A new FSI coupling approach for rigid floating bodies in CFD simulations

In the quest for commercially viable floating offshore wind turbines, a large variety of new floater concepts have been invented in recent years. Detailed CFD simulation of a proposed floater design in a realistic wave environment is a potentially powerful engineering tool allowing assessment of feasibility and optimisation early on in the design phase.

Adding the 6 degrees-of-freedom (DoF) of a rigid floater to the millions of DoF's of the surrounding fluid CFD simulation may at first glance seem like a trivial task. It is, nevertheless, well-documented that if caution is not taken in this coupling, numerical instabilities arise, limiting the usability of CFD as a practical engineering tool for floater design[1].

The main culprit is the strictly tight coupling caused by the fluid incompressibility. Any acceleration of the body will *instantaneously* set up a flow field in the surrounding fluid, thus increasing the fluid momentum. This means that effectively, the fully or partially submerged body reacts to forces as if its mass was augmented by an added mass. The coefficients in the symmetric 6x6 added mass matrix vary with time because of their dependency on the instantaneous water surface and body configuration. It is not difficult to show formally that “naive” iterative partitioned body-fluid coupling methods will be unstable when the added mass exceeds the body mass[2].

In this presentation, we propose a new rigid body-fluid coupling approach which is stabilised by quantifying and taking into account the added mass in each CFD time step. We start each CFD time step with a calculation of the added mass matrix entries, using small *virtual* CFD time steps with prescribed body accelerations along each of the 6 DoF. The updated added mass matrix is then used in the *actual* CFD time step to get the body’s linear and angular accelerations which are compatible with the accompanying acceleration of the surrounding fluid. Once the accelerations are known, they are used to advance the body 6-DoF state variables (position and orientation) and we progress to the next time step.

The proposed coupling strategy was implemented in OpenFOAM’s interfacial flow solver, interIsoFoam, which uses the geometric VoF method, isoAdvector, for the fluid interface representation[3]. In the talk, we will present the proposed coupling algorithm and demonstrate its stability features using generic benchmarks and real 3D floating body simulations.

ACKNOWLEDGEMENT This research was funded by Innovation Fund Denmark as part of the FloatStep Project (grant no. 8055-00075A) where STROMNING, DTU and DHI are partners.

REFERENCES [1] N. Bruinsma, B. T. Paulsen, and N. G. Jacobsen, “Validation and application of a fully nonlinear numerical wave tank for simulating floating offshore wind turbines,” Ocean Eng., 147, pp. 647–658, 2018, doi: 10.1016/j.oceaneng.2017.09.054. [2] P. Causin, J. F. Gerbeau, and F. Nobile, “Added-mass effect in the design of partitioned algorithms for fluid–structure problems,” Comput. Methods Appl. Mech. Eng., 194, pp. 4506–4527, 2005, doi: 10.1016/j.cma.2004.12.005. [3] J. Roenby, H. Bredmose, and H. Jasak, “A computational method for sharp interface advection,” R. Soc. Open Sci., 3, p. 160405, 2016, doi: 10.1098/rsos.160405.