This paper presents an iterative inverse design methodology based on proper orthogonal decomposition (POD) and its applications to the inverse design of turbomachinery blades. In the aerodynamic system with a number of snapshots, the aerodynamic performance with the corresponding aerodynamic shape within the design space can be described as a linear combination of a series of POD basis modes. In the present paper, the description ability of Gappy POD is evaluated firstly and the influence of different parametrization methods and different snapshot approaches are studied and compared in detail. In the POD-based inverse design, the aerodynamic shape can be obtained by only one design process. However, due to the error between the predicted aerodynamic performance by Gappy POD and that obtained from computational fluid dynamics, an iterative inverse design methodology is proposed herein based on the error correction to the target aerodynamic performance. Three inverse design studies of turbomachinery blades are performed. In the first two cases, the profiles of two-dimensional turbine blades are modified to approach the target pressure distributions on the blade surface in subsonic and transonic flow, respectively. In the third case, a three-dimensional supersonic turbine blade is restaggered along span to achieve a given loading distribution in the spanwise direction at the outlet. The design results are presented and compared in detail, demonstrating the effectiveness and improved accuracy of the POD-based iterative inverse design method.

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