Johannes Palm

Estimation of numerical uncertainty in computational fluid dynamics simulations of a passively controlled wave energy converter

The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber. The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5% uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.

Coupled BEM/hp-FEM Modelling of Moored Floaters

A coupling between a dynamic mooring solver based on high-order finite element techniques (MooDy) and a radiation-diffraction based hydrodynamic solver (WEC-Sim) is presented. The high-order scheme gives fast convergence resulting in high-resolution simulations at a lower computational cost. The model is compared against a lumped mass mooring code (MoorDyn) that has an existing coupling to WEC-Sim. The two models are compared for a standard test case and the results are similar, giving confidence in the new WEC-Sim-MooDy coupling. Finally, the coupled model is validated using experimental data of a spread moored cylinder with good agreement.

Mooring cable simulations with snap load capturing for wave energy applications

In a number of experiments and field tests of point absorbers, snap loads have been identified to cause damage on the mooring cables. Snap loads are basically propagating shock waves, which require special care in the numerical modeling of the mooring cable dynamics. In this paper we present a mooring cable model based on a conservative formulation, discretized using the Runge-Kutta discontinuous Galerkin method. The numerical model is thus well suited for correctly capturing snap loads. The numerical model is verified and validated using analytic and experimental data and the computed results are satisfactory.