Laminar-Turbulent Transition in Flow of Pseudoplastic Fluids with Yield Stresses

Abstract

An analysis of the laminar-turbulent transition behavior of power law non-Newtonian fluids with yield stresses reveals that considerable interaction occurs between the characterizing parameters m and Hedstrom number for low power law indexes, m. In particular, for m < 0.4 small yield stresses tend to destabilize the flow whereas large ones stabilize it. The results of this analysis suggest that in order to obtain correct predictions and interpretations of transitional and turbulent flows of nonNewtonian fluids, a correct modeling of the viscous rheological behavior of the fluid is essential. Nomenclature A = a dimensionless parameter defined by Eq. (6) D - pipe diameter / = friction factor He - Hedstrom number, defined by Eq. (17) K = laminar-turbulent transition parameter K = maximum value of K m = power law index in rheological model Re - Reynolds number,.defined by Eq. (8) r = radial coordinate u = v/(u}, dimensionless velocity v = velocity (v} ~ mean velocity T = -du/d£ j] = consistency index in rheological model k = r/rw £ = value of £ where K = K £o = TQ/TW p — fluid density a = dimensionless parameter defined by Eq. (7) r = shear stress TO = yield stress in rheological model