倾斜层中的对流斑图及其临界条件

宁利中; 吴昊; 宁碧波; 田伟利; 宁景昊

doi:10.21656/1000-0887.390102

倾斜层中的对流斑图及其临界条件

doi: 10.21656/1000-0887.390102

¹西安理工大学水利水电学院, 西安 710048;²嘉兴学院建筑工程学院, 浙江嘉兴 314001;³上海大学建筑系, 上海 200444

基金项目: 国家自然科学基金(10872164)

详细信息

作者简介:
宁利中(1961—)，男，教授，博士（通讯作者. E-mail: ninglz@xaut.edu.cn）.

中图分类号: O357
计量
- 文章访问数: 1130
- HTML全文浏览量: 193
- PDF下载量: 375
- 被引次数: 0
出版历程
- 收稿日期: 2018-04-02
- 修回日期: 2018-09-18
- 刊出日期: 2019-04-01

Convection Patterns and Corresponding Critical Conditions in an Inclined Layer

¹Institute of Water Resources and HydroElectric Engineering,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;³Department of Architecture, Shanghai University, Shanghai 200444, P.R.China

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

摘要

摘要: 通过二维流体力学基本方程的数值模拟，探讨了Prandtl(普朗特)数Pr=6.99时，倾斜矩形腔体中的对流斑图和斑图转换的临界条件.根据倾角θ和相对Rayleigh(瑞利)数Ra_r的变化，倾斜矩形腔体中的对流斑图可以分为：单滚动圈对流斑图、充满腔体的多滚动圈对流斑图和过渡阶段的多滚动圈对流斑图.当θ一定时，随着Ra_r的减小，系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图.这时，对流振幅A和Nusselt(努塞尔)数Nu随着Ra_r的增加而增加.当Ra_r=9时，随着θ的增加，系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图，这时对流振幅A随着θ的增加而减小，Nusselt数Nu随着θ的增加而增加.在θ_c-Ra_r平面上对多滚动圈到单滚动圈对流斑图过渡的模拟结果表明，在Ra_r=2时, 腔体中没有发现多滚动圈对流斑图.在Ra_r为2.5左右时，腔体中出现多滚动圈到单滚动圈对流斑图的过渡.当多滚动圈到单滚动圈对流斑图过渡的临界倾角θ_c<10°时，θ_{c随着Ra_r的减小而增加.当θ_c>10°时，θ_c随着Ra_r的增加而增加，在Ra_r≤5时，θ_c随着Ra_r的增加而迅速增加；当Ra_r>5时，θ_c随着Ra_r的增加而缓慢增加.θ_c与Ra_rθ的关系与Ra_r类似}
- 倾斜层 /
- 对流斑图 /
- Rayleigh数 /
- 临界倾角 /
- 流线
Abstract: Through numerical simulation of the basic equations for 2D fluid mechanics, the convection patterns and the critical conditions for pattern transition in an inclined rectangular cavity with Prandtl number Pr=6.99 were studied. According to the variations of inclination angle θ and relative Rayleigh number Ra_r, the convection patterns in the inclined layer can be divided into the convection single-roll pattern, the multi-roll pattern filling the cavity and the multi-roll pattern in the transitional stage. With constant inclination angle θ,the system transforms from the multi-roll pattern filling the cavity to the single-roll pattern with the decrease of relative Rayleigh number Ra_r, where the convection amplitude and Nusselt number Nu increase with Ra_r. For Ra_r=9,the system transforms from the multi-roll pattern filling the cavity to the single-roll pattern with the increase of inclination angle θ,where the convection amplitude decreases with θ,and the Nusselt number increases with θ.The simulation results of the transition from multi-roll to single-roll patterns in plane θ_c-Ra_r show that, for Ra_r=2,the multi-roll pattern is not found in the cavity. For Ra_r=2.5 or so, the transition from the multi-roll pattern to the single-roll pattern appears in the cavity. The critical θ_c value for the transition from the multi-roll to the single-roll patterns increases with the decrease of Ra_r for θ_c<10. The θ_c value increases with Ra_r for θ_c>10, where θ_c increases rapidly with Ra_r for Ra_r≤5,and increases slowly with Ra_r for Ra_r>5. The relation between θ_c and Ra_rθ is similar to θ.
- inclined layer /
- convection pattern /
- Rayleigh number /
- critical inclination angle /
- streamline

HTML全文

参考文献(33)

