Effect of Boundary Layers Asymmetry on Heat Transfer Efficiency in Turbulent Rayleigh-Bénard Convection at Very High Rayleigh Numbers

Urban, P.; Hanzelka, P.; Králı́k, Tomáš; Musilová, Věra; Srnka, A.; Skrbek, L.

doi:10.1103/physrevlett.109.154301

Cited by 50 publications

(64 citation statements)

References 12 publications

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“…This is an order of magnitude smaller than the largest values of φ encountered in the work of Urban et al (2012). Thus, as discussed also by He et al (2013), the concerns expressed by Urban et al (2012) are irrelevant to the present work. 4.2.…”

Section: Non-oberbeck-boussinesq Effectsmentioning

confidence: 80%

Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

Wei

Ahlers

2014

J. Fluid Mech.

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We report measurements of logarithmic temperature profiles Θ(z, r) = A(r) × ln(z/L) + B(r) in the bulk of turbulent Rayleigh-Bénard convection (here Θ is a scaled and timeaveraged local temperature in the fluid, z is the vertical and r the radial position, and L is the sample height). Two samples had aspect ratios Γ ≡ D/L = 1.00 and 0.50 (where D = 190 mm is the diameter). The fluid was a fluorocarbon with a Prandtl number of Pr = 12.3. The measurements covered the Rayleigh-number range 2 × 10 10 Ra 2 × 10 11 for Γ = 1.00 and 3 × 10 11 Ra 2 × 10 12 for Γ = 0.50. In contradistinction to what had been found for Γ = 0.50 and Pr = 0.78 by Ahlers et al. (Phys. measurements revealed no Ra dependence of the amplitude A(r) of the logarithmic term. Within the experimental resolution, the amplitude was also found to be independent of Γ . It varied with r in a manner consistent with the function A(ξ ) = A 1 / 2ξ − ξ 2 , where ξ ≡ (R − r)/R with R = D/2 and A 1 0.0016. The results for A(r) are smaller than those obtained from experiments and direct numerical simulations (Ahlers et al., Phys. Rev. Lett., vol. 109, 2012, art. 114501) at similar values of Ra for Pr = 0.7 and Γ = 1 2 by a factor that depended slightly upon Ra but was close to 2.

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Section: Non-oberbeck-boussinesq Effectsmentioning

confidence: 80%

Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

Wei

Ahlers

2014

J. Fluid Mech.

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“…The relation (17) 37,38 , it has been shown, both numerically 39 and experimentally 40,41 , that the ultimate regime scaling can be realized when the solid boundaries are absent. In RT turbulence, the observation of the ultimate state is not surprising as boundaries play no role in the system and the bulk dynamics dominate the convective turbulence in the mixing zone.…”

Section: Resultsmentioning

confidence: 99%

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Zhou

2013

Physics of Fluids

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We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl number with a spatial resolution of 2048 × 8193 grid points. Our main focus is on the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. Our results show that the buoyancy force balances the inertial force at all scales below the integral length scale and thus validate the basic force-balance assumption of the Bolgiano-Obukhov scenario in 2D RT turbulence. It is further found that the Kolmogorov dissipation scale η(t) ∼ t 1/8 , the kinetic-energy dissipation rate ε u (t) ∼ t −1/2 , and the thermal dissipation rate ε θ (t) ∼ t −1 . All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [Phys. Rev. Lett. 91, 115001 (2003)]. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents ξ r p of the pth-order temperature structure functions are shown to saturate to ξ r ∞ ≃ 0.78 ± 0.15 for the highest orders, p ∼ 10. The value of ξ r ∞ and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [Phys. Rev. Lett. 88, 054503 (2002)], supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems.

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“…This paper extends our recent experimental studies considerably (Urban, Musilová & Skrbek 2011;Urban et al 2012Urban et al , 2014, where we discussed in detail issues such as the influence of the shape (aspect ratio) and material properties of the experimental cells, various corrections to the raw data and advantages of using a clean cryogenic environment. Here, we do not discuss details of experimental corrections applied to the experimentally measured raw data; rather, we concern ourselves exclusively with the non-Oberbeck-Boussinesq effects.…”

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confidence: 88%

Has the ultimate state of turbulent thermal convection been observed?

Skrbek

Urban

2015

J. Fluid Mech.

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An important question in turbulent Rayleigh-Bénard convection is the scaling of the Nusselt number with the Rayleigh number in the so-called ultimate state, corresponding to asymptotically high Rayleigh numbers. A related but separate question is whether the measurements support the so-called Kraichnan law, according to which the Nusselt number varies as the square root of the Rayleigh number (modulo a logarithmic factor). Although there have been claims that the Kraichnan regime has been observed in laboratory experiments with low aspect ratios, the totality of existing experimental results presents a conflicting picture in the highRayleigh-number regime. We analyse the experimental data to show that the claims on the ultimate state leave open an important consideration relating to non-Oberbeck-Boussinesq effects. Thus, the nature of scaling in the ultimate state of Rayleigh-Bénard convection remains open.

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Effect of Boundary Layers Asymmetry on Heat Transfer Efficiency in Turbulent Rayleigh-Bénard Convection at Very High Rayleigh Numbers

Cited by 50 publications

References 12 publications

Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Has the ultimate state of turbulent thermal convection been observed?

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