STOKES-FLOW IN A HALF-FILLED ANNULUS BETWEEN ROTATING COAXIAL CYLINDERS

A model is presented for viscous flow in a cylindrical cavity (a half- filled annulus lying between horizontal, infinitely long concentric cy linders of radii R-i,R-0 rotating with peripheral speeds U-i,U-0). Sto kes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, phi, as a function of radius ratio (R) over bar = R-i/R-0 and speed ratio S = U-i/U-0. 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 potentia lly rich substructure with separatrices and sub-eddies. The behaviour of the streamfunction solution in the neighbourhood of stagnation poin ts on the centreline is investigated by means of a truncated Taylor ex pansion. As (R) over bar and S are varied it is shown that a bifurcati on in the flow structure arises in which a centre becomes a saddle sta gnation point and vice versa. As (R) over bar --> 1, a sequence of 'fl ow bifurcations' leads to a flow structure consisting of a set of nest ed separatrices, and provides the means by which the two-dimensional c avity 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 ar e small (except near S = 1). For S > 0 and moderate to large aspect ra tios the bifurcation characteristics of the two large eddies are quite different and depend on both (R) over bar and S.