Tangential flow development for laminar axial flow in an annulus with a rotating inner cylinder

Abstract
The numerical finite-difference procedure of Gosman et al. (1969) is used to predict the growth of the tangential velocity profile and boundary-layer displacement thickness across an isothermal laminar axial flow through a concentric annulus when the inner cylinder is rotated at speeds which are insufficient to generate Taylor vortices. Solutions are obtained for fully developed and for developing axial flow over the ranges 0.05 < R1/R2 < 0.98, 0.0002 < l < 1.0 and 100 < Re < 1700. The axial velocity profile is predicted to be insensitive to core rotation and, if varied, to influence only marginally the development of the tangential velocity profile; this is such that its dimensionless displacement thickness is related to dimensionless axial distance by a power law except near full development and at very low Reynolds number. Predictions at high Re accord extremely well with measurements. Astill’s (1964) stability criterion for the onset of vortices in tangential developing flow is accordingly presented afresh in terms of system parameters readily available to the designer.

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