scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence

Abstract

In turbulent Rayleigh–Bénard (RB) convection with regular, mono-scale, surface roughness, the scaling exponent$\unicode[STIX]{x1D6FD}$in the relationship between the Nusselt number$Nu$and the Rayleigh number$Ra$,$Nu\sim Ra^{\unicode[STIX]{x1D6FD}}$can be${\approx}1/2$locally, provided that$Ra$is large enough to ensure that the thermal boundary layer thickness$\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$is comparable to the roughness height. However, at even larger$Ra$,$\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$becomes thin enough to follow the irregular surface and$\unicode[STIX]{x1D6FD}$saturates back to the value for smooth walls (Zhuet al.,Phys. Rev. Lett., vol. 119, 2017, 154501). In this paper, we prevent this saturation by employing multiscale roughness. We perform direct numerical simulations of two-dimensional RB convection using an immersed boundary method to capture the rough plates. We find that, for rough boundaries that contain three distinct length scales, a scaling exponent of$\unicode[STIX]{x1D6FD}=0.49\pm 0.02$can be sustained for at least three decades of$Ra$. The physical reason is that the threshold$Ra$at which the scaling exponent$\unicode[STIX]{x1D6FD}$saturates back to the smooth wall value is pushed to larger$Ra$, when the smaller roughness elements fully protrude through the thermal boundary layer. The multiscale roughness employed here may better resemble the irregular surfaces that are encountered in geophysical flows and in some industrial applications.

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

“…Recently, many strategies (6,7) were proposed to achieve high heat flux. The most widely used method is to disturb the boundary-layer structures, such as by creating roughness on the conducting plates (8)(9)(10)(11)(12), which enables a notable increase of heat flux (8,12) but may suppress the global heat transport in some parameter ranges (13). Geometrical confinement provides an additional way to enhance heat transfer via plume condensation (14,15), despite an intermediate range of the cell aspect ratio only.…”

“…The realization of efficient heat transfer thus relies on the minimization of the roles of boundary layers, but manipulating boundary layers is notoriously difficult in thermal turbulence, partly due to the weak shear generated by the large-scale mean flow near the conducting plates. 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).…”

Experimental and numerical shadowgraph in turbulent Rayleigh–Bénard convection with a rough boundary: investigation of plumes

“…Thermal convection over rough surfaces is also an important question for real natural and industrial applications, since most natural surfaces are not hydrodynamically smooth. That is why the analysis of the heat transfer efficiency in thermal convection over rough surfaces has triggered both experimental (Du & Tong, 1998;Ciliberto & Laroche, 1999;García et al, 2012;Xie & Xia, 2017;Rusaouen et al, 2018;Tummers & Steunebrink, 2019), theoretical (Shishkina & Wagner, 2011;Goluskin & Doering, 2016), and numerical efforts (Wagner & Shishkina, 2015;Toppaladoddi et al, 2017;Zhu et al, 2017;Zhang et al, 2018;Zhu et al, 2019).…”

Convection driven by internal heat sources and sinks: Heat transport beyond the mixing-length or “ultimate” scaling regime

“…Another line of work consists in replacing the smooth boundaries of RB convection by rough plates. When the roughness has a single scale, it can lead to γ 0.5 over a finite range of Rayleigh numbers, the belief being that this range extends to arbitrarily large Ra when the roughness involves infinitely many scales in a fractal fashion [27][28][29][30][31][32][33][34][35][36][37].…”