Multiphase flow in ale3d
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Multiphase Flow in ALE3D. Presented by: David Stevens Lawrence Livermore National Laboratory. UCRL-PRES-214865. Introduction to multiphase flow. Spherical Charge. Figure 3 from Fan Zhang et. Al., “Explosive Dispersal of Solid Particles”, Shock Waves , 11 , 431-443, 2001.

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Multiphase Flow in ALE3D

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Multiphase Flow in ALE3D

Presented by:

David Stevens

Lawrence Livermore National Laboratory


Introduction to multiphase flow

Spherical Charge

  • Figure 3 from Fan Zhang et. Al., “Explosive Dispersal of Solid Particles”, Shock Waves, 11, 431-443, 2001.

    • High speed photographs of a 10.6 cm radius charge

    • Frames separated 0.25-0.50 ms

  • The goal is to develop a numerical method capable of accurately capturing such shock/turbulence interactions.

The Multiphase Equations (2-Phase)

  • High particle number concentrations often preclude the use of stochastic particle techniques.

  • The continuum two-phase model of Baer and Nunziato (SNL) with modifications form the basis of the implementation.

  • Each phase is described by evolution equations for mass, momentum, internal energy and volume fraction.

The Treatment of the Multiphase Interactions

  • The model equations are time-split into a pure hydrodynamic phase and a multiphase relaxation phase.

  • The Hydrodynamic phase is composed of a nodal ALE phase and a species Riemann update.

The zonal Riemann update for species quantities

  • A Riemann solver is used to evaluate the species quantities.

  • The Riemann solve is just a new “edge state” formalism that replace the original upwind “edge state” formalism of the Van Leer based advection for zonal scalars remap.

  • Edge states from the advection are cached and converted into fluxes. The combination of a Van Leer predictor followed by a Riemann solve corrector is a standard second-order formalism.

V&V for multiphase model

  • One Dimensional test cases

    • Andrianov’s analytic solutions

    • Rogue et al’s shock tube.

    • Water/air shock tube.

  • Multi-dimensional test cases

    • Zhang particle dispersion experiments (DRDC).

  • Applied Problems

    • Particle dispersion.

    • Particle Jets.

    • DDT.

    • Deflagration modes in HE and propellants.



Method Comparison on the Water-Air Shock Tube

  • High pressure liquid expanding into low pressure air.

  • Challenging problem due to the wide range in densities and sound speeds.

  • Several Riemann Solvers have been compared.

    • Rusanov is a single wave solver.

    • ASW and AUFS are seven wave Riemann solvers.

    • The presence of a predictor appears to outweigh the full amount of terms in the predictor.

Under the hood:The Lagrangian system of primitive variables

Rogue Shock Tube

  • At left is Figure 11 from Rogue, Rodriguez, Haas, and Saurel’s: “Experimental and numerical investigation of the shock-induced fluidization of a particle bed, Shock Waves, 8, 29-45, 1998.

  • This is a series of shadowgraphs of a 2 mm bed of nylon beads being accelerated by a Ma 1.3 shock. Each panel represents a different time in the experiment..

The Rogue Shock Tube

  • Above is Figure 15 from Rogue, et al.

  • Top left is the particle cloud density at 100 us.

  • Bottom right is the gas pressure.

Initial Rogue Shock Tube Comparison

  • Numerical results agree well with the experimental data.

  • The simulated fluidized bed is slightly ahead of the experimental observations.

Deflagration to Detonation Transition

  • The multiphase model has replicated the experimental and simulation results from Baer et al., Combustion and Flame, 65, 15.

  • Detonation Front speeds agree with observations and Mel’s original simulations in both the convective, compressive and detonation regions of the flow.




  • Adaptive mesh refinement is one method for achieving high resolution without imposing O(n4) growth in computational requirements.

Improved Numerics and Mesh Resolution (AMR)

  • Following are simple examples from prototype 1D and 3D shock physics simulations using a combined ALE3D/SAMRAI model.

  • Mathew Dawson (DHS Summer Intern, 2005) examined the role of:

    • Numerical method

    • Number of elements

    • Refinement levels

    • Refinement factor

    • Mesh efficiency

Improved Numerical Methods

  • Traditional methods efficiently track shocks

  • Improved methods required for accurate modeling

    • Actual fluid motion

    • Contact discontinuities

  • HLL, typical numerical method used in production models

    • Carbuncle instability and spurious sollutions

    • HLL/C efficient and robust but adds excessive diffusion around contact discontinuities

  • Artificially upstream flux vector splitting (AUFS)

    • Robust, feasible, reliable

    • Provides resolution on discontinuities and clean solutions

      • Avoids carbuncle instability and kinked mach stems

    • The following 3D results focus on the second-order predictor-corrector AUFS model

  • Numerical Method ComparisonShock Tube Analysis

    • With increasing resolution, AUSF exhibits dramatically better convergence for contact discontinuities







    Density comparison for 200 zones.

    Contact discontinuity at 200 zones.

    NX 50

    NX 100

    NX 200

    NX 400

    Level 1

    Level 2

    Level 3


    Local versus Global Mesh Refinement

    • Local mesh refinement is able to preserve the gains observed with AUSF when compared with global mesh refinement.

    Preferred Numerical Directions

    • Rectangular meshes tend to imprint directional character on spherical problems

    • This problem is influenced by both the numerical method and the accuracy used

    • Higher refinement reduces this problem

  • Further evaluation is required when SAMRAI multiblock capacities are brought online

  • Lineouts at 30, 45, and 60 degrees

    Cross-section of density field

    Gradient Resolution

    • Gradients in 3D are prone to smearing

    • Mitigation of gradient diffusion achieved through increasing refinement

      • Density gradient larger for a tangent lineout as radial resolution increases.

    NX 50

    NX 100

    Density lineout tangent to shockwave

    Density 2D slice using HLL Solver (NX =100)

    Density 2D slice using HLL Solver (NX =50)

    High performance Computing

    • Simulations on 3600 processors were completed successfully

      • Demonstrating robustness of code

      • Optimal refinement parameters in 3D

        • Based on computational efficiency

      • Overall interface and operation capability

    3D Display of zones and corresponding levels with density slice

    3D Display magnified with enhanced zones on the left

    Conclusions And Future Developments

    • Multi-wave Riemann solvers exhibit more accurate results on many Multiphase problems.

    • This performance is reduced by a lack of robustness on more complex problems.

    • Transition to turbulence studies:

      • Rayleigh-Taylor, Richtmyer-Meshkov instabilities

  • Multilevel, multiphase V&V.

  • Deflagration to Detonation studies (DDT)

  • Dynamically fluidized beds.

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