A numerical modeling of the vortex-induced vibration of cascade in turbomachinery using immersed boundary method

Based on the immersed boundary method, a fast simulation for solving unsteady, incompressible, viscous flow associated with the oscillating cascade is established on a quasi-three-dimensional coordinate system. The numerical method is applied to the simulation of the flow passing an oscillating circular cylinder which is forced to move in X direction under prescribed motions in water at rest at low Keulegan-Carpenter numbers. Then vortex-induced vibration of a cylinder with two degrees of freedom which oscillates in in-line direction and transverse direction is simulated using this method. The results are in good agreement with the previous research. Then the method is extended to the oscillating cascade simulation of making various comparisons. It is found that the IBPA (inter blade phase angle) will change as the time goes on, because of the non-uniformity of the flow in the circumferential direction, until the oscillating cascade goes to a stable situation. The reduced velocity and the number of blades are chosen to investigate the effects of them on IBPA. The results indicate that both the reduced velocity and the number of blades are the main factors which influence IBPA. It is worth noting that the coupling process is not necessary to generate any body-fitting grids, which makes it much faster in computational process for such a complicated fluid-structure interaction problem.