Heat-transport enhancement in rotating turbulent Rayleigh-Benard convection

摘要

We present new Nusselt-number (Nu) measurements for slowly rotating turbulent thermal convection in cylindrical samples with aspect ratio Gamma = 1.00 and provide a comprehensive correlation of all available data for that Gamma. In the experiment compressed gasses (nitrogen and sulfur hexafluride) as well as the fluorocarbon C6F14 (3M Fluorinert FC72) and isopropanol were used as the convecting fluids. The data span the Prandtl-number (Pr) range 0.74 < Pr < 35.5 and are for Rayleigh numbers (Ra) from 3 x 10(8) to 4 x 10(11). The relative heat transport Nu(r) (1/Ro) = Nu(1/Ro)/Nu(0) as a function of the dimensionless inverse Rossby number 1/Ro at constant Ra is reported. For Pr approximate to 0.74 and the smallest Ra = 3.6 x 10(8) the maximum enhancement Nu(r,max)-1 due to rotation is about 0.02. With increasing Ra, Nu(r,max)-1 decreased further, and for Ra greater than or similar to 2 x 10(9) heat-transport enhancement was no longer observed. For larger Pr the dependence of Nu(r) on 1/Ro is qualitatively similar for all Pr. As noted before, there is a very small increase of Nu(r) for small 1/Ro, followed by a decrease by a percent or so, before, at a critical value 1/Ro(c), a sharp transition to enhancement by Ekman pumping takes place. While the data revealed no dependence of 1/Ro(c) on Ra, 1/Ro(c) decreased with increasing Pr. This dependence could be described by a power law with an exponent alpha similar or equal to-0.41. Power-law dependencies on Pr and Ra could be used to describe the slope S-Ro(+) = partial derivative Nu(r)/partial derivative(1/Ro) just above 1/Ro(c). The Pr and Ra exponents were beta(1) =-0.16 +/- 0.08 and beta(2) =-0.04 +/- 0.06, respectively. Further increase of 1/Ro led to further increase of Nu(r) until it reached a maximum value Nu(r), max. Beyond the maximum, the Taylor-Proudman (TP) effect, which is expected to lead to reduced vertical fluid transport in the bulk region, lowered Nu(r). Nu(r,max) was largest for the largest Pr. For Pr = 28.9, for example, we measured an increase of the heat transport by up to 40% (Nu(r)-1 = 0.40) for the smallest Ra = 2.2 x 10(9), even though we were unable to reach Nu(r), max over the accessible 1/Ro range. Both Nu(r,max)(Pr, Ra) and its location 1/Romax(Pr, Ra) along the 1/Ro axis increased with Pr and decreased with Ra. Although both could be given by power-lawrepresentations, the uncertainties of the exponents are relatively large.