The development and application of an inviscid inverse method

A two-dimensional inviscid inverse method is developed,verified and applied inthis paper.The method solves the Euler equation in absolute reference frame by a cell-centeredfinite volume method,and the hybrid Runge-Kutta method ls 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 loadingand blade tangential thickness distribution along the blade chord.During the time marchingprocess,the blade shape is periodically updated.When the solution is converged,the bladeshape 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 axialcompressor cascade from a different start.Finally,to demonstrate the powerful capability ofthe method,it is used to redesign the cascade,and final results give an improved aerodynamicperformance.