Large scale circulation transition in thermal convection with large Prandtl number

BAO Yun; HE Jianchao; FANG Mingwei

doi:10.7638/kqdlxxb-2021.0335

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Large scale circulation transition in thermal convection with large Prandtl number

更新时间：2026-05-28

- Large scale circulation transition in thermal convection with large Prandtl number
- Vol. 40, Issue 2, Pages: 174-181(2022)
- 作者机构：
  
  中山大学航空航天学院,深圳,518107
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2021.0335
  CLC： O357.5+3
- Published：2022
- 稿件说明：
移动端阅览
包芸, 何建超, 方明卫. 大Pr数湍流热对流大尺度环流形态变化特性[J]. 空气动力学学报, 2022, 40(2): 174−181.

BAO Yun, HE Jianchao, FANG Mingwei. Large scale circulation transition in thermal convection with large Prandtl number[J]. 2022, 40(2): 174-181.
包芸, 何建超, 方明卫. 大Pr数湍流热对流大尺度环流形态变化特性[J]. 空气动力学学报, 2022, 40(2): 174−181. DOI： 10.7638/kqdlxxb-2021.0335

BAO Yun, HE Jianchao, FANG Mingwei. Large scale circulation transition in thermal convection with large Prandtl number[J]. 2022, 40(2): 174-181. DOI： 10.7638/kqdlxxb-2021.0335.

摘要

大尺度环流是湍流热对流的重要特征之一，为了研究大尺度环流形态的变化特征，本文在大Prandtl数（

）下，较大的Rayleigh数（

）范围内对热对流的流动形态进行研究。采用直接数值模拟（DNS）计算二维湍流热对流，对大

= 10、20的热对流大尺度环流形态进行研究，

范围是1×10

～1×10

，同时与

= 4.3情况进行了对比分析。结果表明：大

数的热对流大尺度环流存在三种形态，方形、椭圆形和圆形，小

数只有椭圆形和圆形两种；方形的最大速度点在侧壁附近，椭圆形大尺度环流的最大速度点在椭圆与角涡的相剪切处，圆形的最大速度点随机出现在大尺度环流周长线上；方形到椭圆形的转变是一种渐变，存在过渡点，而椭圆形到圆形是突变；大尺度环流的长短轴之比，方形时在1.0～1.2之间，椭圆形时在1.2以上，而圆形时基本为1；大尺度环流形态变化影响Reynolds数（

）的变化规律：补偿

数变化规律显示，大尺度环流形态由方形渐变为椭圆形时，

数出现小量下降，过渡点出现极小值，由椭圆形突变为圆形时，

数出现间断式大幅下降。

Abstract

We report a numerical study of large scale circulation (LSC) in two-dimensional turbulent thermal convection with two Prandtl numbers (

= 10

20) and Rayleigh number (

) ranging from 1×10

to 1×10

. To compared with small

some results at

= 4.3 are shown in this article. Three patterns of LSC are found at large Prandtl numbers

i.e. square

ellipse and circle

while only the

latter two patterns are found at small Prandtl numbers

italic/>. For the classical elliptical LSC

the positions of maximum velocity always appear between the LSC and the corner rolls

and the positions appear randomly in the LSC for the circular LSC. Whereas

the maximum velocities appear near the sidewalls for the square LSC. The LSC transition from square to ellipse is a gradual change while the transition from ellipse to circle is a drastic change. The ratio between the major axis and the minor axis of LSC is 1.0～1.2 for square

greater than 1.2 for ellipse

but near 1.0 for circle. The relationship between Reynolds number (

) and

is influenced by the transition of LSC

which can be indicated by the compensated

. The compensated

decreases slightly and then reaches a local minimum when the LSC changes from square to ellipse

while it decreases sharply from ellipse to circle.

