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

Abstract 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.

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