High-Mach-Number Turbulence Modeling using Machine Learning and Direct Numerical Simulation Database

In this paper, a physics-informed machine learning approach is applied to improve the accuracy of the Reynolds stresses modeled by Reynolds-averaged Navier-Stokes (RANS) for high-speed at-plate turbulent boundary layers using an existing DNS database. In the machine-learning technique, the DNS dataset of a Mach 2:5 adiabatic turbulent boundary layer is used as the training flow to construct the invariant basis for learning the functional form of the discrepancy in RANS modeled Reynolds stresses. The functional thus constructed is in turn used to correct the RANS prediction of Reynolds stresses for turbulent boundary layers under two cold-wall hypersonic conditions with nominal freestream Mach numbers of 6 and 8. The study shows that the RANS-modeled Reynolds normal stresses, the turbulent kinetic energy, and the Reynolds-stress anisotropy can be significantly improved using the machine-learning technique. Such a study lays the foundation towards better physics-based turbulence modeling for high-Mach-number turbulent flows