Interface treatment for computational thermo-fluid-structure interaction

Transcription

1 European Trilinos User Group meeting Munich, June 2013, Germany Interface treatment for computational thermo-fluid-structure interaction Georg Hammerl Institute for Computational Mechanics Caroline Danowski, Alexander Popp, Lena Yoshihara, Wolfgang A. Wall Institute for Computational Mechanics Muzio Grilli, Vito Pasquariello, Stefan Hickel, Nikolaus A. Adams Institute of Aerodynamics and Fluid Mechanics Technische Universität München (TUM) Germany

2 Outline Motivation and Introduction Immersed Interface Method for the Fluid Monolithic Thermo-Structure Interaction (TSI) Approach Thermo-Fluid-Structure Interaction (TFSI) Numerical Example Conclusion and Outlook 2

3 Motivation Failure of an Ariane 5 ECA (ESA) in 2002: The independent Inquiry Board reported: The most likely cause for the failure of Flight 157 was the combination of two factors [ ]. [Firstly,] the degraded thermal condition of the nozzle, caused by cracks in the cooling tubes. [Secondly,] the non-exhaustive definition of loads to which the Vulcain 2 engine is subject during flight. (Snecma Magazine, April 2003) Vulcain 2 engine Oscillation modes of a nozzle due to side loads: pendulum, ovalisation, bending [Frey, 2001] 3

4 Introduction Target: A coupled simulation considering fluid, structure and temperature Large-eddy simulation (LES) of turbulent flow including shockboundary-layer interaction Highly nonlinear structural problem (material/geometry) Very high temperature gradients Loose coupling of an immersed interface method for the fluid and a monolithic thermo-structure interaction approach for the solid Focus on the thermal coupling using a fixed interface Mortar coupling with dual Lagrange multipliers for nonconforming interface meshes 4

5 Outline Motivation and Introduction Immersed Interface Method for the Fluid Monolithic Thermo-Structure Interaction (TSI) Approach Thermo-Fluid-Structure Interaction (TFSI) Numerical Example Conclusion and Outlook 5

6 Field Equations of the Fluid Three-dimensional compressible Navier-Stokes equations in conservative form State vector Flux vector with viscous stress tensor heat flux 6

7 Immersed Interface Method Level set function: Geometry of the interface described by a signed wall distance function Interface between fluid and solid defined by the zero level set contour In cut cells: Level set function allows for the computation of interface normals face apertures interface surface extension fluid volume fraction 7

8 Conservative Interface Local modification of the finite volume scheme in the cut cells with pressure viscous effects heat transfer 8

9 Outline Motivation and Introduction Immersed Interface Method for the Fluid Monolithic Thermo-Structure Interaction (TSI) Approach Thermo-Fluid-Structure Interaction (TFSI) Numerical Example Conclusion and Outlook 9

10 Field Equations of TSI Structural field Balance of linear momentum (thermoelasticity) Thermal field Instationary heat conduction with linear, isotropic Fourier's law 10

11 Monolithic TSI System of Equations Large linear block system of equations Solver details: Computational modelling of the volumecoupled problem of thermo-structure interaction by Caroline Danowski (Tuesday morning) 11

12 Outline Motivation and Introduction Immersed Interface Method for the Fluid Monolithic Thermo-Structure Interaction (TSI) Approach Thermo-Fluid-Structure Interaction (TFSI) Numerical Example Conclusion and Outlook 12

13 Coupling of INCA and BACI Two in-house research simulation tools Fluid code INCA of the AER written in Fortran 90 TSI code (part of BACI) of the LNM written in C++ Multiple Program Multiple Data (MPMD) MPI application Single parallel simulation is started within one MPI_COMM_WORLD communicator MPI_COMM_SPLIT used to get local communicators MPI_INTERCOMM_CREATE is used to build point-to-point communication between both codes local communicator local communicator intercommunicator Trilinos 13

14 Coupling of INCA and BACI The TFSI code heavily relies on Trilinos under the hood Iterative solver Aztec_MSR Parallelization based on Epetra_Map Sparse matrix storage via Epetra_CrsMatrix Matrix-matrix computation based on EpetraExt Epetra_Import and Epetra_Export for data gathering and broadcast Smart pointer Teuchos::RCP for garbage collection Last missing piece was Teuchos::TimeMonitor::summarize (thanks to Mark Hoemmen) Important: MPI_COMM_WORLD free zone 14

