Numerical simulations have been performed to study the effects of the gravitational and the centrifugal potentials on the stability of heated, incompressible Taylor-Couette flow. The flow is confined between two differentially heated, concentric cylinders, and the inner cylinder is allowed to rotate. The Navier-Stokes equations and the coupled energy equation are solved using a spectral method. To validate the code, comparisons are made with existing linear stability analysis and with experiments. The code is used to calculate the local and average heat transfer coefficients for a fixed Reynolds number (Re = 100) and a range of Grashof numbers. The investigation is primarily restricted to radius ratios 0.5 and 0.7 for fluids with Prandtl number of about 0.7. The variation of the local coefficients of heat transfer on the cylinder surface is investigated, and maps showing different stable states of the flow are presented. Results are also presented in terms of the equivalent conductivity, and show that heat transfer decreases with Grashof number in axisymmetric Taylor vortex flow regime, and increases with Grashof number after the flow becomes nonaxisymmetric.

1.
Ali
M.
, and
Weidman
P. D.
,
1990
, “
On the Stability of Circular Couette Flow With Radial Heating
,”
J. Fluid Mech.
, Vol.
220
, pp.
53
84
.
2.
Ball
K. S.
, and
Farouk
B.
,
1987
, “
On the Development of Taylor Vortices in a Vertical Annulus With a Heated Rotating Inner Cylinder
,”
Int. J. Num. Meth. Fluids
, Vol.
7
, pp.
857
867
.
3.
Ball
K. S.
, and
Farouk
B.
,
1988
, “
Bifurcation Phenomena in Taylor-Couette Flow With Buoyancy Effects
,”
J. Fluid Mech.
, Vol.
197
, pp.
479
501
.
4.
Ball
K. S.
,
Farouk
B.
, and
Dixit
V. C.
,
1989
, “
An Experimental Study of Heat Transfer in a Vertical Annulus With a Rotating Inner Cylinder
,”
Int. J. Heat Mass Transfer
, Vol.
32
, No.
8
, pp.
1517
1527
.
5.
Brandstater
A.
, and
Swinney
H. L.
,
1987
, “
Strange Attractors in Weakly Turbulent Couette-Taylor Flow
,”
Phys. Rev. A
, Vol.
35
, No.
5
, pp.
2207
2220
.
6.
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., 1988, Spectral Methods in Fluid Dynamics, 3rd ed., Springer-Verlag, Berlin.
7.
Chen
J.
, and
Kuo
J.
,
1990
, “
The Linear Stability of Steady Circular Couette Flow With a Small Radial Temperature Gradient
,”
Phys. Fluids A
, Vol.
2
, No.
9
, pp.
1585
1591
.
8.
Coles
D.
,
1965
, “
Transition in Circular Couette Flow
,”
J. Fluid Mech.
, Vol.
21
, pp.
385
425
.
9.
DiPrima, R. C., and Swinney, H. L., 1981, “Instabilities and Transition in Flow Between Concentric Rotating Cylinders,” Hydrodynamic Instabilities and the Transition to Turbulence, H. L. Swinney and J. P. Gollub, eds., Springer-Verlag, Berlin, pp. 139–180.
10.
Gopalakrishnan, S., Vaghasia, G. K., and Reimers, C. R., 1992, “Crack Propagation in Main Coolant Pumps,” presented at Fifth Int. Workshop on Main Coolant Pumps, April 21–24, Orlando, FL.
11.
Gray
D. D.
, and
Giorgini
A.
,
1976
, “
The Validity of the Boussinesq Approximation for Liquids and Gases
,”
Int. J. Heat Mass Transfer
, Vol.
19
, pp.
545
551
.
12.
Greenspan, H. P., 1968, The Theory of Rotating Fluids, Cambridge University Press, New York.
13.
Kataoka
K.
,
Doi
H.
, and
Komai
T.
,
1977
, “
Heat/Mass Transfer in Taylor Vortex Flow With Constant Axial Flow Rates
,”
Int. J. Heat Mass Transfer
, Vol.
20
, pp.
57
63
.
14.
Kato
H.
,
Kanno
H.
,
Hosokawa
M.
,
Watanabe
A.
,
Shitara
C.
,
Ashizawa
K.
,
Miyano
H.
,
Narabayashi
T.
,
Iikura
T.
,
Hayashi
M.
,
Endoh
A.
, and
Takehara
H.
,
1992
, “
The Development of Advanced Nuclear Primary Loop Recirculating Pump (PLR Pump) for BWR Plant Considering Thermal Fatigue Problem
,”
Industrial and Environmental Applications of Fluid Mechanics
, Proc. of the ASME Winter Annual Meeting, FED-Vol
145
, Sherif et al., eds., pp.
157
162
.
15.
Kedia, R., 1997, “An Investigation of Velocity and Temperature Fields in Taylor-Couette Flows,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
16.
Kreith, F., 1968, “Convection Heat Transfer in Rotating Systems,” Advances in Heat Transfer 5, Academic Press, New York, pp. 129–251.
17.
Lee
Y. N.
, and
Minkowycz
W. J.
,
1989
, “
Heat Transfer Characteristics of the Annulus of Two-Coaxial Cylinders With One Cylinder Rotating
,”
Int. J. Heat Mass Transfer
, Vol.
32
, pp.
711
722
.
18.
Meyer
K. A.
,
1967
, “
Time-Dependent Numerical Study of Taylor Vortex Flow
,”
Phys. Fluids
, Vol.
10
, No.
9
, pp.
1874
1879
.
19.
Moser
R. D.
,
Moin
P.
, and
Leonard
A.
,
1983
, “
A Spectral Numerical Method for the Navier-Stokes Equations With Applications to Taylor-Couette Flow
,”
J. Comput. Phys.
, Vol.
52
, pp.
524
544
.
20.
Roesner
K. G.
,
1978
, “
Hydrodynamic Stability of Cylindrical Couette-Flow
,”
Arch. of Mech.
, Vol.
30
, pp.
619
627
.
21.
Shih, A. C., and Hunt, M. L., 1992, “High-Taylor-Number Couette Flows With a Superposed Isothermal or Heated Axial Flow,” Proc. of the ASME National Heat Transfer Conf., General Papers in Heat Transfer, HTD-Vol. 204, M. Jensen et al, eds. San Diego, CA.
22.
Singer, H. P., 1984, “Techniques of Low Pressure Chemical Vapor Deposition,” Semiconductor International, Denver, CO, May 1984, pp. 72–77.
23.
Taylor
G. I.
,
1923
, “
Stability of a Viscous Liquid Contained Between Two Rotating Cylinders
,”
Phils. Trans. R. Soc. London
, Ser. A, Vol.
223
, pp.
289
343
.
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