Poiseuille flow of power-law fluids in concentric annuli-limiting cases

Abstract

Paper presented at the 6th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 30 June - 2 July, 2008.

The flow of non-Newtonian fluids through an annulus is often encountered in various industrial processes such as transportation of drilling fluids in petroleum industry and extrusion of polymers (in a mandrel region). Roughly speaking there are two approaches how to cope with the description of these flow situations. The numerical approach aims at a calculation of the quantities (e.g. velocity components, flow rate) describing the concrete problem, and with an arbitrary change of the entry parameters (geometry, kinematics, rheological characteristics) it is necessary to repeat the whole procedure from the beginning. The other approach lays emphasis on the functional participation of the individual entry parameters in the whole solution. This method enables to decide which parameters should be altered (and in which way) to obtain more favourable results e.g. from the viewpoint of production rate. In this case the optimum approach is represented by an explicit solution. However in more complicated problems the chance to obtain an explicit solution is rather limited. A number of papers have aimed at an analytical solution of an axial annular flow of power-law fluids, especially a relation: volumetric flow rate vs. pressure gradient. No complete analytical solution has been yet achieved. The only analytical solutions - that have been hitherto derived - concern the limiting cases of the geometrical parameter κ (inner-to-outer diameters ratio) or flow behaviour index n. The present contribution discusses an applicability of these limiting solutions for a broader region of entry parameters and proves that in many cases usage of these relations is fully acceptable (and comparable with an inaccuracy in experimental determination of flow behaviour index n and consistency parameter k of the power-law model).