Phenomenological friction equation for turbulent flow of Bingham fluids

Abstract

Most discussions in the literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In the presentwork, a formula is proposed for the evaluation of the friction coefficient of turbulent flows of Bingham fluids. The developments combine a fresh analysis for the description of the microscales of Kolmogorov and the phenomenological turbulence model of Gioia and Chakraborty [G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006)]. The resulting Blasius-type friction equation is tested against some experimental data and shows good agreement over a significant range of Hedstrom and Reynolds numbers. Comments on pressure measurements in yielding fluids are made. The limits of the proposed model are also discussed.