Turbulent flow of viscoelastic fluid based on the Reynolds stress model

Abstract

This article presents the results of applying a turbulent stress model to the simulation of highviscosity viscoelastic fluid flow in a pipe. The model is used to numerically determine averaged velocity and stress fields within the Navier–Stokes equations. The proposed model takes into account the influence of the Sisko fluid rheology on turbulent momentum transfer, providing a physically sound description of the interaction between turbulence and non-Newtonian effects. Calculations for a Newtonian fluid are performed as a baseline for evaluating the effectiveness of the proposed approach. It is shown that for Sisko fluid, the averaged velocity profile in universal coordinates is systematically shifted upward compared to the Newtonian case, indicating weakening of turbulent momentum transfer and a decrease in hydrodynamic drag. It is established that the level of axial velocity fluctuations exceeds the Newtonian value, while radial fluctuations are lower, indicating pronounced anisotropy of turbulent stresses. The viscoelastic properties of the fluid lead to a reduction in turbulent friction due to the suppression of small-scale vortex structures and, as a consequence, to a reduction in the hydraulic resistance of the pipe.