Wake model of a floating offshore wind turbine under surge motion

Surge motion significantly affects the thrust coefficient variation and wake development characteristics of floating offshore wind turbines (FOWTs). Based on the high-order Gaussian model, this paper proposes a FOWT wake model, designated as HG-DFOWT (high-order Gaussian dynamic floating offshore wind turbine model), which incorporates the additional wind speed induced by FOWT surge motion, to predict the wake distribution and thrust coefficient variation of the wind turbine. The model first corrects the variation in hub position during FOWT surge. Then, it modifies the relative inflow velocity at the rotor plane using the additional velocity induced by surge. Subsequently, a dynamic thrust coefficient model is established based on the first-order sinusoidal surge motion of the FOWT. Finally, the model predictions are compared with wind tunnel experimental results and CFD numerical simulation results to validate the reliability of the model. The results indicate that, under upwind motion, the root mean square error between the model's predicted vertical wake profiles and the wind tunnel experimental results is 4.04%, while under downwind motion, the error is 1.47%. The corrected thrust coefficient shows good consistency with the CFD calculation results, with an average relative error of less than 1% under high-frequency surge conditions (f ≥ 0.072 Hz). In addition, the wake distribution characteristics at different time within a surge cycle are analyzed. It is found that the wake deficit at the same downstream position of the FOWT exhibits periodic fluctuations around the time-averaged value, and the wake center velocity is significantly influenced by the surge frequency, with a fluctuation amplitude reaching 7.1% under high-frequency motion (f = 0.09 Hz). The proposed model provides a reference for layout optimization of floating wind farms.