On the application of generalised Newtonian fluids in the modelling of drag-reducing rigid polymers

Abstract

Drag-reducing polymers with rod-like molecular structure are known to exhibit significant shear-thinning yet only weak elastic properties, making them suited to modelling by generalised Newtonian fluids (GNFs) based on the second invariant of the rate of deformation tensor, D. However only qualitative agreement with experiments is obtained when such models are employed in the direct numerical simulation of turbulent flows. In this study, we investigate GNFs to obtain guidelines for their application in predicting turbulent drag reduction, and show that the appearance of flow-type sensitivity or elastic effects, however small, places a limit on their accuracy. By incorporating a dependence on the third invariant of D, to bring in sensitivity to flow type, we demonstrate that reasonably good quantitative agreement with experimental data can be obtained.