Generative Model Based Parameterization for More Efficient Aerodynamic Optimization of Non-Axisymmetric Endwall

The Non-axisymmetric Endwall Contouring (NEC) technique has been proven effective in reducing the secondary losses of turbine cascades. However, the parameterization of NEC, especially for spline-based techniques, would face a tradeoff between issues such as the dimensionality of the design space, sample variability, and the proportion of abnormal shapes. To address the above issue and achieve a moreefficient NEC optimization, a generative model based parameterization method is proposed. Specifically, to build a comprehensive design space that contains sufficient variability of NEC shapes, the samples of a set of conventional classical NEC parameterization methods are collected, which are combined by representing them with scatter coordinates in a uniform format. Then, to reduce the number of variables to the minimum extent, the Variational Autoencoder (VAE) is used to learn the intrinsic dimensions of the parameterized NEC design space. To ensure the smoothness of the contours and avoid abnormal shapes, a layer of NURBS is incorporated into the neural network architecture of VAE. This proposed model was used for the NEC parameterization of a high-pressure turbine stage testcase with 9 variables. Additionally, the proposed VAE was used for aerodynamic optimization of the non-axisymmetric endwalls, compared to other NEC parameterization approaches. The results demonstrate that the generative model based parameterization method can optimize aerodynamic performance more effectively while maintaining a lower limit on the number of performance evaluations. The effectiveness of our proposed generative model based parameterization method is well demonstrated.