Presentation on theme: "Multiphase Flow in ALE3D"— Presentation transcript:
1Multiphase Flow in ALE3D Presented by:David StevensLawrence Livermore National LaboratoryUCRL-PRES
2Introduction to multiphase flow Spherical ChargeFigure 3 from Fan Zhang et. Al., “Explosive Dispersal of Solid Particles”, Shock Waves, 11, , 2001.High speed photographs of a 10.6 cm radius chargeFrames separated msThe goal is to develop a numerical method capable of accurately capturing such shock/turbulence interactions.
3The 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.
4The 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.
5The 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.
6V&V for multiphase model One Dimensional test casesAndrianov’s analytic solutionsRogue et al’s shock tube.Water/air shock tube.Multi-dimensional test casesZhang particle dispersion experiments (DRDC).Applied ProblemsParticle dispersion.Particle Jets.DDT.Deflagration modes in HE and propellants.
7Method 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.
8Under the hood: The Lagrangian system of primitive variables
9Rogue Shock TubeAt 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..
10The 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.
11Initial Rogue Shock Tube Comparison Numerical results agree well with the experimental data.The simulated fluidized bed is slightly ahead of the experimental observations.
12Deflagration 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.188.8.131.52
13Improved 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 methodNumber of elementsRefinement levelsRefinement factorMesh efficiency
14Improved Numerical Methods Traditional methods efficiently track shocksImproved methods required for accurate modelingActual fluid motionContact discontinuitiesHLL, typical numerical method used in production modelsCarbuncle instability and spurious sollutionsHLL/C efficient and robust but adds excessive diffusion around contact discontinuitiesArtificially upstream flux vector splitting (AUFS)Robust, feasible, reliableProvides resolution on discontinuities and clean solutionsAvoids carbuncle instability and kinked mach stemsThe following 3D results focus on the second-order predictor-corrector AUFS model
15Numerical Method Comparison Shock Tube Analysis With increasing resolution, AUSF exhibits dramatically better convergence for contact discontinuitiesAUSFHLLRusanovAUSFHLLRusanovDensity comparison for 200 zones.Contact discontinuity at 200 zones.
16Local versus Global Mesh Refinement Local mesh refinement is able to preserve the gains observed with AUSF when compared with global mesh refinement.NX 50NX 100NX 200NX 400Level 1Level 2Level 3Level4
17Preferred Numerical Directions Rectangular meshes tend to imprint directional character on spherical problemsThis problem is influenced by both the numerical method and the accuracy usedHigher refinement reduces this problemFurther evaluation is required when SAMRAI multiblock capacities are brought onlineLineouts at 30, 45, and 60 degreesCross-section of density field
18Gradient Resolution Gradients in 3D are prone to smearing Mitigation of gradient diffusion achieved through increasing refinementDensity gradient larger for a tangent lineout as radial resolution increases.NX 50NX 100Density lineout tangent to shockwaveDensity 2D slice using HLL Solver (NX =100)Density 2D slice using HLL Solver (NX =50)
19High performance Computing Simulations on 3600 processors were completed successfullyDemonstrating robustness of codeOptimal refinement parameters in 3DBased on computational efficiencyOverall interface and operation capability3D Display of zones and corresponding levels with density slice3D Display magnified with enhanced zones on the left
20Conclusions 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 instabilitiesMultilevel, multiphase V&V.Deflagration to Detonation studies (DDT)Dynamically fluidized beds.