Modeling and simulation of three-dimensional planar contraction flow of viscoelastic fluids with PTT, Giesekus and FENE-P constitutive models

The planar contraction flow is a representative benchmark problem that is often used as a stringent test for the robustness of the numerical method to predict real flow patterns of viscoelastic fluids. A numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three-dimensional flow of viscoelastic fluids through planar contraction. The viscoelastic rheological responses are described by using three kind differential constitutive models including the Phan-Thien–Tanner (PTT) model, the Giesekus model and the finite extensible nonlinear elastic dumbbell with a peterlin closure approximation (FENE-P) model. The discrete elastic viscous split stress (DEVSS) formulation in cooperating with the inconsistent streamline upwind (SU) scheme is employed to improve the computational stability. The simulation results of flow velocity and stress on different sections of the flow field are compared with Quinzani’s experimental results that detected by laser-doppler velocimetry and flow-induced birefringence technologies. It is found that the simulation results predicted with three kind differential constitutive models agree well with the experimental results. The numerical methodology proposed in the study can be used successfully to predict complex flow patterns of viscoelastic fluids.