When a liquid is forced to flow radially outward in the gap between two coaxial, parallel annular disks—one rotating and one stationary—the liquid occupies the entire gap until the speed of the rotating disk reaches a critical value. Beyond that critical speed, gas from the outer radius starts to enter into the gap, a process referred to as aeration. The higher the rotational speed, the greater is the extent of penetration by the gas into the gap. The extent of gas penetration strongly affects the torque exerted between the two disks because of the large difference in the gas and liquid viscosities. In this study, a reduced-order model is developed to predict the onset of aeration, extent of gas penetration into the gap, and drag torque as a function of the disk's rotational speed, gap between disks, properties of the liquid, and mass flow rate of the liquid forced through the gap. The model developed was validated by comparing predictions with experimental data.

## References

1.
Mellor
,
G. L.
,
Chapple
,
P. J.
, and
Stokes
,
V. K.
,
1968
, “
On the Flow Between a Rotating and a Stationary Disk
,”
J. Fluid Mech.
,
31
(
1
), pp.
95
112
.
2.
Cooper
,
P.
, and
Reshotko
,
E.
,
1975
, “
Turbulent Flow Between a Rotating Disk and a Parallel Wall
,”
AIAA J.
,
13
(
5
), pp.
573
578
.
3.
Sirivat
,
A.
,
1991
, “
Stability Experiment of Flow Between a Stationary and a Rotating Disk
,”
Phys. Fluids A
,
3
(
11
), p.
2664
.
4.
Schouveiler
,
L.
,
Le Gal
,
P.
, and
Chauve
,
M. P.
,
2001
, “
Instabilities of the Flow Between a Rotating and a Stationary Disk
,”
J. Fluid Mech.
,
443
, pp.
329
350
.
5.
Cros
,
A.
, and
Le Gal
,
P.
,
2002
, “
Spatiotemporal Intermittency in the Torsional Couette Flow Between a Rotating and a Stationary Disk
,”
Phys. Fluids
,
14
(
11
), p.
3755
.
6.
Launder
,
B.
,
Poncet
,
S.
, and
Serre
,
E.
,
2010
, “
Laminar, Transitional, and Turbulent Flows in Rotor-Stator Cavities
,”
Annu. Rev. Fluid Mech.
,
42
(
1
), pp.
229
248
.
7.
Cui
,
H.
,
Yao
,
S.
,
Yan
,
Q.
,
Feng
,
S.
, and
Liu
,
Q.
,
2014
, “
Mathematical Model and Experiment Validation of Fluid Torque by Shear Stress Under Influence of Fluid Temperature in Hydro-Viscous Clutch
,”
CJME
,
27
(
1
), pp.
32
40
.
8.
Hu
,
J.
,
Peng
,
Z.
, and
Yuan
,
S.
,
2009
, “
Drag Torque Prediction Model for the Wet Clutches
,”
CJME
,
22
(
2
), pp.
238
243
.
9.
Huang
,
J.
,
Wei
,
J.
, and
Qiu
,
M.
,
2012
, “
Laminar Flow in the Gap Between Two Rotating Parallel Frictional Plates in Hydro-Viscous Drive
,”
CJME
,
25
(
1
), pp.
144
152
.
10.
Iqbal
,
S.
,
Al-Bender
,
F.
,
Pluymers
,
B.
, and
Desmet
,
W.
,
2013
, “
Mathematical Model and Experimental Evaluation of Drag Torque in Disengaged Wet Clutches
,”
ISRN Tribol.
,
2013
, p.
206539
.
11.
Iqbal
,
S.
,
Al-Bender
,
F.
,
Pluymers
,
B.
, and
Desmet
,
W.
,
2013
, “
Experimental Characterization of Drag Torque in Open Multi-Disks Wet Clutches
,”
SAE Int. J. Fuels Lubr.
,
6
(
3
), pp.
894
906
.
12.
Iqbal
,
S.
,
Al-Bender
,
F.
,
Pluymers
,
B.
, and
Desmet
,
W.
,
2013
, “
Model for Predicting Drag Torque in Open Multi-Disks Wet Clutches
,”
ASME J. Fluids Eng.
,
136
(
2
), p.
021103
.
