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.
The performance of an optimized aerodynamic shape is further improved by a second-step optimization using the design knowledge discovered by a data mining technique based on Proper Orthogonal Decomposition(POD) in the present study. Data generated in the first-step optimization by using evolution algorithms is saved as the source data, among which the superior data with improved objectives and maintained constraints is chosen. Only the geometry components of the superior data are picked out and used for constructing the snapshots of POD. Geometry characteristics of the superior data illustrated by POD bases are the design knowledge, by which the second-step optimization can be rapidly achieved. The optimization methods are demonstrated by redesigning a transonic compressor rotor blade, NASA Rotor 37, in the study to maximize the peak adiabatic efficiency, while maintaining the total pressure ratio and mass flow rate.Firstly, the blade is redesigned by using a particle swarm optimization method, and the adiabatic efficiency is increased by 1.29%. Then, the second-step optimization is performed by using the design knowledge, and a 0.25% gain on the adiabatic efficiency is obtained. The results are presented and addressed in detail, demonstrating that geometry variations significantly change the pattern and strength of the shock wave in the blade passage. The former reduces the separation loss,while the latter reduces the shock loss, and both favor an increase of the adiabatic efficiency.
Yanhui DUANWenhua WUPeihong ZHANGFulin TONGZhaolin FANGuiyu ZHOUJiaqi LUO
