一种新的混合流体对流竖向镜面对称对传波斑图
|
摘要
利用SIMPLE算法对混合流体对流的流体力学基本方程组进行了数值模拟,在混合流体分离比ψ=-0.6和矩形腔体长高比Γ=20的情况下,首次发现了一种新的竖向镜面对称对传波斑图,并初步探讨了它的动力学特性.竖向镜面对称对传波斑图的中心为驻波,随着时间的发展驻波的波长伸长.当波长增加到某个临界值时,一个滚动分裂成两个滚动,在这两个滚动之间产生一个具有180°相位差的新滚动.位于中心线上的滚动只有相位的突变及其波长的压缩或者伸长,没有对流滚动的移动,在它的两侧是向左右传播的对流滚动.驻波两次相位突变形成一个周期,驻波周期随着相对Rayleigh(瑞利)数Rar的增加而增加.这种对流结构存在于相对Rayleigh数Rar∈(3.6,4.3]的范围.当相对Rayleigh数Rar≤3.6时,系统出现具有缺陷的行波斑图;当Rar>4.3时系统过渡到行波斑图.说明竖向镜面对称对传波斑图是存在于具有缺陷的行波斑图和行波斑图之间的一种稳定的对流斑图.
The 2D hydrodynamic equations for binary fluid convection were numerically simulated with the SIMPLE method. For separation ratio ψ =-0.6 of the binary fluid mixture and aspect ratio Γ= 20 of the rectangular cell,a new-type counterpropagating wave pattern of vertical mirror symmetry was found for the first time and its dynamics was preliminarily studied. At the center of the counterpropagating wave pattern of vertical mirror symmetry was a standing wave,of which the wavelength extended with time. As the wavelength increased to a certain critical value,a roll split into 2 rolls,and a new roll with a 180° phase difference formed between them 2. The roll located at the center line only has phase mutation and wavelength contraction or extension,without moving toward the left or right.The convective rolls propagating toward the left or right exist on both sides of the center line. The 2 phase mutations of the standing wave form a period,and the standing wave period increases with reduced Rayleigh number Rar. This type of convective structure exists in the range of Rar ∈(3.6,4.3].The convection system produces the traveling wave pattern with defect for Rar ≤ 3.6. The system shifts to the traveling wave pattern for Rar > 4.3. The work shows that the counterpropagating wave pattern of vertical mirror symmetry is a stable flow pattern between the traveling wave pattern with defect and the traveling wave pattern.
The 2D hydrodynamic equations for binary fluid convection were numerically simulated with the SIMPLE method. For separation ratio ψ =-0.6 of the binary fluid mixture and aspect ratio Γ= 20 of the rectangular cell,a new-type counterpropagating wave pattern of vertical mirror symmetry was found for the first time and its dynamics was preliminarily studied. At the center of the counterpropagating wave pattern of vertical mirror symmetry was a standing wave,of which the wavelength extended with time. As the wavelength increased to a certain critical value,a roll split into 2 rolls,and a new roll with a 180° phase difference formed between them 2. The roll located at the center line only has phase mutation and wavelength contraction or extension,without moving toward the left or right.The convective rolls propagating toward the left or right exist on both sides of the center line. The 2 phase mutations of the standing wave form a period,and the standing wave period increases with reduced Rayleigh number Rar. This type of convective structure exists in the range of Rar ∈(3.6,4.3].The convection system produces the traveling wave pattern with defect for Rar ≤ 3.6. The system shifts to the traveling wave pattern for Rar > 4.3. The work shows that the counterpropagating wave pattern of vertical mirror symmetry is a stable flow pattern between the traveling wave pattern with defect and the traveling wave pattern.
引文
[1]Cross M C,Hohenberg P C.Pattern formation outside of equilibrium[J].Reviews of Modern Physics,1993,65(3):851-1112.
[2]Getling A V.Rayleigh-Bénard Convection[M].London:W orld Scientific,1998.
[3]Chandrasekhar S.Hydrodynamic and Hydromagnetic Stability[M].Oxford:Clarendon Press,1961.
[4]Rabinovich M I,Ezersky A B,Weidman P D.The Dynamics of Patterns[M].Singapore:World Scientific,2000.
[5]W alden R W,Kolodner P,Passner A,et al.T raveling waves and chaos in convection in binary fluid m ixtures[J].Physical Review L etters,1985,55(5):496-499.
[6]Niemela J J,Ahlers G,Cannell D S.Localized traveling-wave states in binary-fluid convection[J].Physical Review L etters,1990,64(12):1365-1368.
[7]Harada Y,M asuno Y,Sugihara K.Convective motion in space and time:defect mediated localized traveling w aves[J].V istas in A stronomy,1993,37:107-110.
