1. Multidisciplinary Modeling For Blanket Physics Ramakanth Munipalli, P.-Y. Huang, M.J.Pattison, C.M.Rowell, K.-Y. Szema HyPerComp Inc., 2629 Townsgate Rd., #105, Westlake Village, CA 91361 Alice Ying, Neil Morley, Mohamed Abdou, Sergey Smolentsev UCLA FNST Meeting, UCLA, August 18, 2009

2. TBM Assembly Solid breeder (HCCB) TBM Liquid breeder (DCLL) TBM Outline Progress towards a management software for multiphysical modeling (phase-I completed) Convergence acceleration for liquid metal MHD calculations (phase-II ongoing) Integrated modeling of transport processes in blanket flows (phase-I just started)

3. Helium Ferritic Steel SiC PbLi A Simulation Management System To create a simulation management software with integrated prediction capability for blanket modules (extendable to the divertor and other PFCs) operating in a fusion environment

4. (G) Code coupling and data exchange schematic

5. Highlights of development so far: CAD-centric (as opposed to mesh-centric) modeling Third party software gridding, setup, code launching Data transfer, interpolation across meshes and CAD CAD update, cleanup and deformation Automated mesh generation from blocking information A unified data format for simulation status Detailed GUI design

6. To be done: (Maturation to a complete system) Usage of native CAD formats – open source code from MOAB Usage of simplified primitive problems, leading to complex DCLL geometry Parameterization and feature-based gridding Post-processing – based on geometric primitives selected in problem setup Graphical interface to automate the entire process

7. Top level GUI and new project dialog box

8. Basic CAD editing tool

9. Region editing via CAD

10. Entity selection

11. Inner He Dist. Manifold (Circuit 2) First Wall Grid He Inlet Plenum Outer He Distribution Manifold (Circuit 2) Back Plate Outer He Distribution Manifold (Circuit 1) Inner He Distribution Manifold (Circuit 1) PbLi Outlet Channels (3) PbLi Inlet Channels (3) Grid Plate He Outlet Plenum He Outlet Plenum Divider Plate Plenum Grid Plates Standardization – Sample nomenclature

12. Helium Ferritic Steel SiC PbLi Pb 17 Li Helium Pb 17 LiPb 17 Li Helium Entity-wise grid generation with surface matching

13. Region definition

14. Region definition – grid view

15. Region definition – selection of solvers

16. Intersection of entities

17. BC specifications

18. Data transfer specification

19. Enabling technology: Strongly conservative interpolation

20. LOCAL BICUBIC SURFACE INTERPOLATION (1) Given points calculate control point and knot vector for a continuous surface satisfying The surfaces are obtained by constructing N*m bicubic surfaces.

21. Enabling technology: Parameterized geometry The potential use of templates

22. CAD to Mesh (ANSYS, HIMAG)

23. Flow Solution (HIMAG)

24. Structural Analysis (ANSYS), Interpolation of quantities to other physical solvers Handle deflection if present

25. STATUS Enabling technologies have been prepared: CAD-centric interpolation, data transfer, multisolver execution Preliminary demonstrations have been made A detailed GUI has been prepared

26. 3-D blanket with natural convection, Ha = 6350, N = 1032 ALEX circular-duct experiment, Ha = 6600, N = 10700 HIMAG is a complex geometry modeling software for incompressible two-phase flow MHD at fusion-relevant conditions. While its accuracy has been well established, we are seeking to improve its speed. HyPerComp Incompressible MHD solver for Arbitrary Geometry Free surface flow applications of HIMAG: EM sloshing of liquid metal Liquid metal jet in a magnetic field Ha = 10,000 flow in a square duct

27. Reasons why MHD solutions are slow to compute: 1.The need to resolve and minimize numerical errors in Hartmann layers (Thickness about 1/Ha) 2. The pace of convergence of Poisson equation solvers (for Pressure, Electric potential, divergence of B) 3.Computationally intensive corrections for non-orthogonal meshes 4.Long periods of integration needed to account for flow development, unsteady effects 5.Time taken to develop CAD to CFD mesh for high Ha problems

28. Mathematical methods Method of lines multigrid, FMG: CN, SIMPLE Implicit schemes – time stepping, accuracy CN, AB, SIRK schemes SIMPLE scheme for steady flow Local time stepping Krylov subspace, GMRES Interpolation procedures Data storage: Non-orthogonal correction Rapid prototyping Canonical decomposition of DCLL geometry User interfaces for inlet, fci, bend, etc. Template for multigrid (3-D) – dir. agglomeration Template for hybrid mesh generation blocking Applications of analysis EM coupling between neighboring channels Fringing fields, self-consistent field formulations Wall functions Patched analytical – numerical solution Combination of duct flow solutions Source code maintenance, user support User interfaces for mesh / multigrid template Source code maintenance GUIs for canonical problems Our Approach

29. Research Highlights: (a) Novel mathematical convergence acceleration techniques: HIMAG has been extended to include multigrid methods (sequence of meshes is generated automatically for complex geometries) Variety of implicit schemes included in HIMAG Implicit procedures and sensitivity of numerical parameters has been performed, for optimal code performance Jacobian-Free Newton-Krylov Method (b) Rapid prototyping capabilities in accelerating problem setup, Template based DCLL mesh generation is now possible (c) Variable fidelity modeling for developing better initial conditions and MHD-specific convergence acceleration procedures. (d) Routine use of hybrid meshes is now possible (e) Rapid interpolation across meshes and CPUs can be performed

