Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

Liu, Hao-Ran; Chong, Kai Leong; Yang, Rui; Verzicco, Roberto; Lohse, Detlef

doi:10.1017/jfm.2022.181

Cited by 23 publications

(27 citation statements)

References 45 publications

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“…Indeed, air and water introduce a high jump of the fluid properties at the interface (ρ w /ρ a = 1000 and μ w /μ a = 67.5), thus representing an issue for numerical techniques as demonstrated by a series of works where the jump between the two fluid properties has been reduced to obtain numerical stability -see e.g. Liu et al (2022) and Scapin, Demou & Brandt (2022) -or where the evolution of the two fluids is integrated separately in time and their interaction is taken into account with suitable boundary conditions -see e.g. .…”

Section: Fluid Properties and Compression Coefficientmentioning

confidence: 99%

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On wind–wave interaction phenomena at low Reynolds numbers

2023

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After decades of research efforts, wind–wave interaction mechanisms have been recognized as extremely elusive. The reason is the complex nature of the problem, which combines complex coupling mechanisms between turbulent wind and water waves with the presence of multiple governing parameters, such as the friction Reynolds number of the wind, the water depth and the wind fetch. As shown unequivocally here, the use of suitable flow settings allows us to reduce the complex problem of wind–wave interaction to its essential features, mainly as a function of the sole friction Reynolds number of the wind. The resulting numerical solution allows us to study the interactions between water and air layers with their own fluid properties, and to unveil very interesting features, such as an oblique wave pattern travelling upstream and a wave-induced Stokes sublayer. The latter is responsible for a drag reduction mechanism in the turbulent wind. Despite the simulated flow conditions being far from the intense events occurring at the ocean–atmosphere interface, the basic flow phenomena unveiled here may explain some experimental evidence in wind–wave problems. Among other things, the wave-induced Stokes sublayer may shed light on the large scatter of the drag coefficient data in field measurements where swell waves of arbitrary directions are often present. Hence the present results and the developed approach pave the way for the understanding and modelling of the surface fluxes at the ocean–atmosphere interface, which are of overwhelming importance for climate science.

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Section: Fluid Properties and Compression Coefficientmentioning

confidence: 99%

“…Liu et al. (2022) and Scapin, Demou & Brandt (2022) – or where the evolution of the two fluids is integrated separately in time and their interaction is taken into account with suitable boundary conditions – see e.g. Yang & Shen (2010, 2011).…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

On wind–wave interaction phenomena at low Reynolds numbers

2023

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“…2022 a ), two-layer convection (Zhong, Funfschilling & Ahlers 2009; Xie & Xia 2013; Liu et al. 2022 b ) and convection with phase transitions (Lakkaraju et al. 2013; Wang, Mathai & Sun 2019).…”

Section: Introductionmentioning

confidence: 99%

Morphology evolution of a melting solid layer above its melt heated from below

et al. 2023

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We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to $Ra=10^{11}$ ) and three-dimensional (achieving Rayleigh number up to $Ra=10^9$ ) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wang et al. (Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

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“…The convective flow in each fluid layer is turbulent and possesses the key features of turbulent convection (Xie & Xia 2013; Liu et al. 2021, 2022), which have been observed in single-layer convection (Song, Villermaux & Tong 2011; Wang et al. 2016, 2018 a ; Wang, He & Tong 2019; Wang et al.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, because of the coupling of the large-scale flows between the two immiscible fluid layers (Xie & Xia 2013; Liu et al. 2021, 2022), the liquid interface undergoes strong BL fluctuations with a net convective heat flux passing through the interface. A central finding of this investigation is that the measured BL profiles near the liquid interface can be well described by the BL equations for a solid wall modified by a thermal slip length , which is directly linked to the convective heat flux passing through the liquid interface.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation-induced slip of thermal boundary layers at a stable liquid–liquid interface

Huang

Wang

et al. 2022

J. Fluid Mech.

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We report a systematic experimental study of the mean temperature profile $\theta (\delta z)$ and temperature variance profile $\eta (\delta z)$ across a stable and immiscible liquid–liquid (water–FC770) interface formed in two-layer turbulent Rayleigh–Bénard convection. The measured $\theta (\delta z)$ and $\eta (\delta z)$ as a function of distance $\delta z$ away from the interface for different Rayleigh numbers are found to have the scaling forms $\theta (\delta z/\lambda )$ and $\eta (\delta z/\lambda )$ , respectively, with varying thermal boundary layer (BL) thickness $\lambda$ . By a careful comparison with the simultaneously measured BL profiles near a solid conducting surface, we find that the measured $\theta (\delta z)$ and $\eta (\delta z)$ near the liquid interface can be well described by the BL equations for a solid wall, so long as a thermal slip length $\ell _T$ is introduced to account for the convective heat flux passing through the liquid interface. Direct numerical simulation results further confirm that the turbulent thermal diffusivity $\kappa _t$ near a stable liquid interface has a complete cubic form, $\kappa _t(\xi )/\kappa \sim (\xi +\xi _0)^3$ , where $\kappa$ is the molecular thermal diffusivity of the convecting fluid, $\xi =\delta z/\lambda$ is the normalized distance away from the liquid interface and $\xi _0$ is the normalized slip length associated with $\ell _T$ .

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Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

Cited by 23 publications

References 45 publications

On wind–wave interaction phenomena at low Reynolds numbers

On wind–wave interaction phenomena at low Reynolds numbers

Morphology evolution of a melting solid layer above its melt heated from below

Fluctuation-induced slip of thermal boundary layers at a stable liquid–liquid interface

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