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Abstract
Abstract The vortex dynamics in a two-dimensional oscillatory lid-driven cavity with depth-to-width ratio 1:2 has been investigated, covering a wide range of Reynolds numbers and Stokes numbers where this flow is known to be in the two-dimensional regime. Numerical simulations show that the present flow can be divided into four flow patterns based on the vortex dynamics. The regions of these flow patterns are given in the Stokes number and Reynolds number space. For the flow pattern with lowest Reynolds number, there is no transfer of vortices between two successive oscillation half-cycles while for the three other patterns, vortices are carried over from one oscillation half-cycle to the next. For a given Stokes number, the flow pattern appears sequentially as the Reynolds number increases, showing that the transition between the different flow patterns depends strongly on the Reynolds number. However, if the frequency of oscillation is increased (i.e., the Stokes number is increased) for a given Reynolds number, the extrema of the stream function have less time to grow and the center of the primary vortex has less time to move away from the lid. To compensate these effects, the amplitude has to be increased with increasing frequency to maintain the same flow pattern.
Highlights
Flow in an oscillatory lid-driven cavity has been studied over the years because of its relevance to industrial flows
At t = 0, where the lid velocity is at its largest during the oscillation cycle, the cavity is almost completely occupied by the clockwise primary vortex (CPV ), and the flow here is qualitatively similar to a steady lid-driven cavity flow
As the lid velocity decreases (t = 0.2), flow separation and reattachment cause a bottom left corner vortex (BLCV ), and a bottom right corner vortex (BRCV ) as well as a left wall vortex (LWV ). These three vortices grow in size and strength and the weaker left wall vortex becomes encircled by the stronger bottom left corner vortex from t = 0.20 to 0.22, and (t = 0.25) they merge (LWV + BLCV ) to an anti-clockwise vortex which grows with time, while the clockwise primary vortex shrinks
Summary
Flow in an oscillatory lid-driven cavity has been studied over the years because of its relevance to industrial flows. Ovando et al [15] used numerical simulations to investigate the flow in a rectangular cavity driven by a simultaneous oscillatory motion of the vertical walls, relevant to a piston moving inside a circular cylinder in combustion engines. They found two major generation mechanisms for the primary vortex: (i) vorticity produced by the shear motion induced by the oscillating walls, and (ii) roll-up of vortex sheets as the wall-induced flow changes direction when the fluid meets the vertical walls, as previously observed in experiments by Tabaczynski et al [16] and Allen and Chong [17]
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