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

Figueiredo, Rafael Alves; Oishi, Cassio M.; Cuminato, José Alberto; Alves, M.A.

doi:10.1016/j.jnnfm.2013.01.004

Cited by 20 publications

(21 citation statements)

References 55 publications

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“…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

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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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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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“…On the inlet port, we take the Dirichlet boundary condition for the velocity. On the boundary of the solid walls, the velocity is assumed as u = v = 0 and the homogeneous Neumann boundary condition, i.e.,

\partial u true/ \partial n = \partial v true/ \partial n = 0

, is imposed on the outflow boundary . Actually, when Equations , (11), and (15) are added together, we can obtain Equation .…”

Section: Methodsmentioning

confidence: 99%

Numerical simulation of polymer filling process by a combined finite element/discontinuous Galerkin/level set method

2018

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The filling process in injection molding involves polymer melt and air with large density/viscosity ratios and the transient free surface. It is treated as a challenging viscoelastic-Newtonian two-phase flow problem especially on irregular domains. In this paper, the complex filling process for the irregular cavity is simulated using a combined finite element/discontinuous Galerkin/level set method with application to the socket with five inserts, which is rarely investigated. The rheological behaviour of the viscoelastic fluid is predicted according to the eXtended Pom-Pom (XPP) constitutive model. The level set method proposed from prior literature is utilized to capture the moving interface because of its simplicity and efficiency. The hybrid continuous and discontinuous Galerkin method is utilized to solve the viscoelastic incompressible Navier-Stokes equations. The second order Runge Kutta discontinuous Galerkin (RKDG) method is employed to deal with the XPP constitutive equation and the level set equation due to their hyperbolic natures. This combined algorithm is convenient to cope with the irregular cavity and avoid any stabilization terms. We first investigate the filling process of the rectangular cavity without and with a diamond insert and compare with other numerical and experimental results to illustrate the validity of the coupled method. Moreover, the cavity of the socket with five inserts is considered an application case. We analyze the influences of the inlet velocity and elasticity on physical quantities such as stresses, stretch, etc. The simulation results could provide some numerical predictions for the polymer industry.

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“…The better known constitutive models that have been studied include Oldroyd-B [3][4][5][6], Phan-Thien-Tanner (PTT) [7][8][9][10], FENE-CR [11][12][13], XPP [10,14,15], Giesekus [15,16], among others. Within the class of differential models, the PTT constitutive equation [7] is known to provide a reasonable fit to polymeric solutions and polymer melts and has attracted the attention of several scientists (e.g., [5,9,[17][18][19][20]).…”

Section: Introductionmentioning

confidence: 99%

An assessment of the PTT model on the impacting drop problem

Tomé

Merejolli

Paulo

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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This work presents a numerical method and simulations of axisymmetric free-surface flows of a polymeric fluid using the Phan-Thien-Tanner (PTT) constitutive relationship. The governing equations are solved by finite differences on a staggered grid that employs accurate boundary conditions on the free surface together with bounded, monotone, high-order upwinding approximation of the convection terms. The numerical method is partially verified by solving fully developed flow in a tube and comparing it to a known analytic solution. The problem of a drop impacting on a rigid plate is considered. The effect of varying the five parameters, characterizing the PTT model, is studied extensively, and the results are interpreted physically. The expansion-contraction phenomenon of the viscoelastic drop that occurs when it hits a flat surface is tracked, and the time evolution of the normal and shear components of the extra-stress tensor is analyzed. To further verify the code, the impacting drop of an Oldroyd-B fluid is simulated and the time evolution of the drop width is compared to that of other authors.

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

Cited by 20 publications

References 55 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

Numerical simulation of polymer filling process by a combined finite element/discontinuous Galerkin/level set method

An assessment of the PTT model on the impacting drop problem

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