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In this work, a near-wall model, which couples the inverse of a recentlydeveloped compressible velocity transformation [Griffin, Fu, & Moin, PNAS,118:34, 2021] and an algebraic temperature-velocity relation, is developed forhigh-speed turbulent boundary layers. As input, the model requires the meanflow state at one wall-normal height in the inner layer of the boundary layerand at the boundary-layer edge. As output, the model can predict meantemperature and velocity profiles across the entire inner layer, as well as thewall shear stress and heat flux. The model is tested in an a priori sense usinga wide database of direct numerical simulation high-Mach-number turbulentchannel flows, pipe flows, and boundary layers (48 cases with edge Mach numbersin the range of 0.77--11 and semi-local friction Reynolds numbers in the rangeof 170--5700). The present model is significantly more accurate than theclassical ordinary differential equation (ODE) model for all cases tested. Themodel is deployed as a wall model for large-eddy simulations in channel flowswith bulk Mach numbers in the range of 0.7--4 and friction Reynolds numbers inthe range of 320--1800. When compared to the classical framework, in the aposteriori sense, the present method greatly improves the predicted heat flux,wall stress, and temperature and velocity profiles, especially in cases withstrong heat transfer. In addition, the present model solves one ODE instead oftwo and has a similar computational cost and implementation complexity as thecommonly used ODE model.

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation