A new similarity criterion for real-time hybrid testing of floating wind turbines in wind tunnels: Verification and application

Accurate scaled model testing for floating wind turbines remains challenging due to limitations in traditional similarity approaches. Based on key issues such as aero-hydro mismatch, deficiencies in dynamic effect similarity, and power coefficient dissimilarity under the traditional Froude number similarity criterion, this paper proposes an improved similarity criterion specifically suited for wind tunnel model tests of floating wind turbines. The new criterion introduces three key modifications: (1) matching the tip speed ratio at the optimal power coefficient segment while compensating for power differences, enabling simultaneous power and thrust similarity; (2) deriving the crucial constraint of equal rate of change of tip speed ratio for dynamic aerodynamic similarity, subsequently determining scaling ratios for motion amplitude and frequency; and (3) matching equivalent pitch amplitude and motion frequency with rotational frequency to capture similarity for dynamic effects induced by equivalent wind shear. Validation via unsteady momentum blade element theory calculations (using the NREL 5 MW as prototype) showed significant error reductions: under sinusoidal pitch motion, power coefficient (Cp) and thrust coefficient (Ct) errors decreased by 14.87 % and 6.78 % respectively; under coupled pitch-surge motions, average Cp and Ct errors decreased by 13.68 % and 3.23 %. Wind tunnel verification using a model turbine on a 6-Degree-of-Freedom (6-DoF) motion platform further confirmed the improvement: under forced motion, power and thrust errors decreased by 24.14 % and 9.38 %; in real-time hybrid model applications, the relative error of the surge displacement response decreased by 138.5 % and the pitch displacement response by 116.6 %. This provides clear scientific guidance for the design of model experiments.