Application of grain flow theories to powder lubrication of hydrodynamic bearings requires careful consideration of slip of the flow velocity at the boundaries together with appropriate formulation of the fluctuation (thermal) velocity conditions at the boundaries. Generalized boundary conditions that can be applied to a wide variety of surface and grain material characteristics are developed for a Couette flow configuration. The equations account for both the energy loss at the boundary due to inelastic grain-wall collisions and the energy supplied by the boundary due to collisional momentum supply. The predictions of the model are compared to a number of published results that are based on direct computer simulation of grain-grain collisions. The model’s flexibility is demonstrated by simulating the effects of unequal surface roughnesses.

1.
Campbell
C. S.
,
1993
, “
Boundary Interactions for Two-Dimensional Granular Flows. Part I. Flat Boundaries, Asymmetric Stresses and Couple Stresses
,”
Journal of Fluid Mechanics
, Vol.
247
, pp.
111
136
.
2.
Dai
F.
,
Khonsari
M. M.
, and
Lu
Z. Y.
,
1994
, “
On the Lubrication Mechanism of Grain Flows
,”
Tribology Transactions
, Vol.
37
, pp.
516
424
.
3.
Elrod, H. G., 1988, “Granular Flow as a Tribological Mechanism—A First Look,” Interface Dynamics, Leeds-Lyon Symposium, BHRA, pp. 75–102.
4.
Elrod, H. G., 1990, “Preliminary Theory for Granule-Lubricated Bearings,” Presented at the 1990 Bearing Coordination Meeting, Wright-Patterson AFB, OH, unpublished.
5.
Elrod, H. G., and Brewe, D. E., 1992, “Numerical Experiments with Flows of Elongated Granules,” NASA TM #105567, AVSCOM TR#91-C-006.
6.
Gutt
G. M.
, and
Haff
P. K.
,
1991
, “
Boundary Conditions on Continuum Theories of Granular Flow
,”
Int. J. Multiphase Flow
, Vol.
17
, No.
5
, pp.
621
634
.
7.
Haff
P. K.
,
1983
, “
Grain Flow as a Fluid-Mechanical Phenomenon
,”
Journal of Fluid Mechanics
, Vol.
134
, pp.
401
430
.
8.
Heshmat
H.
,
1992
, “
The Quasi-Hydrodynamic Mechanism of Powder Lubrication: Part II—Lubricant Film Pressure Profile
,”
Lubrication Engineering
, Vol.
48
, pp.
373
383
.
9.
Hui
K.
,
Haff
P. K.
,
Ungar
J. E.
, and
Jackson
R.
,
1984
, “
Boundary Conditions for High-Shear Grain Flows
,”
Journal of Fluid Mechanics
, Vol.
145
, pp.
223
233
.
10.
Jenkins, J. T., and Askari, E., 1993, “Rapid Granular Shear Flows Driven by Identical, Bumpy, Frictionless Boundaries,” Powders and Grains 93, Thornton, C., ed., Balkema, pp. 295–300.
11.
Jenkins
J. T.
, and
Richman
M. W.
,
1986
, “
Boundary Conditions for Plane Flows of Smooth, Nearly Elastic Disks
,”
Journal of Fluid Mechanics
, Vol.
171
, pp.
53
69
.
12.
Jenkins
J. T.
, and
Savage
S. B.
,
1983
, “
A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Spherical Particles
,”
Journal of Fluid Mechanics
, Vol.
130
, pp.
187
202
.
13.
Louge
M. Y.
,
1994
, “
Computer Simulations of Rapid Granular Flows of Spheres Interacting with a Flat, Frictional Boundary
,”
Physics of Fluids
, Vol.
6
, pp.
2253
2269
.
14.
Savage
S. B.
, and
Dai
R.
,
1993
, “
Studies of Granular Shear Flows, Wall Slip Velocities, “Layering”, and Self-Diffusion
,”
Mechanics of Materials
, Vol.
16
, pp.
225
238
.
15.
Yu
C.
,
Craig
K.
, and
Tichy
J.
,
1994
, “
Granular Collision Lubrication
,”
Journal of Rheology
, Vol.
38
, pp.
921
936
.
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