Wave Loading on Bodies in the Free Surface Using Smoothed Particle Hydrodynamics (SPH)

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Abstract

This thesis investigates wave loading on bodies in the free surface using smoothed particle hydrodynamics (SPH). This includes wave loading on fixed bodies, waves generated by heaving bodies in still water and the heave response of a body in waves, representing a wave energy device. SPH is a flexible Lagrangian technique for CFD simulations, which in principle applies to steep and breaking waves without special treatment allowing us to simulate highly nonlinear and potentially violent flows encountered in a real sea. However few detailed tests have been undertaken even with small amplitude waves.This research uses the open-source SPH code SPHysics. First two forms of SPH formulation, standard SPH with artificial viscosity and SPH-Arbitrary Lagrange Euler (ALE) with a Riemann solver, are used to simulate progressive waves in a 2-D tank. The SPH-ALE formulation with a symplectic time integration scheme and cubic spline kernel is found to model progressive waves with negligible dissipation whereas with the standard SPH formulation waves decay markedly along the tank. We then consider two well-defined test cases in two dimensions: progressive waves interacting with a fixed cylinder and waves generated by a heaving semi-immersed cylinder. To reduce computer time in a simple manner a variable particle mass distribution is tested with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. A mass ratio of 1:4 proved effective but increasing to 1:16 caused particle clumping and instability. For wave loading on a half-submerged cylinder the agreement with the experimental data of Dixon et al. (1979) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. For the heaving cylinder, SPH results for the far field wave amplitude and vertical force on the cylinder show good agreement with the data of Yu and Ursell (1961). The variable mass distribution leads to a computer run time speedup of nearly 200% in these cases on a single CPU. The results of the vertical force and wave amplitude are shown to be quite sensitive to the value of the slope limiter in the Riemann solver for the 2-D heaving cylinder problem. A heaving 2-D wedge or 3-D cone whose oscillatory vertical motion is prescribed as the elevation of a focused wave group is a precise test case for numerical free-surface schemes. We consider two forms of repulsive boundary condition (Monaghan & Kos, 1999, and Rogers et al., 2008) and particle boundary force (Kajtar and Monaghan, 2009) for the 2-D wedge case, comparing the result with the experimental data of Drake et al. (2009). The repulsive boundary condition was more effective than the particle boundary force method. Variable particle mass with different kernel sizes was then tested for 2-D problems for mass ratios of 1:4, 1:16 and 1:4:16 with satisfactory results without particle clumping and instability. For the 3-D cone case, SPH reproduces the experimental results very closely for the lower frequency tested where there is no separation from the bottom surface of the body but for the higher frequencies the magnitudes of force minima were underestimated. The mass ratios of 1:8 and 1:8:27 in two and three nested regions are tested for the 3-D cone problem where a computer run time speedup of nearly 500% is achieved on 16 processors for the mass ratio of 1:8.Finally, the floating body of a heaving wave energy device known as the Manchester Bobber is modelled in extreme waves without power take-off. The results for a single float are in approximate agreement with the experiment.

Keyword(s)

Cone; Cylinder; Extreme waves; Floating bodies; Heaving; Manchester Bobber; Smoothed Particle Hydrodynamics; Variable particle mass; Wave energy devices

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