Reynolds number dependence of turbulent heat transfer over irregular rough surfaces

Abstract

To study the scaling of turbulent heat transfer over a rough surface, we performed a series of direct numerical simulations on turbulent heat transfer over a three-dimensional irregular rough surface with varying the friction Reynolds numbers and relative roughness values. We considered rough surfaces with three different relative roughness values of 1/1.9, 1/4.3, and 1/9.0, and the simulations were performed at three friction Reynolds numbers of 115, 250, and 550. The temperature was treated as a passive scalar with a Prandtl number of unity. Regarding the scaling of the Reynolds analogy factor, which is defined as the ratio of the doubled Stanton number to the skin friction coefficient, a correlation function with the skin friction coefficient, equivalent roughness, and Prandtl number provides an accurate account of the effects of relative roughness, roughness Reynolds number, and friction Reynolds number. For scaling the turbulent momentum and energy fluxes, we introduced the decomposition of the turbulent fluxes into the smooth wall profiles at matched friction Reynolds numbers and their deviatoric components. The baseline smooth wall profile was found to account for the effect of the friction Reynolds number, while the deviatoric component incorporated the effect of the roughness Reynolds number. The dispersion fluxes, namely, the dispersive covariance and dispersion heat flux, were dominantly affected by the roughness Reynolds number rather than the friction Reynolds number. To obtain a better understanding of the effect of wall roughness on the momentum and heat transfer mechanisms, we analyzed the spatial and time-averaged momentum and energy equations and discussed the physical mechanisms that caused a decrease in the mean velocity and temperature from smooth wall profiles.