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Onset of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity
Chen, ZW; Li, YS; Zhan, JM;
AbstractDouble-diffusive buoyancy convection in an inclined rectangular closed cavity with imposed temperatures and concentrations along two opposite sidewalls is considered. Attention is restricted to the case where the opposing thermal and solutal buoyancy effects are of equal magnitude (buoyancy ratio R-rho = -1). In this case a quiescent equilibrium solution exists and can remain stable up to a critical thermal Grashof number Gr(c). For both infinite and finite layers, linear stability analysis shows that, when the cavity inclination alpha with respect to gravity decreases from 0 degrees to -90 degrees. Gr(c) for the onset of stationary instability increases exponentially while that for the onset of oscillatory instability decreases exponentially. Below a critical alpha(c), the first onset of instability is oscillatory, rather than stationary. For the infinite layer, the influences of alpha on the critical wave number and frequency of the oscillatory mode are shown and the corresponding flow structure of the eigenfunction consists of counterrotating vortices travelling from one end to the other. For a bounded layer, the neutral stability curves of the first two oscillatory modes, centrosymmetric and anticentrosymmetric, cross each other successively at a series of double Hopf bifurcation points as the aspect ratio increases. These two curves are not smooth, but each contains several abrupt changes, after every one of which a pair of counterrotating vortices is added to the flow field and thus the parity of the mode remains unchanged. The neutral curves showing the influences of Pr and Le are also obtained. The present work expands the work of Bergeon et al. (1999) [8] in which the same physical problem was studied and yet no oscillatory onset of instability was considered. (C) 2012 Elsevier Ltd. All rights reserved.
Department[Chen, Zhi-Wu; Zhan, Jie-Min] Sun Yat Sen Univ, Dept Appl Mech & Engn, Guangzhou 510275, Guangdong, Peoples R China; [Li, Yok-Sheung] Hong Kong Polytech Univ, Dept Civil & Struct Engn, Hong Kong, Hong Kong, Peoples R China; [Chen, Zhi-Wu] Chinese Acad Sci, State Key Lab Trop Oceanog, S China Sea Inst Oceanol, Guangzhou 510301, Guangdong, Peoples R China
KeywordDouble-diffusive Linear Stability Analysis Hopf Bifurcation Oscillatory Instability
Subject AreaThermodynamics ; Engineering, Mechanical ; Mechanics
Funding ProjectLTO
WOS IDWOS:000304785900030
Citation statistics
Cited Times:12[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Recommended Citation
GB/T 7714
Chen, ZW,Li, YS,Zhan, JM,et al. Onset of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity[J]. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER,2012,55(13-14):3633-3640.
APA Chen, ZW,Li, YS,Zhan, JM,& of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity.INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER,55(13-14),3633-3640.
MLA Chen, ZW,et al."Onset of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity".INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 55.13-14(2012):3633-3640.
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