Abstract
This paper considers the development of an isothermal laminar flow of viscoplastic fluid with yield stress in a pipe. A characteristic feature of such a flow is the formation of a non-deformable region in which the fluid behaves like a solid. This phenomenon significantly complicates the numerical solution of the equations of viscoplastic fluid flow, since traditional methods cannot adequately describe the behavior of the fluid in this region. The novelty of this work resides in the application of the effective molecular viscosity methodology and the Bingham-Papanastasiou model, which made it possible to perform an end-to-end calculation of the isothermal flow taking into account the non-deformable region. In the course of the calculations, the velocity and pressure distributions were derived for Reynolds numbers from 71.2 to 740.8 and Bingham numbers in the range from 1.225 to 17.01. An increase in the Reynolds number to Re = 740.8 and a decrease in the Bingham number to Bn = 1.225 lead to a reduction in the region with maximum velocities and a change in the input axial velocity distribution. The radial profiles of the axial velocity remain the same in all cross-sections from z/R = 10 to z/R = 40, which indicates the establishment of a steady-state flow regime of viscoplastic fluid, in which a constant velocity core is formed in the cross-section of the pipe.