The Influence of Inner Cylinder Rotation on Laminar Axial Flows in Eccentric Annuli of Drilling Bore Wells
P. Fang and R.M. Manglik
An extended theoretical study of the effects of annulus radius ratio r* and eccentricity e*, and inner cylinder rotation of drilling bore wells on the axial flow structure and frictional losses is presented. Computational results for a wide range of eccentric annuli geometry (0.1 < r* < 0.9, 0 < e* < 0.95) and inner pipe rotational Reynolds number (0 < Rer < 150) in the sub-critical Taylor number regime (Ta < 10,000) are obtained. The inner-core rotation produces a counter-rotating kidney-shaped vortex in the widest gap of the annulus, which grows with increasing eccentricity and decreasing radius ratio. This lowers the local peak axial velocity but increases the wall gradients, which results in higher friction losses. The combined effects of r*, e*, and Rer on the friction factor, however, are quite complex and their parametric influence is delineated.