Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers

Abstract

A numerical investigation has been carried out to obtain the steady state drag coefficients and flow patterns of a single Newtonian fluid sphere sedimenting in power-law liquids. A finite difference method based simplified marker and cell (SMAC) algorithm has been implemented on a staggered grid arrangement to solve the continuity and momentum equations. For both phases, the convective terms have been discretized using the quadratic upstream interpolation for convective kinematics (QUICK) scheme, and diffusive and non-Newtonian terms with central differencing scheme. An exponential transformation has been applied in the radial direction for the continuous phase computational domain. In order to ensure the accuracy of the solver, extensive validation has been carried out by comparing the present results with the existing literature values for a few limiting cases. Further, in this study the effects of the Reynolds number ( Re o ) , internal to external fluid characteristic viscosity ratio ( k ) and power-law index ( n o ) on the continuous phase flow field, pressure drag ( C dp ) , friction drag ( C df ) and total drag ( C D ) coefficients have been analyzed over the range of parameters: 5 ⩽ Re o ⩽ 500 , 0.1 ⩽ k ⩽ 50 and 0.6 ⩽ n o ⩽ 1.6 . Based on numerical results obtained in this work, a simple correlation has been proposed for the total drag coefficient, which can be used to predict the rate of sedimentation of a fluid sphere in power-law liquids.