Universal scaling laws in turbulent Rayleigh-Bénard convection with and without roughness
Résumé
Experimental measurements of heat-flux and velocity in turbulent Rayleigh-Bénard convection are reported on a wide range of operating conditions, with either smooth or rough boundaries, in water or fluorocarbon, and aspect ratios 1 or 2. The heat-flux, expressed as the dimensionless parameter Nusselt number is found in agreement with Grossmann-Lohse prediction in smooth cells. The new measurements in the rough cell with fluorocarbon, which reaches Rayleigh numbers, Ra, up to 2.5 × 10$^{12}$ at $Pr$ = 11, the Nusselt number show a clear Ra$^{1/2}$ scaling, hinting a fully turbulent regime. The $Nu$ $vs$ Ra relationship is not unique, in that it depends on the cell geometry, plate roughness, Prandtl numbers, as well as details in the experimental setup. The Reynolds number essentially scales like Re ∝ Ra$^{1/2}$ $Pr^{-0.7}$ for all experiments, but show deviations with the various flow configurations. We find that the dimensionless heat-flux, expressed as $RaNu$, has a universal scaling with Reynolds number, collapsing all data, rough or smooth, even those in the literature where the $Nu$ vs Ra scaling is in apparent contradiction.
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