Longitudinal Flow Field

Abstract

The state of the science in predicting the hydrodynamically developed longitudinal field of non-linear viscoelastic fluids in straight tubes of arbitrary but longitudinally constant cross section and in predicting the friction factors is summarized. Laminar and turbulent longitudinal flow fields and related phenomena including recent progress concerning the all-important drag reduction phenomena are addressed. Keywords Non-linear viscoelastic fluids • Longitudinal velocity field • Straight tubes • Arbitrary cross-section • Friction factors • Laminar flow • Turbulent flow • Pseudoplastic behavior • Drag reduction • Drag-reducing additives and applications • Theoretical mechanism of drag reduction • Experimental findings in drag reduction • Factors influencing the effectiveness of drag reductionOnly hydrodynamically developed flows will be reviewed. It should be noted that hydrodynamically developing flows are important as the entrance length L given in terms of either dimensionless quantities L + or L*,can be substantial in particular in laminar flow. Here D h is the hydraulic diameter, and Re + and Re* are the generalized Reynolds number and the Kozicki generalized Reynolds number, respectively, defined in Sect. 2.1.