The nonlinear parabolized stability equations for accurate wall-modeled large-eddy simulations of transitional flows

For the prediction of natural transition, which is ubiquitous in external aerodynamic applications, the nonlinear parabolized stability equations (NLPSE) are computationally efficient, high-fidelity, and physics-based alternative to direct numerical simulations. Gonzalez et al. (CTR Ann. Res. Brief, 2023) and Lozano-Duran et al. (PRF, 2018) have shown that the NLPSE can be coupled to wall-modeled large-eddy simulations (WMLES) to provide a framework that can accurately simulate an H-type transitional boundary layer at affordable resolutions.

Herein we present an extension to this work for boundary layers undergoing K-type and oblique transition. We show that coarse no-slip LES calculations are unable to transition and that WMLES calculations erroneously transition early. In contrast, the proposed simulation framework accurately predicts skin-friction profiles in these two cases at a reduced computational cost, using 95% and 96% fewer control volumes, respectively, compared to the benchmarking wall-resolved LES results. Further, we extend this methodology to complex geometry by implementing general curvilinear numerics in our NLPSE code and simulating a natural laminar flow airfoil (NLF(1)-0416) in this framework.