Inverse method is a very efficient method in turbomachinery aerodynamic design. It takes blade aerodynamic loading as input, and the blade shape and the flow field are computed when calculation converged. However most current inverse methods model turbulent eddy viscosity by Baldwin-Lomax (BL) model or similar approximation, which does not involve local wall distance as a model parameter. Most one- and two-equation turbulence models are not that case, and local wall distance is needed in turbulent work variable(s) transport equation formulation. The usual wall distance computing procedure is the so called "exhaustive search method", which is a time-consuming process. When a flow solver running in analysis mode, the wall distance calculation is not a problem, it can be computed once and stored for subsequent use. But for design mode, this computation intensive process becomes a big challenge. For an inverse design run, the blade shape is updated periodically for about 400 times, if wall distances is re-computed for each blade shape update, the time cost is very appreciable. That is the reason that prohibits the application of higher order (one- and two-equation, compared to BL model) turbulence models in inverse method. In this paper, a novel wall distance calculation method is proposed. The new method transforms the distance searching problem into a length optimization problem, and the steepest descent method is used to find the minimal length from a target point to a wall face. Numerical experiments show that the method can reduce the computing time to approximately 1/10 of the exhaustive search method. Based on this, together with an enhanced blade update method and Spalart-Allmaras turbulence model, a 3D viscous redesign of an axial fan rotor is conducted. Final results demonstrate the effectivity of the proposed method.
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