Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

Tomé, Murilo Francisco; Paulo, Gilcilene Sanchez de; Pinho, F.T.; Alves, M.A.

doi:10.1016/j.jnnfm.2009.12.007

Cited by 33 publications

(34 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…the flow of the surrounding air is omitted). This method was used to simulate the extrudate swell and jet buckling phenomena for the generalized Newtonian fluid model [34,35], and for various viscoelastic constitutive models [36][37][38][39][40][41]. In the level-set method, the position of the interface (or the free surface) is represented with a level-set function that varies continuously across the interface [42].…”

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

View full text Add to dashboard Cite

. 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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…In particular, numerical simulations of unsteady threedimensional extrusion processes are very important when it is necessary to analyze the time evolution of the free surface profile. In this case, results for Oldroyd-B, UCM, and Phan-Thien-Tanner (PTT) fluids were presented in [45][46][47]36]. To our best knowledge, the present work is the first numerical investigation of unsteady three-dimensional extrudate swell using the XPP fluid.…”

Section: Validation Of the Extrudate Swell Problemmentioning

confidence: 93%

Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

Figueiredo

Oishi

Cuminato

et al. 2013

Journal of Non-Newtonian Fluid Mechanics

Self Cite

View full text Add to dashboard Cite

“…The technique employed is well known by many researchers from this area, which is a finite difference method on a staggered grid and the fluid is modelled by a Markerand-Cell approach ( [7]). This metodology have been capable of simulating many problems involving unsteady and steady viscoelastic free surface flows, such as, jet buckling, dieswell, impacting drop and fountain flow (see, as example, [8,14,15,16,17]). …”

Section: Introductionmentioning

confidence: 99%

Numerical Predictions of Steady and Unsteady Flows of Fene-Cr Viscoelastic Fluids With a Newtonian Solvent

Paulo¹,

Oishi²,

Tome³

2014

Proceedings of 10th World Congress on Computational Mechanics

View full text Add to dashboard Cite

show abstract

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

Cited by 33 publications

References 33 publications

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

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

Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

Numerical Predictions of Steady and Unsteady Flows of Fene-Cr Viscoelastic Fluids With a Newtonian Solvent

Contact Info

Product

Resources

About