The stability of developing tangential flow induced by the imposition of an axial velocity on the tangential velocity distribution created by core rotation is theoretically and experimentally investigated. A linear stability analysis is used to examine the influence of axial length, axial Reynolds number and annulus radius ratio on the critical Taylor number for neutral stability when the axial velocity is assumed uniform. Predictions compare favourably with measurements obtained by hot-wire anemometer for air flowing in an annulus of radius ratio 0·9, particularly at small Reynolds number and large values of the axial length parameter.
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References
1.
BeckerK. M.KayeJ.‘Measurements of diabatic flow in an annulus with an inner rotating cylinder’, Trans. ASME, J. Heat Transfer196284, 97–105.
2.
PayneA.MartinB. W.‘Heat transfer to laminar axial flow in a concentric annulus from a rotating inner cylinder’. Proc. Fifth Int. Heat Transfer. Conf. (Japan Soc. mech. Engrs and Soc. chem. Engrs, Japan); Heat Transfer 1974II, FC 2.7, 80–84.
3.
ChandrasekharS.‘The hydrodynamic stability of in viscid flow between co-axial cylinders’, Proc. Nat. acad. Sci. (Washington) 196046, 137–141.
4.
RAYLEIGH‘On the dynamics of revolving fluids’. Science Paper19206, 447–453 (Cambridge University Press).
5.
ChandrasekharS.‘The hydrodynamic stability of viscid flow between co-axial cylinders’, Proc. Nat. acad. Sci. (Washington) 196046, 141–143.
6.
Di PrimaR. C.‘The stability of a viscous fluid between rotating cylinders with an axial flow’, J. fluid Mech.19609, 621–631.
7.
TaylorG. I.‘Stability of a viscous fluid contained between two rotating cylinders’, Phil. Trans. R. Soc. Lond.1923A223. 289–343.
8.
DonnellyR. J.FultzD.‘Experiments on the stability of spiral flow between rotating cylinders’, Proc. Nat. acad. Sci. (Washington) 196046, 1150–1154.
9.
SnyderH. A.‘Experiments on the stability of spiral flow at low axial Reynolds numbers’, Proc. R. Soc. Lond.1962A265, 198–214.
10.
ElliottL.‘Stability of a viscous fluid between rotating cylinders with axial flow and pressure gradient round the cylinders’, Phys. Fluids197316, 577–580.
11.
HughesT. H.ReidW. H.‘The stability of spiral flow between rotating cylinders’, Phil. Trans. R. Soc. Lond.1968A263, 57–91.
12.
HasoonM. A.MartinB. W.‘The stability of viscous axial flow in an annulus with a rotating cylinder’. Proc. R. Soc. (to be published).
13.
AstillK. N.GanleyJ. T.MartinB. W.‘The developing tangential velocity profile for axial flow in an annulus with a rotating inner cylinder’, Proc. R. Soc., Lond.1968A307, 55–69.
14.
SparrowE. M.LinS. H.‘The developing laminar flow and pressure drop in the entrance region of annular ducts’. Trans. ASME. J. bas. Engng196486, 827–834.
15.
AstillK. N.Modes of adiabatic flow in the entrance region of an annulus with an inner rotating cylinder Ph.D. Thesis, Massachusetts Institute of Technology, 1961.
16.
AstillK. N.‘Studies of the developing flow between concentric cylinders with the inner cylinder rotating’. Trans. ASME. J. Heat Transfer196486, 383–392.
17.
KlineS.McClintockF. A.‘The description of uncertainties in single-sample experiments’, Mech. Engng195375, 3–8.
18.
HasoonM. A.Instability criteria in combined developing tangential and axial laminar flow in an annulus with a rotating inner cylinder Ph.D. Thesis. The University of Wales Institute of Science and Technology, 1975.
