No abstract

A scheme for the numerical simulation of incompressible flows is presented. The modeling equations are written in conservation law form. The algorithm, written in a delta form, is very robust without resorting to any degree of relaxation. The well-known cumbersome numerical implementation related to staggered grids is totally removed. The scheme is second-order-accurate in space and first-order in time. An important novelty is the separation of the pressure terms in the physical equations in a pressure flux, facilitating the tackling of different fluids. The algorithm has been applied to laminar and turbulent flows. The results are truly encouraging.

The plastic transforming industry has shown considerable growth in the last years. In this context, commercial simulators have been developed, some of which combine simplified mathematical models with rheological properties of commercial polymers. In spite of the successes, these approximations are not able to capture important details of the flow behavior. The present work addresses some aspects of the polymer melt flow in plane channels using a more elaborate mathematical formulation based on the full momentum and energy conservation laws. The physical equations are discretized using finite differences based on a collocated mesh and second-order spatial accuracy formulas. Solutions featuring the development of hydrodynamic and thermal boundary layers are presented for a commercial polymer.

SUMMARYThis work presents a fully implicit finite difference scheme aimed at simulation of polymer melt flow in channels and mould cavities. This class of problems is characterized by strong material non-linearity and coupling of momentum, heat and mass transfer. The computational approach is based on the generalized Newtonian model and utilizes central discretization for both diffusive and convective terms, collocated meshes and artificial dissipation control to handle spurious pressure modes. The formulation accounts for the full interaction between the thermal effects caused by viscous heating and the momentum diffusion effects dictated by a shear rate and temperature-dependent constitutive model. Solutions for plane channels and asymmetric sudden expansion illustrate application to polymer melt flow.

Identification of stagnant regions of viscoplastic fluid flows in production lines and equipment is of paramount importance owing to potential material degradation and process contamination. The present work introduces an assessment strategy to identify, classify and quantify unyielded regions with the objective of optimizing the flow conditions with the purpose of minimizing stagnant regions. Flow of Carbopol ® 980 in a T-bifurcation channel is adopted to illustrate the procedure. The rheological behavior of Carbopol ® 980 was simulated using the Herschel-Bulkley viscoplastic model regularized by Papanastasiou's exponential approach. The analysis shows that three distinct types of stagnant unyielded regions take place in the bifurcation channel depending upon the Reynolds condition. Furthermore, the rheological characteristics of the fluid indicate the existence of an ideal Reynolds condition which allows the smallest flow stagnant area at the bifurcation zone.