A Surrogate-Based e(N) Method for Compressible Boundary-Layer Transition Prediction

To improve robustness and efficiency of automatic transition prediction in aerodynamic design, a reduced model of linear stability analysis is usually adopted, such as e(N)-envelope or e(N)-database method. Nevertheless, building such a model is challenging when it comes to compressible flows, as the transition mechanism is more complex and multiple flow parameters should be taken into consideration. To address this problem, this paper proposes an efficient surrogate-based e(N) method for compressible boundary layers that uses pretrained surrogate models to substitute linear stability analysis, concerning stability analysis of both Tollmien-Schlichting and Mack modes, as well as transition prediction of flow over arbitrary-shaped airfoils. The proposed method is demonstrated by stability analysis of compressible flat-plate boundary layers at a wide range of Mach numbers of M-infinity=0 similar to 6. It is also validated by transition prediction of flow over a low-speed natural-laminar-flow (NLF) airfoil NLF-0416 and a transonic NLF airfoil NPU-LSC-72613. Besides, a sample partitioning method is presented to accelerate surrogate-model training with large samples. Results show that the predicted growth rates of perturbations, N factors, and corresponding transition locations by our method of using surrogate-based stability analysis agree well with those by a standard e(N) method of solving full linear stability equations.