13.
Kato
,
Y.
,
Murasugi
,
T.
,
Hirano
,
H.
, and
Shibayama
,
T.
,
1993
, “
Fuel Economy Improvement Through Tribological Analysis of the Wet Clutches and Brakes of an Automatic Transmission
,”
SAE
Paper No. 938179.
14.
Kitabayashi
,
H.
,
Li
,
C.
, and
Hiraki
,
H.
,
2003
, “
Analysis of the Various Factors Affecting Drag Torque in Multiple-Plate Wet Clutches
,”
SAE
Paper No. 2003-01-1973.
15.
Li
,
H.
,
Jing
,
Q.
, and
Ma
,
B.
,
2013
, “Modeling and Parametric Study on Drag Torque of Wet Clutch,” SAE-China, FISITA (eds) Proceedings of the FISITA 2012 World Automotive Congress (Lecture Notes in Electrical Engineering, Vol. 193), Springer, Berlin.
16.
Pahlovy
,
S.
,
Mahmud
,
S.
,
Kubota
,
M.
,
Ogawa
,
M.
, and
Takakura
,
N.
,
2014
, “
Multiphase Drag Modeling for Prediction of the Drag Torque Characteristics in Disengaged Wet Clutches
,”
SAE Int. J. Commer. Veh.
,
7
(
2
), pp.
441
447
.
17.
Pahlovy
,
S.
,
Mahmud
,
S.
,
Kubota
,
M.
,
Ogawa
,
M.
, and
Takakura
,
N.
,
2016
, “
New Development of a Gas Cavitation Model for Evaluation of Drag Torque Characteristics in Disengaged Wet Clutches
,”
SAE Int. J. Engines
,
9
(
3
), pp.
1910
1915
.
18.
Takagi
,
Y.
,
Nakata
,
H.
,
Okano
,
Y.
,
Miyagawa
,
M.
, and
Katayama
,
N.
,
2011
, “
Effect of Two-Phase Flow on Drag Torque in a Wet Clutch
,”
,
2
(
2
), p.
021108
.http://stoner.phys.uaic.ro/jarp/
19.
Takagi
,
Y.
,
Okano
,
Y.
,
Miyayaga
,
M.
, and
Katayama
,
N.
,
2012
, “
Numerical and Physical Experiments on Drag Torque in a Wet Clutch
,”
Tribol. Online
,
7
(
4
), pp.
242
248
.
20.
Yuan
,
Y.
,
Liu
,
E. A.
,
Hill
,
J.
, and
Zou
,
Q.
,
2006
, “
An Improved Hydrodynamic Model for Open Wet Transmission Clutches
,”
ASME J. Fluids Eng.
,
129
(
3
), pp.
333
337
.
21.
Yuan
,
S.
,
Peng
,
Z.
, and
Jing
,
C.
,
2011
, “
Experimental Research and Mathematical Model of Drag Torque in Single Plate Wet Clutch
,”
CJME
,
24
(
1
), pp.
91
97
.
22.
Aphale
,
C. R.
,
Cho
,
J.
,
Schultz
,
W. W.
,
Ceccio
,
S. L.
,
Yoshioka
,
T.
, and
Hiraki
,
H.
,
2005
, “
Modeling and Parametric Study of Torque in Open Clutch Plates
,”
ASME J. Tribol.
,
128
(
2
), pp.
422
430
.
23.
Aphale
,
C. R.
,
2007
, “
Drag Reduction at Low and High Reynolds Numbers
,”
Ph.D. dissertation
, University of Michigan, Ann Arbor, MIhttp://hdl.handle.net/2027.42/126354.
24.
Aphale
,
C. R.
,
Schultz
,
W. W.
, and
Ceccio
,
S. L.
,
2009
, “
The Influence of Grooves on the Fully Wetted and Aerated Flow Between Open Clutch Plates
,”
ASME J. Tribol.
,
132
(
1
), p.
011104
.
25.
Aphale
,
C. R.
,
Schultz
,
W. W.
, and
Ceccio
,
S. L.
,
2011
, “
Aeration in Lubrication With Application to Drag Torque Reduction
,”
ASME J. Tribol.
,
133
(
3
), p.
031701
.