Flow reconstructions and aerodynamic shape optimization of turbomachinery blades by POD-based hybrid models

This study presented a hybrid model method based on proper orthogonal decomposition(POD) for flow field reconstructions and aerodynamic design optimization. The POD basis modes have better description performance in a system space compared to the widely used semi-empirical basis functions because they are obtained through singular value decomposition of the system.Instead of the widely used linear regression, nonlinear regression methods are used in the function response of the coefficients of POD basis modes. Moreover, an adaptive Latin hypercube design method with improved space filling and correlation based on a multi-objective optimization approach was employed to supply the necessary samples. Prior to design optimization, the response performance of POD-based hybrid models was first investigated and validated through flow reconstructions of both single-and multiple blade rows. Then, an inverse design was performed to approach a given spanwise flow turning distribution at the outlet of a turbine blade by changing the spanwise stagger angle, based on the hybrid model method. Finally, the span wise blade sweep of a transonic compressor rotor and the spanwise stagger angle of the stator blade of a single low-speed compressor stage were modified to reduce the flow losses with the constraints of mass flow rate, total pressure ratio, and outlet flow turning.The results are presented in detail, demonstrating the good response performance of POD-based hybrid models on missing data reconstructions and the effectiveness of POD-based hybrid model method in aerodynamic design optimization.