关键词

Keywords

references

AHLERS G, GROSSMANN S, LOHSE D. Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection[J]. Reviews of Modern Physics, 2009, 81(2): 503-537. DOI:10.1103/revmodphys.81.503

LOHSE D, XIA K Q. Small-scale properties of turbulent Rayleigh-bénard convection[J]. Annual Review of Fluid Mechanics, 2010, 42: 335-364. DOI:10.1146/annurev.fluid.010908.165152

XIA K Q. Current trends and future directions in turbulent thermal convection[J]. Theoretical and Applied Mechanics Letters, 2013, 3(5): 052001. DOI:10.1063/2.1305201

GLOBE S, DROPKIN D. Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below[J]. Journal of Heat Transfer, 1959, 81(1): 24-28. DOI:10.1115/1.4008124

DAVIS A H. XXXI. Natural convective cooling of wires[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1922, 43(254): 329-339. DOI:10.1080/14786442208565219

DAVIS A H. LXXIX. Natural convective cooling in fluids[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1922, 44(263): 920-940. DOI:10.1080/14786441208562566

HESLOT F, CASTAING B, LIBCHABER A. Transitions to turbulence in helium gas[J]. Physical Review A, General Physics, 1987, 36(12): 5870-5873. DOI:10.1103/physreva.36.5870

SHRAIMAN B I, SIGGIA E D. Heat transport in high-Rayleigh-number convection[J]. Physical Review A, Atomic, Molecular, and Optical Physics, 1990, 42(6): 3650-3653. DOI:10.1103/physreva.42.3650

GROSSMANN S, LOHSE D. Scaling in thermal convection: a unifying theory[J]. Journal of Fluid Mechanics, 2000, 407: 27-56. DOI:10.1017/s0022112099007545

GROSSMANN S, LOHSE D. Thermal convection for large Prandtl numbers[J]. Physical Review Letters, 2001, 86(15): 3316-3319. DOI:10.1103/PhysRevLett.86.3316

SCHMALZL J, BREUER M, HANSEN U. On the validity of two-dimensional numerical approaches to time-dependent thermal convection[J]. Europhysics Letters (EPL), 2004, 67(3): 390-396. DOI:10.1209/epl/i2003-10298-4

VAN DER POEL E P, STEVENS R J A M, LOHSE D. Comparison between two- and three-dimensional Rayleigh–bénard convection[J]. Journal of Fluid Mechanics, 2013, 736: 177-194. DOI:10.1017/jfm.2013.488

HUANG M J, BAO Y, . Characteristics of flow and thermal boundary layer in turbulent Rayleigh-Bénard convection[J]. Acta Physica Sinica, 2016, 65(20): 204702. DOI:10.7498/aps.65.204702

GAO Z Y, LUO J H, BAO Y. Numerical study of heat-transfer in two- and quasi-two-dimensional Rayleigh–Bénard convection[J]. Chinese Physics B, 2018, 27(10): 104702. DOI:10.1088/1674-1056/27/10/104702

ZHANG Y Z, SUN C, BAO Y, et al. How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection[J]. Journal of Fluid Mechanics, 2018, 836: R2. DOI:10.1017/jfm.2017.786

ZHU X J, MATHAI V, STEVENS R J A M, et al. Transition to the ultimate regime in two-dimensional Rayleigh-bénard convection[J]. Physical Review Letters, 2018, 120(14): 144502. DOI:10.1103/PhysRevLett.120.144502

HE J C, FANG M W, GAO Z Y, et al. Effects of Prandtl number in two-dimensional turbulent convection[J]. Chinese Physics B, 2021, 30(9): 094701. DOI:10.1088/1674-1056/ac0781

SHISHKINA O, HORN S, WAGNER S, et al. Thermal boundary layer equation for turbulent Rayleigh-Bénard convection[J]. Physical Review Letters, 2015, 114(11): 114302. DOI:10.1103/PhysRevLett.114.114302

SHISHKINA O, HORN S, EMRAN M S, et al. Mean temperature profiles in turbulent thermal convection[J]. Physical Review Fluids, 2017, 2(11): 113502. DOI:10.1103/physrevfluids.2.113502

CASTILLO-CASTELLANOS A, SERGENT A, ROSSI M. Reversal cycle in square Rayleigh–Bénard cells in turbulent regime[J]. Journal of Fluid Mechanics, 2016, 808: 614-640. DOI:10.1017/jfm.2016.647

