The effect of non-Newtonian behavior on contact formation in an external gear pump

In an extrusion process, an external gear pump can be used to control the flow rate of the system. When extruding polymers, the viscosity is quite high, resulting in negligible inertia and thus laminar flow. The external gear pump contains two gears, one driven by a motor and one driven by means of contact with the other gear. In our previous work, the flow of a viscous fluid through an external gear pump was studied using the finite element method. Local mesh refinement was applied based on the respective distance between boundaries. Furthermore, the rotation of both gears was imposed. In this work, the rotation of one gear is imposed, whereas the other gear is freely rotating. However, the minimum distance between the gears is limited to a minimum value. When this value is reached, contact is assumed and also the rotation of second gear is imposed. A reversion of the torque on this gear results in a release of contact. In this manner, a quasi driver/driven situation is created in the numerical simulations. It is observed that contact is released periodically, and thus cannot be assumed present continuously, as is often prescribed. Non-Newtonian material properties, such as shear thinning and the pressure dependence of the density or the viscosity, alter how long contact is released during a tooth rotation

Chaotic advection in a cavity flow with rigid particles

The effect of freely suspended rigid particles on chaotic materialtransport in a two-dimensional cavity flow is studied. We concentrateon the understanding of the mechanism how the presence of a particleaffects the dynamical system of the flow. In contrast to the casestudied by Vikhansky [A. Vikhansky, Phys. Fluids, vol.15 (2003) 1830],we show that even a regular periodic motion of a single particle caninduce chaotic advection around the particle, as a result of theperturbation of the flow introduced by the freely rotating solidparticle. This perturbation is of a hyperbolic nature. In fact,stretching and folding of the fluid elements are guaranteed by theoccurrence of the hyperbolic flow perturbation centered at theparticle and by the rotation of the freely suspended particle,respectively. The fluid-solid flow problem has been solved by afictitious-domain/finite-element method based on a rigid-ringdescription of the solid particle. A single-particle system isstudied in detail in view of the dynamical systems theory and thenextended to two- and three-particle systems

Stability analysis of injection molding flows

We numerically investigate the stability problem of the injection molding process. It was indicated by Bulters and Schepens Bulters and Schepens 2000 that surface defects of injection molded products may be attributed to a flow instability near the free surface during the filling stage of the mold. We examine the stability of this flow using the extended Pom–Pom constitutive equations. The model allows for controlling the degree of strain hardening of the fluids without affecting the shear behavior considerably. To study the linear stability characteristics of the injection molding process we use a transient finite element algorithm that is able to efficiently handle time dependent viscoelastic flow problems and includes a free surface description to take perturbations of the computational domain into account. It is shown that the fountain flow, which is a model flow for the injection molding process, is subject to a viscoelastic instability. If the various rheologies are compared, we observe that the onset of unstable flow can be delayed by increasing the degree of strain hardening of the fluid by increasing the number of arms in the Pom–Pom model. The most unstable disturbance which is obtained after exponential growth is a swirling flow near the fountain flow surface which is consistent with the experimental findings. © 2004 The Society of Rheology. DOI: 10.1122/1.1753276 I

The deformation fields method revisited: Stable simulation of instationary viscoelastic fluid flow using integral models

The implementation of the deformation fields method for integral models within a finite element context [1,2] has been updated with various techniques to have a numerical stability that is comparable to state-of-the-art implementations of differential models. In particular, the time-dependent stability in shear flow, decoupled schemes for zero or small solvent viscosities and the log-conformation representation now have counterparts in the numerical implementation of integral models leading to similar numerical stability. The new techniques have been tested in transient shear flow and the flow around a cylinder confined between two plates for the integral version of upper-convected Maxwell model and for integral models having a non-constant damping function

Fully implicit interface tracking for a viscous drop under simple shear

In this article we present a novel 3D implicit interface tracking method for sharp interfaces with interfacial tension in the creeping flow regime, employing the finite element method. The interface nodes are allowed to move only in the normal direction and thus remeshing can be avoided, most of the times. The implicit method allows us to overcome certain time step limitations imposed by the mesh capillary time. To validate our method, we use a fairly simple and very well understood problem of a single viscous drop suspended in a viscous matrix that deforms under an applied shear rate. This problem was first studied by Taylor [1] and has been extensively reviewed by Rallison [2] and Stone [3]. The second moment of inertia tensor was used to compute the deformation parameter D and the inclination angle θ and the results are compared to the theory for small deformations of Taylor [1]