Publication Date:
1997-04-25
Description:
A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii Ki,Ro rotating with peripheral speeds Ui,Uo). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, ψ, as a function of radius ratio R = Ri/Ro and speed ratio S = Ui/Uo. Results show that for S 〉 0 (S 〈 0) the flow domain consists of two (one) large eddies (eddy), each having a stagnation point on the centreline and a potentially rich substructure with separatrices and sub-eddies. The behaviour of the streamfunction solution in the neighbourhood of stagnation points on the centreline is investigated by means of a truncated Taylor expansion. As R and S are varied it is shown that a bifurcation in the flow structure arises in which a centre becomes a saddle stagnation point and vice versa. As R → 1, a sequence of 'flow bifurcations' leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gaP limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S 〈 0 and also when S 〉 0 and aspect ratios are small (except near S = 1). For S 〉 0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both R and S.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
