Coupled particle and mesh method in an Euler frame for unsteady flows around the pitching airfoil

Finite difference method (FDM) is a grid-based method which is convenient for implementing multiple resolutions and has high computational efficiency. Smoothed particle hydrodynamics (SPH) is a meshless and particle method which has been widely applied into the fluid flows with free surfaces. In this study, a coupled SPH-FDM approach in an Euler frame is developed to simulate the unsteady flow around a pitching airfoil. In addition, an improved iterative shifting particle technology (IPST) is proposed to satisfy the movement of pitching airfoils. Steady flows around the static airfoils are simulated by SPH-FDM, and the results are compared with results of finite volume mothed (FVM) and literatures. The flows around the pitching airfoil with different conditions are simulated, and the results by coupled SPH-FDM are compared with the results by FVM which uses mesh deformation technology to control the movement of mesh. The numerical results by SPH-FDM in an Euler frame are agreement with the results of FVM or literatures, which verifies the effectiveness of the present method. The results of pithing airfoils show the direction of lift hysteresis loop changes from clockwise to counterclockwise as the pitching axis moves from the leading edge to the trailing edge, which can be well predicted by present SPH-FDM in the Euler frame. In addition, some parameters which may affect the lift hysteresis loop are discussed in this study. The results indicate that the acceleration of the airfoil surface has little effect on the lift hysteresis loop; the shape of airfoil has a weak effect on the lift hysteresis loop; the velocity of the airfoil surface, the position of the pitching axis and the free-stream velocity have predominant effect on the lift hysteresis loop.