Characteristics of higher-harmonic breaking wave forces and secondary load cycles on a single vertical circular cylinder at different Froude numbers

Abstract

A 3D numerical two-phase flow model based on solving Unsteady Reynolds-averaged Navier-Stokes (URANS) equations has been used to simulate spilling breaking waves past a single vertical cylinder installed at the edge of a 1:10 slope. The volume of fluid (VOF) method is employed to capture the free surface, and the k−ω Shear-Stress Transport (k−ω SST) turbulence model is used to simulate turbulence effects. Mesh and time-step refinement studies have been conducted by examining the free surface elevations in front of the cylinder and the total horizontal wave forces on the cylinder. These two quantities have also been compared with experimental data from Irschik et al. [21] to validate the present numerical model. The present numerical results are in good agreement with the measured data. The process of breaking waves past the cylinder is described and explained. Moreover, the ‘secondary load cycle’ phenomenon which may lead to higher-harmonic structural response is observed. The characteristics of higher-harmonic wave forces are discussed further at different Froude numbers by changing cylindrical diameters and incident wave properties for both breaking and non-breaking wave cases. For non-breaking wave cases, pronounced secondary load cycles are observed for the Froude number exceeding about 0.4, and the magnitudes of the secondary loads are about 8.1%–12.6% of the peak-to-peak wave force (crest to trough value). However, for breaking wave cases, the critical value of the Froude number to observe the pronounced secondary load cycles reduces to 0.35. The relative magnitude of the secondary load to the peak-to-peak wave force reduces to a range of 2.4%–7.6% due to the high slamming force. The duration of the secondary load cycle is not greater than 0.242T for all the cases, where T is incident wave period. For a vertical cylinder with a larger diameter, the pronounced secondary load cycle occurs with a larger wave steepness.