Numerical Modelling of Viscous and Viscoelastic Fluids Flow in the Channel with T-Junction

Abstract

In this work the numerical solution of the viscous and viscoelastic fluids flow for generalized Newtonian and Oldroyd-B fluids are considered. The governing system of equations is the system of generalized Navier-Stokes equations for incompressible laminar fluids flow. For the stress tensor on the right hand side of this system two different mathematical models for viscous and viscoelastic fluids flow are used, Newtonian model and Oldroyd-B model. For the numerical simulation of generalized Newtonian and Oldroyd-B fluids flow in the tested domain a cross model for viscosity function $\mu (\dot{\gamma })$ is considered. The finite volume method combined with the artificial compressibility method is used for the spatial discretization. For the time discretization the explicit multistage Runge-Kutta scheme is used. Computational domain is formed by the branched channel with one inlet and two outlet parts. The crosssection is square and the branch is perpendicular to the main pipe. The numerical results of generalized Newtonian and generalized Oldroyd-B fluids flow obtained by this method are presented.