Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries

Rusaouen, Eleonore; Liot, Olivier; Castaing, B.; Salort, Julien; Chillà, Francesca

doi:10.1017/jfm.2017.852

Cited by 28 publications

(26 citation statements)

References 34 publications

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“…Roughness of the horizontal plates is an obvious candidate to trigger boundary layer instabilities possibly leading to an enhancement of the heat flux (Ciliberto & Laroche 1999) and possibly to the socalled ultimate regime predicted by Kraichnan (Kraichnan 1962;Roche et al 2010). The wave-length and typical amplitude of our topography is however much larger than the typical roughness used in experiments (Rusaouën et al 2018). Note also that roughness does not always lead to a heat transfer enhancement (Zhang et al 2018).…”

Section: Effect Of the Topography On The Heat Fluxmentioning

confidence: 82%

Rayleigh–Bénard convection with a melting boundary

2018

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We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical Rayleigh-Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier-Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appears as the depth-and therefore the effective Rayleigh number-of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells. †

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Section: Effect Of the Topography On The Heat Fluxmentioning

confidence: 82%

Rayleigh–Bénard convection with a melting boundary

2018

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“…In regime III they found that these scaling exponents saturate to 0.30 to 0.50, respectively, with increasing λ. Rusaouën et al (2018) performed RB experiments with water in cylindrical containers for Ra up to 10 12 . They performed a set of measurements using smooth and rough plates with cubic roughness elements in a square lattice.…”

Section: Introductionmentioning

confidence: 99%

scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence

et al. 2019

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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.

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“…For instance, the use of rough plates disrupts the boundary layer structure and enhances the heat transport significantly, with γ 0.5 over some finite range of Rayleigh number. However, recent studies have shown that this effect is significant at moderate Rayleigh numbers only, while, for strong imposed temperature gradients and fixed geometry, the system settles back into the boundary layer controlled regime (16)(17)(18). Global rotation offers another way to alter the boundary layer dynamics and increase the exponent γ (19,20), albeit for an intermediate range of Ra only, and with a heat flux that is smaller than its nonrotating counterpart (21).…”

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confidence: 99%

Radiative heating achieves the ultimate regime of thermal convection

Lepot

Aumaître

Gallet

2018

Proc. Natl. Acad. Sci. U.S.A.

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The absorption of light or radiation drives turbulent convection inside stars, supernovae, frozen lakes, and Earth's mantle. In these contexts, the goal of laboratory and numerical studies is to determine the relation between the internal temperature gradients and the heat flux transported by the turbulent flow. This is the constitutive law of turbulent convection, to be input into large-scale models of such natural flows. However, in contrast with the radiative heating of natural flows, laboratory experiments have focused on convection driven by heating and cooling plates; the heat transport is then severely restricted by boundary layers near the plates, which prevents the realization of the mixing length scaling law used in evolution models of geophysical and astrophysical flows. There is therefore an important discrepancy between the scaling laws measured in laboratory experiments and those used, e.g., in stellar evolution models. Here we provide experimental and numerical evidence that radiatively driven convection spontaneously achieves the mixing length scaling regime, also known as the "ultimate" regime of thermal convection. This constitutes a clear observation of this regime of turbulent convection. Our study therefore bridges the gap between models of natural flows and laboratory experiments. It opens an experimental avenue for a priori determinations of the constitutive laws to be implemented into models of geophysical and astrophysical flows, as opposed to empirical fits of these constitutive laws to the scarce observational data.

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Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries

Cited by 28 publications

References 34 publications

Rayleigh–Bénard convection with a melting boundary

Rayleigh–Bénard convection with a melting boundary

scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence

Radiative heating achieves the ultimate regime of thermal convection

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