Development of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics I. Pantle Fachgebiet Strömungsmaschinen Karlsruher Institut für Technologie KIT
Motivation FSI can be: Structural vibrations excite fluid waves/acoustical waves in fluids Fluid flow excites structural vibrations which in turn excite acoustical waves Fluid flow excites structural deformations which hold an equilibrium state
Motivation/Context FSI
Hybrid Approach Hybrid Integrated Approach Hybrid = 2 specialized codes for CFD and CSD Integrated = 1 code for both simulation types
Hybrid Approach Advantages/Disadvantages Hybrid Approach Integrated Approach Codes for CFD and CSD are highly adapted for specific problem One code for both fluid simulations and structural simulations For CFD typically Euler formulation: describes fluid state and its changes within control volume For CSD typically Lagrangian formulation: describes movement of control unit rather than its interior state 2 grids, one for CFD and CSD each, cell search and interpolation algorithm necessary 1 grid possible, however, two sets of conservation equations valid for fluid and structure Grid movement on CFD side requires correction terms due to cell deformation Border region must be treated with a specific approach to avoid singularities
Hybrid Approach Characteristics of CFD and CSD Solver CFD: SPARC-FNX (KIT) CSD: Z88 (Univ. of Bayreuth) Compressible Navier-Stokes, block-structured Finite Volume code Finite Element structural code (about 20 element types possible) Laminar, Reynolds-Averaged Navier-Stokes turbulence modeling, Large Eddy Simulation with various sub-grid scale models Covering plane stress, plate bending, axis symmetric and spatial structures Parallelized with MPICH 3 types of solvers: Contains driving interface for FSI: Fast Cholesky solver with Jennings storage FSI-interfaces organizes cell-to-cell search algorithm on contact faces of fluid and structural mesh, manages interpolation of loads to the CSD side and of grid deformations back to the CFD side Sparse matrix iterative solver with Conjugate Gradient preconditioning (for very large structures) With unsteady CFD simulations: FSI-interface manages temporal exchange Direct sparse matrix with multi-cpu support
Unsteadyness Steady and Unsteady Approach Steady Approach: for equilibrium deformations (inner red part) Unsteady Approach: for vibrations (whole chart)
Grid-to-grid Interpolation Contact Surfaces of Grids - 2 different cell distributions - interpolation of fluid loads to the solid structure (CFD to CSD) - interpolation of the structure deformations to the CFD grid (CSD to CFD) - unsteady case: interpolation of contact surface velocities
Grid-to-grid Interpolation Curvature creates errors to some extent! Interpolation errors Geometrical gaps
Steady Example Steady flow through elastic pipeline Blue: CFD grid Brown: CSD grid
Steady Example CFD Cells 552,960 hexahedons Node s Data Type CSD 329.876 tetrahedons 69,167 nodes No slip at walls Static pressure ps=104,755 Pa Mass flow rate: 0.13*104 Laminar flow, ideal gas Young modulus: 1.1 MPa Poisson ration: 0.44 Reduction of degrees of freedom: translational movement of pipeline not allowed
Steady Example
Steady Example Developed fluid flow before FSI is started: solid structure not deformed Some iterations after FSI is started: solid structure as well as flow profile is deformed
Steady Example Sequence until equlibrium stated between Comparision of external structural diameter at equilibrium versus fluid loads and structural tension is transmural pressure reached
Steady Example 2 types of interpolation: cell search algorithm starts from CFD side (upper) or from CSD side (lower) cells on both sides of similar size
Steady Example Conservative Interpolation Alternative Interpolation If CSD cell size much finer than CFD cell size Alternative interpolation (starting from CSD side) gives smoother fluid force distribution on the CSD contact face
Unsteady Example Elastic plate mounted behind square cylinder in crossflow: vortex street excites elastic plate s vibrations
Unsteady Example CFD Cells 425,984 hexahedons Node s Data Flow Type CSD 14,908 tetrahedons 3,964 nodes No slip at walls Farfield: U=0.512 m/s Static pressure ps=98,888.72 Pa Periodic boundaries Laminar flow, ideal gas Young modulus: 1.0 MPa Poisson ration: 0.35 No reduction of degrees of freedom except for the mounting of the plate at the cylinder
Unsteady Example One period T of vibration: ¼ T steps
Unsteady Example
Unsteady Example - Unsteadiness for implicit time dependant scheme implemented - Test cases and validation still in progress - Preliminary validation according to Wood, C., Gil, A. J., Hassan, O., Bonet, J., 2008, A Partitioned Coupling Approach for Dynamic FluidStructure Interaction with Applications to Biological Membranes, International Journal for Numerical Methods in Fluids, Vol. 57, Issue 5, pp. 555-581 - At present, Young modulus at 106 Pa for stabilization of the simulation, should be at 105 Pa - At present, amplitude of plate vibration at 1.2 cm, should be at 0.5 cm - At present, frequency of plate vibration at 3 Hz, should be at 1 Hz
Conclusions FSI simulation tool created by attaching Z88 to SPARC Unsteady and steady simulations possible Still, algorithm verification and validation not yet terminated Validating measurements in progress; present validation data from other simulations