中国物理B ›› 2021, Vol. 30 ›› Issue (9): 94701-094701.doi: 10.1088/1674-1056/ac0781

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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. 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
  • 收稿日期:2021-03-21 修回日期:2021-05-07 接受日期:2021-06-03 出版日期:2021-08-19 发布日期:2021-09-06
  • 通讯作者: Yun Bao E-mail:stsby@mail.sysu.edu.cn
  • 基金资助:
    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).

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. 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
  • Received:2021-03-21 Revised:2021-05-07 Accepted:2021-06-03 Online:2021-08-19 Published:2021-09-06
  • Contact: Yun Bao E-mail:stsby@mail.sysu.edu.cn
  • Supported by:
    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).

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摘要： 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 δθ～Ra-0.30 approximately, but the local values vary a lot for different Pr, which become more uniform with Pr increasing.

关键词: turbulent convection, Prandtl number, direct numerical simulations (DNS)

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 δθ～Ra-0.30 approximately, but the local values vary a lot for different Pr, which become more uniform with Pr increasing.

Key words: turbulent convection, Prandtl number, direct numerical simulations (DNS)

中图分类号:  (Turbulent convective heat transfer)

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