IV O l O g O g O g H kcal moleK: ( ) ( ) ( ) ( ) . /.3 2 2 298 15 92 67


Frozen Ozone:Simplest Case of 3-Phase Deflagration

Distance from Surface ( microns )

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70

Te

mp

era

ture

(

K )

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Mo

le F

ractio

n

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

GA

S

SO

LID

r (cm/s) = 0.2526 xliq (micron) = 24.07 Ts (K) = 158.06

FROZEN OZONE COMBUSTION AT 1 ATM & 40 K

T

O2

O

O3

LIQ

UID

Distance from Surface (microns)

0.1 1 10 100 1000

Spe

cies

Pro

duct

ion

Rat

e (m

oles

/cc-

s)-4

-3

-2

-1

0

1

2

3

4

5

R(O3)

R(O)

R(O2)

ZONE BZONE A ZONE C ZONE D

P = 1 atm T0 = 40 KGas/Surface Reaction Probability = 0

Gas-Phase Species-Production Rates in Frozen-Ozone Combustion

RxnsIb & IIIf

Rxn IIf Rxn If Rxn IIIf


Comparison of Ozone Model to Experiment

• 10% O2 / 90% O3 liquid at 90 K: rexptl ~ 0.4 cm/s (Streng 1960)

• Single-component evaporation model with mixture-corrected liquid density, thermal conductivity, and enthalpy:

rcalc = 0.30 cm/s

What can explain the discrepancy?

• Multi-component Evaporation

• Liquid-Phase Diffusion

• O3/O2 Phase Separation in Liquid


Multi-component Evaporation in Ozone Model

• O2 at surface evaporates faster than O3, enriching the surface concentration of O3 from feedstock value

• O3 surface concentration becomes new eigenvalue; necessitates 4th iteration loop

• Necessitates consideration of molecular diffusion in the liquid phase

O3-O3 Strong interaction

O2-O2 Weak interaction

O2-O3 Moderate interaction


Liquid-Layer Molecular Diffusion

O3

O2

LOW RATE OF ESCAPE

HIGH RATE OF ESCAPE

DiffusionalFlow of O3

DiffusionalFlow of O2

LIQUID GAS

mg

cm sY

g

cmr

cm

sO O O3 2 30

3 3FH IK FH IK FHIK

mg

cm sY

g

cmr

cm

sO O O2 2 20

3 2FH IK FH IK FHIK

Condition for steady-state surface regression: rO3 = rO2

m

Y

m

YO

O

O

O

3

30

2

20

YO30=> New Eigenvalue


Calculational Price of Including Multi-Component Evaporation in Continuum Model







Converged Eigenvalues

xliq, Ts, and m








Converged Eigenvalues xliq, Ts, and



Surface Mole Fraction Relation Satisfied?

xliq

Ts

xliq

Ts

m

m

0O3

Y

Multi-ComponentEvaporation – Ozone

Single-ComponentEvaporation – Ozone

3 Eigenvalues3 Nested Loops

4 Eigenvalues4 Nested Loops

Multi-ComponentEvaporation – 6 species

6+2 Eigenvalues6+2 Nested Loops

Solve

Liq./Solid

Solve

Surface

Solve

Gas/Liq.

Choose

Solve

Surface

Solve

Liq./Solid

Solve

Surface

Solve

Gas/Liq.

Conv

Solve

Surface

(Assuming Oatoms not in liq.)


RDX


RDX Burning-Rate Model Results Compared

Davidson & BecksteadLiau & YangPrasad, Yetter, & Smooke

MODEL VAPORPRESSURE

SENSITIVITY OFBURN RATE TO

VAPOR PRESSURE

LIQUID RDXDECOMPOSITION

P, Y, & Snone - input exptl. Ts

instead none 40% at 1 atm

L & YPRDX(600K)=0.69 atm

(vapor-liquid data) high <1% at 1 atm

D & BPRDX(600K)=0.17 atm

(vapor-solid data) low 25% at 1 atm


C-Phase Decomposition Mechanisms Used by Different Models for RDX

3 CH2O + 3 N2O H570K = - 47 kcal/mole (D&B, PY&S, L&Y)

3 H2CN + 3 NO2 H570K = + 180 kcal/mole (D&B, PY&S)

3 HCN + 3 HONO H570K = + 19 kcal/mole

3 HCN + 3 NO2 + 3 H H570K = + 256 kcal/mole

3 HCN + (3/2) NO +(3/2) NO2 + (3/2) H2O H570K = + 34 kcal/mole (L&Y)

RDX(liq.)

