Aerodynamic shape optimization using a physics-informed hot-start method combined with modified metric-based proper orthogonal decomposition

Aerodynamic shape optimization based on computational fluid dynamics still has a huge demand for improvement in the optimization effect and efficiency when optimizing the unstable flow of airfoils. This article presents a physics-informed hot-start method combined with modified metric-based proper orthogonal decomposition (MPOD-ML-Phys). The data-based filtering strategy is a core step in the original metric-based proper orthogonal decomposition method (MPOD), but existing filtering strategies generate a significant amount of additional computational consumption. Therefore, this article applies machine learning methods to data-based filtering strategy in MPOD and establishes a modified MPOD method (MPOD-ML). In addition, during the MPOD-ML process, a lot of hidden physical knowledge that is beneficial for optimization will also be generated. This article combines Bayesian optimization to construct an MPOD-ML-Phys method, which fully utilizes the flow physical knowledge in MPOD-ML. The efficiency and effect of MPOD-ML and MPOD-ML-Phys are validated by two typical cases: inverse and direct design for airfoils. The results indicate that both MPOD-ML and MPOD-ML-Phys methods can effectively improve the overall optimization efficiency. However, the intervention of machine learning models has significantly reduced the robustness of the MPOD-ML method, while the embedding of physical knowledge makes MPOD-ML-Phys more robust. Meanwhile, the optimized airfoil obtained by MPOD-ML-Phys has better drag divergence characteristics, a later flow separation point, and better flow stability.