FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Development of an Integrated Computational Simulation Method

for Fluid Driven Structure Movementand Acoustics

I. Pantle

Fachgebiet StrömungsmaschinenKarlsruher Institut für Technologie

KIT

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

FSI can be:Structural vibrations excite fluid waves/acoustical waves in fluidsFluid flow excites structural vibrations which in turn excite acoustical waves

Fluid flow excites structural deformations which hold an equilibrium state

Motivation

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

FSI

Motivation/Context

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Hybrid IntegratedApproach

Hybrid = 2 specialized codesfor CFD and CSD

Integrated = 1 code for bothsimulation types

Hybrid Approach

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Advantages/Disadvantages

Border region must be treated with a specific approach to avoid singularities

Grid movement on CFD side requires correction terms due to cell deformation

1 grid possible, however, two sets of conservation equations valid for fluid and

structure

2 grids, one for CFD and CSD each, cell search and interpolation algorithm necessary

For CFD typically Euler formulation: describes fluid state and its changes within control volumeFor CSD typically Lagrangian formulation: describes movement of control unit rather than its

interior state

One code for both fluid simulations and structural simulations

Codes for CFD and CSD are highly adapted for specific problem

Integrated ApproachHybrid Approach

Hybrid Approach

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Characteristics of CFD and CSD Solver

Covering plane stress, plate bending, axis symmetric and spatial structures

Laminar, Reynolds-Averaged Navier-Stokes turbulence modeling, Large Eddy Simulation

with various sub-grid scale models

Fast Cholesky solver with Jennings storageContains driving interface for FSI:

Sparse matrix iterative solver with Conjugate Gradient preconditioning (for very large

structures)

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

Direct sparse matrix with multi-cpu supportWith unsteady CFD simulations: FSI-interface manages temporal exchange

3 types of solvers:Parallelized with MPICH

Finite Element structural code (about 20 element types possible)

Compressible Navier-Stokes, block-structured Finite Volume code

CSD: Z88 (Univ. of Bayreuth)CFD: SPARC-FNX (KIT)

Hybrid Approach

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Steady and UnsteadyApproach

Steady Approach: for equilibriumdeformations (inner red part)

Unsteady Approach: for vibrations(whole chart)

Unsteadyness

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

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

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Curvature createserrors to some extent!

Interpolation errorsGeometrical gaps

Grid-to-grid Interpolation

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Steady flow through elastic pipeline

Blue: CFD gridBrown: CSD grid

Steady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Reduction of degrees of freedom: translational movement of pipeline not allowed

Laminar flow, ideal gasType

Young modulus: 1.1 MPaPoisson ration: 0.44

No slip at wallsStatic pressure ps=104,755 PaMass flow rate: 0.13*104

Data

69,167 nodesNodes

329.876 tetrahedons552,960 hexahedonsCells

CSDCFD

Steady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Steady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Developed fluid flow – before FSI is started: solid structure not deformed

Some iterations after FSI is started: solid structure as well as flow profileis deformed

Steady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Sequence until equlibrium stated betweenfluid loads and structural tension is reached

Comparision of external structural diameter at equilibrium versus transmural pressure

Steady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

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

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

If CSD cell size much finer than CFD cell sizeAlternative interpolation (starting from CSD side) gives smoother fluid force distribution on the CSD contact face

Conservative Interpolation

Alternative Interpolation

Steady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Elastic plate mounted behind square cylinder in crossflow: vortex street excites elastic plate’s vibrations

Unsteady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

No reduction of degrees of freedom except for the mounting of the plate at the cylinder

Laminar flow, ideal gasFlow Type

Young modulus: 1.0 MPaPoisson ration: 0.35

No slip at wallsFarfield: U=0.512 m/sStatic pressure ps=98,888.72 PaPeriodic boundaries

Data

3,964 nodesNodes

14,908 tetrahedons425,984 hexahedonsCells

CSDCFD

Unsteady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

One period Tof vibration:

¼ T steps

Unsteady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

Unsteady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

- 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 Fluid-Structure 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

Unsteady Example

FSM – FSI – 21.05.2010 – Dr.-Ing. Iris Pantle

FSI simulation tool created by attachingZ88 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

Conclusions