An efficient sparse surrogate model for aerodynamic characteristics of a supersonic compressor cascade with uncertain geometric deformations

The increasing demand for high-load compressors necessitates research and design of supersonic compressor blades. Geometric deformations of the blades resulting from manufacturing errors introduce uncertainties in their aerodynamic characteristics. For uncertainty analysis, Polynomial Chaos Expansion (PCE) has gained popularity among engineers in various disciplines. However, as the number of random variables used to describe uncertainties increases, the efficiency of the PCE method diminishes. To overcome this limitation, an Efficient Sparse Surrogate Model (ESSM) was first proposed. The ESSM combines PCE to approximate global characteristics and Gaussian process modeling to capture local variability, resulting in a highly accurate model. Additionally, by utilizing an iteratively diffeomorphic modulation under observable response preserving homotopy, important PCE basis functions are adaptively selected, leading to a sparse surrogate model that significantly reduces the required training samples. Then using the ESSM, efficient Uncertainty Quantification (UQ) and global sensitivity analysis were conducted to evaluate the impact of uncertain geometric deformations on the aerodynamic characteristics of a supersonic compressor cascade. Principal Component Analysis (PCA) was employed in conjunction with an Improved Class Shape Transformation (ICST) to characterize geometric deformations caused by manufacturing errors. The proposed ICST method exhibits enhanced accuracy in fitting near the leading and trailing edges compared to the CST method. PCA enables a 50% reduction in the number of random variables needed to describe geometric deformations. The UQ results establish a quantitative correlation between geometric deformations and supersonic aerodynamics, and the sensitivity analysis identifies some specific forms of geometric deformations that significantly impact the aerodynamics. Finally, the study investigated the flow mechanisms associated with typical geometric deformation forms, further providing recommendations for manufacturing and testing of supersonic blades to prevent performance deterioration.