A numerical study of flow interaction between a cylinder and an oscillating airfoil by using an immersed boundary method

The dynamic performance of an oscillating airfoil subjected to the wake of a circular cylinder is studied in this paper. Two-dimensional numerical simulations are conducted at Re = 1100 by using an immersed boundary method together with the adaptive mesh refinement technique. The effects of two parameters, the gap between the cylinder and the airfoil and the oscillation frequency, are of particular interest to the present study. Therefore, dynamic responses are presented as functions of the two parameters, including the fluid forces, the associated frequency characteristics, and the energy exchange between the airfoil and the fluid. The results show that the cylinder wake can significantly reduce the drag as well as the energy extraction of the lift on the airfoil. Different synchronization behaviors between the airfoil's oscillation and the wake pattern have been observed for some specific cases, i.e., the 1:1, 1:2 and 1:3 patterns. Remarkably, the 1:2 pattern is associated with an asymmetric vortex shedding pattern, which can further result in non-zero time-averaged lift and moment on the airfoil even though both the upstream vortices from the cylinder and the oscillation of the airfoil are periodic. Due to the strong nonlinear interaction between the cylinder wake and the airfoil's oscillation, new frequency branches associated with nonlinear frequency superposition are formed in the responses of the airfoil and their characteristics have been demonstrated. The present study also finds that the oscillation amplitudes are important in determining the synchronization behavior.