A Nonlinear Potential Flow Model Based On The Weak-Scatterer Hypothesis And Its Engineering Application

With the development and utilization of marine renewable energy,marine structures such as monopile-supported offshore wind turbines and point-absorber wave energy converters have been widely used.Generally speaking,the horizontal scale of these structures is relatively small compared with the characteristic wavelength,and these structures are often subject to many nonlinearities such as those arising from the harsh ocean environment and large-amplitude motions.However,these nonlinear phenomena can not be well modeled by conventional analysis tools such as the linear and second-order wave diffraction–radiation models.In this paper,a novel nonlinear potential flow model based on the weak-scatterer hypothesis is developed to better deal with the nonlinear hydrodynamic problems for small-scale marine structures under the condition of large wave steepness.In the proposed numerical model,the incident wave is simulated by a dedicated wave model,including the nolinear regular waves and focused waves.The corresponding boundary value problem about the scattered velocity potential is solved by the higher-order boundary element method at each time step.In the time marching process,the standard 4th-order Runge-Kutta time-integration scheme together with an arbitrary Lagrangian-Eulerian approach is adopted on the free surface.The direct and indirect calculation methods of hydrodynamic loads are established,and the 4th-order Runge-Kutta method is used to solve the motion equation of a rigid body.Two efficient mesh deformation algorithms are integrated to adapt to the changes of instantaneous wetted body surface and free surface with time.A spring analogy method is used to update the mesh on the instantaneous wetted body surface,and the radial basis function interpolation method is used for the mesh deformation on the free surface.In addition,some smoothing techniques are used to deal with the saw-tooth instability during the numerical simulation of strongly nonlinear wave–structure interaction problem.Firstly,the proposed model is verified by the wave run-up and higher-harmonic wave forces on a vertical cylinder under the action of regular waves,the generation and propagation of nonlinear focused waves,and the comparative study on the interaction of focused waves with a fixed vertical cylinder.The accuracy and superiority of the numerical model in this paper are verified by comparison with previous theoretical,numerical and experimental results.Then,the high-frequency resonance response of a bottom-hinged monopile under the action of regular and focused waves is investigated by using this model,focusing on the third-harmonic resonance in pitch motion.In the case of regular waves,the effects of the incident wave amplitude and structural damping on the high-frequency resonance response of the monopile are studied.For focused waves,the effects of the peak frequency,input wave amplitude and structural damping on the ringing response of the monopile are discussed,and the time-frequency characteristics of the response are analyzed by wavelet transforms.The numerical results show that the higher-harmonic component plays an important role in the response when the incident wave amplitude is large enough and the damping ratio is small.Further,based on the modified blade element momentum theory,the proposed model in this paper and the p-y curve method for calculating the pile-soil interaction,a coupled model is established for computing the overall dynamic response of a monopile-supported offshore wind turbine under the combined action of the wind and waves.As a result,the coupling calculation of aero-hydro-soil loads on and dynamic response analysis of monopile-supported offshore wind turbines are realized under different working conditions.Firstly,the thrust and power of the NREL 5-MW baseline wind turbine are verified under the action of steady wind.It indicates that the present results are all in good agreement with the results of FAST program for different wind speeds.The overall dynamic response of the wind turbine is subsequently calculated and analyzed under the action of the steady wind and regular/irregular waves.For the case of steady wind and regular waves,the hub displacement is composed of the mean drift,wave frequency and high-frequency components,and the high-frequency response has a more significant effect on the hub velocity.In addition,the amplitude of high-frequency resonance response calculated by the quasi-dynamic method is larger than that by the coupled dynamic method.This is mainly because the quasi-dynamic method ignores the aerodynamic damping caused by the motion of the wind turbine.For the case of steady wind and irregular waves,it can be found that there are significant high-frequency resonance responses at several specific moments during a long time series,which should be paid special attention to in practical design.Finally,the nonlinear potential flow model established in this paper is used to analyze the hydrodynamic performance of a point-absorber wave energy converter(WEC)in regular waves and the survivability of the device in focused waves.For regular wave tests,the effects of wave steepness on the power absorption of the WEC and the power take-off(PTO)force are highlighted by comparison with a linear frequency-domain model,and the influence of the PTO damping coefficient on the performance is discussed.For focused wave tests,the numerical results of the motion responses of the buoy and the mooring force are compared with the experimental data.The time–frequency characteristics of the motion responses of the buoy are further analysed based on wavelet transforms.It appears that the low-frequency slow drift in the surge displacement and high-frequency response in the pitch angle are well captured by the present model.