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