[8]M a Y-P,Burke J,Knobloch E.Defect-mediated snaking:a new growth mechanism for localized structures[J].Physica D:Nonlinear Phenomena,2010,239(19):1867-1883.
[9]W atanabe T,Iima M,Nishiura Y.Spontaneous formation of travelling localized structures and their asym ptotic behaviours in binary fluid convection[J].J ournal of Fluid M echanics,2012,712:219-243.
[10]M uller H W,T veitereid M,T rainoff S.Rayleigh-Bénard problem with imposed weak throughflow:tw o coupled G inzburg-Landau equations[J].Physical Review E,1993,48(1):263-272.
[11]王卓运,宁利中,王娜,等.基于振幅方程组的行波对流的数值模拟[J].西安理工大学学报,2014,30(2):163-169.(W AN G Z huo-yun,N IN G Li-zhong,W AN G N a,et al.N um erical sim ulation of traveling w ave convection based on am plitude equations[J].J ournal of Xi’an University of T echnology,2014,30(2):163-169.(in C hinese))
[12]Yahata H.T ravelling convection rolls in a binary fluid mixture[J].Progress of Theoretical Physics,1991,85(5):933-937.
[13]Barten W,Lucke M,Kamps M.Localized traveling-wave convection in binary-fluid mixtures[J].Physical Review L etters,1991,66(20):2621-2624.
[14]Barten W,Lücke M,Kamps M,et al.Convection in binary fluid mixtures I:extended travelingw ave and stationary states[J].Physical Review E,1995,51(6):5636-5661.
[15]Barten W,Lücke M,Kamps M,et al.Convection in binary fluid mixtures II:localized traveling w aves[J].Physical Review E,1995,51(6):5662-5682.
[16]NING Li-zhong,Harada Y,Yahata H.Localized traveling waves in binary fluid convection[J].Progress of T heoretical Physics,1996,96(4):669-682.
[17]NING Li-zhong,Harada Y,Yahata H.M odulated traveling waves in binary fluid convection in an interm ediate-aspect-ratio rectangular cell[J].Progress of T heoretical Physics,1997,97(6):831-848.
[18]NING Li-zhong,Harada Y,Yahata H.Formation process of the traveling-wave state with a defect in binary fluid convection[J].Progress of T heoretical Physics,1997,98(3):551-566.
[19]NING Li-zhong,Harada Y,Yahata H,et al.Fully-developed traveling wave convection in binary fluid m ixtures w ith lateral flow s[J].Progress of T heoretical Physics,2001,106(3):503-512.
[20]宁利中,齐昕,周洋,等.混合流体Rayleigh-Benard行波对流中的缺陷结构[J].物理学报,2009,58(4):2528-2534.(N IN G Li-zhong,Q I X in,Z H O U Yang,et al.D efect structures of Rayleigh-Benard travelling w ave convection in binary fluid m ixtures[J].A cta Physica Sinica,2009,58(4):2528-2534.(in Chinese))
[21]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:物理学力学天文学),2009,39(5):746-751.(NING Li-zhong,YU Li,YUAN Zhe,et al.Evolution of traveling w ave patterns along upper branch of bifurcation diagram in binary fluid convection[J].Science in China(Series G:Physics,M echanics&A stronomy),2009,39(5):746-751.(in C hinese))
[22]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.(N IN G Li-zhong,W AN G N a,YU AN Z he,et al.Influence of separation ratio on Rayleigh-Bénard convection solutions in a binary fluid m ixture[J].Acta Physica Sinica,2014,63(10):104401.doi:10.7498/aps.63.104401.(in Chinese))
[23]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.(N IN G Li-zhong,W AN G Yong-qi,YU AN Zhe,et al.T w o types of patterns of localized traveling w ave convection in binary fluid m ixtures w ith different structures[J].Chinese Science Bulletin,2016,61(8):872-880.(in C hinese))
[24]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 Li-zhong,HU Biao,NING Bi-bo,et al.Partition and grow th of convection patterns in Poiseuille-Rayleigh-Bénard flow[J].A cta Physica Sinica,2016,65(21):214401.doi:10.7498/aps.65.214401.(in C hinese))
[25]NING Li-zhong,QI Xin,YUAN Zhe,et al.A counter propagating wave state with a periodically horizontal m otion of defects[J].J ournal of H ydrodynamics,2008,20(5):567-573.