[1]	〖JP2〗CROSS M C, HOHENBERG P C. Pattern formation outside of equilibrium[J]. Reviews of Modern Physics,1993,65(3): 951-1112.
[2]	BODENSCHATZ E, PESCH W, AHLERS G. Recent developments in Rayleigh-Bénard convection[J]. Annual Reviews of Fluid Mechanics,2000,32: 709-778.
[3]	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.
[4]	YAHATA H. Travelling convection rolls in a binary fluid mixture[J]. Progress of Theoretical Physics,1991,85(5): 933-937.
[5]	NING L Z, HARADA Y, YAHATA H. Modulated traveling waves in binary fluid convection in an intermediate-aspect-ratio rectangular cell[J]. Progress of Theoretical Physics,1997,97(6): 831-848.
[6]	NING L Z, HARADA Y, YAHATA H. Localized traveling waves in binary fluid convection[J]. Progress of Theoretical Physics,1996,96(4): 669-682.
[7]	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.
[8]	KNOBLOCH E, MERCADER I, BATISTE O, et al. Convectons in periodic and bounded domains[J]. Fluid Dynamics Research,2010,42: 025505. DOI: 10.1088/0169-5983/42/2/025505.
[9]	TARAUT A V, SMORODIN B L, LCKE M. Collisions of localized convection structures in binary fluid mixtures[J]. New Journal of Physics,2012,14(9): 093055. DOI: 10.1088/1367-2630/14/9/093055.
[10]	MERCADER I, BATISTE O, ALONSO A, et al. Travelling convectons in binary fluid convection[J]. Journal of Fluid Mechanics,2013,722: 240-265.
[11]	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.
[12]	BARTEN W, LCKE M, KAMPS M, et al. Convection in binary fluid mixture II: localized traveling waves[J]. Physical Review E,1995,51: 5662-5680.
[13]	JUNG D, LCKE M. Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong Soret effect[J].Physical Review Letters,2002,89(5): 054502. DOI: 10.1103/PhysRevLett.89.054502.
[14]	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))
[15]	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. DOI: 10.7498/aps.63.104401.(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. DOI: 10.7498/aps.63.104401.(in Chinese))
[16]	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(G辑): 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 (Series G): Physica, Mechanica & Astronomica,2009,39(5): 746-751.(in Chinese))
[17]	宁利中, 胡彪, 宁碧波, 等. Poiseuille-Rayleigh-Bénard流动中对流斑图的分区和成长[J]. 物理学报, 2016,65(21): 214401. DOI: 10.7498/aps.65.214401.(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. DOI: 10.7498/aps.65.214401.(in Chinese))
[18]	宁利中, 齐昕, 周洋, 等. 混合流体Rayleigh-Bénard行波对流中的缺陷结构[J]. 物理学报, 2009,58(4): 2528-2534.(NING Lizhong, QI Xin, ZHOU Yang, et al. Defect structures of Rayleigh-Bénard travelling wave convection in binary fluid mixtures[J]. Acta Physica Sinica,2009,58(4): 2528-2534.(in Chinese))
[19]	NING L Z, QI X, YUAN Z, et al. A counter propagating wave state with a periodically horizontal motion of defects[J]. Journal of Hydrodynamics,2008,20(5): 567-573.
[20]	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. DOI: 10.1063/1.4923235.
[21]	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))
[22]	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))
[23]	CLEVER R M. Finite amplitude longitudinal convection rolls in an inclined layer[J]. Journal of Heat Transfer,1973,95: 407-408.
[24]	CLEVER R M, BUSSE F H. Instabilities of longitudinal convection rolls in an inclined layer[J]. Journal of Fluid Mechanics,1977,81: 107-125.
[25]	DANIELS K E, BODENSCHATZ E. Defect turbulence in inclined layer convection[J].Physical Review Letters,2002,88: 034501. DOI: 10.1103/PhysRevLett.88.034501.
[26]	DANIELS K E, PLAPP B B, BODENSCHATZ E. Pattern formation in inclined layer convection[J]. Physical Review Letters,2000,84: 5320-5323.
[27]	HART J E. Stability of the flow in a differentially heated inclined box[J]. Journal of Fluid Mechanics,1971,47(3): 547-576.
[28]	HART J E. Transition to a wavy vortex regime in convective flow between inclined plates[J]. Journal of Fluid Mechanics,1971,48: 265-271.
[29]	RUTH D W. On the transition to transverse rolls in inclined infinite fluid layers-steady solutions[J]. International Journal of Heat & Mass Transfer,1980,23: 733-737.
[30]	RUTH D W, RAITHBY G D, HOLLANDS K D T. On the secondary instability in inclined air layers[J]. Journal of Fluid Mechanics,1980,96: 481-492.
[31]	RUTH D W, RAITHBY G D, HOLLANDS K D T. On free convection experiments in inclined air layers heated from below[J]. Journal of Fluid Mechanics,1980,96: 461-469.
[32]	DANIELS K E, BRAUSCH O, PESCH W, et al. Competition and bistability of ordered undulations and undulation chaos in inclined layer convection[J]. Journal of Fluid Mechanics,2008,597: 261-282.
[33]	BUSSE F H, CLEVER R M. Three-dimensional convection in an inclined layer heated from below[J]. Journal of Engineering Mathematics,1992,26: 1-19.