Weapons and Materials Research Burning-Rate Models and Their Successors Martin S. Miller MURI Kickoff Meeting 17 OCT 02

Weapons and Materials Research Goals of Briefing Convey complexity of phenomena Concepts - continuum-mechanics paradigm Recent modeling approaches Frozen ozone RDX Propellants The MURI challenges

Weapons and Materials Research PHENOMENA

Weapons and Materials Research 98% NC (13.16%N) MPa

Weapons and Materials Research 28.7% NC(12.68%N) 22% Nitroglycerine 47.3% Nitroguanidine MPa

Weapons and Materials Research 76% RDX (5 micron) 12% CAB 4% NC(12.6%N) 8% Energetic Plasticizer MPa

Weapons and Materials Research 80% HMX ( 200/20 micron) 20% Polydiethylene Glycol Adipate MPa

Weapons and Materials Research CONCEPTS

Weapons and Materials Research Propellant Combustion & Modeling Abstraction RDX Composite Propellant 15.5 atm

Weapons and Materials Research Conservation Equations for 1-D, Steady-State Combustion at Constant Pressure conductionconvectiondiffusionreaction diffusionconvectionreaction

Weapons and Materials Research Energy Fluxes at the Phase Boundaries convection diffusion conduction T(x)

Weapons and Materials Research An Example of a Surface Regression Mechanism: Single-Component Evaporation

Weapons and Materials Research 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, T s ) Solution eigenvalues: x liq, T s, }

Weapons and Materials Research Iteration Scheme for 3-Phase Problem

Weapons and Materials Research MODELS

Weapons and Materials Research Solid-Propellant Combustion-Modeling Timeline

Weapons and Materials Research FROZEN OZONE

Weapons and Materials Research 3 Reversible Gas-Phase Reactions Heterogeneous Reaction Considered Ozone Chemistry

Weapons and Materials Research Frozen Ozone: Simplest Case of 3-Phase Deflagration

Weapons and Materials Research Comparison of Ozone Model to Experiment 10% O 2 / 90% O 3 liquid at 90 K: r exptl ~ 0.4 cm/s (Streng 1960) Single-component evaporation model with mixture-corrected liquid density, thermal conductivity, and enthalpy: r calc = 0.30 cm/s What can explain the discrepancy? Multi-component Evaporation Liquid-Phase Diffusion O3/O2 Phase Separation in Liquid

Weapons and Materials Research Multi-component Evaporation in Ozone Model O 2 at surface evaporates faster than O 3, enriching the surface concentration of O 3 from feedstock value O 3 surface concentration becomes new eigenvalue; necessitates 4th iteration loop Necessitates consideration of molecular diffusion in the liquid phase

Weapons and Materials Research Liquid-Layer Molecular Diffusion

Weapons and Materials Research Calculational Price of Including Multi-Component Evaporation in Continuum Model x liq TsTs TsTs Multi-Component Evaporation – Ozone Single-Component Evaporation – Ozone 3 Eigenvalues 3 Nested Loops 4 Eigenvalues 4 Nested Loops Multi-Component Evaporation – 6 species 6+2 Eigenvalues 6+2 Nested Loops (Assuming O atoms not in liq.)

Weapons and Materials Research RDX

Weapons and Materials Research RDX Burning-Rate Model Results Compared Davidson & Beckstead Liau & YangPrasad, Yetter, & Smooke

Weapons and Materials Research C-Phase Decomposition Mechanisms Used by Different Models for RDX 3 CH2O + 3 N2O  H 570K = - 47 kcal/mole (D&B, PY&S, L&Y) 3 H2CN + 3 NO2  H 570K = kcal/mole (D&B, PY&S) 3 HCN + 3 HONO  H 570K = + 19 kcal/mole 3 HCN + 3 NO2 + 3 H  H 570K = kcal/mole 3 HCN + (3/2) NO +(3/2) NO2 + (3/2) H2O  H 570K = + 34 kcal/mole (L&Y) RDX(liq.) { NO2 + CH2O  NO + CO + H2O  H 570K = - 42 kcal/mole (D&B, PY&S, L&Y) k1 k2 k3

Weapons and Materials Research RDX Liquid-Phase Reactions Assumed by Different Models ** RDX => (3/2)NO + (3/2)NO2 + (3/2)H2O

Weapons and Materials Research GUN PROPELLANTS

Weapons and Materials Research 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 = A s exp(-E s /RT s ) NG 2 H 2 CO + 2 NO 2 + HONO + CO [ 2 H 2 CO + 2 NO 2 + HONO + CO ] x 0.14 [ 2 H 2 CO + (CHO) NO 2 + NO + CO + HCO ] x 0.59 [ 3 H 2 CO + 2 NO 2 + CH 2 ] x 0.27 } 2.3 H 2 CO (CHO) NO HONO NO CO HCO CH 2 Gas-Phase Reactants GASSOLID

Weapons and Materials Research “Pyrolysis” Laws from Zenin Microthermocouple Data

Weapons and Materials Research CYCLOPS v1.0: Burning-Rate Predictor for Multi-Ingredient Propellants with NC

Weapons and Materials Research Nitrate-Ester Linear Burning Rates

Weapons and Materials Research Flame Structure

Weapons and Materials Research Species Mole Fractions in the Dark-Zone of Double-Base Propellant (~ M9) EXPERIMENTAL

Weapons and Materials Research Nitramine-Propellant Burning Rates & Flame Structure

Weapons and Materials Research CHALLENGES & OPPORTUNITIES

Weapons and Materials Research Barriers to Development of a Predictive Model 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

Weapons and Materials Research 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?

Weapons and Materials Research Continuum Model of the Molecule/Liquid-Interface Potential

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

Weapons and Materials Research Vapor-Pressure Estimation Theory for Pure LJ Fluids

Weapons and Materials Research THE END