Effect of sidewall thermal conductivity on Rayleigh-Bénard convection:  a numerical study

LIU Miaomiao; WANG Qi; WAN Zhenhua; SUN Dejun

doi:10.7638/kqdlxxb-2021.0320

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Effect of sidewall thermal conductivity on Rayleigh-Bénard convection: a numerical study

更新时间：2026-05-28

- Effect of sidewall thermal conductivity on Rayleigh-Bénard convection: a numerical study
- Vol. 40, Issue 2, Pages: 165-173(2022)
- 作者机构：
  
  中国科学技术大学近代力学系,合肥,230027
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2021.0320
  CLC： V211.3
- Published：2022
- 稿件说明：
移动端阅览
刘苗苗, 王启, 万振华, 等. 侧壁效应对Rayleigh-Bénard对流影响的数值模拟研究[J]. 空气动力学学报, 2022, 40(2): 165−173.

LIU Miaomiao, WANG Qi, WAN Zhenhua, et al. Effect of sidewall thermal conductivity on Rayleigh-Bénard convection: a numerical study[J]. 2022, 40(2): 165-173.
刘苗苗, 王启, 万振华, 等. 侧壁效应对Rayleigh-Bénard对流影响的数值模拟研究[J]. 空气动力学学报, 2022, 40(2): 165−173. DOI： 10.7638/kqdlxxb-2021.0320

LIU Miaomiao, WANG Qi, WAN Zhenhua, et al. Effect of sidewall thermal conductivity on Rayleigh-Bénard convection: a numerical study[J]. 2022, 40(2): 165-173. DOI： 10.7638/kqdlxxb-2021.0320.

摘要

Rayleigh-Bénard（RB）对流的研究中通常使用侧壁绝热的温度边界条件，然而实际的对流换热设备中侧壁存在导热性且会对系统传热和流动特性产生影响。为探究侧壁导热性对RB对流的影响，本文采用侧壁等温假设，即侧壁温度为上下壁面温度的平均值，使用二维和三维直接数值模拟的方法研究了侧壁恒温的RB对流。流体工质为普朗特数

= 5.3的水，二维和三维方腔宽高比

为1。将侧壁等温的计算结果与经典的侧壁绝热的RB对流结果进行比较，研究表明：侧壁等温时，二维和三维系统中均存在上下壁面

不相等的情形，该特性发生在有限的

值区间内，且与系统内的流动结构密切相关；侧壁恒温时，系统的传热效率要高于侧壁绝热情况下的传热效率，这是由于侧壁恒温条件下，一部分热量可以直接通过侧壁来传递，从而绕开温度边界层。当采用恒温边界条件时，流场的强度减弱，从而系统的

要小于侧壁绝热条件下对应的

。

Abstract

In the study of Rayleigh-Bénard (RB) convection

it is usually assumed that sidewalls are adiabatic. However

this is not always the case in real heat exchangers. Consequently

the flow structures and heat transfer will be inevitably affected by non-adiabatic walls. The effect of the thermal conductivity of sidewalls on RB convection is investigated by two- and three-dimensional direct numerical simulations with the sidewall temperature being set to the mean of the top and bottom temperatures. The working fluid is water with the Prandtl number

= 5.3 a

nd the aspect ratio

of the simulation box is fixed to

= 1. The results are further compared with those of traditional RB convection with adiabatic sidewalls. It is found that in a certain range of the Rayleigh number

the Nusselt numbers

of the top and bottom plates are not equal

which is closely related to the flow structures. The global heat transport is higher for the isothermal sidewall case than that of the adiabatic sidewall case. This is because

in the former case

part of the heat can be transferred directly through sidewalls instead of being absorbed by the thermal boundary layer. For the isothermal sidewall case

the global Reynolds number is smaller than that of the adiabatic sidewall case due to lower turbulence insensity.

关键词

Keywords

references

SUGIYAMA K, NI R, STEVENS R J, et al. Flow reversals in thermally driven turbulence[J]. Physical Review Letters, 2010, 105(3): 034503. DOI:10.1103/physrevlett.105.034503

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(1): 335-364. DOI:10.1146/annurev.fluid.010908.165152

ZHOU Q, XIA K Q. Advances and outlook in turbulent Rayleigh-Benard convection[J]. Advances in Mechanics, 2012, 42(3): 231-251. (in Chinese)

VERZICCO R. Sidewall finite-conductivity effects in confined turbulent thermal convection[J]. Journal of Fluid Mechanics, 2002, 473: 201-210. DOI:10.1017/s0022112002002501

STEVENS R J A M, LOHSE D, VERZICCO R. Sidewall effects in Rayleigh–Bénard convection[J]. Journal of Fluid Mechanics, 2014, 741: 1-27. DOI:10.1017/jfm.2013.664

