Numerical Study of Effect of Stress Tensor for Viscous and Viscoelastic Fluids Flow

Abstract

This work deals with the numerical simulation of viscous and viscoelastic fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar fluids. Two models for the stress tensor are tested. For viscous fluids flow Newtonian model is used. By the combination of Newtonian and simple viscoelastic (Maxwell) models the behaviour of the mixture of viscous and viscoelastic fluids can be described. This model is called Oldroyd-B model. Both presented models (Newtonian and Oldroyd-B) can be generalized for the numerical modelling of the generalized Newtonian and Oldroyd-B fluids flow. In this case the viscosity is no more constant but is defined as a shear rate dependent viscosity function \(\mu (\dot{\gamma })\). One of the most frequently used shear-thinning models is the generalized cross model. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge–Kutta time integration. Steady state solution is achieved for \(t \rightarrow \infty \). In this case the artificial compressibility method can be applied. The numerical results of generalized Newtonian and generalized Oldroyd-B fluids flow obtained by this method are presented and compared.