Helical Flow of a Viscoplastic Material Through the Developing Region of Annular Spaces

Abstract

The laminar helical flow of a viscoplastic (or highly shear-thinning) material through the developing region of concentric annular spaces was examined. This physical situation is important in a variety of applications, including the flow of drilling muds through petroleum wells. The velocity, pressure and viscosity fields were obtained by solving the mass- and momentum-conservation equations via a finite-volume method. The Generalized Newtonian Liquid model was adopted as constitutive equation. The Carreau model was employed as viscosity function, whose parameters were obtained via a least-squares to fit to data obtained for a viscoplastic material. Solutions are presented for a wide range of Reynolds and Taylor numbers, within the subcritical regime.