Periodicity of Convection Under Lateral Local Heating

NING Lizhong; ZHANG Di; NING Bibo; LI Kaiji; TIAN Weili; TENG Sufen

doi:10.21656/1000-0887.400091

Volume 41 Issue 2

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(2): 125-133

NING Lizhong, ZHANG Di, NING Bibo, LI Kaiji, TIAN Weili, TENG Sufen. Periodicity of Convection Under Lateral Local Heating[J]. Applied Mathematics and Mechanics, 2020, 41(2): 125-133. doi: 10.21656/1000-0887.400091

Citation:

PDF( 5967 KB)

Periodicity of Convection Under Lateral Local Heating

doi: 10.21656/1000-0887.400091

¹State Key Laboratory of EcoHydraulics in Northwest Arid Region of China,Xi’an University of Technology, Xi’an 710048, P.R.China;²College of Civil Engineering and Architecture, Jiaxing University, Jiaxing, Zhejiang 314001, P.R. China;³Lanzhou Construction Investment (Holding) Group Co. Ltd., Lanzhou 730000, P.R.China;⁴Department of Architecture, Shanghai University, Shanghai 200444, P.R. China

Funds: The National Natural Science Foundation of China(10872164)

Received Date: 2019-03-11
Rev Recd Date: 2019-03-27
Publish Date: 2020-02-01

Abstract

Abstract

The periodicity of convection under lateral local heating with Prandtl number Pr=0.027 2 was studied through numerical simulation of hydrodynamic equations. The results show that, convection develops in the order of steady-state convection, single-local-period convection, double-local-period convection and quasi-period convection with the increase of Grashof number Gr. Convection is steady for Gr＜3.6×10³. In the range of 3.6×10³＜Gr＜6.78×10⁴,convection has a single local period; in the range of 6.78×10⁴＜Gr＜3.5×10⁶, convection has double local periods; for Gr＞3.5×10⁶,convection has a quasi period. In the steady convection case, the position of the convection roll corresponding to the heating zone on the wall does not change with time. In the single-local-period convection case, the core of the convection roll corresponding to the upper heating zone on the wall moves periodically with time. In the double-local-period convection case, the cores of the convection rolls corresponding to the 2 heating zones on the wall move periodically with time. In the quasi-period convection case, there are small convection rolls with quasi-period variations in the upper and lower parts of the convection loop corresponding to the lower unheated zone on the wall. In the range of the convection periods mentioned above, the convection period decreases with the increase of Grashof number Gr for given Prandtl number Pr.
- lateral local heating,
- single-local-period convection,
- double-local-period convection,
- quasi-period convection

FullText(HTML)

References(26)

