Smoothed Particle Hydrodynamic Modelling of Wave Impact

Abstract

Hydraulic structures can be prone to impulsive wave impact, which is a highly stochastic and uncertain process. This type of impact, defined by extreme pressure peaks and a very short duration, is not only caused by breaking waves, but also by non-breaking standing waves on structures with an overhang, such as culverts and steel gates. In this study, the capabilities of the Lagrangian numerical tool Smoothed Particle Hydrodynamics (SPH) are validated by means of experimental research conducted at the Hydraulics lab of the Delft university of Technology, in which two short overhang configurations were subjected to multiple non-breaking wave conditions. SPH distinguishes itself by discretizing the numerical domain in particles instead of a grid, unlike traditional computational fluid dynamics (CFD). In doing so, it excels in free surface modelling and complex wave-structure interaction. In this thesis, the theory of pressure-impulse is applied, which is defined as the integral of the pressure over the impact duration. This method is more stable than using pressure peaks and can be used to obtain the reaction forces on hydraulic structures. However, the theory is in development and subject of recent literature. This research includes the theoretical pressure-impulse model, which is based on the Laplace equation and solely includes the vertical impact by assuming a circular profile under the overhang with a constant impact velocity. Furthermore, a new conceptual model is introduced, which is based on integration by the particle velocities in both horizontal and vertical direction as described by Linear Wave Theory. The assumptions of the velocity fields of both models are assessed by the SPH method. As a result, modifications are proposed to the conceptual model and validated with the experiment. SPH shows good agreement with the experiment in terms of wave generation, pressure distribution and pressure-impulse profile. However, the lack of air in the numerical model result in overestimations of the pressure peaks. The more air is entrapped in the experimental wave impact, the higher the deviation. That said, the impact duration also becomes longer the more air is entrapped while the SPH model shows a somewhat constant and shorter duration. As a result, the pressure-impulse profiles shows corrective behavior over the vertical, mitigates the absence of air and thus greatly increases the accuracy and stability of the results. Finally, an analytical validation is performed in which the theoretical models for overhang configurations and design formulae for vertical walls are compared to SPH and the experiment.