[26]胡军,尹协远.双流体Poiseuille-Rayleigh-Bénard流动中脉冲扰动的时空演化[J].中国科学技术大学学报,2007,37(10):1267-1272.(HU Jun,YIN Xie-yuan.Spatio-temporal evolution of pulse like perturbation for Poiseuille-Rayleigh-Bénard flow s in binary fluids[J].J ournal of University of Science and T echnology of China,2007,37(10):1267-1272.(in C hinese))
[27]HU Jun,YIN Xie-yuan.T wo-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids w ith Soret effect[J].Progress in Nature Science,2007,17(12):1389-1396.
[28]ZHAO Bing-xin,T IAN Zhen-fu.Numerical investigation of binary fluid convection with a weak negative separation ratio in finite containers[J].Physics of Fluids,2015,27:074102.
[29]T araut A V,Smorodin B L,Lucke M.Collisions of localized convection structures in binary fluid m ixtures[J].New J ournal of Physics,2012,14(9):093055.
[30]M ercader I,Batiste O,Alonso A,et al.T ravelling convectons in binary fluid convection[J].Journal of Fluid M echanics,2013,722:240-266.
[31]M ercader I,Batiste O,Alonso A,et al.Convectons in periodic and bounded domains[J].Fluid Dynamics Research,2010,42:025505.doi:10.1088/0169-5983/42/2/025505.
[32]M ercader I,Batiste O,Alonso A,et al.Convectons,anticonvectons and multiconvectons in binary fluid convection[J].J ournal of Fluid M echanics,2011,667:586-606.
[33]Batiste O,Knobloch E,Alonso A,et al.Spatially localized binary-fluid convection[J].Journal of Fluid M echanics,2006,560:149-158.
[34]Bensimon D,Kolodner P,Surko C M,et al.Competing and coexisting dynamical states of travelling-w ave convection in an annulus[J].J ournal of Fluid M echanics,1990,217:441-467.
[35]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.(H U Biao,N IN G Li-zhong,N IN G Bi-bo,et al.Effects of horizontal flow on perturbation grow th and convection periodicity[J].A pplied M athematics and M echanics,2017,38(10):1103-1111.(in C hinese))
[2]Getling A V.Rayleigh-Bénard Convection[M].London:W orld Scientific,1998.
[3]Chandrasekhar S.Hydrodynamic and Hydromagnetic Stability[M].Oxford:Clarendon Press,1961.
[4]Rabinovich M I,Ezersky A B,Weidman P D.The Dynamics of Patterns[M].Singapore:World Scientific,2000.
[5]W alden R W,Kolodner P,Passner A,et al.T raveling waves and chaos in convection in binary fluid m ixtures[J].Physical Review L etters,1985,55(5):496-499.
[6]Niemela J J,Ahlers G,Cannell D S.Localized traveling-wave states in binary-fluid convection[J].Physical Review L etters,1990,64(12):1365-1368.
[7]Harada Y,M asuno Y,Sugihara K.Convective motion in space and time:defect mediated localized traveling w aves[J].V istas in A stronomy,1993,37:107-110.
[8]M a Y-P,Burke J,Knobloch E.Defect-mediated snaking:a new growth mechanism for localized structures[J].Physica D:Nonlinear Phenomena,2010,239(19):1867-1883.
[9]W atanabe T,Iima M,Nishiura Y.Spontaneous formation of travelling localized structures and their asym ptotic behaviours in binary fluid convection[J].J ournal of Fluid M echanics,2012,712:219-243.
[10]M uller H W,T veitereid M,T rainoff S.Rayleigh-Bénard problem with imposed weak throughflow:tw o coupled G inzburg-Landau equations[J].Physical Review E,1993,48(1):263-272.
[11]王卓运,宁利中,王娜,等.基于振幅方程组的行波对流的数值模拟[J].西安理工大学学报,2014,30(2):163-169.(W AN G Z huo-yun,N IN G Li-zhong,W AN G N a,et al.N um erical sim ulation of traveling w ave convection based on am plitude equations[J].J ournal of Xi’an University of T echnology,2014,30(2):163-169.(in C hinese))
[12]Yahata H.T ravelling convection rolls in a binary fluid mixture[J].Progress of Theoretical Physics,1991,85(5):933-937.
[13]Barten W,Lucke M,Kamps M.Localized traveling-wave convection in binary-fluid mixtures[J].Physical Review L etters,1991,66(20):2621-2624.
[14]Barten W,Lücke M,Kamps M,et al.Convection in binary fluid mixtures I:extended travelingw ave and stationary states[J].Physical Review E,1995,51(6):5636-5661.
[15]Barten W,Lücke M,Kamps M,et al.Convection in binary fluid mixtures II:localized traveling w aves[J].Physical Review E,1995,51(6):5662-5682.
[16]NING Li-zhong,Harada Y,Yahata H.Localized traveling waves in binary fluid convection[J].Progress of T heoretical Physics,1996,96(4):669-682.
