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Modeled Reynolds stress is a major source of model-form uncertainties inReynolds-averaged Navier-Stokes (RANS) simulations. Recently, aphysics-informed machine-learning (PIML) approach has been proposed forreconstructing the discrepancies in RANS-modeled Reynolds stresses. The meritsof the PIML framework has been demonstrated in several canonical incompressibleflows. However, its performance on high-Mach-number flows is still not clear.In this work we use the PIML approach to predict the discrepancies in RANSmodeled Reynolds stresses in high-Mach-number flat-plate turbulent boundarylayers by using an existing DNS database. Specifically, the discrepancyfunction is first constructed using a DNS training flow and then used tocorrect RANS-predicted Reynolds stresses under flow conditions different fromthe DNS. The machine-learning technique is shown to significantly improveRANS-modeled turbulent normal stresses, the turbulent kinetic energy, and theReynolds-stress anisotropy. Improvements are consistently observed whendifferent training datasets are used. Moreover, a high-dimensionalvisualization technique and distance metrics are used to provide a prioriassessment of prediction confidence based only on RANS simulations. This studydemonstrates that the PIML approach is a computationally affordable techniquefor improving the accuracy of RANS-modeled Reynolds stresses forhigh-Mach-number turbulent flows when there is a lack of experiments andhigh-fidelity simulations.

Prediction of Reynolds Stresses in High-Mach-Number Turbulent Boundary Layers using Physics-Informed Machine Learning