Large Scale Fluid-Structure Interaction by coupling OpenFOAM with external codes Thomas Gallinger * Alexander Kupzok Roland Wüchner Kai-Uwe Bletzinger Lehrstuhl für Statik Technische Universität München member of
Very Thin Shell/Membrane Wind - Interaction high Reynolds number flow complex wind characteristic complex geometries very light and flexible structures optimized structures (formfinding, shape optimization, shape adaptivity) large displacements aeroelastic effects Vision: Numerical Wind Tunnel Source: Architekturbüro Rasch & Bradatsch Motivation
Agenda Motivation & Objective Solution Approach Governing Equations Coupling Algorithm Software Environment Validation: Experimental FSI Benchmark Silsoe Cube Application: Outlook A.R.I.E.S. a mobile canopy structure Agenda
Solution Approach - Governing Equations Fluid field: Incompressible Navier Stokes Equations for Newtonian fluids momentum equation: 1 ( t ) ( ν ) u+ u d u = p+ u t ρ in F Ω continuity equation: u = 0 boundary & (, ) = ( ), (, ) = ( ) u x t u t p x t p t Γ Γ on F Γ initial conditions: (,0) = ( ), (,0) = ( ) u x u x p x p x 0 0 Governing Equations
Solution Approach - Governing Equations Fluid field: Structure field: Incompressible NSE Nonlinear Elastodynamics t 1 ( t ) ( ν ) u+ u d u = p+ u ρ momentum equation: 2 t d σ = f in S Ω constitutive equation: σ = D ε u = 0 boundary & (, ) = ( ), σ(, ) = σ ( ) d x t d t x t t Γ Γ on S Γ initial conditions: (,0) = ( ), σ(,0) = σ ( ) d x d x x x 0 0 Governing Equations
Solution Approach - Governing Equations Fluid field: Incompressible NSE Coupling Conditions at FS interface Γ : continuity of displacements: Structure field: Nonlinear Elastodynamics t 1 ( t ) ( ν ) u+ u d u = p+ u ρ d Γ FS = d Γ FS 2 t d σ = f continuity of surface traction: u = 0 t Γ FS = t Γ FS σ = D ε Governing Equations
Solution Approach Coupling Algorithm Partitioned approach with subiteration Structure field: geometric nonlinear Generalized-α time stepping Coupling: Dirichlet-Neumann type coupling Fixed point iteration with adaptive underrelaxation Fluid field: transient PISO ( Pressure Implicit with Operator Splitting ) Coupling Algorithm
Solution Approach Coupling Algorithm advance in interfield iteration: n n+1 Structure field: geometric nonlinear Generalized-α time stepping n 1 Predict interface forces σ + Γ n 1 n 1 n 1 n 1 n 1 Solve Md&& + + + + + + N ( d ) = R ( σ ) Evaluate interface displacements n 1 d + Γ Coupling Algorithm
Solution Approach Coupling Algorithm advance in interfield iteration: n n+1 Structure field: geometric nonlinear Generalized-α time stepping Coupling: Dirichlet-Neumann type coupling Fixed point with adaptive underrelaxation (Aitken method) Map interface displacements Calculate Aitken Relax displacements d n+ 1 Φ n+ 1 Γ dγ n n+ 1 T n+ 1 ( ΔdΓ ΔdΓ ) ΔdΓ i = ri 1 + n n+ 1 2 ( ΔdΓ ΔdΓ ) r (1 ) d% r d r d n + 1 n + 1 n Γ = i Γ + (1 i) Γ Coupling Algorithm
Solution Approach Coupling Algorithm advance in interfield iteration: n n+1 Structure field: geometric nonlinear Generalized-α time stepping Coupling: Dirichlet-Neumann type coupling Fixed point with adaptive underrelaxation Fluid field: seggregated with transient PISO Coupling Algorithm Apply boundary displacement Move fluid mesh Momentum predictor ( γ n 1) d % + = 0 pressure solution explicit vel. correction Evaluate boundary pressure % n 1 d + Γ n + 1 n n + 1 n + 1 n t u + u u ( ν u ) = p n 1 p + Γ
Solution Approach Coupling Algorithm advance in interfield iteration: n n+1 Structure field: geometric nonlinear Generalized-α time stepping Coupling: Dirichlet-Neumann type coupling Fixed point with adaptive underrelaxation Fluid field: seggregated with transient PISO Proove convergence: n 1 n 1 If e.g. d% + + Γ d% Γ ε goto Structure field else ti t i + 1 L2 Coupling Algorithm
Software Overview CSD-Design and Simulation: CARAT Coupling tool: CoMA CFD-Simulation: OpenFOAM Ansys CFX-11 mapping Software overview
Multi-Code Approach Advantages: Plug n Play system high flexibility use of best-suited codes for single-fields possible approach can be and is used for any surface-coupled problem, e.g.: FFI, Heat transfer, optimization of aeroelastic problems But: high coding effort setup more complicated Coupling Environment
Concept and Features CoMA = Coupling for Multiphysics Analysis General tool for control of surface-coupled simulations Important aspects: communication and parallelization interface data transfer coupling strategies Coupling Environment
Important aspects I communication and parallelization Single fields can work in parallel, based on domain decomposition Only exchange with subset of processes Per process multiple partitions with different tags and different discretizations possible Therefore: no restrictions on parallelization / decomposition concept in use Communication between CoMA and single field processes by Files easy to implement, existing single-field communication doesn t have to be touched MPI fast and efficient, first choice for large systems. Existing single field communication concept has to be enhanced and only small changes implemented (sub-communicator concept) Communication
Important aspects II data transfer at interfaces Mapping of node-based quantities at non-matching surface meshes Surface mesh discretization: 3-noded, 4-noded (is transformed) Mapping algorithm based on neighborhood-search and interpolation Quantities to be mapped can be Interpolated, e.g. displacements Summed up, e.g. forces Data transfer is conservative! Surface element-based quantities (FVM methods) have to be transformed before exchange (up to now) Class structure