[17]NING Li-zhong,Harada Y,Yahata H.M odulated traveling waves in binary fluid convection in an interm ediate-aspect-ratio rectangular cell[J].Progress of T heoretical Physics,1997,97(6):831-848.
[18]NING Li-zhong,Harada Y,Yahata H.Formation process of the traveling-wave state with a defect in binary fluid convection[J].Progress of T heoretical Physics,1997,98(3):551-566.
[19]NING Li-zhong,Harada Y,Yahata H,et al.Fully-developed traveling wave convection in binary fluid m ixtures w ith lateral flow s[J].Progress of T heoretical Physics,2001,106(3):503-512.
[20]宁利中,齐昕,周洋,等.混合流体Rayleigh-Benard行波对流中的缺陷结构[J].物理学报,2009,58(4):2528-2534.(N IN G Li-zhong,Q I X in,Z H O U Yang,et al.D efect structures of Rayleigh-Benard travelling w ave convection in binary fluid m ixtures[J].A cta Physica Sinica,2009,58(4):2528-2534.(in Chinese))
[21]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:物理学力学天文学),2009,39(5):746-751.(NING Li-zhong,YU Li,YUAN Zhe,et al.Evolution of traveling w ave patterns along upper branch of bifurcation diagram in binary fluid convection[J].Science in China(Series G:Physics,M echanics&A stronomy),2009,39(5):746-751.(in C hinese))
[22]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.(N IN G Li-zhong,W AN G N a,YU AN Z he,et al.Influence of separation ratio on Rayleigh-Bénard convection solutions in a binary fluid m ixture[J].Acta Physica Sinica,2014,63(10):104401.doi:10.7498/aps.63.104401.(in Chinese))
[23]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.(N IN G Li-zhong,W AN G Yong-qi,YU AN Zhe,et al.T w o types of patterns of localized traveling w ave convection in binary fluid m ixtures w ith different structures[J].Chinese Science Bulletin,2016,61(8):872-880.(in C hinese))
[24]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 Li-zhong,HU Biao,NING Bi-bo,et al.Partition and grow th of convection patterns in Poiseuille-Rayleigh-Bénard flow[J].A cta Physica Sinica,2016,65(21):214401.doi:10.7498/aps.65.214401.(in C hinese))
[25]NING Li-zhong,QI Xin,YUAN Zhe,et al.A counter propagating wave state with a periodically horizontal m otion of defects[J].J ournal of H ydrodynamics,2008,20(5):567-573.
[26]胡军,尹协远.双流体Poiseuille-Rayleigh-Bénard流动中脉冲扰动的时空演化[J].中国科学技术大学学报,2007,37(10):1267-1272.(HU Jun,YIN Xie-yuan.Spatio-temporal evolution of pulse like perturbation for Poiseuille-Rayleigh-Bénard flow s in binary fluids[J].J ournal of University of Science and T echnology of China,2007,37(10):1267-1272.(in C hinese))
[27]HU Jun,YIN Xie-yuan.T wo-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids w ith Soret effect[J].Progress in Nature Science,2007,17(12):1389-1396.
[28]ZHAO Bing-xin,T IAN Zhen-fu.Numerical investigation of binary fluid convection with a weak negative separation ratio in finite containers[J].Physics of Fluids,2015,27:074102.
[29]T araut A V,Smorodin B L,Lucke M.Collisions of localized convection structures in binary fluid m ixtures[J].New J ournal of Physics,2012,14(9):093055.
[30]M ercader I,Batiste O,Alonso A,et al.T ravelling convectons in binary fluid convection[J].Journal of Fluid M echanics,2013,722:240-266.
[31]M ercader I,Batiste O,Alonso A,et al.Convectons in periodic and bounded domains[J].Fluid Dynamics Research,2010,42:025505.doi:10.1088/0169-5983/42/2/025505.
[32]M ercader I,Batiste O,Alonso A,et al.Convectons,anticonvectons and multiconvectons in binary fluid convection[J].J ournal of Fluid M echanics,2011,667:586-606.
[33]Batiste O,Knobloch E,Alonso A,et al.Spatially localized binary-fluid convection[J].Journal of Fluid M echanics,2006,560:149-158.
[34]Bensimon D,Kolodner P,Surko C M,et al.Competing and coexisting dynamical states of travelling-w ave convection in an annulus[J].J ournal of Fluid M echanics,1990,217:441-467.
[35]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.(H U Biao,N IN G Li-zhong,N IN G Bi-bo,et al.Effects of horizontal flow on perturbation grow th and convection periodicity[J].A pplied M athematics and M echanics,2017,38(10):1103-1111.(in C hinese))