This paper presents a novel iterative viscous inverse design method for turbomachinery blading. It is made up of two steps: the first one consists of an analysis by means of a Navier-Stokes solver; the second one is an inverse design by means of an Euler solver. The inverse design resorts to the concept of permeable wall, and recycles the ingredients of Demeulenaere’s inviscid inverse design method that was proven fast and robust. The re-design of the LS89 turbine nozzle blade, starting from different arbitrary profiles at subsonic and transonic flow regimes, demonstrates the merits of this approach. The method may result in more than one blade profile that meets the objective, i.e., that produces the viscous target pressure distribution. To select one particular solution among all candidates, a target mass flow is enforced by adjusting the outlet static pressure. The resulting profiles are smooth (oscillation-free). The design of turbine blades with arbitrary pressure distribution at transonic and supersonic outflow illustrates the correct behavior of the method for a large range of applications. The approach is flexible because only the pitch chord ratio is fixed and no limitations are imposed on the stagger angle.

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