Multiphase Flow in ALE3DMultiphase Flow in ALE3D

Presented by:

David Stevens

Lawrence Livermore National Laboratory

UCRL-PRES-214865

Introduction to multiphase flowIntroduction to multiphase flow

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-

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

Spherical Charge

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.

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The Treatment of the Multiphase InteractionsThe 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 quantitiesThe 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.

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V&V for multiphase modelV&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

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.

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Under the hood:The Lagrangian system of primitive variables

Under the hood:The Lagrangian system of primitive variables

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Rogue Shock TubeRogue 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 TubeThe 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 ComparisonInitial 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 TransitionDeflagration 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.

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Improved Numerics and Mesh Resolution (AMR)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

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

Improved Numerical MethodsImproved 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

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.

AUSF HLL Rusanov

AUSF HLL Rusanov

Local versus Global Mesh RefinementLocal versus Global Mesh Refinement

Level 1 Level 2 Level 3 Level4

NX 50 NX 100 NX 200 NX 400

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

Preferred Numerical DirectionsPreferred 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

Cross-section of density field

Lineouts at 30, 45, and 60 degrees

Higher refinement reduces this problem

Further evaluation is required when SAMRAI multiblock capacities are brought online

Gradient ResolutionGradient 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.

Density lineout tangent to shockwave

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

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

NX 50 NX 100

High performance ComputingHigh 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 DevelopmentsConclusions And Future Developments

Transition to turbulence studies: Rayleigh-Taylor, Richtmyer-

Meshkov instabilities

Multilevel, multiphase V&V.Deflagration to Detonation

studies (DDT)Dynamically fluidized beds.

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.