Growth and Dynamics of Convection Patterns With Horizontal Flow

NING Lizhong; NING Bibo; HU Biao; TIAN Weili

doi:10.21656/1000-0887.410104

Volume 41 Issue 10

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(10): 1146-1156

NING Lizhong, NING Bibo, HU Biao, TIAN Weili. Growth and Dynamics of Convection Patterns With Horizontal Flow[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1146-1156. doi: 10.21656/1000-0887.410104

Citation:

PDF( 4501 KB)

Growth and Dynamics of Convection Patterns With Horizontal Flow

doi: 10.21656/1000-0887.410104

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;³Jiangxi Provincial Water Conservancy Planning, Design & Research Institute,Nanchang 330029, P.R.China;⁴Department of Architecture, Shanghai University, Shanghai 200444, P.R.China

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

Received Date: 2020-04-10
Rev Recd Date: 2020-05-25
Publish Date: 2020-10-01

Abstract

Abstract

The growth and dynamic characteristics of convection patterns with horizontal flow for Prandtl number Pr=0.72 were numerically simulated with 2D basic equations of fluid mechanics. The results show that, for given relative Rayleigh number Ra_r=5(Rayleigh number Ra=8 540) and Reynolds number Re=22.5, the growth of the traveling wave convection pattern can be divided into 3 stages: the convection development stage, the exponential growth stage and the periodic variation stage (including the transition adaptation region and the stable periodic variation region). The average wave number in the traveling wave convection decreases with time or with the growth of the convection pattern. The exponential growth stage length in traveling wave convection becomes shorter and the growth rate of the maximum vertical velocity of convection increases with relative Rayleigh number Ra_r.For Reynolds number Re=5,the growth rate of the maximum vertical velocity of convection relates with the variation of relative Rayleigh number Ra_r in the form of γ_m=0.004 8Ra^{6.065 3}_r.In the periodic variation stage, after the transition adaptation region of the convection pattern and parameters in traveling wave convection, the convection enters the stable periodic variation region of the convection pattern and parameters. For given relative Rayleigh number Ra_r=5,dimensionless period T_t of traveling wave convection varying with Re can be expressed as T_t=0.001 4Re^{2.363 5}.
- horizontal flow,
- average wave number,
- exponential growth stage,
- periodic variation stage,
- growth rate

FullText(HTML)

References(27)

