Heat transport by turbulent Rayleigh-Benard convection for Pr similar or equal to 0.8 and 4 x 10(11) less than or similar to Ra less than or similar to 2 x 10(14): ultimate-state transition for aspect ratio Gamma=1.00
Identifieur interne : 000728 ( Hal/Checkpoint ); précédent : 000727; suivant : 000729Heat transport by turbulent Rayleigh-Benard convection for Pr similar or equal to 0.8 and 4 x 10(11) less than or similar to Ra less than or similar to 2 x 10(14): ultimate-state transition for aspect ratio Gamma=1.00
Auteurs : Xiaozhou He [Allemagne] ; Denis Funfschilling [France] ; Eberhard Bodenschatz [Allemagne] ; Guenter Ahlers [Allemagne]Source :
- New Journal of Physics [ 1367-2630 ] ; 2012-07-25.
English descriptors
- mix :
Abstract
We report experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh-Benard convection (RBC) in a cylindrical sample of aspect ratio Gamma equivalent to D/L = 1.00 (D = 1.12m is the diameter and L = 1.12m the height) and compare them with previously reported results for Gamma = 0.50. The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range 4 x 10(11) less than or similar to Ra less than or similar to 2 x 10(14) and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra-1* similar or equal to 2 x 10(13) we find Nu = N0Ra gamma eff with gamma(eff) = 0.321 +/- 0.002 and N-0 = 0.0776, consistent with classical turbulent RBC in a system with laminar boundary layers (BLs) below the top and above the bottom plate and with the prediction of Grossmann and Lohse. For Ra > Ra-1* the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for Gamma = 0.50, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of Ra-1* as it does for Gamma = 0.50. This differs from an earlier estimate by Roche et al (2010 New J. Phys. 12 085014), which yielded a transition at Ra-U similar or equal to 1.3 x 10(11) Gamma(-2.5 +/- 0.5). A Gamma-independent Ra-1* would suggest that the BL shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global Gamma-dependent flow mode. Within the resolution of the measurements the heat transport above Ra-1* is equal for the two Gamma values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of Nu in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system. Several previous measurements for Gamma = 1.00 are re-examined and compared with the present results. None of them identified the ultimate-state transition.
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DOI: 10.1088/1367-2630/14/6/063030
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<front><div type="abstract" xml:lang="en">We report experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh-Benard convection (RBC) in a cylindrical sample of aspect ratio Gamma equivalent to D/L = 1.00 (D = 1.12m is the diameter and L = 1.12m the height) and compare them with previously reported results for Gamma = 0.50. The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range 4 x 10(11) less than or similar to Ra less than or similar to 2 x 10(14) and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra-1* similar or equal to 2 x 10(13) we find Nu = N0Ra gamma eff with gamma(eff) = 0.321 +/- 0.002 and N-0 = 0.0776, consistent with classical turbulent RBC in a system with laminar boundary layers (BLs) below the top and above the bottom plate and with the prediction of Grossmann and Lohse. For Ra > Ra-1* the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for Gamma = 0.50, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of Ra-1* as it does for Gamma = 0.50. This differs from an earlier estimate by Roche et al (2010 New J. Phys. 12 085014), which yielded a transition at Ra-U similar or equal to 1.3 x 10(11) Gamma(-2.5 +/- 0.5). A Gamma-independent Ra-1* would suggest that the BL shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global Gamma-dependent flow mode. Within the resolution of the measurements the heat transport above Ra-1* is equal for the two Gamma values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of Nu in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system. Several previous measurements for Gamma = 1.00 are re-examined and compared with the present results. None of them identified the ultimate-state transition.</div>
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<abstract xml:lang="en">We report experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh-Benard convection (RBC) in a cylindrical sample of aspect ratio Gamma equivalent to D/L = 1.00 (D = 1.12m is the diameter and L = 1.12m the height) and compare them with previously reported results for Gamma = 0.50. The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range 4 x 10(11) less than or similar to Ra less than or similar to 2 x 10(14) and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra-1* similar or equal to 2 x 10(13) we find Nu = N0Ra gamma eff with gamma(eff) = 0.321 +/- 0.002 and N-0 = 0.0776, consistent with classical turbulent RBC in a system with laminar boundary layers (BLs) below the top and above the bottom plate and with the prediction of Grossmann and Lohse. For Ra > Ra-1* the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for Gamma = 0.50, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of Ra-1* as it does for Gamma = 0.50. This differs from an earlier estimate by Roche et al (2010 New J. Phys. 12 085014), which yielded a transition at Ra-U similar or equal to 1.3 x 10(11) Gamma(-2.5 +/- 0.5). A Gamma-independent Ra-1* would suggest that the BL shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global Gamma-dependent flow mode. Within the resolution of the measurements the heat transport above Ra-1* is equal for the two Gamma values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of Nu in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system. Several previous measurements for Gamma = 1.00 are re-examined and compared with the present results. None of them identified the ultimate-state transition.</abstract>
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