15 Coupling Conditions of TFSI No slip condition Balance of forces Temperature coupling Balance of heat fluxes 15

16 Dirichlet-Neumann Partitioning Step 1 : Dirichlet values of the solid are applied to the fluid Step 2 : Fluid is advanced in time (including subcycling) Step 3 : Neumann loads of the fluid are applied to the solid Step 4 : TSI system is advanced in time 16

17 Coupling of non-conforming interfaces Exchange from states and loads for arbitrary interface meshes Step 1 : Step 3 : Discrete projection operators?? e.g. direct force motion transfer (consistent interpolation, least-square interpolation), localized Lagrange multiplier methods, mortar methods Desired properties Flux transmission consistency Computational efficiency 17

18 Mortar with dual Lagrange multipliers FE discretization for fluid and structural interface necessary structure side T S fluid side (carries LM) T F Dual shape functions lead to biorthogonality e.g. bilinear 3D (quad4) 18

19 Mortar with dual Lagrange multipliers Discrete coupling matrices dual LM make D diagonal mixed shape functions in M require accurate segmentation, triangulation and projection operations Computationally cheap conversion 19

20 Mortar with dual Lagrange multipliers - convergence Optimal rates of spatial convergence are preserved [Klöppel, 2010] 20

21 Mortar with dual shape functions FV and FEM Fluid interface data available at centroids of level set facets 3D surface Delaunay triangulation of centroids to obtain dual mesh 21

22 Outline Motivation and Introduction Immersed Interface Method for the Fluid Monolithic Thermo-Structure Interaction (TSI) Approach Thermo-Fluid-Structure Interaction (TFSI) Numerical Example Conclusion and Outlook 22

23 Numerical Example Viscous laminar boundary layer flow of over a hot plate (initially ) [Birken, 2010] Rigid structure with zero coefficient of thermal expansion Initial steady state solution for the fluid Subcycling fluid : structure = 100 : 1 with 23

24 Temperature evolution Exponential decay of the interface temperature Increased cooling of the structure close to fluid inflow Solid Fluid 24

25 Interface temperature (t=0.05 s) Fluid mesh cartesian: 200x8 (streamwise x spanwise) Varying solid interface mesh (from 200x8 to 50x2) Boundary effects due to dual mesh! 25

26 Conservative heat flux transfer Conservation in a weak sense with mortar coupling Relative error err conforming 200x8 0.0 mortar 200x8 0.0 mortar 170x5 <10e-7 mortar 100x4 0.0 mortar 97x5 mortar 73x3 <10e-7 <10e-7 mortar 50x

27 Outline Motivation and Introduction Immersed Interface Method for the Fluid Monolithic Thermo-Structure Interaction (TSI) Approach Thermo-Fluid-Structure Interaction (TFSI) Numerical Example Conclusion and Outlook 27

28 Conclusion & Outlook Conclusion Loosely coupled approach for thermo-fluidstructure interaction problems based on Dirichlet-Neumann partitioning Dual mortar approach for non-conforming interface meshes Multiple Program Multiple Data MPI application in an MPI_COMM_WORLD free zone Outlook Application to realistic rocket nozzle configurations 28

29 References Frey, M., and Hagemann, G. (2000): Restricted shock separation in rocket nozzles, Journal of propulsion and power, Vol. 16, pp Grilli, M., Hickel, S., Hu X.Y., and N.A. Adams (2009): Conservative Immersed Boundary for compressible flows, Academy Colloquium on Immersed Boundary Methods: current status and future research directions, Amsterdam, The Netherlands Klöppel, T., Popp, A., Küttler, U., and W.A. Wall (2010): Fluid-structure interaction for non-conforming interfaces based on a dual mortar formulation, Computer Methods in Applied Mechanics and Engineering, Vol. 200, pp Hammerl, G., Danowski, C., Grilli, M., Adams, N.A., and W.A. Wall (2012): A coupled thermo-fluid-structure interaction approach based on an immersed interface method and a monolithic thermo-structure approach, Proceedings of 1st ECCOMAS YIC, Aveiro, Portugal, April Birken, P., Quint, K., Hartmann, S., and A. Meister (2010): Time-adaptive fluidstructure interaction method for thermal coupling, Computing and Visualization in Science 13: ,

30 Euro TUG Interface treatment for TFSI Munich, June 3 rd, 2013 Thank you for your attention! Georg Hammerl hammerl@lnm.mw.tum.de Institute for Computational Mechanics Technische Universität München (TUM) Germany 30