References

[1]	CROSS M C, HOHENBERG P C. Pattern formation outside of equilibrium[J]. Reviews of Modern Physics,1993,65(3): 851-1112.
[2]	BODENSCHATZ E, PESCH W, AHLERS G. Recent developments in Rayleigh-Bénard convection[J]. Annual Review of Fluid Mechanics,2000,32(1): 709-778.
[3]	NING L Z, HARADA Y, YAHATA H. Formation process of the traveling wave state with a defect in binary fluid convection[J]. Progress of Theoretical Physics,1997,98(3): 551-566.
[4]	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(7): 074102.
[5]	MERCADER I, BATISTE O, ALONSO A, et al. Traveling convectons in binary fluid convection[J]. Journal of Fluid Mechanics,2013,722: 240-265.
[6]	WATANABE T, IIMA M, NISHIURA Y. Spontaneous formation of travelling localized structures and their asymptotic behaviour in binary fluid convection[J]. Journal of Fluid Mechanics,2012,712: 219-243.
[7]	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.
[8]	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))
[9]	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))
[10]	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))
[11]	余荔, 宁利中, 魏炳乾, 等. Rayleigh-Benard 对流及其在工程中的应用[J]. 水资源与水工程学报, 2008,19(3): 52-54.(YU Li, NING Lizhong, WEI Binqian, et al. Rayleigh-Benard convection and application in engineering[J]. Journal of Water Resources and Water Engineering,2008,19(3): 52-54.(in Chinese))
[12]	JUNG D, LUCKE M, BUCHEL P. Influence of through-flow on linear pattern formation properties in binary mixture convection[J]. Physical Review E,1996,54(2): 1510-1529.
[13]	BUCHEL P, LUCKE M. Influence of through flow on binary fluid convection[J]. Physical Review E,2000,61(4): 3793-3810.
[14]	ROTH D, BUCHEL P, LUCKE M, et al. Influence of boundaries on pattern selection in through-flow[J]. Physica D: Nonlinear Phenomena,1996,97(1/3): 253-263.
[15]	JUNG D, LUCKE M, SZPRYNGER A. Influence of inlet and bulk noise on Rayleigh-Benard convection with lateral flow[J]. Physical Review E,2001,63(5): 056301.
[16]	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-Bénard flow[J]. Acta Physica Sinica,2016,65(21): 214401.(in Chinese))
[17]	胡彪, 宁利中, 宁碧波, 等. 局部行波对水平来流的依赖性[J]. 水动力学研究与进展, 2017,32(1): 110-116.(HU Biao, NING Lizhong, NING Bibo, et al. The dependence of localized traveling wave on horizontal flow[J]. Chinese Journal of Hydrodynamics,2017,32(1): 110-116.(in Chinese))
[18]	宁利中, 周洋, 王思怡, 等. Poiseuille-Rayleigh-Benard流动中的局部行波对流[J]. 水动力学研究与进展, 2010,25(3): 299-306.(NING Lizhong, ZHOU Yang, WANG Siyi, et al. Localized traveling wave convection in Poiseuille-Rayleigh-Benard flows[J]. Chinese Journal of Hydrodynamics,2010,25(3): 299-306.(in Chinese))
[19]	胡彪, 宁利中, 宁碧波, 等. 周期性加热Poiseuille-Rayleigh-Benard流动中局部行波的研究[J]. 水动力学研究与进展, 2017,32(3): 336-343.(HU Biao, NING Lizhong, NING Bibo, et al. Localized traveling waves in Poiseuille-Rayleigh-Benard flows under periodic heating[J]. Chinese Journal of Hydrodynamics,2017,32(3): 336-343.(in Chinese))
[20]	赵秉新, 田振夫. 底部加热平面Poiseuille流中的局部行波结构[J]. 水动力学研究与进展, 2012,27(6): 649-658.(ZHAO Bingxin, TIAN Zhenfu. Localized traveling wave convection in plan Poiseuille flow heated from below[J]. Chinese Journal of Hydrodynamics,2012,27(6): 649-658.(in Chinese))
[21]	赵秉新. 水平流作用下的混合流体行波对流[J]. 水动力学研究与进展, 2012,27(3): 264-274.(ZHAO Bingxin. Traveling wave convection in binary fluid mixtures with lateral flow[J]. Chinese Journal of Hydrodynamics,2012,27(3): 264-274.(in Chinese))
[22]	NING L Z, QI X, HARADA Y, et al. A periodically localized traveling wave state of binary fluid convection with horizontal flows[J]. Journal of Hydrodynamics,2006,18(2): 199-205.
[23]	李国栋, 黄永念. 水平流作用下行波对流的成长及周期性重复[J]. 物理学报, 2004,53(11): 3800-3805.(LI Goudong, HUANG Yongnian. Growth and periodic repeating of traveling-wave convection with through-flow[J]. Acta Physica Sinica,2004,53(11): 3800-3805.(in Chinese))
[24]	NING L Z, HARADA Y, YAHATA H, et al. The spatio-temporal structure of binary fluid convection with horizontal flow[J]. Journal of Hydrodynamics,2004,16(2): 151-157.
[25]	NING L Z, HARADA Y, YAHATA H, et al. Fully-developed traveling wave convection in binary fluid mixtures with lateral flow[J]. Progress of Theoretical Physics,2001,106(3): 503-512.
[26]	宁利中, 吴昊, 宁碧波, 等. 倾斜层中的对流斑图及其临界条件[J]. 应用数学和力学, 2019,40(4): 398-407.(NING Lizhong, WU Hao, NING Bibo, et al. Convection patterns and corresponding critical condition in an inclined layer[J]. Applied Mathematics and Mechanics,2019,40(4): 398-407.(in Chinese))
[27]	宁利中, 张珂, 宁碧波, 等. 侧向加热腔体中的多圈型对流斑图[J]. 应用数学和力学, 2020,41(3): 250-259.(NING Lizhong, ZHANG Ke, NING Bibo, et al. Multi-roll type convection pattern in cavity heated laterally[J]. Applied Mathematics and Mechanics,2020,41(3): 250-259.(in Chinese))