Heat transport by turbulent Rayleigh–Bénard convection forPr≃ 0.8 and 3 × 1012≲Ra≲ 1015: aspect ratio Γ = 0.50

Ahlers, Guenter; He, Xiaozhou; Fünfschilling, Denis; Bodenschatz, Eberhard

doi:10.1088/1367-2630/14/10/103012

Cited by 68 publications

(120 citation statements)

References 82 publications

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“…For RB flow, the transition to an ultimate regime was first qualitatively predicted by Kraichnan (1962), and later quantitatively by Grossmann & Lohse (2000, 2001 and then experimentally found by He et al (2012b,a); Ahlers et al (2012); Roche et al (2010). It lies outside the present reach of DNS.…”

Section: Introductionmentioning

confidence: 80%

Exploring the phase diagram of fully turbulent Taylor–Couette flow

et al. 2014

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Direct numerical simulations of Taylor-Couette flow (TC), i.e. the flow between two coaxial and independently rotating cylinders were performed. Shear Reynolds numbers of up to 3 · 10 5 , corresponding to Taylor numbers of T a = 4.6 · 10 10 , were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect-and rotation-ratios, but depends significantly on the radius-ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius-ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15% of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner vs outer Reynolds number parameter space and in the Taylor vs inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech. 164, 155-183, 1986) phase diagram towards the ultimate regime.

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Section: Introductionmentioning

confidence: 80%

Exploring the phase diagram of fully turbulent Taylor–Couette flow

et al. 2014

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“…It should be noted that for the SF 6 experiments there are more data points in (b). The reason is that this approach does not require experimental values of T c (which for (a) we calculated using Ahlers et al (2012a)), and we used all T b , T t data points tabulated in Ahlers et al (2012b). The theoretically estimated Nu = Nu(Ra) scalings, for both the nearly constant Pr SF 6 Göttingen data ,b) (a,b) and the Brno cryogenic He data where Pr increases at the high-Ra end (Urban et al 2014) (c,d), indicate no transition to the ultimate state.…”

Section: Discussionmentioning

confidence: 99%

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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“…New experimental heat-flux measurements have been reported recently by the MPIDS group in Göttingen for Rayleigh numbers beyond 10 12 , using pressurized SF 6 as the working fluid (Ahlers et al , 2012bFunfschilling, Bodenschatz & Ahlers 2009;He et al 2012). They have obtained several possible effective scaling exponents, possibly less steep than γ = 1/3, but eventually close to γ = 0.36 for Ra > 10…”

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Boundary layer structure in a rough Rayleigh–Bénard cell filled with air

et al. 2015

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In this experimental work, the aim is to understand how turbulent thermal flows are enhanced by the destabilization of the boundary layers. Square-stud roughness elements have been added on the bottom plate of a rectangular Rayleigh-Bénard cell in air, to trigger instabilities in the boundary layers. The top plate is kept smooth. The cell proportions are identical to those of the water cell previously operated and described by Salort et al. (Phys. Fluids, vol. 26, 2014, 015112), but six times larger. The very large size of the Barrel of Ilmenau allows detailed velocity fields to be obtained using particle image velocimetry very close to the roughness elements. We found that the flow is quite different at low Rayleigh numbers, where there is no heat-transfer enhancement, and at high Rayleigh numbers where there is a heat-transfer enhancement due to the roughness. Below the transition, the fluid inside the notch, i.e. between the studs, is essentially at rest, though it is slowly recirculating. The velocity profiles on the top of obstacles and in grooves are fairly compatible with those obtained in the smooth case. Above the transition, on the other hand, we observe large incursions of the bulk inside the notch, and the velocity profiles on the top of obstacles are closer to the logarithmic profiles expected in the case of turbulent boundary layers.

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Heat transport by turbulent Rayleigh–Bénard convection forPr≃ 0.8 and 3 × 10¹²≲Ra≲ 10¹⁵: aspect ratio Γ = 0.50

Cited by 68 publications

References 82 publications

Exploring the phase diagram of fully turbulent Taylor–Couette flow

Exploring the phase diagram of fully turbulent Taylor–Couette flow

Has the ultimate state of turbulent thermal convection been observed?

Boundary layer structure in a rough Rayleigh–Bénard cell filled with air

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