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TECHNICAL PAPERS

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

[+] Author and Article Information
S. Sriram, S. Pushpavanam

Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai-600 036, India

Abhijit P. Deshpande1

Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai-600 036, Indiaabhijit@che.iitm.ac.in

1

Author to whom correspondence should be addressed.

J. Fluids Eng 128(3), 413-420 (Nov 16, 2005) (8 pages) doi:10.1115/1.2173289 History: Received October 03, 2005; Revised November 16, 2005

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.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometric details of the cavity

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Figure 2

Schematic diagram of the experimental setup: (A) cavity, (B) top plate, (C) guide plate arrangement, (D) drive wheel, (E) connecting rod assembly, (F1, F2) ball bearings, (G) permanent magnet DC motor, and (H) thyristor drive

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Figure 3

Comparison of temporal variation of ũ and ṽ at point 1 in the cavity from the PIV measurements with CFD simulations (μ=0.0235Pas, Re=348, St=845)

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Figure 4

Comparison of temporal variation of ũ and ṽ at point 2 in the cavity from the PIV measurements with CFD simulations (μ=0.0235Pas, Re=348, St=845)

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Figure 5

Trajectories of ũ and ṽ from PIV measurements and 3D CFD simulations (a) point 1 and (b) point 2 (μ=0.0235Pas, Re=348, St=845)

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Figure 6

Power spectra of x and y component velocities from experimental measurements and CFD simulations at point 1 (a) ũ and (b) ṽ (μ=0.0235Pas, Re=348, St=845)

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Figure 7

Power spectra of x and y component velocities from experimental measurements and CFD simulations at point 2 (a) ũ and (b) ṽ (μ=0.0235Pas, Re=348, St=845)

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Figure 8

Comparison of velocity profiles of ũ measured at the central z plane at plate positions 2 and 4 along x=0.05 with CFD simulations (μ=0.0235Pas, ω=1.7(s−1), Re=348, St=845). The simulation result of Iwatsu (3) at plate position 2 (ω=1, Re=400) is given as the inset.

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Figure 9

Comparison of velocity profiles of ṽ measured at the central z plane at plate positions 2 and 4 along y=0.075 from PIV measurements with CFD simulations (μ=0.0235Pas, ω=1.7(s−1), Re=348, St=845). The simulation result of Iwatsu (3) at plate position 2 (ω=1, Re=400) is given as the inset.

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Figure 10

Flow variation in different z planes at plate position 2: comparison of the streamline patterns from PIV planar measurements and CFD simulations (ac) PIV, (df) 3D CFD, and (g) 2D CFD (μ=0.0143Pas, Re=1040, St=2024). The arrow indicates the instantaneous position and direction of the plate.

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Figure 11

Streamlines of velocity fields from planar measurements at the central z plane showing the representative evolution of flow as a function of Re and St at different plate positions. The arrow indicates the instantaneous position and direction of the plate.

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Figure 12

Profiles of the experimentally measured nondimensionalized vertical component velocity in the central z plane along the horizontal plane y=0.075 for different Re, St: (a) Re=5, St=13(μ=0.771Pas), (b) Re=28, St=54(μ=0.147Pas), (c) Re=1255, St=2024μ=0.0143Pas(μ=0.0143Pas), (d) Re=2064, St=4053(μ=0.0047Pas), and (e) Re=3691, St=6001(μ=0.0047Pas)

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