Roughness effects in turbulent forced convection

Abstract

We conducted direct numerical simulations (DNSs) of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal channel is used to circumvent the high cost of simulating high Reynolds number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal channel agrees well with that of the conventional full-span channel, indicating it can be readily used for heat-transfer studies at a much reduced cost compared to conventional DNS. As the roughness Reynolds number, $k^{+}$, is increased, the Hama roughness function, $\Delta U^{+}$, increases in the transitionally rough regime before tending towards the fully rough asymptote of ${\kappa }_m^{-1}\log (k^{+})+C$, where $C$ is a constant that depends on the particular roughness geometry and ${\kappa }_m\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $R{e}_b$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\Delta {\Theta }^{+}$, appears to tend towards a constant value, $\Delta {\Theta }_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $R{e}_b$ in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness $k_s/k$ and the temperature difference $\Delta {\Theta }_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat transfer roughness lengths, $z_{0m}/z_{0h}$, being linearly proportional to $z_{0m}^{+}$, the momentum roughness length [continued]...

arXiv commentAccepted (In press) in the Journal of Fluid Mechanics

References in corpus (5)

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• Turbulent flow over transitionally rough surfaces with varying roughness densities
• The minimal-span channel for rough-wall turbulent flows
• Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows
• Changes in the boundary-layer structure at the edge of the ultimate regime in vertical natural convection

Cited by in corpus (7)

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• Large Eddy Simulations of Fully-Developed Turbulent Flows Over Additively Manufactured Rough Surfaces
• The ultimate state of turbulent permeable-channel flow
• Large eddy simulations of conjugate heat transfer in boundary layers over laser-scanned ice roughness
• Spanwise wall forcing can reduce turbulent heat transfer more than drag