BurningRate Models and Their Successors

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Burning-Rate Modelsand Their Successors

• Martin S. Miller
• MURI Kickoff Meeting
• 17 OCT 02

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Goals of Briefing

• Convey complexity of phenomena
• Concepts - continuum-mechanics paradigm
• Recent modeling approaches
• Frozen ozone
• RDX
• Propellants
• The MURI challenges

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PHENOMENA
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98 NC (13.16N)
2.8 mm/s _at_ 1 MPa
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28.7 NC(12.68N)22 Nitroglycerine47.3
Nitroguanidine
2.3 mm/s _at_ 1 MPa
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76 RDX (5 micron)12 CAB4 NC(12.6N)8
Energetic Plasticizer
0.8 mm/s _at_ 1 MPa
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80 HMX (200/20 micron)20 Polydiethylene Glycol
Adipate
0.5 mm/s _at_ 1 MPa
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CONCEPTS
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Propellant Combustion Modeling Abstraction
RDX Composite Propellant M43 _at_ 15.5 atm
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Conservation Equations for 1-D, Steady-State
Combustion at Constant Pressure
conduction
convection
diffusion
reaction
diffusion
convection
reaction
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Energy Fluxes at the Phase Boundaries
convection
diffusion
conduction
convection
T(x)
diffusion
conduction
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An Example of a Surface Regression
MechanismSingle-Component Evaporation
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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)

Solution eigenvalues xliq , Ts,
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Iteration Scheme for 3-Phase Problem
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MODELS
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Solid-Propellant Combustion-Modeling Timeline
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FROZEN OZONE
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Ozone Chemistry

• 3 Reversible Gas-Phase Reactions
• Heterogeneous Reaction Considered

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Frozen OzoneSimplest Case of 3-Phase
Deflagration
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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

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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

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Liquid-Layer Molecular Diffusion
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Calculational Price of Including Multi-Component
Evaporation in Continuum Model
Multi-Component Evaporation 6 species
Multi-Component Evaporation Ozone
Single-Component Evaporation Ozone
xliq
xliq
Ts
Ts
3 Eigenvalues 3 Nested Loops
62 Eigenvalues 62 Nested Loops
4 Eigenvalues 4 Nested Loops
(Assuming O atoms not in liq.)
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RDX
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RDX Burning-Rate Model Results Compared
Davidson Beckstead
Liau Yang
Prasad, Yetter, Smooke
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C-Phase Decomposition Mechanisms Used by
Different Models for RDX
3 CH2O 3 N2O DH570K - 47 kcal/mole
(DB, PYS, LY)
k1
RDX(liq.)

3 H2CN 3 NO2 DH570K 180 kcal/mole
(DB, PYS) 3 HCN 3 HONO DH570K 19
kcal/mole 3 HCN 3 NO2 3 H DH570K 256
kcal/mole 3 HCN (3/2) NO (3/2) NO2 (3/2)
H2O DH570K 34 kcal/mole (LY)
k2
k3
NO2 CH2O ? NO CO H2O DH570K - 42
kcal/mole (DB, PYS, LY)
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RDX Liquid-Phase Reactions Assumed by Different
Models
RDX gt (3/2)NO (3/2)NO2 (3/2)H2O
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GUN PROPELLANTS
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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

Gas-Phase Reactants
2 H2CO (CHO)2 2 NO2 NO CO HCO x
0.59
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
2 H2CO 2 NO2 HONO CO x 0.14
3 H2CO 2 NO2 CH2 x 0.27
GAS
SOLID
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Pyrolysis Laws from Zenin Microthermocouple Data
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CYCLOPS v1.0 Burning-Rate Predictorfor
Multi-Ingredient Propellants with NC
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Nitrate-Ester Linear Burning Rates
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Flame Structure
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Species Mole Fractions in the Dark-Zoneof
Double-Base Propellant ( M9)
EXPERIMENTAL
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Nitramine-Propellant Burning Rates Flame
Structure
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CHALLENGESOPPORTUNITIES
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Barriers to Development of a Predictive Model

• Chemical kinetics
• High-density transport

• Reactions
• Bubble formation, dynamics
• Mixture equations of state
• Mixture molecular diffusion
• Mixture thermal conductivity

• Reactions
• Mixture equations of state
• Mixture thermal conductivity

• Evaporation of mixtures
• Critical phenomena of mixtures
• Heterogeneous reactions
• Non-planar surface phenomena

• Mixture melting
• Polymer softening

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Issues in Developing a Molecular-Dynamics
Description of EM Combustion

• Gas phase
• Most easily and accurately done with
  continuum-mechanics formulation (gt80 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?

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Continuum Model of theMolecule/Liquid-Interface
Potential
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Heat-of-Vaporization Estimation Theory for Pure
LJ Fluids(Gas-Phase LJ Parameters Used)
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Vapor-Pressure Estimation Theory for Pure LJ
Fluids
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THE END