Fluctuating Thermal Boundary Layers and Heat Transfer in Turbulent Rayleigh–Bénard Convection

Ching, Emily S. C.; Dung, On Yu; Shishkina, Olga

doi:10.1007/s10955-017-1739-5

Cited by 14 publications

(15 citation statements)

References 30 publications

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“…with e = 2π/(3 √ 3) ≈ 1.2 as well as for c = 2: (47) and (48) are found to be in good agreement with DNS results for Pr = 4.38 and Pr = 2547.9 respectively, as reported in [37]. For intermediate values of Pr between 4.38 and 2547.9, (45) with a fitted value of c is shown to be in good agreement with DNS results [42].…”

Section: Theoretical Modelsupporting

confidence: 83%

“…In [37,42] we have shown that (45) describes the temperature profiles obtained in DNS of RBC very well in the large-Pr regime, from Pr = 4.38 to Pr = 2547.9. The DNS simulations were conducted in a cylindrical container with a diameter-to-height aspect ratio 1, using the finite-volume computational code Goldfish [43].…”

Section: Validation Of the Modelmentioning

confidence: 82%

“…For the particular case of very large Pr, the thermal BL is deeply nested within the viscous BL and the eddy thermal diffusivity can be approximated by (28). Thus, (42) is reduced to the form reported in [37]:…”

Section: Theoretical Modelmentioning

confidence: 99%

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Mean temperature profiles in turbulent thermal convection

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To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation including the effects of fluctuations has to be solved. In Shishkina et al. [Phys. Rev. Lett. 114, 114302 (2015)], the thermal BL equation with the fluctuations taken into account as an eddy thermal diffusivity has been solved for large Prandtl-number fluids for which the eddy thermal diffusivity and the velocity field can be approximated, respectively, as a cubic and a linear function of the distance from the plate. In the present work, we make use of the idea of Prandtl's mixing length model and relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal BL equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters for fluids with a general Prandtl number. With a proper choice of the parameters, our predictions of the temperature profiles are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10(7) to 10(9)

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Section: Theoretical Modelsupporting

confidence: 83%

Section: Validation Of the Modelmentioning

confidence: 82%

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Mean temperature profiles in turbulent thermal convection

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“…In particular, the value of θ ′ (0) [φ ′ (ξ)] −1/2 is a pure constant. This together with(18) immediately imply the following scaling relation for the Nusselt number with the Reynolds and the Prandtl numbers, which thus in general holds for natural boundary-layer dominated large-Prandtl-number thermal convection:Nu ∼ Re 1/2 Pr 1/2 . (20)Note that apart from RBC, the scaling(20) was found also in other different configurations of natural large-Prandtl-number thermal convective flows, for example, in horizontal convection, where the fluid layer is heated through one region of the bottom and cooled through another region of the bottom [23-25] and also in vertical convection, where the fluid is heated through one vertical surface of the fluid layer and cooled though another vertical surface…”

mentioning

confidence: 78%

“…[6,16]. This approach can be generalized to include the influence of the turbulent fluctuations within the BL [17][18][19] and also can be adapted to the case of a non-vanishing pressure gradient within the BL (or to the case of a non-constant wind above the horizontal isothermal plate, which approaches the plate at arbitrary angle), see [20,21].…”

Section: Driven) Boundary-layer Dominated Thermal Convectionmentioning

confidence: 99%

Scaling relations in large-Prandtl-number natural thermal convection

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In this study, we follow Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], who derived various scalings regimes for the dependence of the Nusselt number Nu and the Reynolds number Re on the Rayleigh number Ra and the Prandtl number Pr. We focus on theoretical arguments as well as on numerical simulations for the case of large-Pr natural thermal convection. Based on an analysis of self-similarity of the boundary layer equations, we derive that in this case the limiting large-Pr boundary-layer dominated regime is I-infinity(<), introduced and defined by Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], with the scaling relations Nu similar to Pr-0 Ra-1/3 and Re similar to Pr-1 Ra-2/3. Our direct numerical simulations for Ra from 10(4) to 10(9) and Pr from 0.1 to 200 showthat the regime I-infinity(<) is almost indistinguishable from the regime III infinity, where the kinetic dissipation is bulk-dominated. With increasing Ra, the scaling relations undergo a transition to those in IVu of Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], where the thermal dissipation is determined by its bulk contribution

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Bulk temperature and heat transport in turbulent Rayleigh–Bénard convection of fluids with temperature-dependent properties

Weiss

Ahlers

et al. 2018

J. Fluid Mech.

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We critically analyse the different ways to evaluate the dependence of the Nusselt number ($\mathit{Nu}$) on the Rayleigh number ($\mathit{Ra}$) in measurements of the heat transport in turbulent Rayleigh–Bénard convection under general non-Oberbeck–Boussinesq conditions and show the sensitivity of this dependence to the choice of the reference temperature at which the fluid properties are evaluated. For the case when the fluid properties depend significantly on the temperature and any pressure dependence is insignificant we propose a method to estimate the centre temperature. The theoretical predictions show very good agreement with the Göttingen measurements by He et al. (New J. Phys., vol. 14, 2012, 063030). We further show too the values of the normalized heat transport $\mathit{Nu}/\mathit{Ra}^{1/3}$ are independent of whether they are evaluated in the whole convection cell or in the lower or upper part of the cell if the correct reference temperatures are used.

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Fluctuating Thermal Boundary Layers and Heat Transfer in Turbulent Rayleigh–Bénard Convection

Cited by 14 publications

References 30 publications

Mean temperature profiles in turbulent thermal convection

Mean temperature profiles in turbulent thermal convection

Scaling relations in large-Prandtl-number natural thermal convection

Bulk temperature and heat transport in turbulent Rayleigh–Bénard convection of fluids with temperature-dependent properties

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