The influence of the rheological model used in pipe-flow prediction techniques for homogeneous non-Newtonian fluids

Abstract

Pressure gradients were measured for shear-thinning (5% CMC), Bingham plastic (7% bentonite), and viscoplastic (6% kaolin) fluids in pipe diameters of Ø40 to Ø200 mm, in laminar and turbulent flow. The fluids were characterized as power law, Bingham plastic, and Herschel-Bulkley fluids respectively, and additionally as Casson fluids. The study considered the effect of the rheological model in reproducing experimental laminar flow, and on transitional velocity and turbulent flow predictions. For the fluids tested, the model was found to have little effect on laminar flow calculations. Transitional velocities were predicted using three well-known techniques and found to depend on the model, although no preferences were apparent. Errors in transitional velocity predictions varied from 2.5 to 31%. Turbulent predictions too were made using three common and widely published methods, and varied significantly with rheology. All the methods, however, predicted turbulent flow similarly when using the Casson model, with errors of between 4 and 11%. It is concluded, at least for the types of time-independent, homogeneous/pseudohomogeneous, non-Newtonian fluids investigated, that for pipe flow in the practical range 40 s−1<(8V/D)<1,000 s−140 s−1<(8V/D)<1,000 s−1, laminar flow pressure gradient predictions are insensitive to the rheological model. Transitional velocity and turbulent flow pressure gradient predictions, however, are significantly affected by the rheological model used, so care must be taken to correctly characterize fluids for which these predictions are required.