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Chin. Phys. B, 2021, Vol. 30(9): 094701    DOI: 10.1088/1674-1056/ac0781

Effects of Prandtl number in two-dimensional turbulent convection

Jian-Chao He(何建超)1, Ming-Wei Fang(方明卫)1, Zhen-Yuan Gao(高振源)2,3, Shi-Di Huang(黄仕迪)2,3, and Yun Bao(包芸)1,†
1 School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, China;
2 Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China;
3 Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen 518055, China
Abstract  We report a numerical study of the Prandtl-number (Pr) effects in two-dimensional turbulent Rayleigh-Bénard convection. The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number (Ra) range from 107 to 1010. We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr, and the flow pattern becomes plume-dominated at high Pr. The evolution in flow pattern is quantified by the Reynolds number (Re), with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and -0.87 to -0.93, respectively. It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr, but their difference becomes marginal as Ra increases. For the thermal boundary layer, the spatially averaged thicknesses for all the Pr numbers can be described by δθRa-0.30 approximately, but the local values vary a lot for different Pr, which become more uniform with Pr increasing.
Keywords:  turbulent convection      Prandtl number      direct numerical simulations (DNS)  
Received:  21 March 2021      Revised:  07 May 2021      Accepted manuscript online:  03 June 2021
PACS:  47.27.te (Turbulent convective heat transfer)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11961160719, 11702128, 91752201, and 11772362), the Shenzhen Fundamental Research Program (Grant No. JCYJ20190807160413162), the Fundamental Research Funds for the Central Universities (Sun Yat-sen University under Grant No. 19lgzd15), and the Department of Science and Technology of Guangdong Province, China (Grant No. 2019B21203001).
Corresponding Authors:  Yun Bao     E-mail:

Cite this article: 

Jian-Chao He(何建超), Ming-Wei Fang(方明卫), Zhen-Yuan Gao(高振源), Shi-Di Huang(黄仕迪), and Yun Bao(包芸) Effects of Prandtl number in two-dimensional turbulent convection 2021 Chin. Phys. B 30 094701

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