Numerical simulation of an oscillating cascade based on immersed boundary method

A fast explicit numerical method is established to solve the unsteady flow with an oscillating cascade on the basis of the immersed boundary method. In order to consider more practical problems, a turbulence model is introduced into this method. The specific method is to solve the Reynolds averaged Navier-Stokes equations with low Reynolds number turbulence model, i.e., Lam-Bremhorst model, which is one of the k-ε models. In order to validate the method, two simulation cases, laminar boundary layer and turbulent boundary layer are carried out and results agree well with the Blasius solution and the law of wall. Based on these benchmark cases, a numerical simulation at high Reynolds number for an oscillating cascade is then established. It is found that the oscillating of cascade is greatly influenced by the reduced velocity which is just the same solution of the laminar results. It is worth noting that the coupling process is not necessary to generating any body-fitting grid, which makes it much faster in computational process for such a cascade problem.