Effects of Particle Blockage and Eccentricity in Location on the Non-Newtonian Fluid Hydrodynamics around a Sphere

Abstract

The flow of an incompressible non-Newtonian fluid over an eccentrically located sphere confined in a circular tube was investigated using three-dimensional steady state Computational Fluid Dynamics simulations. Pseudoplastic fluids with different power-law indices of 0.57, 0.76, and 0.94 were considered. The effects of ratio of particle diameter to tube diameter (blockage ratio, BR) and ratio of offset of the sphere position from the tube axis to the tube radius (eccentricity, Ec) on the hydrodynamic phenomena around the sphere are reported over a range of particle Reynolds numbers (Rep). The simulations were carried out in the range (0.1 ≤ Rep ≤ 40, 0.01 ≤ BR ≤ 0.5, and 0.0 ≤ Ec ≤ 0.6). The drag coefficient predictions for an unconfined sphere were found to be sensitive to the value of the consistency index parameter (K) in the viscous flow regime, especially at lower n values. At lower particle Reynolds numbers and centrally located sphere, the enhancement in drag coefficient due to blockage ratio was felt least by the fluid with the lowest n value. Even at higher Rep, higher blockage ratios still could cause significant enhancements in the drag coefficients (∼20%) for centrally located spheres. Irrespective of the power-law index, eccentric location of the sphere caused a decline in the overall drag coefficient due to the dominant influence of the lower hemisphere which was closer to the tube wall. At the highest particle Reynolds numbers, eccentricity, and blockage ratio, asymmetric fluid flow distribution caused opposing effects by decreasing the viscous drag coefficient and increasing the form drag coefficient relative to those obtained with the centrally confined sphere. Sharp variations in the shear rate dependent viscosity at the sphere surface could be associated with boundary layer separation. Wall effects at higher blockage ratio suppressed the boundary layer separation in the case of the fluid with the highest power-law index. Eccentricity also caused accelerated boundary layer separation at the upper hemisphere and absence of boundary layer separation along the lower hemisphere. At lower blockage ratios a maximum in the lift coefficient versus particle Reynolds number was usually observed. This study will be relevant in applications such as aseptic food processing, petroleum well drilling, fluidization, and particle transport in microfluidic devices.