Heat transfer in rough-wall turbulent thermal convection in the ultimate regime

Abstract

Heat and momentum transfer in wall-bounded turbulent flow, coupled with the effects of wallroughness, is one of the outstanding questions in turbulence research. In the standard Rayleigh-Bénard problem for natural thermal convection, it is notoriously difficult to reach the so-called ultimate regime in which the near-wall boundary layers are turbulent. Following the analyses proposed by Kraichnan [Phys. Fluids 5, 1374-1389(1962] and Grossmann & Lohse [Phys. Fluids 23, 045108 (2011)], we instead utilize recent direct numerical simulations of forced convection over a rough wall in a minimal channel [MacDonald, Hutchins & Chung, J. Fluid Mech. 861, 138-162 (2019)] to directly study these turbulent boundary layers. We focus on the heat transport (in dimensionless form, the Nusselt number N u) or equivalently the heat transfer coefficient (the Stanton number C h ). Extending the analyses of Kraichnan and Grossmann & Lohse, we assume logarithmic temperature profiles with a roughness-induced shift to predict an effective scaling of N u ∼ Ra 0.42 , where Ra is the dimensionless temperature difference, corresponding to C h ∼ Re −0.16 , where Re is the centerline Reynolds number. This is pronouncedly different from the skin-friction coefficient C f , which in the fully rough turbulent regime is independent of Re, due to the dominant pressure drag. In rough-wall turbulence the absence of the analog to pressure drag in the temperature advection equation is the origin for the very different scaling properties of the heat transfer as compared to the momentum transfer. This analysis suggests that, unlike momentum transfer, the asymptotic ultimate regime, where N u ∼ Ra 1/2 , will never be reached for heat transfer at finite Ra.

The -dependence of the critical roughness height in two-dimensional turbulent Rayleigh–Bénard convection

“…2017; MacDonald et al. 2019; Emran & Shishkina 2020) further revealed that at height the exponent decreases back to the exponent in the smooth cell, due to the competition between the turbulent bulk and BL flow.…”

“…With sinusoidally rough upper and lower surfaces in two dimensions, Toppaladoddi, Succi & Wettlaufer (2015 numerically showed that the Nu(Ra) scaling exponent reaches the value of 0.5 for a certain roughness wavelength. Recent studies (Zhu et al 2017;MacDonald et al 2019;Emran & Shishkina 2020) further revealed that at height Ra the Nu(Ra) exponent decreases back to the exponent in the smooth cell, due to the competition between the turbulent bulk and BL flow.…”

Ultimate heat transfer in ‘wall-bounded’ convective turbulence

“…2017, 2019; MacDonald et al. 2019; Tummers & Steunebrink 2019). This transient scaling would not imply the transition to the asymptotic ultimate scaling, because a further increase in leads to saturation down to the classical scaling .…”

Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement

“…As an example, the introduction of wall roughness has been widely adopted to disrupt boundary layers by enhancing the detachment of the thermal boundary layer from the tips of rough elements (8)(9)(10)(11). As the analog to pressure drag is absent in the temperature advection equation (18), however, the system settles back to the boundary-layer-controlled regime for large imposed temperature differences (9,12). Another attempt is to perform the lateral confinement of turbulent flows (14,15), which has been successful in manipulating the flow structures in the convective bulk, yet the laminar boundary layers still limit the global heat flux.…”