NUMERICAL MODELING OF HELICAL FLOW OF PSEUDOPLASTIC FLUIDS

Abstract

The laminar helical flow of non-Newtonian pseudoplastic fluids in concentric and eccentric annuli with a rotating inner cylinder has been investigated numerically. A finite volume algorithm with a nonstaggered grid system is used to analyze the problem. A nonorthogonal curvilinear coordinate system is employed to handle the irregular geometry of aneccentric annulus. The power-law constitutive equation is used to model the shear rate dependent viscosity of a pseudoplastic fluid. The computer code is validated against an available analytical solution for helical flow in a concentric annulus. It is observed that for a certain axial pressure gradient the axial flow rate increases within creasing rotational speed of the inner cylinder. The torque needed to rotate the inner cylinder decreases with increasing axial pressure gradient. These are explained in terms of the shear-thinning effect of a pseudoplastic fluid. The discharge as well as torque are found to increase with increasing eccentricity. The flow field in an eccentric annulus is complex in nature since vigorous secondary flow is produced in addition to the primary axial helical flow. The location and extent of the secondary flow is studied and theresults are presented for various eccentricities. The results will be useful in planning oil and gas well drilling operations.