Roughness effects in turbulent forced convection. (19th December 2018) - MacDonald, M.; Hutchins, N.; Chung, D.
Abstract : We conducted direct numerical simulations 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-span 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-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, k^+, is increased, the Hama roughness function, [STIX]x0394U^+, increases in the transitionally rough regime before tending towards the fully rough asymptote of [STIX]x1D705_m^-1(k^+)+C, where C is a constant that depends on the particular roughness geometry and [STIX]x1D705_m≈ 0.4 is the von Kármán constant. 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, [STIX]x0394[STIX]x1D6E9^+, appears to tend towards a constant value, [STIX]x0394[STIX]x1D6E9_FR^+ . This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with Re_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 [STIX]x0394[STIX]x1D6E9_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 the inner-normalised momentum roughness length, z_0m^+, where the constant of proportionality is related to [STIX]x0394[STIX]x1D6E9_FR^+ . 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 are observed. Instantaneous visualisations 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.