Wall model for large-eddy simulation of high-speed flows over rough surfaces*

Computational fluid dynamics (CFD) for Entry, Descent, and Landing (EDL) vehicles face unique challenges due to the ubiquity of complex aero/thermo-physics. Current CFD models are incapable of accurately predicting multiple aero/thermo-dynamic phenomena, especially those involving roughness-enhanced heating and shearing levels. To address this challenge, we have developed a wall model for large-eddy simulation (LES) using machine learning (ML) techniques, which accounts for compressibility and roughness effects in high-speed regimes. A DNS database of compressible turbulent flow over rough walls has been constructed, encompassing various roughness topographies, different Mach numbers, and Reynolds numbers. This database serves as the foundation for training our ML-based wall model. Information-theoretic dimensionless learning, based on the Buckingham-π theorem, is used to determine the most relevant non-dimensional inputs and outputs for the wall model. The predictive capability of the wall model is assessed a-posteriori in compressible turbulent channel flows with both smooth and rough walls, a high-pressure turbine blade with roughness, a compression ramp with roughness, and an EDL-like vehicle with roughness. The results demonstrate that the new wall model can predict drag and heat flux for high-speed flows in hydraulically smooth, transitionally, and fully rough regimes with an accuracy of within 10%.