Viscoelastic flow past a confined cylinder of a low density polyethylene melt

Baaijens, F.P.T.; Selen, Sjaak H.A; Baaijens, Hans P. W.; Peters, G.W.M.; Meijer, H.E.H.

doi:10.1016/s0377-0257(96)01519-4

Cited by 127 publications

(61 citation statements)

References 36 publications

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“…The numbers for the stationary drag coefficient are compared in Table 1. Compared to the values of Warichet and Legat [10] and Baaijens et al [11] our values differ only by 0.01% for low up to 0.1% for high We. Fig.…”

Section: à3contrasting

confidence: 80%

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Instationary Eulerian viscoelastic flow simulations using time separable Rivlin–Sawyers constitutive equations

Peters

Hulsen

Brule

2000

Journal of Non-Newtonian Fluid Mechanics

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A time dependent method for solving integral constitutive equations of the Rivlin±Sawyers type is introduced. The deformation history is represented by a finite number of deformation fields. Using these fields the stress integral is approximated as a finite sum. When the flow evolves the deformation fields are convected and deformed. The approach presented in this paper is the first Eulerian method that can handle integral equations in a time dependent way. The method is validated by using the upper-convected Maxwell (UCM) benchmark of a sphere moving in a tube. We show that the method converges with mesh and time step refinement and that the results are accurate, comparable to the results obtained with the differential equivalent of the UCM model. To demonstrate that complicated linear spectra are easily incorporated, results of a Rouse model simulation of 100 modes are presented. We also compare results on a falling sphere problem to the results obtained by a Lagrangian method as reported by Rasmussen and Hassager [H.K. Rasmussen, O. Hassager, On the sedimentation velocity of spheres in a polymeric liquid, Chem. Eng. Sci. 51 (1996) 1431±1440]. The model being employed is the PSM model, for which no differential equivalent exists. #

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Section: à3contrasting

confidence: 80%

“…Currently the maximum (reliable) Weissenberg number, computed by the most sophisticated methods, is 2.6 ( [10,11]). The methods used to reach these high Weissenberg numbers are time independent methods.…”

Section: à3mentioning

confidence: 99%

Instationary Eulerian viscoelastic flow simulations using time separable Rivlin–Sawyers constitutive equations

Peters

Hulsen

Brule

2000

Journal of Non-Newtonian Fluid Mechanics

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“…We will use discontinuous bilinear polynomials (Q 1 ) for the space T h . The combination of the DEVSS formulation with DG has been introduced by Baaijens et al [7] and it has been proved by Fortin et al [8] that it leads to a proper mixed velocity-stress scheme.…”

Section: Numerical Discretizationmentioning

confidence: 99%

“…This gives a two-dimensional Trouton ratio of 1/(2α) = 50, still leading to subtantial strain-hardening, but compared to the Oldroyd-B the stretch is much more restricted. For polymer melts a larger value, for example α = 0.25 as in [7], with even more restricted strain-hardening seems to be more appropriate.…”

Section: Giesekus Modelmentioning

confidence: 99%

Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms

Hulsen

Fattal

Kupferman

2005

Journal of Non-Newtonian Fluid Mechanics

326

332

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The log conformation representation proposed in [1] has been implemented in a fem context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and attribute the high Weissenberg problem to the failure of the numerical scheme to balance exponential growth. A slightly different derivation of the log based evolution equation than in [1] is also presented. We show numerical results for the flow around a cylinder for an Oldroyd-B and a Giesekus model. We provide evidence that the numerical instability identified in the 1D problem is also the actual reason for the failure of the standard fem implementation of the problem. With the log conformation representation we are able to obtain solutions far beyond the limiting Weissenberg numbers in the standard scheme. However it turns out that, although in large parts of the flow the solution converges, we have not been able to obtain convergence in localized regions of the flow. Possible reasons for this are: artefacts of the model (Oldroyd-B) or unresolved small scales (Giesekus). However, more work is necessary, including the use of more refined meshes and/or higher-order schemes, before any conclusion can be made on the local convergence problems.

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“…In this study, the mathematical model of two-dimensional extrudate swell of viscoelastic uid was established using Giesekus' di erential model. A stable solving method for the nonlinear problem was employed (DEVSS/SUPG) combined with a front tracking method proposed by Baaijens et al and Soula mani et al [22,23]. The investigation of 2D extrudate swell predicted by di erential viscoelastic rheological model was successfully carried out and compared to experimental data.…”

Section: Introductionmentioning

confidence: 99%

Study on the Viscoelastic Fluid Behavior in Hollow Fiber Membrane Fabrication Process Using Giesekus’ Model

2017

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Abstract. In the present study, attempts are made to study the behavior of a viscoelastic uid in the hollow ber membrane production process. For this purpose, the uid is considered to obey the Giesekus' model and ow is taken as steady, two-dimensional and isothermal one. The ow eld is obtained using DEVSS/SUPG scheme combined with a free surface tracking method. The obtained results are compared to the case of Newtonian uid. It is shown that the extrudate swell is 20% more in the case of viscoelastic uid. Moreover, the elastic behavior of the viscoelastic uid signi cantly a ects the velocity eld in the extrudate outside the die. It causes the uid ow to become reversed in the middle part of the extrudate as the direct result of the stress relaxation process, whereas such a behavior is not seen for Newtonian uid. Also, the First Normal Stress Di erence (FNSD) distribution in the extrudate is obtained and its variation is discussed. Furthermore, the e ects of operational parameters, including die back pressure and take-up velocity, are investigated. Finally, the predicted extrudate swell for various operation conditions is compared to experimental results showing good agreement between experimental and simulated data.

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Viscoelastic flow past a confined cylinder of a low density polyethylene melt

Cited by 127 publications

References 36 publications

Instationary Eulerian viscoelastic flow simulations using time separable Rivlin–Sawyers constitutive equations

Instationary Eulerian viscoelastic flow simulations using time separable Rivlin–Sawyers constitutive equations

Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms

Study on the Viscoelastic Fluid Behavior in Hollow Fiber Membrane Fabrication Process Using Giesekus’ Model

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