An aerodynamic inverse method that is developed for viscous flow over airfoils, is implemented into ANSYS-CFX as a User-Defined Function (UDF). The implementation is validated, it is then assessed in the redesign of a compressor and a turbine stage in two-dimensional visocus flow. In the inverse method, one of the design choices is to prescribe a target pressure distribution on the airfoil surfaces. The airfoil walls are assumed to be moving with a virtual velocity that would asymptotically drive the airfoil to the shape that would correspond to the specified target pressure distribution. This virtual velocity distribution is computed from the difference between the current and the target pressure distributions. The inverse design approach is fully consistent with the viscous flow assumption and is independent of the CFD approach taken. The Arbitrary Lagrangian-Eulerian formulation of the unsteady Reynolds-Averaged Navier Stokes equations is solved in a time accurate fashion with the airfoil motion being the source of unsteadiness. At each time step, the airfoil shape is modified and dynamic meshing is used to remesh the fluid flow domain. An axial compressor stage and turbine stage are redesigned using ANSYS-CFX running in inverse mode so as to demonstrate the ability of this approach to improve the aerodynamic performance of both compressor and turbine stages.

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