Flow of power-law liquids past a solid sphere with and without radial mass flux at moderate Reynolds numbers

Abstract

In this work, the flow of power-law fluids past a solid sphere with and without radial mass flux has been investigated numerically using a finite difference method based SMAC-implicit algorithm implemented on a spherical staggered grid arrangement. It is clearly shown that the flow and drag phenomena are strongly affected by the pertinent dimensionless parameters like Reynolds number (Re), power-law index (n) and the radial mass flux (φ). The effect of suction (φ < 0) on the flow profile is seen to be strong at high Reynolds numbers in the case of shear-thinning fluids (n < 1), whereas the reverse is seen in Newtonian and shear-thickening fluids (n ≥ 1). On the other hand, irrespective of the value of power-law index, the effect of injection (φ > 0) on the flow profile is significant at all Reynolds numbers. Regardless of the value of the power-law index, the pressure drag coefficient decreases as the value of φ decreases. On the other hand, the friction and total drag coefficients decrease as the value of φ decreases for Newtonian and shear-thinning fluids, whereas an opposite trend is seen in shear-thickening fluids. However, the total drag coefficient is reduced for suction (φ < 0) and augmented for injection (φ > 0) compared to that in the absence of radial mass flux. This is so for all values of power-law index. The present numerical results have been correlated empirically, thereby enabling the prediction of the drag coefficient (hence terminal velocity) in a new application.