Viscoelastic Contraction Flows Research Articles

Rheological transient effects on steady-state contraction flows

It may be assumed that the steady-state kinematics of viscoelastic contraction flows depends on the time-independent rheological properties only. This idea is supported by the large number of references explaining steady simulation results by considering only steady-state material functions. Even with numerical simulations, it would be difficult to prove such a statement wrong. However, using the Bautista-Manero-Puig class of models allows to obtain the same steady rheological response but with different transient evolution. Here, we considered two fluids, one displaying a monotonic trend towards the steady-state and the other with at least one visible overshoot in the material functions. Our results show that for the transient evolution with the overshoot fluid, a significant increase in the steady pressure drop is gathered. In addition, vortex response is quite different for the two fluids. This research gives evidence that the transient evolution in rheometrical functions has great impact on steady-state flow behavior.

An Experimental Investigation of Viscoelastic Flow in a Contraction Channel.

In order to assess the predictive capability of the S–MDCPP model, which may describe the viscoelastic behavior of the low-density polyethylene melts, a planar contraction flow benchmark problem is calculated in this investigation. A pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) method is adopted to overcome oscillations of the pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique in combination with the streamline upwind Petrov-Galerkin (SUPG) method are employed to calculate the viscoelastic flow. The equal low-order finite elements interpolation approximations for velocity-pressure-stress variables can be applied to calculate the viscoelastic contraction flows for LDPE melts. The predicted velocities agree well with the experimental results of particle imagine velocity (PIV) method, and the pattern of principal stress difference calculated by the S-MDCPP model has good agreement with the results measured by the flow induced birefringence (FIB) device. Numerical and experimental results show that the S-MDCPP model is capable of accurately capturing the rheological behaviors of branched polymers in complex flow.

Application of the natural stress formulation for solving unsteady viscoelastic contraction flows

We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.

On modelling viscoelastic flow through abrupt circular 8:1 contractions – matching experimental pressure-drops and vortex structures

This study compares and contrasts computational predictions against experimental data for some viscoelastic contraction flows. Nigen and Walters [1], provides the comparative data-set, the specific flow of interest is an 8:1 abrupt circular contraction, and the constitutive model is that of swanINNFM(q) [swIM]. Taken against increasing flow-rate, such a model is observed to capture significant vortex-enhancement in these axisymmetric flows, reflecting well the counterpart experimental findings. In addition, rich vortex characteristics are reflected, through evolving patterns of salient-corner, lip-vortex and elastic-corner vortices. A systematic parametric analysis is conducted over three independent and governing material parameters in the model, whilst attempting to interpret rheological adjustment against such changes in flow-structure. Specifically, this has involved variation in solvent-fraction (β), finite-extensibility parameter (L), and extensional-based dissipative parameter (λD).

Numerical vs experimental pressure drops for Boger fluids in sharp-corner contraction flow

This paper addresses the problem of matching experimental findings with numerical prediction for the extreme experimental levels of pressure-drops observed in the 4:1 sharp-corner contraction flows, as reported by Nigen and Walters [“Viscoelastic contraction flows: Comparison of axisymmetric and planar configurations,” J. Non- Newtonian Fluid Mech. 102, 343–359 (2002)]. In this connection, we report on significant success in achieving quantitative agreement between predictions and experiments. This has been made possible by using a new swanINNFM model, employing an additional dissipative function. Notably, one can observe that extremely large pressure-drops may be attained with a suitable selection of the extensional viscous time scale. In addition, and on vortex structure, the early and immediate vortex enhancement for Boger fluids in axisymmetric contractions has also been reproduced, which is shown to be absent in planar counterparts.

Interaction effects in multi-outlet viscoelastic contraction flow

This paper describes an experimental study of interaction effects in viscoelastic contraction flows with an array of multiple, parallel outlets. The study focuses on edge effects, that is, effects of the finite size of an array, on flow rate distribution and flow stability. The experiments were carried out with a PEG-PEO Boger fluid in glass microfluidic chips with three parallel, abrupt contractions, variable outlet spacing, and free outflow. We used micro-Particle Image Velocimetry (μ-PIV) to measure the velocity field, and particle streak imaging to visualise the flow. The two most important conclusions of our study are: 1. the flow in the three outlet case is more unsteady than in the single outlet case, which possibly leads to flow rate fluctuations in the individual outlets, and 2. if the distance between the outlets is smaller than the distance between the outer outlets and the side walls of the upstream channel, the flow rate in the central outflow channel is lower than that in the outer two channels. The difference in flow rate reduces with increasing vortex size; at the highest tested flow rates the flow rate in the middle channel is even higher than that in the outer channels. These results are relevant for industrial production processes involving multi-outlet viscoelastic extrusion flow, such as fibre spinning.

