A general framework for predicting mean profiles in compressible turbulent boundary layers with established scaling laws

A prediction framework for the mean quantities in a compressible turbulent boundary layer (TBL) with given Reynolds number, free-stream Mach number and wall-to-recovery ratio as inputs is proposed based on the established scaling laws regarding the velocity transformations, skin-friction coefficient and temperature–velocity (TV) relations. The established velocity transformations that perform well for collapsing the compressible mean profiles onto incompressible ones in the inner layer are used for the scaling of such inner-layer components of mean velocity, while the wake velocity scaling is determined such that self-consistency is achieved under the scaling law for the skin-friction coefficient. A total of 44 compressible TBLs from six direct numerical simulations databases are used to validate the proposed framework, with free-stream Mach numbers ranging from 0.5 to 14, friction Reynolds numbers ranging from 100 to 2400, and wall-to-recovery ratios ranging from 0.15 to 1.9. When incorporated with the scaling laws for velocity transformation from Griffin et al. (2021, Proc. Natl Acad. Sci. , vol. 118, e2111144118), the skin-friction coefficient from Zhao & Fu (2025, J. Fluid Mech. , vol. 1012, R3) and the TV relation from Duan & Martín (2011, J. Fluid Mech. , vol. 684, pp. 25–59), the prediction errors in the mean velocity and temperature profiles remain within $4.0\,\%$ and $6.0\,\%$ , respectively, across all tested cases. Correspondingly, the skin-friction and wall-heat-transfer coefficients are also accurately predicted, with root mean square prediction errors of approximately $3 \,\%$ . When adopting different velocity transformation methods that are valid for inner-layer scaling, the root mean square prediction errors in the mean velocity and temperature profiles remain below $2.3\,\%$ and $3.6\,\%$ , respectively, which further highlights the universality of the proposed framework.