A two-dimensional Navier-Stokes inverse solver for compressor and turbine blade design

A two-dimensional viscous inverse method for the design of compressor and turbine blades is presented. It iteratively modifies an initial geometry until a prescribed pressure distribution is reached on the blade surface. The method solves the time-dependent Navier-Stokes equations in a numerical domain of which some boundaries (the blade walls) move during the transient part of the computation. The geometry modification algorithm is based on the transpiration principle: a normal velocity distribution is computed from the difference between the actual and prescribed pressure distributions, and is used to modify the blade shape. A time iteration is then performed on this new blade shape, taking into account the grid movement during the time stepping. A two-dimensional upwind finite-volume Navier-Stokes solver has been developed. The multiblock strategy allows for a selective concentration of the discretization points in the zones of higher gradients. Applications to turbine and compressor blade design illustrate the accuracy of the flow computation, the capabilities and efficiency of the inverse method.