Aerodynamic evaluation of cascade flow with actual geometric uncertainties using an adaptive sparse arbitrary polynomial chaos expansion

In this paper, an adaptive sparse arbitrary polynomial chaos expansion (PCE) is first proposed to quantify the performance impact of realistic multi-dimensional manufacturing uncertainties. The Stieltjes algorithm is employed to generate the PCE basis functions concerning geometric variations with arbitrary distributions. The basis-adaptive Bayesian compressive sensing algorithm is introduced to retain a small number of significant PCE basis functions, requiring fewer model training samples while preserving fitting accuracy. Second, several benchmark tests are used to verify the computational efficiency and accuracy of the proposed method. Eventually, the coexistence effects of six typical machining deviations on the aerodynamic performance and flow fields of a controlled diffusion compressor cascade are investigated. The probability distributions of the machining deviations are approximated by limited measurement data using kernel density estimation. By uncertainty quantification, it can be learned that the mean performance seriously deteriorates with increasing incidences, while the performance at negative incidences is more dispersed. By global sensitivity analysis, the leading-edge profile error should be given high priority when working at negative incidences, and the inlet metal angle error would be carefully inspected first when the cascade works at high positive incidences. Furthermore, controlling the manufacturing accuracy of the suction surface profile error can play a certain role in improving the robustness of aerodynamic performance in off-design conditions. Through flow field analysis, it further proves that actual leading-edge errors are the most important ones to aerodynamics and reveals how the effects of leading-edge errors propagate in the cascade passage, thus affecting the aerodynamic loss.