Creeping flows of power-law fluids through periodic arrays of elliptical cylinders

• Published in: Journal of non-Newtonian fluid mechanics 2003-04, Vol.111 (2), p.211-228
• Main Authors: Woods, J.K., Spelt, P.D.M., Lee, P.D., Selerland, T., Lawrence, C.J.
• Format: Article
• Language: English
• Subjects: Elliptical cylinders; Exact sciences and technology; Flows through porous media; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Low-reynolds-number (creeping) flows; Non-newtonian fluid flows; Nonhomogeneous flows; Permeability; Physics; Power-law fluids
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/S0377-0257(03)00056-9

Results from numerical simulations and lubrication theory are presented for creeping flows of power-law fluids through periodic arrays of elliptical cylinders. Flows are considered in the plane perpendicular to the axes of the cylinders, both along an axis of the array (on-axis flow) and at an angle to the axes of the array (off-axis flows). Results are presented for the apparent permeability tensor and for the dimensionless velocity variances (which can also be used to approximate the added mass coefficient for a cylinder in the array). The apparent permeability values obtained for on-axis flows of power-law fluids are shown to obey a simple scaling, which relates the apparent permeability tensor for power-law fluids to the corresponding permeability for Newtonian fluids; this scaling arises because of the choice of length scale used in the definition of the apparent permeability tensor for power-law fluids. The off-axis flow results are shown to be related to the on-axis results in a straightforward manner. The results are summarised in the form of closure relations for the apparent permeability tensor and velocity variances for off-axis flows of power-law fluids through arrays of elliptical cylinders for a range of aspect ratios using look-up graphs for only a few scalars.