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arXiv2026

On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling

We study the validity of the generalized Reynolds analogy (GRA) in compressible turbulent boundary layers over prism-shaped roughness by mining direct numerical simulation data of Mach 2 and Mach 4 compressible turbulent boundary layers with adiabatic and cooled surfaces. Although the direct influence of roughness strongly disrupts the near-wall coupling between momentum and energy, we show that this breakdown is confined to the roughness sublayer. Above this layer, the enthalpy and velocity fields recover a smooth-wall-like similarity, and the GRA becomes asymptotically valid by naturally accounting for roughness-enhanced wall shear stress and heat flux. Building on these results, we propose a GRA-based wall model for predicting heat transfer over rough surfaces, which is coupled with a drag-predictive physics-based method developed for prism-shaped roughness by means of compressibility transformations.

physics.flu-dyn↗

arXiv2023

Assessment of heat transfer and Mach number effects on high-speed turbulent boundary layers

High-speed vehicles experience a highly challenging environment in which the free-stream Mach number and surface temperature greatly influence aerodynamic drag and heat transfer. The interplay of these two parameters strongly affects the near-wall dynamics of high-speed turbulent boundary layers in a non-trivial way, breaking similarity arguments on velocity and temperature fields, typically derived for adiabatic cases. In this work, we present direct numerical simulations of flat-plate zero-pressure-gradient turbulent boundary layers spanning three free-stream Mach numbers [2,4,6] and four wall temperature conditions (from adiabatic to very cold walls), emphasising the choice of the diabatic parameter $\mathitΘ$ (Zhang, Bi, Hussain & She, J. Fluid Mech., vol. 739, pp. 392-420) to recover a similar flow organisation at different Mach numbers. We link qualitative observations on flow patterns to first- and second-order statistics to explain the strong decoupling of temperature-velocity fluctuations that occurs at reduced wall temperatures and high Mach numbers. For these cases, we find that the mean temperature gradient in the near-wall region can reach such a strong intensity that it promotes the formation of a secondary peak of thermal production in the viscous sublayer, which is in direct contrast with the monotonic behaviour of adiabatic profiles. We propose different physical mechanisms induced by wall-cooling and compressibility that result in apparently similar flow features, such as a higher peak in the streamwise velocity turbulence intensity, and distinct ones, such as the separation of turbulent scales.

physics.flu-dyn↗