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 wide parameter range, superordinate influences compressibility, wall heat pressure gradient terms governing equations are identified visualized. allows us both to determine what degree cases corresponding different Mach number, pressure-gradient conditions have physically comparable behaviour design boundary-layer with specific sought-after behaviour. To this end, newly formulated identities skin-friction coefficient $c_f$ heat-transfer $c_h$ wall-normal integrals non-dimensional total-enthalpy derived evaluated. As individual resulting stay formally close equations, further evaluation common arguments ‘strong’ Reynolds analogy an perspective. A particular formulation Eckert number $Ec$ is proposed as similarity parameter, mapping numbers conditions.