Data Transfer at non-matching Meshes Interpolation e.g. displacements (structure fluid) Fluid elements, nodal values unknown u u ( ξ, η) = N ( ξ, η) u F S i Si Si Structure elements, nodal values known conservative summation e.g. loads (fluid structure) Values known Sj f = N ( ξ, η ) f i Sj i i Fi f Sj = N Sj ( ξi, ηi ) f Fi = N Sj ( ξi, ηi ) f Fi = j j i i j 1 i f Si Values unknown Coupling Environment
Validation doubly curved Surface field variable field variable difference < 1%! Coupling Environment
Important aspects III coupling strategies Basic coupling concepts: One-way coupling just pass information from side A to side B Two-way coupling without subiteration (explicit) with subiteration (implicit) Coupling strategies
Important aspects III coupling strategies Coupling in CoMA is based on concept of Exchange points One exchange point is basically defined as: A quantity with a certain dimension A sender and reciever processgroup Data transfer type (summation/interpolation) Order of appearance e.g. displacements in FSI: 3 From structure to fluid Interpolation 1 Exchange points are grouped together into an exchangepointgroup By a combination of exchange points different coupling strategies possible Coupling strategies
Important aspects III coupling strategies Additional features per exchange point are (acceleration strategies): Predictor for implicit coupling Order 0 to 3, based on history of quantity Underrelaxation for implicit coupling constant or Aitken Convergence proove e.g. Max steps, L2-Norm,... concept of exchange points is easily extendible, e.g. transfer of an adaptive set of eigenforms Coupling strategies
FluidFieldSolver solver based on OpenFOAM-libraries incompressible NSE using structured and unstructured meshes turbulence modelling: RANS (+LES) necessary extensions: communication with CoMA extensions to PSTREAM-library implicit coupling necessitates reset of mesh motion within a timestep extensions to mesh motion library drawback: non-conforming OF-version Coupling Environment
Agenda Motivation & Objective Solution Approach Governing Equations Coupling Algorithm Software Environment Validation: Experimental FSI Benchmark Silsoe Cube Application: Outlook A.R.I.E.S. a mobile canopy structure Agenda
Validation: Numerical FSI Benchmark numerical benchmark for FSI problems proposed by Turek & Hron within DFG Research Group 493 contribution to solution database interaction between elastic object and laminar incompressible flow simulation setup: rigid elastic beam no slip pressure outlet parabolic inlet velocity Validation Example
Validation: Numerical FSI Benchmark 9 different calculations to validate single-field and coupled solutions CFD 1..3 - fluid only: CSD 1..3 - structure only: FSI 1..3 coupled: differing inlet velocity, Re = [20, 100, 200] differing E-Moduls, static and dynamic differing density, inlet velocity and E-Modulus Validation Example
Technische Universität München Results Coupled Computations y A FSI 2: transient behavior, converges against const. amplitude and frequency Validation Example x
Results Coupled Computations A FSI 2: transient behavior, converges against const. amplitude and frequency FSI2 disp_x FSI2 disp_y y x 0,005 FSI2 disp_x 0,10 FSI2 disp_y 0,000 0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 0,08 0,06 displacement [m] -0,005-0,010-0,015 displacement [m] 0,04 0,02 0,00 0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0-0,02-0,020-0,04-0,06-0,025-0,08-0,030 time [s] -0,10 time [s] X - direction frequency tip displacement [*10-3 m] reference 3,80-14,58 ± 12,44 own 3,86 14,28 ± 12,25 difference [%] 1,70 2,12 ± 1,54 Y - direction frequency tip displacement [*10-3 m] reference 2,00 1,23 ± 80,6 own 1,94 1,24 ± 80,4 difference [%] 3,00 0,80 ± 0,23 Validation Example
Results Coupled Computation FSI 1..3 - coupled: comparing beam s tip displacement reference own difference FSI 1 0.0008209 0.0007999 2.55 [%] FSI 2 ±0.08060 ±0.08040 0.23 [%] FSI 3 ±0.03438 ±0.03473 1.02 [%] Validation Example
Validation: SILSOE Cube presentation of Majjid Hojat side view 1,500 1,000 0,500 Cp (mean) 0,000-0,500-1,000-1,500 0,000 0,500 1,000 1,500 2,000 2,500 3,000 normalized length Richards et al., Wind Pressure on a 6 m cube, J. Wind Eng. Ind. Aerodyn. Validation Example
A.R.I.E.S mobile canopy structure Gengnagel, 2006
Setup CSD simulation form finding given: desired final geometry solution: 1. find the right pre-stress distribution 2. correct deformation of side trusses redo form finding computation with pre-stress from previous form finding step continue computation with pre-stressed structure
Setup CSD simulation
Setup CFD simulation
CFD simulation
Steady State results wind from back side displacements and pressure distribution
Steady State results wind from front side pressure distribution and displacements
Technische Universität München max. inflow velocity [m/s] Unstead FSI wind gust from front side simulation time [s] v10m,max = 30 m/s
Agenda Motivation & Objective Solution Approach Governing Equations Coupling Algorithm Software Environment Validation: Experimental FSI Benchmark Silsoe Cube Application: Outlook A.R.I.E.S. a mobile canopy structure Agenda
Outlook numerical prediction of natural wind as inlet condition further investigation of code coupling strategies general shape optimization of surface-coupled problems with different shape parametrizations and accordingly developed solution strategies WIP: Experimental Benchmark Outlook
Thank you for your attention! The End