#### Project Leader:

#### Project Members:

- Marcel König
- Silvan Brändli

## Introduction:

In many fluid-structure interaction (FSI) simulations performed in Naval Architecture and Ocean Engineering, the structure is considered to be rigid. Although the assumption of a rigid body is justified in many cases, there are several problems where the deformation of the structure needs to be taken into account. Problems of this type are, for example:

**Sloshing:**Free-surface motions in tanks, causing impacts at the tank wall.**Slamming:**Impact at ship hull, caused by the relative motion between the ship hull and the water surface.**Springing:**Ship hull bending-oscillation due to periodic excitation by waves.**Whipping:**Ship hull bending-oscillation due to slamming.

In order to model and simulate these problems accurately, a full coupling of a fluid and a structural solver needs to be considered. Therefore, in a first approach a FSI simulation tool [1] has been realized based on the opensource fluid solver *OpenFOAM* [2] which uses the finite volume method. In this approach, the structure has been discretized by means of the finite element methods and the corresponding equation of motion has been solved in *OpenFOAM* utilizing the Newmark method for time integration. The needed mass and stiffness matrices have been obtained from the commercial finite element code *ANSYS* [3]. A sloshing simulation of a tank has been performed with this FSI tool and the influence of the deformation of the tank due to the fluid loads has been studied. Figure 1 shows the pressure for two different points at the top of the tank. From this it is evident, that the pressure is significantly smaller when taking the deformation of the tank into account. This can be explained by the fact, that part of the kinetic energy of the fluid is transformed into the deformation of the tank.

Figure 1: Pressure history

One period of the simulation is visualized in the animation. The interface between fluid and gas is shown in grey and the tank walls are colored according to the magnitude of their deformation. The arrows illustrate the deformation in the cutting plane, demonstrating how the tank walls react to the pressure of the fluid.

Animation 1: Sloshing simulation showing deformations

## Outline of the Project:

The aim of this project is to develop a FSI-solver capable of simulating different FSI-problems such as described above. Therefore the fluid solver *OpenFOAM* will be coupled with the inhouse finite element code *AdhoC ^{4}* to be able to simulate FSI problems arising in Naval Architecture and Ocean Engineering.

## Publications:

- [1] Brändli, S.:
*Simulation der Fluid-Struktur-Interaktion mit OpenFOAM*, Diploma Thesis at TU Hamburg-Harburg in cooperation with Prof. Moustafa Abdel-Maksoud (TUHH) and Daniel Schmode (FutureShip), 2010.

- [2]
*OpenFOAM*

- [3]
*ANSYS*

- [4] Geller S.;Kollmannsberger S.; Bettah M., Scholz D.; Krafczyk M.; Düster A.; Rank E.:
*An explicit model for three-dimensional fluid-structure interaction using LBM and p-FEM*. In:*Fluid-Structure Interaction II*, ed. by Bungartz, H.-J. and Schäfer, M., p. 285-325, Springer Verlag 2010

- [5] Kollmannsberger, S.; Geller, S.; Düster, A.; Rank, E.; Toelke, J.; Krafczyk, M.:
*Fixed-grid Fluid-Structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p-FEM approach*. International Journal for Numerical Methods in Engineering 2009

- [6] Scholz, D.; Kollmannsberger, S.; Düster, A., Rank, E.:
*Thin solids for fluid-structure-interaction*. In:*Fluid-Structure Interaction*, ed. by Bungartz, H.-J. and Schäfer, M., p. 294-335, Springer Verlag 2006