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The effect of compressibility on the stability of wall-bounded Kolmogorov flow
Manela A; Zhang J(张俊); Zhang, J; Chinese Acad Sci, Inst Mech, Lab High Temp Gas Dynam, Beijing 100190, Peoples R China.
Source PublicationJOURNAL OF FLUID MECHANICS
2012-03-01
Volume694Pages:29-49
ISSN0022-1120
AbstractWe extend the stability analysis of incompressible Kolmogorov flow, induced by a spatially periodic external force in an unbounded domain, to a compressible hard-sphere gas confined between two parallel isothermal walls. The two-dimensional problem is studied by means of temporal stability analysis of a 'slip flow' continuum-limit model and the direct simulation Monte Carlo (DSMC) method. The neutral curve is obtained in terms of the Reynolds (Re) and Knudsen (Kn) numbers, for a given non-dimensional wavenumber (2 pi n) of the external force. In the incompressible limit (Kn, Kn Re -> 0), the problem is governed only by the Reynolds number, and our neutral curve coincides with the critical Reynolds number (Re-cr) calculated in previous incompressible analyses. Fluid compressibility (Kn, Kn Re not equal 0) affects the flow field through the generation of viscous dissipation, coupling flow shear rates with irreversible heat production, and resulting in elevated bulk-fluid temperatures. This mechanism has a stabilizing effect on the system, thus increasing Re-cr (compared to its incompressible value) with increasing Kn. When compressibility effects become strong enough, transition to instability changes type from `exchange of stabilities' to 'overstability', and perturbations are dominated by fluctuations in the thermodynamic fields. Most remarkably, compressibility confines the instability to small (O(10(-3))) Knudsen numbers, above which the Kolmogorov flow is stable for all R e. Good agreement is found between 'slip flow' and DSMC analyses, suggesting the former as a useful alternative in studying the effects of various parameters on the onset of instability, particularly in the context of small Knudsen numbers considered.
KeywordGas Dynamics Instability Rarefied Gas Flow Rarefied-gas Instability Simulation Regime Taylor
Subject Area稀薄气体力学
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Indexed BySCI ; EI
Language英语
WOS IDWOS:000300667200003
Funding OrganizationPart of this work was supported by the National Natural Science Foundation of China (Grant Nos. 10921062 and 11002147). We thank Professor J. Fan for his support and helpful comments during this work.
Department高温气体动力学国家重点实验室
Classification一类
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Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/46541
Collection高温气体动力学国家重点实验室
Corresponding AuthorZhang, J; Chinese Acad Sci, Inst Mech, Lab High Temp Gas Dynam, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Manela A,Zhang J,Zhang, J,et al. The effect of compressibility on the stability of wall-bounded Kolmogorov flow[J]. JOURNAL OF FLUID MECHANICS,2012,694:29-49.
APA Manela A,张俊,Zhang, J,&Chinese Acad Sci, Inst Mech, Lab High Temp Gas Dynam, Beijing 100190, Peoples R China..(2012).The effect of compressibility on the stability of wall-bounded Kolmogorov flow.JOURNAL OF FLUID MECHANICS,694,29-49.
MLA Manela A,et al."The effect of compressibility on the stability of wall-bounded Kolmogorov flow".JOURNAL OF FLUID MECHANICS 694(2012):29-49.
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