Journal ArticleDOI
Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures
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In this article, the steady flow in rectangular cavities is investigated both numerically and experimentally, and it is found that the basic two-dimensional flow is not always unique.Abstract:
The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.read more
Citations
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Journal ArticleDOI
Fluid mechanics in the driven cavity
P. N. Shankar,M. D. Deshpande +1 more
TL;DR: In this article, a review of the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls is presented. But the use of direct numerical simulation appears very promising.
Journal ArticleDOI
Advances in global linear instability analysis of nonparallel and three-dimensional flows
TL;DR: A summary of physical insights gained into three-dimensional linear instability through solution of the two-dimensional partial-differential-equation-based nonsymmetric real or complex generalised eigenvalue problem is presented in this article.
Journal ArticleDOI
Mixed convection in two-sided lid-driven differentially heated square cavity
Hakan F. Öztop,Ihsan Dagtekin +1 more
TL;DR: In this article, a two-dimensional mixed convection problem in a vertical two-sided lid-driven differentially heated square cavity is investigated numerically and the Richardson number, Ri=Gr/Re2 emerges as a measure of relative importance of natural and forced convection modes on the heat transfer.
Journal ArticleDOI
Accurate three-dimensional lid-driven cavity flow
TL;DR: In this paper, a Chebyshev-collocation method in space is introduced, which allows an accurate calculation of three-dimensional lid-driven cavity flows using an Adams-Bashforth backward-Euler scheme.
Journal ArticleDOI
Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem
TL;DR: In this article, a linear stability analysis of the basic flow becomes unstable at higher Reynolds numbers to four different three-dimensional modes depending on the aspect ratio of the cavity's cross section.
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