Multicellular natural convective flows in narrow horizontal air-filled concentric annuli are considered numerically in this paper. The results show that the multiplicity of the multicellular upper flows reported in the literature can be credited to the existence of an imperfect bifurcation with two stable branches. The emergence and extinction of the buoyancy-driven cells have been proved to be identical on both branches. The appearance of another secondary flow, the origin of which is purely hydrodynamic and located within the crescent base flow at the vertical portions of the annulus, has also been evidenced at moderate values of the Rayleigh number. As Ra is increased a reverse transition from a multicellular structure to a unicellular pattern occurs through a gradual decrease in the number of cells. In addition, it is shown that shear-driven instabilities cannot develop for radius ratios larger than a value close to R = 1.15.

1.
Bishop E. H., and Carley C. T., 1966, “Photographic Studies of Natural Convection between Concentric Cylinders,” Proc. Heat Transf. Fluid Mech. Inst., pp. 63–78.
2.
A.
,
Caltagirone
J. P.
,
Mojtabi
A.
, and
Vafai
K.
,
1992
, “
Free Two-dimensional Convective Bifurcation in a Horizontal Annulus
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
114
, pp.
99
106
.
3.
Chikhaoui A., Marcillat J. F., and Sani R. L., 1988, “Successive Transitions in Thermal Convection within a Vertical Enclosure,” Natural Convection in Enclosures, ASME HTD-Vol. 99, pp. 29–35.
4.
Desrayaud G., 1987, “Analyse de stabilite´ line´aire dans un milieu semi-transparent. De´termination expe´rimentale des limites de stabilite´ dans un milieu transparent,” these de doctorat es sciences physiques.
5.
Fant D. B., Rothmayer A., and Prusa J., 1989, “Natural Convective Flow Instability between Horizontal Concentric Cylinders,” Numerical Methods in Laminar and Turbulent Flow, Vol. 6, Part 2, Pineridge Press, Swansea, UK, pp. 1047–1065.
6.
Fant
D. B.
,
Prusa
J.
, and
Rothmayer
A.
,
1990
, “
Unsteady Multi-Cellular Natural Convection in a Narrow Horizontal Cylindrical Annulus
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
112
, pp.
379
387
.
7.
Kim C. J., and Ro S. T., 1994, “Numerical Investigation on Bifurcative Natural Convection in an Air-Filled Horizontal Annulus,” 10th Int. Heat Transfer Conference, Vol. 7, pp. 85–90.
8.
Korpela
S. A.
,
Gozum
D.
, and
Baxi
C. B.
,
1973
, “
On the Stability of the Conduction Regime of Natural Convection in a Vertical Slot
,”
Int. J. Heat Mass Transfer
, Vol.
16
, pp.
1683
1690
.
9.
Lauriat G., 1980, “Numerical Study of Natural Convection in a Narrow Cavity: An Examination of High Order Accurate Schemes,” ASME Paper No. 80-HT-90.
10.
Lauriat G., and Desrayaud G., 1985, “Natural Convection in Air-Filled Cavities of High Aspect Ratios: Discrepancies between Experimental and Theoretical Results,” ASME Paper No. 85-HT-37.
11.
Le
Que´re´ P.
,
1990
, “
A Note on Multiple and Unsteady Solutions in Two-Dimensional Convection in Tall Cavity
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
112
, pp.
965
974
.
12.
Powe
R. E.
,
Carley
C. T.
, and
Bishop
E. H.
,
1969
, “
Free Convective Flow Patterns in Cylindrical Annuli
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
91
, pp.
310
314
.
13.
Rao
Y.
,
Miki
Y.
,
Fukuda
K.
,
Takata
Y.
, and
Hasegawa
S.
,
1985
, “
Flow Patterns of Natural Convection in Horizontal Cylindrical Annuli
,”
Int. J. Heat Mass Transfer
, Vol.
28
, No.
3
, pp.
705
714
.
14.
Roux
B.
,
Grondin
J.
,
Bontoux
P.
, and
de
Vahl Davis G.
,
1980
, “
Reverse Transition from Multicellular to Monocellular Motion in Vertical Fluid Layer
,”
Phys. Chem. Hydro.
, Vol.
3F
, pp.
292
297
.
15.
Wakitani
S.
,
1997
, “
Development of Multicellular Solutions in Natural Convection in an Air-Filled Vertical Cavity
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
119
, pp.
97
101
.
This content is only available via PDF.