Scaling approaches and scale effects in wave–flexible structure interaction

Abstract

Laboratory models are important for research, to inform design solutions and to calibrate and validate numerical models. Unfortunately, model-prototype similarity is often difficult to achieve in small models, resulting in scale effects. For Wave–Flexible Structure Interaction (WFSI), scale effects arise when the fluid and/or structure properties are incorrectly scaled. The present study provides a systematic investigation of scale effects for wave impacts on flexible and rigid plates based on numerical modelling supported by small-scale laboratory tests. Non-breaking and breaking wave impacts were simulated with regular and solitary waves for the prototypes and up to 40 times smaller models. These were scaled according to the scaling approaches (i) precise Froude (fluid and plate properties scaled), (ii) traditional Froude–Cauchy (fluid properties unscaled, plate properties scaled), (iii) traditional Froude (fluid and plate properties unscaled) and (iv) a new WFSI approach (partial conservation of the WFSI governing parameters). The numerical results confirmed the absence of scale effects for (i). Non-breaking wave impacts were correctly predicted for (ii), however, up to 132% scale effects were observed in the breaking wave pressures due to the unscaled fluid properties. The plate displacements were underestimated by up to 98% for (iii). The new approach (iv) was successfully validated based on non-breaking waves, with less than 4.3% deviations for the maximum regular wave forces and plate displacements. Additionally, less than 3% deviations for the maximum solitary wave force and plate displacement were observed. The new scaling approach provides a more versatile alternative to traditional Froude–Cauchy scaling laws to support laboratory investigations of WFSI.