30. Poisson solver with Neumann BCs Hunt’s fully developed channel flow 3-D circular duct Ha = 10, Re = 10, c w = 0.1 3-D rectangular duct Ha = 0, Re = 15,250 3-D rectangular duct Ha = 100, Re = 10, c w = 0.1 Poisson solver acceleration by sparse matrix storage and inversion

31. Ha = 0 Ha = 31.6 Ha = 100 A steady flow pressure correction solver (Can provide faster initial conditions to HIMAG even for unsteady flows)

32. A sequence of three meshes used in a traditional nested multigrid algorithm An unnested, automated approach to the multigrid method for complex geometries

33. Fully developed MHD result with un-nested multigrid

34. Automated production of multigrid mesh sequence Template based multigrid method is being used for complex geometries

35. Crank-Nicholson Scheme Adams-Bashforth schemes Hybrid Adams Schemes (Adams-Bashforth for convection and Adams-Moulton for viscous terms) 2 nd order 3 rd order Semi-Implicit RK schemes f – non-stiff terms g – stiff terms IMPLICIT SCHEMES (ongoing)

36. Mapping simpler solutions to complex geometries: Faster initialization

37. Propagation of flow profiles along channels with bend

38. Graphical Processing Units (GPUs) The GPU is a highly parallel, multi-threaded, many-core processor with tremendous computational horsepower and very high memory bandwidth. Significant speedup can be achieved using GPUs for data-parallel computational efforts. We have demonstrated good speed up on off- the-shelf GPUs for isolated hyperbolic equation solvers as well as for Poisson-type systems and are now porting this success to HIMAG.

39. High order accurate Poisson solver speedup Poisson solver speedup using GPUs

40. STATUS We have incorporated various new methods into HIMAG for speeding up calculations. Each of these methods comes with added sensitivities. However, a net speedup of an order of magnitude or more has been observed in many important problems. We hope to complete all code upgrades in about a year from now.

41. Integrated Mass Transport Prediction for Blanket Systems Mass transfer and solid-liquid interaction processes in blanket systems are strongly coupled with MHD flow physics in blanket systems. We are attempting to perform 3-D integrated simulations with best available submodels for these processes

42. Scope of this SBIR project Improved prediction of transport processes such as Tritium permeation, corrosion of structural materials, deposition phenomena under conditions of strong heat flux and fusion relevant magnetic fields. Physical models accommodated in a modular manner – scope for enhancement/revision Coupled multispecies Eulerian / Lagrangian framework will provide means to model particulate transport Code will be able to handle complex geometry and will couple with existing simulation software for other physics

43. Principal Tasks in Phase-I Model assessment Problem formulation Setup dilution approximation: Tritium transport Dilution of Iron in PbLi Dispersed phase model Implementation Verification Coupling strategies Verification and Validation, Sensitivity study

44. Issues to be Considered How does radiation affect trap sites and porosity of steels? Suitable model for nucleation of Tritium – impurity particles/ionisation from radiation Require accurate values for transport coefficients and dissociation/recombination Fluid flow field, MHD effects and temperature field are all coupled and will affect the mass transport. Need to work toward a full model incorporating all these effects.

45. General Equation for Species Transport Source term Soret coefficient AdvectionDiffusionThermopheresis Trapping coefficientRelease coefficient Concn. of species i Trapped particles Empty trap sites Total trap sites Consider the transport of a passive scalar. Important terms arise from advection and diffusion as well as sources due to radioactive or chemical processes.

46. Boundary Conditions = no. of atoms “s” in “m” dissociationrecombination Sievert’s Law Diffusion-limited transfer through wall When absorbed by metals, tritium molecules dissociate into individual atoms – where dissociation and recombination effects dominate, net flow to surface given by: Full equation for interface is: diffusion dissociation into m reaction with another species

47. Diffusion Coefficients for PbLi Typically use equation of form Factor of 3 differences at 540ºC Note that diffusion through steel may be order of magnitude higher May get high concentration gradients at wall boundaries as T diffuses into wall – time scale for diffusion from bulk to walls much greater than recirculation time. D0D0 E0E0 D at 540ºCSource 4.03 × 10 -8 -195002.25 × 10 -9 Reiter, 1991 2.3 × 10 -9 -66008.66× 10 -10 Shibuya et al., 1987 2.99 × 10 -8 -168712.46× 10 -9 Aiello & Ciampichetti, 2004

48. Solubility of Tritium in PbLi Typically use equation of form Factor 50 difference at 540ºC Solubility is low – values may not be accurate, particularly those obtained with absorption methods Due to low solubility, may get bubble formation – require suitable model for nucleation S0S0 ESES Source 1.24× 10 -3 -1350Reiter, 1991 5.733-32236Aiello & Ciampichetti, 2004

49. Corrosion of Steel Components One can construct simple models for erosion and deposition of iron with a knowledge of solubility and diffusion coefficients. These can then be coupled to a flow field from CFD analysis (e.g. Mistalangelo, 2007). Experimental work in Latvia has shown MHD effects not only enhance corrosion rate of EUROFER, but result in uneven erosion with wave-like structures. Explained as being due to feedback effects: – Higher erosion rates are associated with high velocity gradients at wall. – Higher velocity gradients are higher where depth of erosion is greater.