Reproduction of slow-drift motions of a floating wind turbine using second-order hydrodynamics and Operational Modal Analysis

Abstract

Slow-drift forcing and damping are important for an accurate reproduction of the low-frequency motion of floating offshore wind turbines. In this study we present a numerical model that includes both inviscid slow-drift forcing through full quadratic transfer functions (QTFs) and viscous forcing. To accommodate a linear damping matrix that represents all the damping effects on the floater, the classical Morison formulation of the drag forcing with relative velocity is simplified into a pure forcing term and a linear constant damping term. The frequency-dependent radiation properties are also replaced by constant matrices. We investigate the application of Operational Modal Analysis (OMA) to estimate the damping ratios from the test data, and also pursue a calibration method where the linear damping is calibrated in the modal space and subsequently transformed back to the physical space. The model is compared to wave basin data for four environmental conditions including the 50-year sea state. The damping ratios estimated with OMA generally increase with the sea state. The measured response can be generally well reproduced by the model when the damping is calibrated for each sea state. Due to the neglection of first-order motion effects in the applied QTFs and to the damping introduced by the mooring lines, however, the surge response is underpredicted for the severe sea states, and the yaw motion is always underpredicted. The commonly used approach where the damping is calibrated to the decay tests is found to provide less accurate results than the approach of calibrating the modal damping ratios for the given sea state. The damping ratios estimated with OMA are found similar to the calibrated values for mild pink-noise sea states, while significant differences exist for the stronger Pierson-Moskowitz sea states. Thus the potential and limitations for OMA application in different sea states is discussed. In summary, the model is found able to generally predict the measured response, provided that the damping is properly calibrated for each sea state.