Semi-analytical load models describing the progressive immersion of a fixed vertical cylinder in a breaking wave

Abstract

This paper is part of the DIMPACT (Design of floating wind turbines and impacts of energetic steep and breaking waves) project concerning slamming loads on floating offshore wind turbines. Two semi-analytical models accounting for the progressive immersion of a vertical cylinder in a breaking wave are presented. These models are based on the rate of change of the fluid momentum and the continuity of the added mass during immersion. The first model is based on the Generalized von Kármán Model where the real shape of the body and its added mass are accounted for. To account for the nonlinearity of the flow kinematics, the second-order terms of the momentum equation are considered in the inertia load. The total load is obtained by adding the drag force using a variable drag coefficient. To better predict the slamming load, a second model based on Wagner’s theory is presented. The Modified Logvinovich Model provides the pressure distribution at the first instants of impact. It is assumed that the flow does not separate from the structure. The load models are applied in a strip-theory approach under the Froude–Krylov assumption. For comparison, a Navier–Stokes solver is used to generate four phase-focused breaking waves. The resulting free surface shape and the ambient kinematics of the two-dimensional waves are used in the semi-analytical models. The present models are compared with existing slamming load formulations and a three-dimensional numerical simulation with an actual cylinder, where the load on four sections of the cylinder are considered. The force in the deeply immersed sections is in good agreement in all models considered. In the partially submerged section, the proposed load formulations and the three-dimensional simulation predict a similar load. Other standard engineering formulas predict a much lower force in this section. In the area impacted by the crest, the Froude–Krylov-based approaches predict a much higher force than that given by the Navier–Stokes result, likely due to the free surface being disturbed by the cylinder.