Stability of multiple steady states of convection in laterally heated cavities

A. Yu Gelfgat, P. Z. Bar-Yoseph, Alexander Yarin

Research output: Contribution to journalArticle

76 Citations (Scopus)

Abstract

A parametric study of multiple steady states, their stability, onset of oscillatory instability, and some supercritical unsteady regimes of convective flow of a Boussinesq fluid in laterally heated rectangular cavities is presented. Cavities with four no-slip boundaries, isothermal vertical and perfectly insulated horizontal boundaries are considered. Four distinct branches of steady-state flows are found for this configuration. A complete study of stability of each branch is performed for the aspect ratio A (length/height) of the cavity varying continuously from 1 to 11 and for two fixed values of the Prandtl number: Pr = 0 and Pr = 0.015. The results are represented as stability diagrams showing the critical parameters (critical Grashof number and the frequency at the onset of the oscillatory instability) corresponding to transitions from steady to oscillatory states, appearance of multi-roll states, merging of multiple states and backwards transitions from multi-roll to single-roll states. For better comparison with the existing experimental data, an additional stability study for varying Prandtl number (0.015 ≤ Pr ≤ 0.03) and fixed value of the aspect ratio A = 4 was carried out. It was shown that the dependence of the critical Grashof number on the aspect ratio and the Prandtl number is very complicated and a very detailed parametric study is required to reproduce it correctly. Comparison with the available experimental data for A = 4 shows that the results of a two-dimensional stability analysis are in good agreement with the experimental results if the width ratio (width/height) of the experimental container is sufficiently large. The study is carried out numerically with the use of two independent numerical approaches based on the global Galerkin and finite-volume methods.

Original languageEnglish
Pages (from-to)315-334
Number of pages20
JournalJournal of Fluid Mechanics
Volume388
Publication statusPublished - 1999 Jun 10
Externally publishedYes

Fingerprint

convection
cavities
Prandtl number
aspect ratio
Aspect ratio
Grashof number
dimensional stability
equilibrium flow
convective flow
Dimensional stability
finite volume method
Finite volume method
containers
Merging
Containers
Convection
slip
diagrams
Fluids
fluids

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Gelfgat, A. Y., Bar-Yoseph, P. Z., & Yarin, A. (1999). Stability of multiple steady states of convection in laterally heated cavities. Journal of Fluid Mechanics, 388, 315-334.

Stability of multiple steady states of convection in laterally heated cavities. / Gelfgat, A. Yu; Bar-Yoseph, P. Z.; Yarin, Alexander.

In: Journal of Fluid Mechanics, Vol. 388, 10.06.1999, p. 315-334.

Research output: Contribution to journalArticle

Gelfgat, AY, Bar-Yoseph, PZ & Yarin, A 1999, 'Stability of multiple steady states of convection in laterally heated cavities', Journal of Fluid Mechanics, vol. 388, pp. 315-334.
Gelfgat, A. Yu ; Bar-Yoseph, P. Z. ; Yarin, Alexander. / Stability of multiple steady states of convection in laterally heated cavities. In: Journal of Fluid Mechanics. 1999 ; Vol. 388. pp. 315-334.
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