Simulation of Oldroyd-B Viscoelastic Fluid in Axisymmetric Straight Channel by Using a Hybrid Finite Element/Volume Method

Abstract

In this study, incompressible viscoelastic fluid through the axisymmetric circular channel is simulated with Oldroyd-B model. The simulation is performed based on a hybrid finite volume/element method, which consists of Taylor-Galerkin finite element discretisation, and a cell vertex fluctuation-distribution finite volume method. In this context, the momentum and continuity equations are treated with a finite element method, while a finite volume approach is applied to solve the Oldroyd-B constitutive model. Analytical expressions are presented for the velocity and stress components in fully developed channel flow of Oldroyd-B fluid. For this complex fluid, we see an excellent agreement between the analytic and the numerical solutions. The study of axisymmetric circular channel problem based on a hybrid numerical method represents a great challenge. The novelty here is to study the temporal convergence-rate of the system solution that is taken to be steady state, incompressible, axisymmetric, and laminar, which did not address by researchers previously. Here, the rate of convergence for all solution components is presented, where a large level of convergence is appeared for stress compared to the other solution components. Moreover, the pressure drops and stress response across the flow are provided with respect to difference in solvent-fraction  and Weissenberg number . A significant effect from the viscoelastic parameters upon the level of the stress has been detected, while for the pressure response the change is semi-modest. For the stress response the findings reveal that, with decreasing solvent-fraction , the maxima level of stress components are strongly amplifies.