A numerical study of constitutive models endowed with Pom-Pom molecular attributes

The branched polymer melts are modeled respectively in this investigation by the existing XPP and PTT–XPP models, along with the proposed S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model developed on the basis of the existing MDCPP model. A pressure stabilized mass equation is formulated with the finite increment calculus (FIC) process to restrain and further eliminate spurious oscillations of pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique is employed, in order to retain an elliptic contribution in the weak form of the momentum equation. An inconsistent streamline-upwind (SU) method is applied to spatially discretize the constitutive equations. The mass, momentum conservation and constitutive equations are discretized and solved by the iterative stabilized fractional step algorithm along with the Crank–Nicolson implicit difference scheme. Thus the finite elements with equal low-order interpolation approximations for velocity–pressure–stress variables can be devised to numerically simulate the viscoelastic contraction flows for branched LDPE melts. The influences of the three viscoelastic constitutive models and the branched arms at the end of the Pom-Pom molecule on the rheological behaviors occurring in this complex flow are discussed. The numerical results demonstrate that the proposed S-MDCPP model is capable of reproducing some properties similar to those predicted by the XPP model in high shear flow and, on the other hand, reproducing some properties similar to those predicted by the PTT–XPP model in high elongational flow. Furthermore, the proposed S-MDCPP model is capable of well identifying the macromolecule topological structures of branched polymer melts.

Three-dimensional numerical simulation of viscoelastic contraction flows using the Pom–Pom differential constitutive model

A three-dimensional finite element method is applied for analyzing the viscoelastic flow of branched LDPE through 3D planar contraction geometry. For describing the viscoelastic properties of the flowing material, a recently proposed eXtended Pom–Pom model is used. The main purpose of our study is to evaluate the ability of this model to capture some specific 3D effects in the case of converging entry flow of relatively high strain-hardening polyethylene melts. A special attention is paid to the vortex region. Like in our previous study [I. Sirakov, A. Ainser, J. Guillet, Three-dimensional numerical simulation of viscoelastic planar contraction flow, in: Proceedings of the Fourth International ESAFORM Conference, Liege, 23–25 April 2001] (where the Phan-Thien Tanner (PTT) model was used), the calculations predict an open vortex in which the material is involved in a complicated spiral motion, directed from the vertical plane of symmetry to the side wall of the contraction. Quantitative comparisons with experiments are done on the vortex size in the width direction (contraction z-axis).

Viscoelastic contraction flows: comparison of axisymmetric and planar configurations

This is an experimental study, which investigates the behaviour of two constant-viscosity polymer solutions (so called Boger fluids) in both axisymmetric and planar contractions. To provide a means of investigating the role of fluid elasticity, experiments are also carried out on Newtonian liquids with the same shear viscosity as the Boger fluids. In the axisymmetric contractions, the experimental results are as expected, with so called “vortex enhancement” in the Boger fluids, associated with increased pressure losses due to viscoelasticity. Behaviour in the planar contractions for the same liquids is provocatively different from that found in the axisymmetric geometries. Now, vortex enhancement is absent. Furthermore, it is impossible to distinguish between the pressure-drop/flow-rate data for the Boger and Newtonian fluids.

Three dimensional numerical simulations of viscoelastic flows through planar contractions

We present in this paper a fully three dimensional (3D) convergent numerical study of planar viscoelastic contraction flows. A 3D finite volume method (FVM) with the primary variable elastic viscous split stress (EVSS) formulation is employed, and a very efficient 3D block solver coupled with block correction is developed to speed up the convergence rate. Full 3D simulations of viscoelastic flows in 4:1 planar abrupt contractions are carried out using experimental conditions. Upstream vortex patterns comparable with the existing flow visualisation observations are captured using the upper convected Maxwell model for a Boger fluid and the Phan-Thien–Tanner model for a shear thinning fluid. Comprehensive comparisons between numerical simulation results and data measured in the dynamic fields in a 4:1 planar abrupt contraction are made, and the results indicate that the experimental measurements can be quantitatively reproduced if the fluid is well characterised by an appropriate viscoelastic model. It is confirmed numerically that the shear thinning of the fluid reduces the intensity of the singularity of viscoelastic flow near the re-entrant corner. With the Oldroyd-B model, by extensive computations on successively refined meshes with the minimum dimensionless size being 0.16–0.014 on the contraction plane in 2D configuration, it is revealed that, although the asymptotic flow behavior near the re-entrant corner and the build-up of the overall pressure and extensional stresses as well as the kinematic behavior along the centreline are insensitive to mesh refinement, completely different vortex activities may be predicted if the mesh is not sufficiently fine. It is verified numerically that, depending on the flow inertia and rheological properties of fluids, both the lip vortex mechanism and the corner vortex mechanism may be responsible for the vortex activities of viscoelastic fluids in 4:1 planar contraction flow, and the elasticity number E and Mach number M of the flow can be used to determine the vortex mechanism approximately. It is clear that the development process of the vortex activities could be underestimated with 2D simplification, and overpredicted with the creeping flow assumption, particularly when R e>0.5. Therefore, in planar contraction flow analyses, numerical artifacts may be produced with a coarse mesh, and 2D flow simulation is only a good approximation to the fully 3D flow if the upstream aspect ratio W/ H in the experiment is at least 10.