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Research Papers: Hydrodynamic Lubrication

Aeration in Lubrication With Application to Drag Torque Reduction

[+] Author and Article Information
Chinar R. Aphale

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48105caphale@umich.edu

William W. Schultz

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48105schultz@umich.edu

Steven L. Ceccio

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48105ceccio@umich.edu

J. Tribol 133(3), 031701 (Jul 12, 2011) (7 pages) doi:10.1115/1.4004303 History: Received September 18, 2010; Revised May 07, 2011; Published July 12, 2011; Online July 12, 2011

The aeration of an oil film flowing between the faces of two closely spaced circular plates (one stationary, and one rotating) is examined experimentally, numerically, and with an improved lubrication model. The gap between the plates is small compared to their radii, making lubrication theory appropriate for modeling the flow. However, standard lubrication boundary conditions suggested by Reynolds (1886, "On the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil," Philos. Trans. R. Soc. London, 177 , pp. 157-234) of p = 0 and pn  = 0 (Dirichlet and Neumann conditions on pressure) at the gas-liquid interface do not allow for the inclusion of a contact line model, a phenomenon that is important in the inception of aeration. Hence, the standard theory does not adequately predict the experimentally observed onset of aeration. In the present work, we modify the Neumann boundary condition to include both interfacial tension effects and the dynamics of the interface contact angle. The resulting one-dimensional Cartesian two-phase model is formulated to incorporate the prescribed contact line condition and tracks the interface shape and its motion. This model is then implemented in an axisymmetric, two-dimensional model of the rotating disk flow and used to predict the onset of aeration for varying surface tension and static contact angles. The results of the modified lubrication model are compared with experimental observations and with a numerical computation of the aerating flow using a volume of fluid method.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 4

The drag torque, T, versus the rotation rate, ω, as computed with the volume of fluid model, illustrating the influence of the contact angle on the inception of aeration. A larger contact angle, θc, indicates a lesser affinity for the liquid, and; as a result, aeration is promoted as the contact angle increases.

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Figure 5

Commonly used contact line models relating the contact angle, θc, with the velocity of contact line, Vcl . The common model is shown on the left, the model proposed by Hocking [9] is shown on the right.

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Figure 6

The geometry of the two-dimensional model using Cartesian coordinates. The coordinate system moves with the velocity of the contact line, Vcl . The fluid attaches to the moving plate while the gas attaches to the stationary plate.

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Figure 7

The geometry of the axisymmetric, two-dimensional model. The two interfaces shown are for the two ranges of contact angle, θc, given by a solid line (0o<θc<90o) and by the dashed-dotted line (90o<θc<180o). The dashed line indicates the region where the lubrication equations are solved. The solid line is the portion of the interface that is modeled by a third order polynomial. Three matching conditions link the two regions at junction point A where R =− ro .

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Figure 8

The drag torque, T, versus the rotation rate, ω, as computed with the axisymmetric, two-dimensional lubrication model, illustrating the influence of the contact angle on the inception of aeration. The experimental data for the aluminum plate θc = 9o and the Teflon coated plate with θc = 45o (square) are shown with the analytical results with θc = 9o (solid line) and θc = 45o (dashed line). A larger contact angle, θc, indicates a lesser affinity for the liquid, and; as a result, aeration is promoted as the contact angle increases.

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Figure 3

The drag torque, T, versus the rotation rate, ω, as computed with the volume of fluid model. The sharp drop in drag torque at a particular rotation rate is coincident with aeration. An increase in the surface tension promotes aeration. The computations were performed using the contact angle of the aluminum plate, and the corresponding experimental results are shown (circle).

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Figure 2

The experimentally obtained results of coating the Aluminum disk with Teflon. The two curves for Teflon coated stationary plates are shown with squares. The circles denote the case when the stationary plate surface is aluminum.

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Figure 1

Schematic of the experimental assembly (left) with different modes of aeration shown (right). Liquid flows in axially from a passage within the rotating shaft and is expelled radially outward due to the centrifugal action of the rotating plate. When aeration occurs, the gas interface moves radially inwards, with the gas layer forming on the stationary plate.

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