LAUSR

Abstract This paper presents a quantitative evaluation of the Reynolds analogy factor $s=2c_h/c_f$ 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 $s$ is found in the parameter range investigated. Mach-number influences on $s$ are found to be small; $s$ decreases slightly with increasing Mach number. The influence of pressure gradients on $s$ 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.