科研之友
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摘要
The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-Benard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio Gamma of a closed cylindrical cell and the Rayleigh number Ra. The Prandtl number is Pr = 0.7 throughout the study. The aspect ratio Gamma is varied between 0.5 and 12 for a Rayleigh number range between 10(7) and 10(9). The Nusselt number Nu is the dimensionless measure of the global turbulent heat transfer. For small and moderate aspect ratios, the global heat transfer law Nu = A x Ra(beta) shows a power law dependence of both fit coefficients A and beta on the aspect ratio. A minimum of Nu(Gamma) is found at Gamma approximate to 2.5 and Gamma approximate to 2.25 for Ra = 10(7) and Ra = 10(8), respectively. This is the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations in the convection cell. For larger aspect ratios Gamma greater than or similar to 8, our data indicate that the heat transfer becomes independent of the aspect ratio of the cylindrical cell. The aspect ratio dependence of the turbulent heat transfer for small and moderate Gamma is in line with a varying amount of energy contained in the LSC, as quantified by the Karhunen-Loeve or proper orthogonal decomposition (POD) analysis of the turbulent convection field. The POD analysis is conducted here by the snapshot method for at least 100 independent realizations of the turbulent fields. The primary POD mode, which replicates the time-averaged LSC patterns, transports about 50% of the global heat for Gamma >= 1. The snapshot analysis enables a systematic disentanglement of the contributions of POD modes to the global turbulent heat transfer. Although the smallest scale - the Kolmogorov scale eta(K) - and the largest scale - the cell height H - are widely separated in a turbulent flow field, the LSC patterns in fully turbulent fields exhibit strikingly similar texture to those in the weakly nonlinear regime right above the onset of convection. Pentagonal or hexagonal circulation cells are observed preferentially if the aspect ratio is sufficiently large (Gamma greater than or similar to 8).
- 出版日期2010-7-25
