Reynolds analogy factor in self-similar compressible turbulent boundary layers with pressure gradients

This paper presents a quantitative evaluation of the Reynolds analogy factor for self-similar turbulent boundary layers with pressure gradients in the streamwise direction via direct numerical simulation. Both sub- and supersonic cases are considered at nearly adiabatic wall conditions. The Reynolds analogy factor is found to be greatly increased for adverse-pressure-gradient cases and decreased for favourable-pressure-gradient cases. Although the boundary layers considered cover a comparatively large Reynolds-number range from small to moderate Reynolds numbers, no Reynolds-number dependency of is found in the parameter range investigated. Mach-number influences on are found to be small; decreases slightly with increasing Mach number. The influence of pressure gradients on turns out to be well approximated by the analytical relation derived by So (Intl J. Heat Mass Transfer, vol. 37, 1994, pp. 27-41) for incompressible flow if a fixed, calibrated Reynolds number is used. Moreover, the effects of non-self-similarity prior to the self-similar region are assessed.