Applications of the Multi-Material DEM Model

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Applications of the Multi-Material DEM Model

• Presented by
• David Stevens, Jaroslaw Knap, Timothy Dunn
• September 2007
• Lawrence Livermore National Laboratory

This work was performed under the auspices of the
U.S. Department of Energy by the University of
California Lawrence Livermore National Laboratory
under Contract No. W-7405-Eng-48.
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Introduction

• Multiphase flow is important in many shock-driven
  applications
• This talk will describe several ways in which we
  have adapted the multiphase DEM method of
  Chinnayya et al to handle
• Complex geometries
• Curvi-Linear coordinates
• Deviatoric strength
• Interface reconstruction
• Adaptive mesh refinement.

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Multiphase flow model development

• The multiphase model is built upon an Eulerian
  treatment of each phase.
• This treatment uses a hierarchy of flux-nozzling
  pairs defined by the number of waves used in the
  numerical solver.
• Saurell and Abgrall (1999) are the basis for the
  flux-nozzling pairs for the Rusanov (1 wave) and
  HLL (2 waves) solvers.
• The DEM method of Chinnayya et al. (2003) allows
  the use of HLLC.

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DEM Generalizations

• The following formulation is not limited to the
  Euler Equations

Upon Integration by Parts and simplifying
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Discrete Equation Method

• The most promising model is DEM or Discrete
  Equation Method and is based on an acoustic
  Riemann Solver.
• DEM allows the use of very sophisticated single
  phase solvers in a multiphase context.
• Flows with deviatoric stresses can easily be
  incorporated.
• The following results were presented at the
  latest International Detonation Symposium in
  2006.

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AUSF

• AUSF (Sun and Takayama, JCP, 2003) is the Riemann
  solver used in our version of DEM.
• Extends easily to unstructured meshes
• Extends easily to arbitrary equations of state.

Coordinate Rotation and Wave Selection
In 1D this method is identical to HLLC.
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AUSF Validation

• We have compared AUSF on a number of analytic
  planar and spherical test problems

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The Rogue Shock Tube

• At right is Figure 15 from Experimental and
  numerical investigation of the shock-induced
  fluidization of a particle bed, Shock Waves, 8,
  29-45, 1998.
• Numerical results agree well with the
  experimental data.
• The simulated fluidized bed is slightly ahead of
  the experimental observations.

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Numerical Method Comparison

• Fan Zhang et. al., Explosive Dispersal of Solid
  Particles, Shock Waves, 11, 431-443, 2001 has
  proven to be a useful data set for model
  validation.
• DEM appears to best match the experimental data.

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Reactive Multiphase flows

• Long mixing time scales are often the rate
  limiting step for many turbulent reacting flows.
• Air and fuel products can compete as oxidizers in
  cases when combustion of embedded metals is
  present.
• Mixing effects on reaction rates
• Pre-initiation
• Enhancement of slower rate reactions
• Extended reaction times
• Long-lived non-reacted fuel parcels.
• These mixing effects require a model for
  subgrid-scale heterogeneity.

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Prescribed PDF Methods for Reactive flows

• Mixture fraction and reaction progress variables
  are powerful tools for simplifying reaction
  chemistry.
• Several widely used closures result from assuming
  a prescribed beta PDF for the mixture fraction.
• Simple covariance closures
• Flamelet models
• Infinitely fast chemistry
• Binned PDF for use with an equilibrium chemistry
  package.
• Finite rate kinetics

Beta PDF distribution
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Infinite Rate Chemistry

• Single Reaction model loosely based on Kuhl,
  Howard, and Fried, Proceedings 34th Int.. ICT
  conference Energetic Materials Reactions of
  Propellants, Explosives, and Pyrotechnics, 2003.
• Detonation Products (F) mix with air (A) to
  completely combust to product (P).

Figure 4. Le Chatelier diagram for combustion of
TNT explosion products in air.
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Equilibrium Chemistry

• The mean and varience of the mixture fraction PDF
  is tracked in this simulation.
• The mixture fraction is defined as 1 inside the
  charge and 0 outside.
• Only the adiabat for the pure fuel stage at high
  energies is needed.
• Upon mixing at lower energies, an entire plane of
  equilibrium calculations are needed.

Charge Position
4 inch L/D1 TNT cylinder detonation in Air
Equilibrium chemistry calculations as a function
of T,P and Mixture fraction.
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Adaptive Mesh Refinement (AMR)

• Our approach to AMR combines block structured AMR
  and an unstructured local discretization.
• The unstructured local discretization handles
  reduced and enhanced connectivity in the form of
  multi-block meshes with no modification to the
  numerics.
• Block Structured AMR is used to handle
  inter-domain communication via rotations and
  translations. All O(n2) operations have been
  eliminated.
• Zone-centered data for all state variables
  dramatically simplifies computer science
  requirements.

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Summary

• We have describes ways in which we have adapted
  DEM to incorporate additional physics and
  geometrical complexity
• turbulent and kinetic effects are being
  incorporated by the use of assumed subgrid PDF
  methods
• Particle size distributions.
• Burned as Mixed model.
• Equilibrium Chemistry.
• Progress variables for finite rate kinetics.
• AMR,
• deviatoric strength
• interface reconstruction.