| An aerodynamic inverse design method for turbomachinery cascades is presented and is implemented in a finite volume method. In this design method, the mass-averaged swirl schedule and the blade thickness distribution are prescribed. The design method then provides the blade shape that would accomplish this loading by imposing the appropriate pressure jump across the blades and satisfying the blade boundary condition, the latter implies that the flow is tangent to the blade surfaces. This inverse design method is implemented using a cell-vertex finite volume method which solves the Euler equations on unstructured triangular meshes. A five-stage Runge-Kutta pseudo-time integration scheme is used to march the solution to steady state. Non-linear artificial viscosity is added to eliminate pressure-velocity decoupling and to capture shocks. Convergence is accelerated using local time stepping and implicit residual smoothing. The boundary conditions at inflow and outflow are based on the method of characteristics. The finite volume discretization method is validated against some standard cases of internal flow as well as linear cascades.The inverse design method is first validated for three different cascades namely, a parabolic cascade, a compressor cascade and a turbine inlet guide vane. It is then used to obtain a shock-free design of an impulse transonic cascade and of the ONERA transonic compressor cascade. A parametric study has shown that the blade profile is rather sensitive to the prescribed loading distributions and that, in most cases, a smooth loading distribution results in a shock-free cascade design. |