AHLERS G. Effect of sidewall conductance on heat-transport measurements for turbulent Rayleigh-Bénard convection[J]. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2001, 63(1 pt 2): 015303. DOI:10.1103/physreve.63.015303

ROCHE P E, CASTAING B, CHABAUD B, et al. Side wall effects in Rayleigh Bénard experiments[J]. The European Physical Journal B - Condensed Matter and Complex Systems, 2001, 24(3): 405-408. DOI:10.1007/s10051-001-8690-5

NIEMELA J J, SREENIVASAN K R. Confined turbulent convection[J]. Journal of Fluid Mechanics, 2003, 481: 355-384. DOI:10.1017/s0022112003004087

LEONG W H, HOLLANDS K G T, BRUNGER A P. On a physically-realizable benchmark problem in internal natural convection[J]. International Journal of Heat and Mass Transfer, 1998, 41(23): 3817-3828. DOI:10.1016/S0017-9310(98)00095-7

LEONG W H, HOLLANDS K G T, BRUNGER A P. Experimental Nusselt numbers for a cubical-cavity benchmark problem in natural convection[J]. International Journal of Heat and Mass Transfer, 1999, 42(11): 1979-1989. DOI:10.1016/S0017-9310(98)00299-3

SEZAI I, MOHAMAD A A. Natural convection in a rectangular cavity heated from below and cooled from top as well as the sides[J]. Physics of Fluids, 2000, 12(2): 432-443. DOI:10.1063/1.870321

CUESTA I, GRAU F X. Rayleigh-Bénard convection in a perfectly conducting cubical cavity at Pr = 0.7[C ] //CHT'01-Advances in Comput-ational Heat Transfer II. Proceedings of a Second Symposium. Begel House Inc. , 2001.

PALLARES J, ARROYO M P, GRAU F X, et al. Experimental laminar Rayleigh-Bénard convection in a cubical cavity at moderate Rayleigh and Prandtl numbers[J]. Experiments in Fluids, 2001, 31(2): 208-218. DOI:10.1007/s003480100275

PALLARES J, CUESTA I, GRAU F X. Laminar and turbulent Rayleigh-Bénard convection in a perfectly conducting cubical cavity[J]. International Journal of Heat and Fluid Flow, 2002, 23(3): 346-358. DOI:10.1016/S0142-727X(02)00182-0

PEPPER D W, HOLLANDS K G T. Summary of benchmark numerical studies for 3-d natural convection in an air-filled enclosure[J]. Numerical Heat Transfer, Part A: Applications, 2002, 42(1-2): 1-11. DOI:10.1080/10407780290059396

PAUL M R, CHIAM K H, CROSS M C, et al. Pattern formation and dynamics in Rayleigh-Bénard convection: numerical simulations of experimentally realistic geometries[J]. Physica D: Nonlinear Phenomena, 2003, 184(1-4): 114-126. DOI:10.1016/S0167-2789(03)00216-1

PUIGJANER D, HERRERO J, SIMÓ C, et al. Bifurcation analysis of steady Rayleigh–Bénard convection in a cubical cavity with conducting sidewalls[J]. Journal of Fluid Mechanics, 2008, 598: 393-427. DOI:10.1017/s0022112007000080

BOROŃSKA K, TUCKERMAN L S. Extreme multiplicity in cylindrical Rayleigh-Bénard convection. I. Time dependence and oscillations[J]. Physical Review E, 2010, 81(3): 036320. DOI:10.1103/physreve.81.036320

HÉBERT F, HUFSCHMID R, SCHEEL J, et al. Onset of Rayleigh-Bénard convection in cylindrical containers[J]. Physical Review E, 2010, 81(4): 046318. DOI:10.1103/physreve.81.046318

HU Y P, LI Y R, LI M H, et al. Effects of enclosure geometry and thermal boundary condition on Rayleigh-Bénard convection of cold water near its maximum density[J]. International Journal of Thermal Sciences, 2017, 120: 220-232. DOI:10.1016/j.ijthermalsci.2017.06.013

YU J, GOLDFADEN A, FLAGSTAD M, et al. Onset of Rayleigh-Bénard convection for intermediate aspect ratio cylindrical containers[J]. Physics of Fluids, 2017, 29(2): 024107. DOI:10.1063/1.4976543

KOIZUMI H, HOSOKAWA I, ITO H. Effects of side-wall temperature on the flow pattern of Rayleigh-Bénard cells in an enclosure[J]. Heat Transfer - Japanese Research, 1998, 27(6): 462-471. DOI:10.1002/(sici)1520-6556(1998)27: 6462: aid-htj53.0.co;2-d

