Wave Pattern Analysis for the Determination of Wave-Induced Resistance and Side Forces
Extending the Transverse Wave Cut Method to Side Forces
J.B. Krämer (TU Delft - Mechanical Engineering)
G.D. Weymouth – Mentor (TU Delft - Mechanical Engineering)
H.J. de Koning Gans – Mentor (TU Delft - Mechanical Engineering)
J.O. (Oriol) Colomes Gene – Graduation committee member (TU Delft - Civil Engineering & Geosciences)
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Abstract
Accurately predicting wave-induced forces plays an important role in ship design. Currently, pressure integration is the standard method for calculating wave-induced forces from panel methods. For Computational Fluid Dynamics (CFD) and experiments, it is not even possible to separate the wave-induced forces from the viscous forces. Pressure integration is limited by discretization, which can compromise the accuracy of the results. Wave pattern analysis offers an alternative by calculating wave-induced forces from the far-field wave elevation, thereby reducing the influence of discretization.
The transverse wave cut method (TWC) uses wave elevation measured along a single line perpendicular to the ship's path. Previous research has demonstrated that wave resistance can be determined using this method. Since only wave elevation data is necessary, wave resistance could even be calculated from experimental data.
No effort has been made yet to extend this method to calculate wave-induced side forces. This research investigates whether side forces can be accurately determined using the TWC method and evaluates its performance against conventional pressure integration in panel methods and CFD simulations.
The TWC method is derived from the conservation of momentum around the ship hull. The method applies a Fourier transform to the measured wave elevation to determine the free wave spectrum, which describes the wave field as a superposition of individual wave components. By reformulating the final expression, it is shown that the same spectral coefficients used to calculate the wave resistance can also be used to determine the wave-induced side force, without requiring any additional measurements or calculations.
The TWC method was compared with pressure integration results for a submerged spheroid using a panel method. Multiple test cases were considered, all of which showed good agreement between the two approaches. The TWC method was therefore successfully validated for calculating wave-induced side forces.
By plotting the free wave spectrum, the contributions of individual wave components at different propagation angles can be observed. As expected, the wave resistance was found to be dominated by the transverse wave components, while the side force was caused almost entirely by the diverging wave system.
In CFD simulations, the cell size strongly influences the quality of the simulated wave pattern. Coarser meshes introduce more numerical damping, causing the wave pattern to decay faster than physically expected. This was confirmed by evaluating the TWC method at multiple longitudinal locations, where the decay rate was extracted and compared across refinement levels. The numerical damping prevented accurate force predictions. However, the TWC method proved to be a useful diagnostic tool, providing a quantitative measure of wave decay and indicating the quality of the simulation.
Overall, the TWC method can accurately predict wave-induced side forces from a simulated wave field, showing good agreement with pressure integration for panel method results. In CFD simulations, its accuracy is limited by mesh resolution and numerical dissipation, but it can still be used as a diagnostic tool.