Direct numerical simulation of turbulent forced convection with roughness

We present direct numerical simulations of turbulent forced convection over explicitly gridded three-dimensional sinusoidal roughness. The minimal channel is used to circumvent the high cost of simulating high Reynolds number flows, in which only the near-wall flow is captured. As the roughness Reynolds number, k⁺, is increased, the Hama roughness function, ΔU⁺, tends towards the fully rough asymptote which scales with the logarithm of k⁺. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, Re_b. Meanwhile, the temperature difference between smooth- and rough-wall flows, ΔΘ⁺, appears to tend towards a constant value. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with Re_b in the fully rough regime. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress is observed. Instantaneous visualizations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.