Modelling detonation waves in heterogeneous energetic materials

The computation of detonation waves in heterogeneous explosives involves compressible multiphase mixtures due to the chemical decomposition of the energetic material as well as its heterogeneous initial formulation. Also material interfaces are present between the explosive and the surrounding inert or reactive materials. We develop a new method for the modelling of interface problems and multiphase mixtures in the particular limit where phases pressures and velocities relax towards equilibrium very fast. This method is a variant of the discrete equations for multiphase mixtures proposed by Abgrall and Saurel [J. Comput. Phys. 186 (2) (2003) 361]. The new discrete model is adapted to reacting flows with mass, momentum and energy transfer. The model is based on the pure material equation of state only (no mixture equation of state is used) for the computation of the reaction zone of detonation waves. The algorithm is full Eulerian and fulfills interface conditions between mixtures and pure materials automatically. It is validated over a set of difficult test problems with exact solution and its multi-dimensional capabilities are shown over problems involving a large number of materials.

[1]  T. Young,et al.  CHEMEQ - A Subroutine for Solving Stiff Ordinary Differential Equations , 1980 .

[2]  M. Lallemand,et al.  Pressure relaxation procedures for multiphase compressible flows , 2005 .

[3]  R. Abgrall.  How to Prevent Pressure Oscillations in Multicomponent Flow Calculations , 1996 .

[4]  Richard Saurel,et al.  Mathematical and numerical modeling of two-phase compressible flows with micro-inertia , 2002 .

[5]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[6]  Keh-Ming Shyue,et al.  An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems , 1998 .

[7]  Alexandre J. Chorin,et al.  Random choice methods with applications to reacting gas flow , 1977 .

[8]  D. Benson.  Computational methods in Lagrangian and Eulerian hydrocodes , 1992 .

[9]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[10]  M. Baer,et al.  A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials , 1986 .

[11]  G. Strang.  On the Construction and Comparison of Difference Schemes , 1968 .

[12]  P. Raviart,et al.  Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.

[13]  Steven F. Son,et al.  Two-phase modeling of DDT: Structure of the velocity-relaxation zone , 1997 .

[14]  Ronald Fedkiw,et al.  An Isobaric Fix for the Overheating Problem in Multimaterial Compressible Flows , 1999 .

[15]  R Abgrall.  HOW TO PREVENT PRESSURE OSCILLATIONS IN MULTICOMPONENT FLOWS: A QUASI-CONSERVATIVE APPROACH , 1996 .

[16]  Rémi Abgrall,et al.  Proposition de méthodes et modèles eulériens pour les problèmes à interfaces entre fluides compressibles en présence de transfert de chaleur , 2002 .

[17]  R. Abgrall,et al.  A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows , 1999 .

[18]  D. Stewart,et al.  Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations , 2001 .

[19]  Richard Saurel,et al.  Modelling evaporation fronts with reactive Riemann solvers , 2005 .

[20]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[21]  Jean-Marc Hérard,et al.  Some recent finite volume schemes to compute Euler equations using real gas EOS , 2002 .

[22]  B. V. Leer,et al.  A quasi-steady state solver for the stiff ordinary differential equations of reaction kinetics , 2000 .

[23]  Steven F. Son,et al.  Two-Phase Modeling of DDT in Granular Materials: Reduced Equations , 2000 .

[24]  Smadar Karni,et al.  Multicomponent Flow Calculations by a Consistent Primitive Algorithm , 1994 .

[25]  Richard Saurel,et al.  A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation , 2001, Journal of Fluid Mechanics.

[26]  D. Mott,et al.  New Quasi-Steady-State And Partial-Equilibrium Methods For Integrating Chemically Reacting Systems , 1999 .

[27]  Rémi Abgrall,et al.  A Simple Method for Compressible Multifluid Flows , 1999, SIAM J. Sci. Comput..

[28]  Smadar Karni,et al.  Hybrid Multifluid Algorithms , 1996, SIAM J. Sci. Comput..

[29]  Rémi Abgrall,et al.  Discrete equations for physical and numerical compressible multiphase mixtures , 2003 .

[30]  P. B. Butler,et al.  Shock Development and Transition to Detonation Initiated by Burning in Porous Propellant Beds , 1981 .

[31]  Heuzé.  Equations of state of detonation products: Influence of the repulsive intermolecular potential. , 1986, Physical review. A, General physics.

[32]  S. Marsh.  Lasl Shock Hugoniot Data , 1980 .

[33]  J. Chan,et al.  Shock initiation and detonation models in one and two dimensions. [PBX-9404, RX-03-BB] , 1979 .

[34]  J. Craggs.  Applied Mathematical Sciences , 1973 .