Analysis of Spatiotemporal Variations and Flow Structures in a Periodically Driven Cavity

Abstract

The time-dependent fluid flow in a square cavity was studied using model fluids of glycerol-water solution at different frequencies and amplitudes of motion of the top plate. The range of Reynolds numbers in our investigation varied from 5 to 3700. The experiments were carried out in a square cavity with a periodically driven lid, and planar velocity measurements were obtained using particle image velocimetry. The flow was driven by moving the top surface of the cavity in a simple harmonic motion. The aspect ratio, defined as the ratio of cavity length to the cavity height, is unity. The ratio of cavity spanwise width to the length of the cavity is 0.2. The temporal variation of velocity at fixed locations in the cavity exhibits a periodic variation. The basic frequency of the fluid motion at a point in the flow domain was observed to be the same as that of plate motion for low Reynolds number Re. However, existence of dominant secondary frequencies was observed along the central vertical plane. The velocity variation as a function of time at a fixed position and the velocity profiles along horizontal and vertical planes are also quantitatively described. These were compared to computational fluid dynamics (CFD) simulations based on the finite volume technique. Comprehensive details of the flow as a function of Reynolds number are analyzed. The evolution of secondary vortices at different plate positions as a function of Reynolds number is also presented. The planar velocity measurements acquired are indicative of the flow behavior in a periodically driven cavity with a narrow span width even at high Re. At very low Re, the flow throughout the periodically driven cavity qualitatively resembles the classical steady lid-driven cavity flow. At high Re, the entire cavity is occupied with multiple vortices. The qualitative features of the bulk flow observed are valid even for cavities with infinite span width.