Dynamic responses of pitching hydrofoil in laminar–turbulent transition regime

Abstract

Recently, the problem of a transitional boundary layer around a pitching foil has been attracting increasing attention. To determine the underlying physical mechanisms, in this study, a pitching hydrofoil is numerically investigated using the shear stress transport (SST) k–ω turbulence model coupled with the γ–Re˜θt transition model. First, the prediction of the static performance is compared with the experimental measurements and XFOIL data to validate and verify the numerical accuracy of the proposed method. Subsequently, the flow morphologies induced by sinusoidal and non-sinusoidal pitching laws are analyzed and compared in different reduced frequencies. The results indicate that reducing the empirical coefficient, A1, in the SST k–ω turbulence model can generate the flow separation in advance, thus improving the prediction of the hydraulic performance at a high angle of attack. The dynamic behavior of the laminar separation bubble is strongly associated with the pitching method and velocity. The collapse of the laminar separation bubble can destabilize the local boundary layer, generating multi-laminar separation bubbles. When new separation bubbles form and shed, a turbulent boundary layer moves downstream and is adsorbed on the surface simultaneously. The turbulence flow passes through the trailing edge, destroying the local vortex, contributing to a transiently elevated hydrodynamic lift. During a rapid pitching down, a counterclockwise trailing edge vortex becomes increasingly unstable, repeating the processes of inception, development, and shedding. The Theodorsen model fails to produce a reasonable hysteresis loop owing to the assumption of a fully attached flow. The results of a hybrid of the Theodorsen and Øye models show noticeable improvement in the dynamic lift prediction. The empirical coefficient, ks, of the Snel model is optimized, improving the predictions of low-frequency pitching significantly. All dynamic stall models present the same trend: low-frequency motions show better agreement than high-frequency ones. In the former, modeling of a non-sinusoidal pitching is closer to the transient numerical results than that of a sinusoidal motion.