Hydrodynamic characteristics of a pitching hydrofoil in unsteady uniform inflow with special emphasis on the hysteresis effect

Numerical flow simulations on a Clark-Y pitching hydrofoil are carried out to study the effect of an unsteady uniform inflow on the dynamic characteristics and the corresponding flow structure. The representative hysteresis phenomenon of pitching hydrofoil is observed and analyzed emphatically. In this study, the pitching motion trajectory is a triangular wave with mean incidence of α₀ = 10° and amplitude of Δα₀ = 5° at a pitching frequency f* of 2 Hz. The amplitude of unsteady uniform velocity ΔU is set 0, 0.75, 1.50, 3.0 respectively, and the frequency of unsteady uniform velocity f of 1, 2, 4 were chosen. The numerical method is validated through the experimental results at ΔU = 0. Results revealed that pitching motion and unsteady uniform inflow both lead to the occurrence of hysteresis effect, and two hysteresis effect quantization parameters (the hysteresis parameter ε_CL and hysteresis area S_CL) were defined. Results showed that the relationship between ΔU, f and the two parameters is respectively linear and nonlinear. Meanwhile, the values of ΔU, f directly determine the contribution of unsteady uniform inflow to hydrodynamic hysteresis effect. In addition, ΔU and f have a significant impact on the flow structures and the development of vortices. However, ΔU and f don't change vortex structure directly, but affect the formation and dwell time of vortex structure significantly, thus leading to the different hydrodynamic characteristics.