Linear stability analysis of cylindrical Rayleigh-Benard convection

被引:39
作者
Wang, Bo-Fu [1 ]
Ma, Dong-Jun [2 ]
Chen, Cheng [3 ]
Sun, De-Jun [1 ]
机构
[1] Univ Sci & Technol China, Dept Modern Mech, Hefei 230027, Peoples R China
[2] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA
[3] China Aerodynam Res & Dev Ctr, Low Speed Aerodynam Inst, Mianyang 622762, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
bifurcation; buoyancy-driven instability; convection in cavities; VERTICAL CYLINDERS; NATURAL-CONVECTION; THERMOCONVECTIVE INSTABILITY; CIRCULAR-CYLINDER; PATTERN-FORMATION; FLUID LAYER; SCHEME; FLOWS;
D O I
10.1017/jfm.2012.360
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The instabilities and transitions of flow in a vertical cylindrical cavity with heated bottom, cooled top and insulated sidewall are investigated by linear stability analysis. The stability boundaries for the axisymmetric flow are derived for Prandtl numbers from 0.02 to 1, for aspect ratio A (A = H/R = height/radius) equal to 1, 0.9, 0.8, 0.7, respectively. We found that there still exists stable non-trivial axisymmetric flow beyond the second bifurcation in certain ranges of Prandtl number for A D 1, 0 : 9 and 0.8, excluding the A = 0.7 case. The finding for A = 0.7 is that very frequent changes of critical mode (azimuthal Fourier mode) of the second bifurcation occur when the Prandtl number is changed, where five kinds of steady modes m = 1, 2, 8, 9, 10 and three kinds of oscillatory modes m = 3, 4, 6 are presented. These multiple modes indicate different flow structures triggered at the transitions. The instability mechanism of the flow is explained by kinetic energy transfer analysis, which shows that the radial or axial shear of base flow combined with buoyancy mechanism leads to the instability results.
引用
收藏
页码:27 / 39
页数:13
相关论文
共 30 条
[1]  
[Anonymous], 1998, Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods, DOI DOI 10.1137/1.9780898719628
[2]   Recent developments in Rayleigh-Benard convection [J].
Bodenschatz, E ;
Pesch, W ;
Ahlers, G .
ANNUAL REVIEW OF FLUID MECHANICS, 2000, 32 :709-778
[3]   Standing and travelling waves in cylindrical Rayleigh-Benard convection [J].
Boronska, Katarzyna ;
Tuckerman, Laurette S. .
JOURNAL OF FLUID MECHANICS, 2006, 559 (279-298) :279-298
[4]   Extreme multiplicity in cylindrical Rayleigh-Benard convection. II. Bifurcation diagram and symmetry classification [J].
Boronska, Katarzyna ;
Tuckerman, Laurette S. .
PHYSICAL REVIEW E, 2010, 81 (03)
[5]   Extreme multiplicity in cylindrical Rayleigh-Benard convection. I. Time dependence and oscillations [J].
Boronska, Katarzyna ;
Tuckerman, Laurette S. .
PHYSICAL REVIEW E, 2010, 81 (03)
[6]   THE EFFECT OF WALL CONDUCTION ON THE STABILITY OF A FLUID IN A RIGHT CIRCULAR-CYLINDER HEATED FROM BELOW [J].
BUELL, JC ;
CATTON, I .
JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME, 1983, 105 (02) :255-260
[7]   FINITE-AMPLITUDE AXISYMMETRIC THERMOCONVECTIVE FLOWS IN A BOUNDED CYLINDRICAL LAYER OF FLUID [J].
CHARLSON, GS ;
SANI, RL .
JOURNAL OF FLUID MECHANICS, 1975, 71 (SEP23) :209-229
[8]   THERMOCONVECTIVE INSTABILITY IN A BOUNDED CYLINDRICAL FLUID LAYER [J].
CHARLSON, GS ;
SANI, RL .
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 1970, 13 (09) :1479-&
[9]   THERMOCONVECTIVE INSTABILITY IN A BOUNDED CYLINDRICAL FLUID LAYER [J].
CHARLSON, GS ;
SANI, RL .
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 1971, 14 (12) :2157-&
[10]   PATTERN-FORMATION OUTSIDE OF EQUILIBRIUM [J].
CROSS, MC ;
HOHENBERG, PC .
REVIEWS OF MODERN PHYSICS, 1993, 65 (03) :851-1112