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Research Papers: Multiphase Flows

Lumped Parameter Analysis of an Enclosed Incompressible Squeeze Film and a Central Gas Bubble

[+] Author and Article Information
M. Anderson

Department of Mechanical Engineering, University of Idaho, Moscow, ID 83844anderson@uidaho.edu

C. Richards

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164cill@wsu.edu

R. Richards, D. Bahr

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164

J. Fluids Eng 130(2), 021303 (Jan 25, 2008) (8 pages) doi:10.1115/1.2829587 History: Received April 04, 2007; Revised September 21, 2007; Published January 25, 2008

A lumped-parameter dynamic model for an enclosed incompressible squeeze film with a central gas bubble has been derived. A new approach was applied to derive closed-form expressions for the lumped-parameter mass and damping coefficients caused by liquid motion. It was assumed that plate motions were small and the fluid behaved as a continuum. The values of the lumped-parameter mass and damping were found to depend on the aspect ratio and nondimensional squeeze-film thickness. The nondimensional thickness was given by the ratio of the actual squeeze-film thickness to the viscous penetration depth of the liquid. A nondimensional squeeze-film thickness of a value of 5 was found to divide between categories of thick and thin incompressible squeeze films. Amplification of the liquid mass and damping over and above squeeze films open to the atmosphere at the edges was found. The amplification was attributed to converging flow caused by enclosed boundaries. Comparisons between the lumped-parameter model predictions and finite-element computations showed a surprising degree of accuracy for the lumped-parameter model despite large liquid velocities in the squeeze film.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 6

Liquid mass versus bubble size

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Figure 1

Cavity geometry. (a) Isometric view and (b) side view.

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Figure 2

Radial liquid velocity for a thick cavity h⪢lv, h=200μm, ri=2.5mm, ro=5mm, W=−j0.0314m∕s, f=500Hz, and time t=8.6ms: (a) and (b) surface plots and (c) solid line, finite element; dashed line, analytical model

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Figure 3

Radial liquid velocity for a thin cavity h⪡lv, h=200μm, ri=2.5mm, ro=5mm, W=−j6.28μm∕s, f=0.1Hz, and time t=43s: (a) and (b) surface plots and (c) solid line, finite element; dashed line, analytical model

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Figure 4

Accuracy for thick- and thin-cavity limits for liquid mass: (a) thick-cavity limit and (b) thin-cavity limit

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Figure 5

Accuracy for thick- and thin-cavity limits for liquid damping

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