The development and application of an inviscid inverse method

A two-dimensional inviscid inverse method is developed, verified and applied in this paper. The method solves the Euler equation in absolute reference frame by a cell-centered finite volume method, and the hybrid Runge-Kutta method is used for time integration. Different from the direct method, the inverse method imposes a unique “transpiration” boundary condition on the blade surfaces. The inputs of inverse method are pressure loading and blade tangential thickness distribution along the blade chord. During the time marching process, the blade shape is periodically updated. When the solution is converged, the blade shape will be stabled. In the paper, the principle of the inverse method is described in detail. Then the developed inverse method is verified against a consistence test: recover an axial compressor cascade from a different start. Finally, to demonstrate the powerful capability of the method, it is used to redesign the cascade, and final results give an improved aerodynamic performance.