Chinar R. Aphale e-mail: caphale@umich.edu William W. Schultz e-mail: schultz@umich.edu Steven L. Ceccio e-mail: ceccio@umich.edu Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48105 Aeration in Lubrication With Application to Drag Torque Reduction 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 lubrica- tion 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 ¼ 0 and p n ¼ 0 (Dirichlet and Neumann conditions on pressure) at the gas-liq- uid 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-dimen- sional 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. [DOI: 10.1115/1.4004303] Keywords: aerating lubrication flow, clutch, surface tension, contact angle, groove, drag reduction 1 Introduction In a disengaged or open clutch, one plate typically rotates while the other is stationary. Oil is passed between open clutch plates to provide lubrication during clutch re-engagement and to transfer heat away from the plates. However, the shearing of this liquid between the open clutch plates result in viscous drag. Conse- quently, it is beneficial to introduce air between the two plates while they are disengaged, reducing the drag and subsequent para- sitic losses. Open-clutch drag has been examined by Schade [1], Lloyd [2], Fish [3], and Aphale [4], [5]. Schade first suggested that air might be present between the plate surfaces at high rota- tion rates, which was subsequently observed to occur. Aphale [4] examined the conditions necessary for incipient aeration, and in a separate work [5] studied how the presence of grooves on the face of one plate can enhance the aeration process. In the present work, we examine how lubrication theory, appropriately formulated, can be used to predict the onset of aeration between two rotating disk, the geometry of a typical set of clutch plates. We will show how the interfacial properties of the fluid and gas (e.g., the oil and air) strongly influence the conditions for the inception of aeration in lubricating flow. Figure 1 presents a schematic diagram of the flow geometry under consideration. Two disks, separated by a narrow gap, are rotating about the same axis. A pocket is present in one disk, pro- ducing an annular ring of inner radius R i and outer radius R o . The minimum spacing between the plates is h. The radial and axial dimensions are r and z, as shown. A liquid is pumped into the cav- ity between the disks at an inlet that lies along the axis of rotation, and the liquid flows both circumferentially and radially until it exits from the gap at the outer radii of the disks. Important param- eters include the flow rate of the liquid, Q, and the properties of the fluid (usually an oil) such as the density, q, viscosity, l, and surface tension, r. The drag torque that is developed between the plates is T, and in the present study, we will consider one plate rotating with speed x, and one stationary plate. Note that a finite flow of fluid through the gap can occur simply ars a result of cen- trifuging, but in the present case, the flow rate of liquid will be prescribed via pumping. Aeration can occur naturally between the rotating disks due to centrifugal forces that act on the liquid flowing through the gap. Figure 1 also shows the type of aerated flows that could develop in the gap between the plates. Without aeration, the flow is consid- ered fully flooded. But, under certain flow conditions, a pocket of gas can penetrate from the outer radii of the disks to partially aer- ate the gap flow. The cavity usually forms on the stationary plate. If the gas pocket extends across the radial extent of the gap, the flow is fully aerated. Also shown, is an idealized topology of the air pocket that will be discussed below. The onset of aeration on smooth clutch plates (e.g., without surface grooves, roughness, or other patterns) depends on a variety of flow and physical parame- ters, including the rotation rates of the plates, the liquid flow-rate, the liquid properties and the gap thickness. Air penetration toward the inner radii of the clutch plates necessitates the formation of a free surface and contact line on the drying, stationary plate. This suggests that interfacial properties of the oil and plate surfaces will be an important consideration. The gap between the two plates is small compared to the plate radii. Therefore, lubrication theory can be successfully used to model the flow [4]. However, difficulties with the standard lubrication model are encountered during the onset and develop- ment of aeration since aeration in lubricating flows depends strongly on the contact line condition. Reynolds [6] proposed a simple gas-liquid interface conditions for lubricating flow where p ¼ 0 and p n ¼ 0 (Dirichlet and Neumann conditions on pres- sure) at the gas-liquid interface. The former interface condition Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received September 18, 2010; final manuscript received May 7, 2011; published online July 12, 2011. Assoc. Editor: Dong Zhu. 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