Author:
GELFGAT A. YU.,BAR-YOSEPH P. Z.,YARIN A. L.
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 [les ] Pr [les ] 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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
83 articles.
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