References

[1]	CROSS M C, HOHENBERG P C. Pattern formation outside of equilibrium[J]. Reviews of Modern Physics,1993,65(3): 998-1011.
[2]	BODENSCHATZ E, PESCH W, AHLERS G. Recent developments in Rayleigh-Bénard convection[J]. Annual Review of Fluid Mechanics,2000,32: 709-778.
[3]	KNOBLOCH E, MERCADER I, BATISTE O, et al. Convectons in periodic and bounded domains[J]. Fluid Dynamics Research,2010,42(2): 025505.
[4]	MERCADER I, BATISTE O, ALONSO A, et al. Convectons, anticonvectons and multiconvectons in binary fluid convection[J]. Journal of Fluid Mechanics,2011,667: 586-606.
[5]	NING L Z, HARADA Y, YAHATA H. Localized traveling waves in binary fluid convection[J]. Progress of Theoretical Physics,1996,96(4): 669-682.
[6]	MERCADER I, BATISTE O, ALONSO A, et al. Traveling convectons in binary fluid convection[J]. Journal of Fluid Mechanics,2013,722: 240-265.
[7]	WATANABE T, IIMA M, NISHIURA Y. Spontaneous formation of travelling localized structures and their asymptotic behaviours in binary fluid convection[J]. Journal of Fluid Mechanics,2012,712: 219-243.
[8]	TARAUT A V, SMORODIN B L, LUCKE M. Collisions of localized convection structures in binary fluid mixtures[J]. New Journal of Physics,2012,14(9): 093055.
[9]	宁利中, 王永起, 袁喆, 等. 两种不同结构的混合流体局部行波对流斑图[J]. 科学通报, 2016,61(8): 872-880. （NING Lizhong, WANG Yongqi, YUAN Zhe, et al. Two types of patterns of localized traveling wave convection in binary fluid mixtures with different structures[J]. Chinese Science Bulletin,2016,61(8): 872-880.(in Chinese))
[10]	宁利中, 余荔, 袁喆, 等. 沿混合流体对流分叉曲线上部分支行波斑图的演化[J]. 中国科学: 物理力学天文学, 2009,39(5): 746-751.(NING Lizhong, YU Li, YUAN Zhe, et al. Evolution of traveling wave patterns along upper branch of bifurcation diagram in binary fluid convection[J]. Scientia Sinica： Physica, Mechanica & Astronomica,2009,39(5): 746-751.(in Chinese))
[11]	ZHAO B X, TIAN Z F. Numerical investigation of binary fluid convection with a weak negative separation ratio in finite containers[J]. Physics of Fluids,2015,27: 074102.
[12]	宁利中, 王娜, 袁喆, 等. 分离比对混合流体Rayleigh-Bénard对流解的影响[J]. 物理学报, 2014,63(10): 104401.(NING Lizhong, WANG Na, YUAN Zhe, et al. Influence of separation ratio on Rayleigh-Bénard convection solutions in a binary fluid mixture[J]. Acta Physica Sinica,2014,63(10): 104401.(in Chinese))
[13]	宁利中, 胡彪, 宁碧波, 等. Poiseuille-Rayleigh-Benard流动中对流斑图的分区和成长[J]. 物理学报, 2016,65(21): 214401.(NING Lizhong, HU Biao, NING Bibo, et al. Partition and growth of convection patterns in Poiseuille-Rayleigh-Benard flow[J]. Acta Physica Sinica,2016,65(21): 214401.(in Chinese))
[14]	宁利中, 胡彪, 周洋, 等. 底部周期加热的局部对流斑图[J]. 应用力学学报, 2016,33(4): 684-689.(NING Lizhong, HU Biao, ZHOU Yang, et al. Patterns of localized convection heated periodically from below[J]. Chinese Journal of Applied Mechanics,2016,33(4): 684-689.(in Chinese))
[15]	宁利中, 渠亚伟, 宁碧波, 等. 一种新的混合流体对流竖向镜面对称对传波斑图[J]. 应用数学和力学, 2017,38(11): 1230-1239.(NING Lizhong, QU Yawei, NING Bibo, et al. A new type of counterpropagating wave pattern of vertical mirror symmetry in binary fluid convection[J]. Applied Mathematics and Mechanics,2017,38(11): 1230-1239.(in Chinese))
[16]	胡彪, 宁利中, 宁碧波, 等. 水平来流对扰动成长和对流周期性的影响[J]. 应用数学和力学, 2017,38(10): 1103-1111.（HU Biao, NING Lizhong, NING Bibo, et al. Effects of horizontal flow on perturbation growth and the convection periodicity[J]. Applied Mathematics and Mechanics,2017,38(10): 1103-1111.(in Chinese))
[17]	IVEY G N. Experiments on transient natural convection in a cavity[J]. Journal of Fluid Mechanics,1984,144: 389-401.
[18]	BATCHELOR G K. Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures[J]. Quarterly of Applied Mathematics,1954,12(3): 209-233.
[19]	PATTERSON J C, IMBERGER J. Unsteady natural convection in a rectangular cavity[J]. Journal of Fluid Mechanics,1980,100(1): 65-86.
[20]	XU F, PATTERSON J C, LEI C. Heat transfer through coupled thermal boundary layers induced by a suddenly generated temperature difference[J]. International Journal of Heat & Mass Transfer,2009,52(21): 4966-4975.
[21]	XU F, PATTERSON J C, LEI C. On the double-layer structure of the thermal boundary layer in a differentially heated cavity[J]. International Journal of Heat & Mass Transfer,2008〖STHZ〗, 51(15): 3803-3815.
[22]	XU F, PATTERSON J C, LEI C. Temperature oscillations in a differentially heated cavity with and without a fine on the sidewall[J]. International Communications in Heat & Mass Transfer,2010,37(4): 350-359.
[23]	XU F. Convective instability of the vertical thermal boundary layer in a differentially heated cavity[J]. International Communications in Heat & Mass Transfer,2014,52(3): 8-14.
[24]	徐丰, 崔会敏. 侧加热腔内的自然对流[J]. 力学进展, 2014,44(1): 98-136.(XU Feng, CUI Huimin. Natural convection in a differentially heated cavity[J]. Advances in Mechanics,2014,44(1): 98-136.(in Chinese))
[25]	YAHATA H. Thermal convection in a vertical slot with lateral heating[J]. Journal of the Physical Society of Japan,1997,66(11): 3434-3443.
[26]	李开继, 宁利中, 宁碧波, 等. 格拉晓夫数 Gr 对侧向局部加热腔体内对流结构的影响[J]. 力学季刊, 2016,37(1): 131-138.(LI Kaiji, NING Lizhong, NING Bibo, et al. Effect of Grashof number Gr on convection structure of rectangular cavity heated locally from side[J]. Chinese Quarterly of Mechanics,2016,37(1): 131-138.(in Chinese))