{NO2 + CH2O NO + CO + H2O H570K = - 42 kcal/mole (D&B, PY&S, L&Y)

k1

k2

k3


RDX Liquid-Phase Reactions Assumed by Different Models

MODEL RDX-> 3CH2O+3N2O

k1 = A exp(-E/RT)

A E

RDX-> 3NO2+3H2CN

k2 = A exp(-E/RT)

A E

CH2O+NO2-> CO+NO+H2O

k3 = A T2.77 exp(-E/RT)

A E

P, Y, & S 6.0E13 36.0 1.6E17 45.0 802.0 13.73

L & Y 6.0E13 36.0 3.2E17 ** 45.0 802.0 13.73

D & B 6.0E13 36.0 0.8E17 45.0 802.0 13.73

** RDX => (3/2)NO + (3/2)NO2 + (3/2)H2O


GUN PROPELLANTS


ARL Burn-Rate Predictor: A New Approach

• Assumption 1: Universality and availability of an empirical pyrolysis law for the given class of propellants

• Assumption 2: Condensed-phase decomposition products can be estimated for each ingredient, e.g.,

• Assumption 3: Decomposition of the propellant into gas-phase reactants can be approximated as the non-interactive decomposition of each of its ingredients

r = As exp(-Es/RTs)

NG 2 H2CO + 2 NO2 + HONO + CO

[ 2 H2CO + 2 NO2 + HONO + CO ] x 0.14

[ 2 H2CO + (CHO)2 + 2 NO2 + NO + CO + HCO ] x 0.59

[ 3 H2CO + 2 NO2 + CH2 ] x 0.27 }2.3 H2CO + 0.6 (CHO)2 + 2.0 NO2

+ 0.1 HONO + 0.6 NO + 0.7 CO

+ 0.6 HCO + 0.3 CH2

Gas-Phase Reactants

GASSOLID


“Pyrolysis” Laws from Zenin Microthermocouple Data


CYCLOPS v1.0: Burning-Rate Predictorfor Multi-Ingredient Propellants with NC

Mononitrate: 6 w%

Trinitrate: 75 w%

DEGDN: 25 w%

NC (13.1 %N): 60 w%

CODEINPUT

MONTE-CARLOCALC. OF NITRATE-STATE

DISTRIBUTION FOR GIVEN %N

NC2 2 NO2 + 0.5 CHOCHO + 1.5 CH2O + 1.5 HCO + CH + CO

NC3 3 NO2 + CHOCHO + 2 CH2O + CH + CO

NC1 NO2 + 3 CH2O + 2 HCO + CH

NG 3 HONO + 2 HCO + CO

DEGDN NO2 + 3 CH2O + CH2

0.288 NO2 0.070 HONO 0.061 CHOCHO

0.285 CH2O

0.083 HCO

0.045 CH2

0.076 CH

0.092 CO

NASCENTGAS-PHASE REACTANTS(mole fractions)

Condensed Phase Gas Flame

DECOMPOSITIONPRODUCTSDATABASE

NG: 15 w%

Dinitrate: 19 w%

59 S

peci

es, 3

65 R

eact

ions

,C

ondu

ctio

n, C

onve

ctio

n,

Mol

ecul

ar D

iffu

sion


Nitrate-Ester Linear Burning Rates

Pressure ( MPa )

0.1 1 10 100 1000

Lin

ear

Bu

rnin

g R

ate

( c

m/s

)

0.1

1

10

100Experiment, M10: Miller (1985)Experiment, M10: AFATL (1982)Experiment, M10: Atwood, et al. (1988)CYCLOPS Code

M10

Pressure (MPa)

0.001 0.01 0.1 1 10 100

Lin

ear

Bu

rnin

g R

ate

(cm

/s)

0.001

0.01

0.1

1

10

100

Data of Andreev (1957) Data of Andreev (1940) 3% gelData of Andreev (1959) 3% gelCYCLOPS Code (NG4 Product Set)

NG


Flame Structure

Distance from Surface in Gas (cm)0.01 0.1 1

Gas

Tem

per

atu

re (

K)

