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**Multiphase Flow in ALE3D**

Presented by: David Stevens Lawrence Livermore National Laboratory UCRL-PRES

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**Introduction to multiphase flow**

Spherical Charge Figure 3 from Fan Zhang et. Al., “Explosive Dispersal of Solid Particles”, Shock Waves, 11, , 2001. High speed photographs of a 10.6 cm radius charge Frames separated ms The goal is to develop a numerical method capable of accurately capturing such shock/turbulence interactions.

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**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 Interactions**

The Hydrodynamic phase is composed of a nodal ALE phase and a species Riemann update. The model equations are time-split into a pure hydrodynamic phase and a multiphase relaxation phase.

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**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.

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**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.

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**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**

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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..

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**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.

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**Initial Rogue Shock Tube Comparison**

Numerical results agree well with the experimental data. The simulated fluidized bed is slightly ahead of the experimental observations.

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**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

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**Improved Numerics and Mesh Resolution (AMR)**

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

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**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

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**Numerical Method Comparison Shock 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.

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**Local versus Global Mesh Refinement**

Local mesh refinement is able to preserve the gains observed with AUSF when compared with global mesh refinement. NX 50 NX 100 NX 200 NX 400 Level 1 Level 2 Level 3 Level4

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**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

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**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)

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**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

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**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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