Flow fields in an annulus between two rotating cylinders with a porous lining have been numerically examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The effects of porous sleeve thickness and its properties on the flows and their stability in the annulus are numerically investigated. Three-dimensional momentum equations for the porous and fluid layers are formulated separately and solved simultaneously in terms of velocity and vorticity. The solutions have covered a wide range of the governing parameters (105Da102,2000Ta5000,0.8b¯0.95). The results obtained show that the presence of a porous sleeve generally has a stabilizing effect on the flows in the annulus.

1.
Rayleigh
,
L.
, 1879, “
On the Stability, or Instability, of Certain Fluid Motions
,”
Proc. London Math. Soc.
0024-6115,
s1-11
, pp.
57
72
.
2.
Taylor
,
G. I.
, 1921, “
Experiments With Rotating Fluids
,”
Proc. Cambridge Philos. Soc.
0068-6735,
20
, pp.
77
99
.
3.
Taylor
,
G. I.
, 1923, “
Stability of a Viscous Liquid Contained Between Two Rotating Cylinders
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
223
, pp.
289
343
.
4.
Walowit
,
J.
,
Tsao
,
S.
, and
DiPrima
,
R. C.
, 1964, “
Stability of Flow Between Arbitrarily Spaced Concentric Cylindrical Surfaces Including the Effect of a Radial Temperature Gradient
,”
ASME J. Appl. Mech.
0021-8936,
31
, pp.
585
593
.
5.
Davis
,
S. H.
, 1969, “
On the Principle of Exchange of Stabilities
,”
Proc. R. Soc. London, Ser. A
1364-5021,
310
, pp.
341
358
.
6.
Yih
,
C. -S.
, 1972a, “
Spectral Theory of Taylor Vortices
,”
Archive for Rational Mechanics and Analysis
,
46
, pp.
218
240
.
7.
Yih
,
C. -S.
, 1972b, “
Spectral Theory of Taylor Vortices Part II. Proof of Nonoscillation
,”
Archive for Rational Mechanics and Analysis
,
47
, pp.
288
300
.
8.
Al-Mubaiyedh
,
U.
,
Sureshkumar
,
A. R.
, and
Khomami
,
B.
, 2002, “
The Effect of Viscous Heating on the Stability of Taylor-Couette Flow
,”
J. Fluid Mech.
0022-1120,
462
, pp.
111
132
.
9.
Muller
,
S. J.
,
Larson
,
R. G.
, and
Shaqfeh
,
E. S. G.
, 1989, “
A Purely Elastic Transition in Taylor-Couette Flow
,”
Rheol. Acta
0035-4511,
28
, pp.
499
503
.
10.
White
,
M. J.
, and
Muller
,
S. J.
, 2002, “
Experimental Studies on the Stability of Newtonian Taylor-Couette Flow in the Presence of Viscous Heating
,”
J. Fluid Mech.
0022-1120,
462
, pp.
133
161
.
11.
Lockett
,
T. J.
,
Richardson
,
S. M.
, and
Worraker
,
W. J.
, 1992, “
The Stability of Inelastic Non-Newtonian Fluids in Couette Flow Between Concentric Cylinders: A Finite Element Study
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
43
, pp.
165
177
.
12.
Channabasappa
,
M. N.
,
Ranganna
,
G.
, and
Rajappa
,
B.
, 1984, “
Stability of Viscous Flow in a Rotating Porous Medium in the Form of an Annulus: The Small-Gap Problem
,”
Int. J. Numer. Methods Fluids
0271-2091,
4
, pp.
803
811
.
13.
Chang
,
M. -H.
, 2003, “
Hydrodynamic Stability of Taylor–Dean Flow Between Rotating Porous Cylinders With Radial Flow
,”
Phys. Fluids
1070-6631,
15
, pp.
1178
1188
.
14.
Subotic
,
M.
, and
Lai
,
F. C.
, 2008, “
Flows Between Rotating Cylinders With a Porous Lining
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
102601
.
15.
Drazin
,
P. G.
, and
Reid
,
W. H.
, 1991,
Hydrodynamic Stability
,
Press Syndicate of the University of Cambridge
,
Cambridge
.
16.
Chandrasekhar
,
S.
, 1961,
Hydrodynamic and Hydromagnetic Stability
,
Oxford University Press
,
Oxford
.
17.
Coronado-Matutti
,
O.
,
Souza Mendes
,
P. R.
, and
Carvalho
,
M. S.
, 2004, “
Instability of Inelastic Shear-Thinning Liquids in a Couette Flow Between Concentric Cylinders
,”
ASME J. Fluids Eng.
0098-2202,
126
, pp.
385
390
.
18.
Fusegi
,
T.
, and
Farouk
,
B.
, 1986, “
Predictions of Fluid Flow and Heat Transfer Problems by the Vorticity–Velocity Formulation of the Navier–Stokes Equations
,”
J. Comput. Phys.
0021-9991,
65
, pp.
227
243
.
19.
Orlandi
,
P.
, 1987, “
Vorticity-Velocity Formulation for High Re Flows
,”
Comput. Fluids
0045-7930,
15
, pp.
137
149
.
20.
Speziale
,
C. G.
, 1987, “
On the Advantages of Vorticity–Velocity Formulation of the Equations of Fluid Dynamics
,”
J. Comput. Phys.
0021-9991,
73
, pp.
476
480
.
21.
Dennis
,
S. C. R.
, and
Hudson
,
J. D.
, 1995, “
Methods of Solution of the Velocity-Vorticity Formulation of the Navier-Stokes Equations
,”
J. Comput. Phys.
0021-9991,
122
, pp.
300
306
.
22.
Neale
,
G.
, and
Nader
,
W.
, 1974, “
Practical Significance of Brinkman Extension of Darcy’s Law. Coupled Parallel Flow Within a Channel and a Bounding Porous Medium
,”
Can. J. Chem. Eng.
0008-4034,
52
, pp.
475
478
.
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