500

1000

1500

2000

2500

3000

CYCLOPS Code PredictionVanderhoff, et al. (1992) by NO AbsorptionVanderhoff, et al. (1992) by OH Absorption

JA2 @ 16 atm

Distance from Surface in Gas (cm)0.01 0.1 1

NO

Mol

e F

ract

ion

0.00

0.05

0.10

0.15

0.20

0.25

CYCLOPS Code PredictionVanderhoff, et al. (1992)

JA2 @ 16 atm


Species Mole Fractions in the Dark-Zoneof Double-Base Propellant (~ M9)

P a ra m e te rs H e lle r &G o rd o n (1 9 55 )

L e ng e lle , e t a l.(19 8 4 )

V a nde r ho ff, e ta l. (1 9 9 1)

C Y C L O P S(p re se nt ca lc .)

P (a tm ) 1 6 9 1 7 1 7

T D Z (K ) 16 0 0 15 0 0 15 0 0 15 4 3

N O 24 % 21 % 24 % 25 %

C O 3 3 3 8 3 2

H 2 8 8 8

N 2 4 2 0.4

H 2 O 2 0 2 0 1 9

C O 2 1 0 9 1 0

H C N 0.4 0.4

C H 4 0.8 2 .6 0.9

C 2 H 4 0.8 0 .8 0.1

EXPERIMENTAL


Nitramine-Propellant Burning Rates& Flame Structure

RDX/TPE Propellant @ 293K:80% RDX, 20% BAMO/AMMO (50/50 Mix)

Pressure (MPa)

0.1 1 10 100

Lin

ear

Bu

rnin

g R

ate

(cm

/s)

0.01

0.1

1

10

Data of Zenin (2000)CYCLOPS: NTRB pyrolysis lawCYCLOPS: RDX/BA pyrolysis law


CHALLENGES&

OPPORTUNITIES


Barriers to Development of a Predictive Model

LIQUIDSOLID GASM

EL

T I

NT

ER

FA

CE

GA

S /

SU

RF

AC

E

• Chemical kinetics

• High-density transport

• Evaporation of mixtures

• Critical phenomena of mixtures

• Heterogeneous reactions

• Non-planar surface phenomena

• Reactions

• Bubble formation, dynamics

• Mixture equations of state

• Mixture molecular diffusion

• Mixture thermal conductivity

• Reactions

• Mixture equations of state

• Mixture thermal conductivity

• Mixture melting

• Polymer softening


Issues in Developing a Molecular-Dynamics Description of EM Combustion

• Gas phase:

– Most easily and accurately done with continuum-mechanics formulation (>80 species, 550 rxns)

• Condensed phases:

– no reliable reaction mechanisms, and those that exist have only a few reactions with uncertain rates

– MD would likely have no competitor for the foreseeable future

– How to couple a MD description with a continuum description of the gas-phase processes?

• Surface-regression mechanism:

– MD coupled with quantum-structure calculations might be able to rationalize pyrolysis law data and provide predictions

– How to couple a MD surface-regression mechanism to the continuum description of the gas phase, as in multi-component evaporation

• MD-calibrated continuum models the answer?


rz

d

L IQ U ID

G A S

a 0

z = 0

dV adadz2=a

n dV n dz r r drLJ2 ( )

612

4)(rr

rLJ

where

( ) ( ( )) ( ( ))d n f x d g x d 8 3 x dd

a( )

0

f xa

x

x x x xx( )

( ) ( ) ( ) ( )arctan ( )

1

10 9

9

8 1

63

48 1

315

192 1

945

384 1

105

384

105

7680

9

2 4 2 3 2 2 2

g xa

x

xx( )

( )arctan ( )

1

4 2 1

1

2 40

3

2

6

0

3

0

32

32

71

aanH vap

5 0 50.3

0.2

0.1

0

V( )d

d

(d)

Continuum Model of theMolecule/Liquid-Interface Potential


Heat-of-Vaporization Estimation Theory for Pure LJ Fluids(Gas-Phase LJ Parameters Used)

6

0

3

0

32

32

71

aanH vap


Vapor-Pressure Estimation Theory for Pure LJ Fluids

5 0 50.3

0.2

0.1

0

V( )d

d

out liq c e cn P E E v E E 1

4( ) ( )

E f H

f c c H

c

c

c vap

vap

1 2

1

26

0 725

9 8 10

.

.

pRT

RTM

vapout

4

8


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