KOIZUMI H. Effects of sidewall temperature on the flow pattern and the bifurcation to chaos of Rayleigh-benard cells in an enclosure (aspect ratio of enclosure: 6: 4: 1)[J]. JSME International Journal Series B, 2003, 46(3): 377-384. DOI:10.1299/jsmeb.46.377

CORCIONE M. Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above[J]. International Journal of Thermal Sciences, 2003, 42(2): 199-208. DOI:10.1016/S1290-0729(02)00019-4

MOON J Y, CHUNG B J. Influence of Prandtl number, height and lateral cooling condition on laminar natural convection in a rectangular enclosure[J]. Heat and Mass Transfer, 2019, 55(6): 1593-1605. DOI:10.1007/s00231-018-02540-7

VASU U, TIWARI S, SAHU S. Effect of side wall conditions and aspect ratio on convective pattern formation in Rayleigh-Benard convection[J]. International Journal of Thermal Sciences, 2019, 139: 246-268. DOI:10.1016/j.ijthermalsci.2019.01.031

ROCHE P E, CASTAING B, CHABAUD B, et al. Heat transfer in turbulent Rayleigh-bénard convection below the ultimate regime[J]. Journal of Low Temperature Physics, 2004, 134(5-6): 1011-1042. DOI:10.1023/B: JOLT.0000016727.23228.78

MADANAN U, GOLDSTEIN R J. Effect of sidewall conductance on nusselt number for Rayleigh-bénard convection: a semi-analytical and experimental correction[J]. Journal of Heat Transfer, 2019, 141(12). DOI:10.1115/1.4044659

IVANČIĆ A, OLIVA A, SEGARRA C D P, et al. Heat transfer simulation in vertical cylindrical enclosures for supercritical Rayleigh number and arbitrary side-wall conductivity[J]. International Journal of Heat and Mass Transfer, 1999, 42(2): 323-343. DOI:10.1016/S0017-9310(98)00113-6

STRINGANO G, VERZICCO R. Mean flow structure in thermal convection in a cylindrical cell of aspect ratio one half[J]. Journal of Fluid Mechanics, 2006, 548: 1. DOI:10.1017/s0022112005007378

URBAN P, HANZELKA P, MUSILOVÁ V, et al. Heat transfer in cryogenic helium gas by turbulent Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1[J]. New Journal of Physics, 2014, 16(5): 053042. DOI:10.1088/1367-2630/16/5/053042

XU M, PAUL M R. Chaotic Rayleigh-Bénard convection with finite sidewalls[J]. Physical Review E, 2018, 98(1-1): 012201. DOI:10.1103/PhysRevE.98.012201

DANILOV N I, MITIN K A, BERDNIKOV V S. Effect of conjugate heat transfer on the side and horizontal walls on the structure of convective flow in the Rayleigh-Benard convection mode[J]. Journal of Physics: Conference Series, 2019, 1382(1): 012078. DOI:10.1088/1742-6596/1382/1/012078

MADANAN U, GOLDSTEIN R J. Thermal convection in horizontal rectangular enclosures at moderate Rayleigh numbers: Effect of sidewall conductance and aspect ratio[J]. International Journal of Heat and Mass Transfer, 2019, 136: 178-185. DOI:10.1016/j.ijheatmasstransfer.2019.02.076

WAN Z H, WEI P, VERZICCO R, et al. Effect of sidewall on heat transfer and flow structure in Rayleigh–Bénard convection[J]. Journal of Fluid Mechanics, 2019, 881: 218-243. DOI:10.1017/jfm.2019.770

PANDEY S, PARK Y G, HA M Y. An exhaustive review of studies on natural convection in enclosures with and without internal bodies of various shapes[J]. International Journal of Heat and Mass Transfer, 2019, 138: 762-795. DOI:10.1016/j.ijheatmasstransfer.2019.04.097

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Direct numerical simulation of gas injection into a high-enthalpy turbulent boundary layer based on OpenCFD-Comb

Numerical simulation of the stably stratified thermohaline flow with horizontal shear

Heat transfer models for porous media in porous-walled turbulent flows

Study on drag characteristics of an ellipsoidal particle under wall constraint

Numerical study on the orientation effects of roughness elements on turbulence statistics

Related Author

Liu Hongwei

Li Xinliang

Zeng Guangkang

YANG Yantao

XUN Weikang

DONG Yuhong

ZHANG Jinlong

ZHAO Zehao

Related Institution

School of Engineering Science, University of Chinese Academy of Sciences, Beijing

State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing

State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing

Shanghai Institute of Aircraft Mechanics and Control, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai

Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai

AI问答

⁰