On modeling turbulent fluid flows in concentric annular pipes

The possibility of using a rheological model of a bi-viscous fluid to describe laminar and turbulent flows of Newtonian and non-Newtonian fluids in concentric annular pipes is considered. For low shear rates, common rheological models (Newton, Bingham, Ostwald, Herschel−Bulkley, Shulman−Casson, etc.) are used, and for high shear rates, a generalization of L. Prandtl’s model is applied. Considering the averaged characteristics of the flow, a model of turbulent flow and velocity distribution equations in concentric annular pipes are constructed, which ensure the continuity of the dependence of hydraulic resistance on the fluid flow rate and expand the possibilities of its application in applied problems of hydromechanics. The results of calculations of the parameters of laminar and turbulent fluid flows in concentric annular pipes for Newton, Bingham, Ostwald, Herschel−Bulkley and Shulman−Casson fluids are presented. Based on the analysis of numerical simulation results, some features of turbulent fluid flows are examined. The presence of turbulence asymmetry in concentric annular pipes is noted, which manifests itself in the occurrence of turbulent flow first in the fluid layers adjacent to the inner pipe, and then to the outer one. Critical values of the parameters (flow rate, Reynolds number) for the occurrence of turbulent flows are determined by the diameters of the annular pipes and the rheological properties of the fluid, and can differ significantly for the internal and external regions of the flow. The effect of turbulence on the removal (displacing) capacity of the fluid flow is shown.