Transonic flow reconstruction by an adaptive proper orthogonal decomposition hybrid model

Abstract

A proper orthogonal decomposition (POD) based hybrid surrogate model and the applications to transonic flow reconstructions are presented in the paper. In the implementations, the radial basis function (RBF) model response instead of the least-square linear regression is employed in order to improve the coefficients of POD basis modes; moreover, an adaptive sampling strategy with both the model response error and sample independence taken into account is studied to reduce the sample number, while maintaining sufficient response accuracy. Firstly, the POD-RBF surrogate model is studied and compared with the least-square-based POD through pressure reconstruction studies on the twodimensional blade surface. The results demonstrate that the non-linear model response method significantly improves the coefficients of the basis modes and thus the averaged description error. Meanwhile, the beneficial gains on the convergence performance of the response error versus the number of basis modes are obtained. Then by comparing with the uniform sampling and the resampling strategy with taking only the response error into account, the adaptive sampling method proposed in the paper obtains the best performance on reducing the averaged description error. Finally, the flow characteristics of the flow fields on the suction surface, at the blade tip, in the blade passage of the sampled three-dimensional transonic compressor rotor blades with different spanwise sweeps based on the baseline blade, NASA Rotor 67 are illustrated through the flow basis modes. Compared with the suction flow, the flow at the blade tip contains more intensive flow characteristics including shock, tip-leakage flow and shock-leakage interaction, resulting in a higher averaged description error. Besides, the missed flow fields in the passages of the test blades are reconstructed from the flow basis modes by using the adaptive POD-RBF hybrid model and the corresponding aerodynamic parameters are then predicted. The spanwise distributions of the circumferentially averaged aerodynamic parameters at the blade outlet reconstructed from POD-RBF model are consistent well with the numerical solutions. The results demonstrate that the adaptive POD-RBF hybrid surrogate model is effective and accurate enough for reconstructing the transonic flow. In order to further evaluate the response performance of the adaptive POD-RBF model, statistic analysis is carried out for a group of hybrid models with different sampling strategies and different numbers of samples. Generally, although the number of adaptive samples is much less, the mean value and standard deviation of the adaptive model are close enough to those of the static model with sufficient uniform samples. Besides, the standard deviations of a lot of aerodynamic parameters of interest exhibit significant peaks near the blade tip, further demonstrating that the flow at the blade tip is more intensive in the three-dimensional transonic rotor blade passage.