A Lagrangian–Eulerian approach for the numerical simulation of free-surface flow of a viscoelastic material

Etienne, Jocelyn; Hinch, E. J.; Li, Jie

doi:10.1016/j.jnnfm.2006.04.003

Cited by 34 publications

(24 citation statements)

References 26 publications

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“…Various numerical methods have been employed to solve this problem.Étienne et al [14] used a Lagrangian-Eulerian approach, while Owens et al [15] preferred a spectral method combined with a SUPG method. Fan et al [16] used a Galerkin/least-square approach combined with a h-p finite element method to produce very accurate solutions.…”

Section: Resultsmentioning

confidence: 99%

An adaptive remeshing strategy for viscoelastic fluid flow simulations

Guénette

Fortin

Kane

et al. 2008

Journal of Non-Newtonian Fluid Mechanics

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Section: Resultsmentioning

confidence: 99%

An adaptive remeshing strategy for viscoelastic fluid flow simulations

Guénette

Fortin

Kane

et al. 2008

Journal of Non-Newtonian Fluid Mechanics

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“…Automatic adaptive remeshing techniques were later developed in [21,22] to give more flexibility to transient Lagrangian simulations of nonNewtonian free-surface flows when large deformations occur. The arbitrary-Lagrangian-Eulerian method has also been used to simulate the filament stretching [23,24] and extrudate swell [25,26] of viscoelastic liquids. Finally, a few works on the simulation of free-surface viscoelastic flows with the mesh-free smoothed particle hydrodynamics method have been reported in [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

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“…The formulation is based on time-discontinuous/Galerkin-least squares formulation. Recently Etienne et al [34] have presented an ALE technique based method and simulated problems of drag on a cylinder and collapse of a column involving polymer melts.…”

Section: Flow Simulation Methodsmentioning

confidence: 99%