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

Multiphase Flow in ALE3D

Presented by:

David Stevens

Lawrence Livermore National Laboratory

UCRL-PRES-214865


Introduction to multiphase flow

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

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 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

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

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

Water

Air

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

Under the hood:The Lagrangian system of primitive variables


Rogue shock tube

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

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

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

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.

5.3

1.1

0.5


Improved numerics and mesh resolution amr

  • 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

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 comparison shock tube analysis

    Numerical Method ComparisonShock Tube Analysis

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

    AUSF

    HLL

    Rusanov

    AUSF

    HLL

    Rusanov

    Density comparison for 200 zones.

    Contact discontinuity at 200 zones.


    Local versus global mesh refinement

    NX 50

    NX 100

    NX 200

    NX 400

    Level 1

    Level 2

    Level 3

    Level4

    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

    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

    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

    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

    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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