About the influences of compressibility, heat transfer and pressure gradients in compressible turbulent boundary layers

This paper presents a comprehensive analysis of the momentum and energy transfer in compressible turbulent boundary layers based on integral identities. By considering data obtained from direct numerical simulations for a wide parameter range, the superordinate influences of compressibility, wall heat transfer and pressure gradient on the terms of the governing equations are identified and visualized. This allows us both to determine to what degree cases corresponding to different Mach number, heat transfer and pressure-gradient conditions have physically comparable behaviour and to design turbulent boundary-layer cases with specific sought-after behaviour. To this end, newly formulated identities for the skin-friction coefficient c(f) and the specific heat-transfer coefficient c(h) from wall-normal integrals based on the non-dimensional compressible momentum and total-enthalpy equations are derived and evaluated. As the individual terms of the resulting identities stay formally close to the terms of the governing equations, the integral analysis further allows the evaluation of common arguments derived from the 'strong' Reynolds analogy from an integral perspective. A particular formulation of the Eckert number Ec is proposed as a similarity parameter, mapping cases with different Mach numbers and wall heat transfer conditions.

Automated summary

This paper presents a comprehensive analysis of momentum and energy transfer in compressible turbulent boundary layers based on integral identities. The superordinate influences of compressibility, wall heat transfer, and pressure gradient on the governing equations are identified and visualized using data from direct numerical simulations. Newly formulated identities for skin-friction coefficient and specific heat-transfer coefficient are derived, allowing for comparison of different cases and design of turbulent boundary-layer cases with specific behavior. The proposed formulation of the Eckert number serves as a similarity parameter, mapping cases with different Mach numbers and wall heat transfer conditions.