Lin Wenxian, Armfield S W
Solar Energy Research Institute, Yunnan Normal University, Kunming, Yunnan 650092, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066312. doi: 10.1103/PhysRevE.86.066312. Epub 2012 Dec 14.
Recent studies have used scaling analysis to obtain simple power-law relations that accurately predict the Prandtl (Pr) number dependency of natural-convection boundary layers subjected to both isothermal and ramped heating conditions, when Pr>1. The analysis used in those studies cannot be extended to Pr<1 fluids, and it is not clear at present whether such simple scaling relations can be developed for Pr<1 fluids. In the present study, the Pr>1 scalings are shown to perform well for the start-up stage of the Pr<1 flow, but not for the fully developed flow. The Pr>1 scalings are modified to provide unified Prandtl number scalings for fully developed natural-convection boundary layers for both Pr≳1 and Pr≲1, with the unknown powers obtained empirically via direct numerical simulation. The modified scalings are shown to perform well for the fully developed flow, with the exception being the prediction of the inner viscous boundary-layer thickness.
最近的研究利用标度分析获得了简单的幂律关系，当普朗特数（Pr）>1时，这些关系能准确预测等温加热和斜坡加热条件下自然对流边界层的普朗特数依赖性。这些研究中使用的分析方法不能扩展到Pr<1的流体，目前尚不清楚是否能为Pr<1的流体建立这样简单的标度关系。在本研究中，结果表明Pr>1的标度关系在Pr<1流动的启动阶段表现良好，但在充分发展的流动中则不然。对Pr>1的标度关系进行了修正，以提供适用于Pr≳1和Pr≲1的充分发展自然对流边界层的统一普朗特数标度关系，其中未知幂次通过直接数值模拟凭经验获得。结果表明，修正后的标度关系在充分发展的流动中表现良好，但对内粘性边界层厚度的预测除外。
