Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids

A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

The dilation-free semi-staggered finite volume method presented in Sabin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown Copyright (C) 2007 Published by Elsevier B.V. All rights reserved

Computational analysis of viscoelastic free surface flows

The demand for increasingly small and lightweight products require micro-scale components made of materials which are durable and light. Polymers have therefore become a popular choice since they can be used to produce materials which meet industrial requirements. Many of these polymers are viscoelastic fluids. The reduction in the sizes of components make physical experimentation difficult and costly. Therefore computational tools are being sought to replace old methods of testing. This research has been concerned with the development of a finite volume algorithm for viscoelastic flow which can be readily applied to real world applications. A major part of the research involved the implementation of the Oldroyd-B constitutive equations and associated solution methods, in the 3-D multi-physics software environment PHYSICA+. This provides an unstructured finite volume solution technique for viscoelastic flow. This algorithm is validated using the 4:1 planar contraction and results are reported. The developed viscoelastic algorithm has also been coupled with two interface tracking techniques one of which includes surface tension effects. These techniques are the Scalar Equation Algorithm (SEA) and the Level Set Method (LSM). With both techniques the algorithms are able to take into account flow effects from both fluids (ie. air and polymer) in a two-fluid system. The LSM technique maintains a sharp interface overcoming the smearing of the interface which generally affects interface tracking techniques on Eulerian fixed grids, for example SEA, and enables the curvature of the interface to be calculated accurately to implement surface tension effects. This integrated viscoelastic flow solver and free surface algorithm is then illustrated by predicting two industrial flow processes as used in the electronic packaging industry

Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows

We find three types of steady solutions and remarkable flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical simulations with spectral element method. The solutions are called "convective", "transition", and "elastic" in ascending order of Wi. In the convective region in the Re-Wi parameter space, the convective effect and the pressure gradient balance on average. As Wi increases, the elastic effect becomes suddenly comparable and the first transition sets in. Through the transition, a separation vortex disappears and a jet flow induced close to the wall by the viscoelasticity moves into the bulk; The viscous drag significantly drops and the elastic wall friction rises sharply. This transition is caused by an elastic force in the streamwise direction due to the competition of the convective and elastic effects. In the transition region, the convective and elastic effects balance. When the elastic effect dominates the convective effect, the second transition occurs but it is relatively moderate. The second one seems to be governed by so-called Weissenberg effect. These transitions are not sensitive to driving forces. By the scaling analysis, it is shown that the stress component is proportional to the Reynolds number on the boundary of the first transition in the Re-Wi space. This scaling coincides well with the numerical result.Comment: 33pages, 23figures, submitted to Physical Review

Further developments on theoretical and computational rheology

Tese financiada pela FCT - Fundação para a Ciência e a Tecnologia, Ciência.Inovação2010, POPH, União Europeia FEDERTese de doutoramento. Engenharia Química e Biológica. Faculdade de Engenharia. Universidade do Porto. 201

STEADY FLOW OF A THIN VISCOELASTIC JET

The symmetric two-dimensional flow of a thin viscoelastic fluid jet emerging from a vertical channel is examined theoretically in this study. The fluid is assumed to be a polymeric solution, modeled following the Oldroyd-B constitutive equation. The influence of inertia, elasticity and gravity in the presence of surface tension is investigated for steady flow only. Special emphasis is placed on the initial stages ofjet development. The viscoelastic boundary-layer equations are solved by expanding the flow field in terms of orthonormal shape functions. In contrast to the commonly used depth-averaging technique, the proposed method predicts the shape of the free surface, as well as the velocity and stress components within the fluid. It was found that the jet reaches the same uniform thickness regardless of Reynolds number in the absence of gravity. However, the distance to reach the uniform thickness depends on inertia. Presence of gravity enhances the jet contraction and leads to possible jet break up. Presence of surface tension tends to prohibit the contraction and flatten the jet surface. In contrast to the Newtonian flow, viscoelastic flow displays uniform flow much farther from the channel exit. Swelling is observed as Deborah number increases. The velocity and stress components profiles suggest that elasticity tends to play different role to inertia. Surface tension tends to flatten the jet surface similar to the Newtonian jet, but the stress components are not affected much in the case of a viscoelastic jet. The numerical solution is validated with experiment and good qualitative agreement is achieved

Numerical Simulations of Planar Extrusion and Fused Filament Fabrication of Non-Newtonian Fluids

Autocorrelation and convergence of RR for WHtR, male. Autocorrelation and convergence of RR for WHtR, male. (DOCX 19 kb