PANDEY A, VERMA M K, BARMA M. Reversals in infinite-Prandtl-number Rayleigh-bénard convection[J]. Physical Review E, 2018, 98(2): 023109. DOI:10.1103/physreve.98.023109

ZHANG Y, ZHOU Q, SUN C. Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection[J]. Journal of Fluid Mechanics, 2017, 814: 165-184. DOI:10.1017/jfm.2017.19

XU A, SHI L, XI H D. Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection[J]. Physics of Fluids, 2019, 31(12): 125101. DOI:10.1063/1.5129818

NG C S, OOI A, LOHSE D, et al. Vertical natural convection: application of the unifying theory of thermal convection[J]. Journal of Fluid Mechanics, 2015, 764: 349-361. DOI:10.1017/jfm.2014.712

CHILLÀ F, SCHUMACHER J. New perspectives in turbulent Rayleigh-Bénard convection[J]. The European Physical Journal E, 2012, 35(7): 58. DOI:10.1140/epje/i2012-12058-1

STEVENS R J A M, VAN DER POEL E P, GROSSMANN S, et al. The unifying theory of scaling in thermal convection: the updated prefactors[J]. Journal of Fluid Mechanics, 2013, 730: 295-308. DOI:10.1017/jfm.2013.298

CHONG K L, WAGNER S, KACZOROWSKI M, et al. Effect of Prandtl number on heat transport enhancement in Rayleigh-Bénard convection under geometrical confinement[J]. Physical Review Fluids, 2018, 3: 013501. DOI:10.1103/physrevfluids.3.013501

SILANO G, SREENIVASAN K R, VERZICCO R. Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10–1 and 104 and Rayleigh numbers between 105 and 109[J]. Journal of Fluid Mechanics, 2010, 662: 409-446. DOI:10.1017/s0022112010003290

SHISHKINA O, EMRAN M S, GROSSMANN S, et al. Scaling relations in large-Prandtl-number natural thermal convection[J]. Physical Review Fluids, 2017, 2(10): 103502. DOI:10.1103/physrevfluids.2.103502

VERZICCO R, CAMUSSI R. Prandtl number effects in convective turbulence[J]. Journal of Fluid Mechanics, 1999, 383: 55-73. DOI:10.1017/s0022112098003619

BREUER M, WESSLING S, SCHMALZL J, et al. Effect of inertia in Rayleigh-Bénard convection[J]. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2004, 69(2 pt 2): 026302. doi:10.1103/physreve.69.026302

LI X M, HE J D, TIAN Y, et al. Effects of Prandtl number in quasi-two-dimensional Rayleigh–bénard convection[J]. Journal of Fluid Mechanics, 2021, 915: A60. DOI:10.1017/jfm.2021.21

SUN C, XI H D, XIA K Q. Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5[J]. Physical Review Letters, 2005, 95(7): 074502. DOI:10.1103/PhysRevLett.95.074502

BROWN E, NIKOLAENKO A, AHLERS G. Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection[J]. Physical Review Letters, 2005, 95(8): 084503. DOI:10.1103/PhysRevLett.95.084503

BAO Y, GAO Z Y, YE M X, et al. Numerical study of Prandtl number effects in turbulent thermal convection[J]. Acta Physica Sinica, 2018, 67(1): 014701. DOI:10.7498/aps.67.20171518

BAO Y, LUO J, YE M. Parallel direct method of DNS for two-dimensional turbulent Rayleigh-bénard convection[J]. Journal of Mechanics, 2018, 34(2): 159-166. DOI:10.1017/jmech.2017.54

LUO J H, BAO Y. Simulation of turbulent thermal convection and its characteristics at very high Ra[J]. Computer Aided Engineering, 2017, 26(4): 65-70. (in Chinese)

BAO Y, HE J C, GAO Z Y, et al. Effect of plume motion path on heat transfer characteristics in two-dimensional turbulent thermal convection[J]. Acta Physica Sinica, 2019, 68(16): 164701. DOI:10.7498/aps.68.20190323

SUGIYAMA K, CALZAVARINI E, GROSSMANN S, et al. Flow organization in two-dimensional non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water[J]. Journal of Fluid Mechanics, 2009, 637: 105-135. DOI:10.1017/s0022112009008027

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