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.

References

References
1.
Schade
,
C.
, 1971,
“Effects of Transmission Fluid on Clutch Performance,”
SAE Paper No. 710734.
2.
Lloyd
,
F.
, 1974,
“Parameters Contributing to Power Loss in Disengaged Wet Clutch Drag Losses,”
SAE Paper No. 740676.
3.
Fish
,
R.
, 1991,
“Using the SAE No. 2 Machine to Evaluate Wet Clutch Drag Losses,”
SAE Technical Paper Series No. 910803.
4.
Aphale
,
C.
,
Cho
,
J.
,
Schultz
,
W.
,
Ceccio
,
S.
,
Yoshioka
,
T.
, and
Hiraki
,
H.
, 2006, “
Modeling and Parametric Study of Torque in Open Clutch Plates
,”
J. Tribology
,
128
(
2
), pp.
422
430
.
5.
Aphale
,
C.
,
Schultz
,
W.
, and
Ceccio
,
S.
, 2010, “
The Influence of Grooves on the Fully Wetted and Aerated Flow Between Open Clutch Plates
,”
J. Tribology
,
132
(
1
), p.
011104
.
6.
Reynolds
,
O.
, 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
.
7.
Bretherton
,
F.
, 1961, “
The Motion of Long Bubbles in Tubes
,”
J. Fluid Mech.
,
10
, pp.
166
188
.
8.
Dussan
,
E.
, 1979, “
On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines
,”
Ann. Rev. Fluid Mech.
,
11
, pp.
371
400
.
9.
Hocking
,
L.
, 1976, “
A Moving Fluid Interface on a Rough Surface
,”
J. Fluid Mech.
,
76
, pp.
801
817
.
You do not currently have access to this content.