Numerical modelling of viscoelastic liquids using a finite-volume method

Darwish, M.; Whiteman, J. R.; Bevis, M.

doi:10.1016/0377-0257(92)80066-7

Cited by 53 publications

(47 citation statements)

References 14 publications

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“…While the meshes used in [7] were too coarse for quantitative results, the medium meshes of [8] clearly show a reduction in the size of the corner vortex, from x r /D = 0.15 at Weissenberg number of We = 0 (Newtonian case) to approximately 0 at We = 1.5, thus corroborating the experimental findings of Townsend and Walters regarding elimination of recirculation regions by viscoelasticity effects.…”

Section: Introductionsupporting

confidence: 78%

“…Compared with other works, the present level of mesh refinement is similar to that used by Hawa and Rusak [13] (their base mesh had δx = 0.05) who solved the Newtonian problem with a vorticity/stream function formulation using a finite-difference method; in relation to works dealing with viscoelastic flow simulations in planar expansions at very low Re, Mesh-2 is much finer than those previously used [5,7,8]. Numerical accuracy was assessed for both Newtonian and viscoelastic fluids with a Reynolds number of 60, in the middle of the range here considered (Re = 0.01-100) but for which the flow is already asymmetric for both fluid types.…”

Section: Meshes and Quantification Of Accuracymentioning

confidence: 90%

“…Representative purely numerical studies of viscoelastic flow through planar expansions (E = 4) are those of Darwish et al [7] and Missirlis et al [8]; both employ the upper convected Maxwell model (UCM) under creeping flow conditions (Re = 0.2) and since flow asymmetries were not expected, only half of the full domain was actually used in these numerical studies (the symmetry assumption is then quite adequate). While the meshes used in [7] were too coarse for quantitative results, the medium meshes of [8] clearly show a reduction in the size of the corner vortex, from x r /D = 0.15 at Weissenberg number of We = 0 (Newtonian case) to approximately 0 at We = 1.5, thus corroborating the experimental findings of Townsend and Walters regarding elimination of recirculation regions by viscoelasticity effects.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries

Oliveira

2003

Journal of Non-Newtonian Fluid Mechanics

110

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The flow of viscoelastic liquids with constant shear viscosity through symmetric sudden expansions is studied by numerical means. The geometry considered is planar and the constitutive model follows the modified FENE-CR equation, valid for relative dilute solutions of polymeric fluids. For Newtonian liquids in a 1:3 expansion we predict the result that the flow becomes asymmetric for a Reynolds number (based on upstream mean velocity and channel height) of about 54, in agreement with previously published results. For the non-Newtonian case the transition depends on both the concentration and the extensibility parameters of the model, and the trend is for the pitch-fork bifurcation to occur at higher Reynolds numbers. Detailed simulations are carried out for increasing Reynolds number, at fixed concentration and Weissenberg number, and for increasing concentration at a fixed Reynolds number of 60. The results given comprise size and strength of the recirculation zones, bifurcation diagrams, and streamline plots.

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Section: Introductionsupporting

confidence: 78%

Section: Meshes and Quantification Of Accuracymentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries

Oliveira

2003

Journal of Non-Newtonian Fluid Mechanics

110

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“…The results for the flows with expansion ratio of 3 : 40 showed good qualitative agreement with some experimental cases conducted by Townsend and Walters [11]. Darwish et al [13] and Missirlis et al [14] applied upper-convected Maxwell (UCM) model and developed finite volume method to simulate the creeping flows of viscoelastic fluid in a 1 : 4 sudden expansion at Re = 0.1. Poole et al [15,16] numerically investigated the creeping flow of viscoelastic fluid with three different models (UCM, Oldroyd-B, and the linear form of PTT model) through a 1 : 3 planar sudden expansion and studied the effect of expansion ratio on the creeping flow of viscoelastic fluid obeying UCM model.…”

Section: Introductionsupporting

confidence: 71%

Modeling Asymmetric Flow of Viscoelastic Fluid in Symmetric Planar Sudden Expansion Geometry Based on User-Defined Function in FLUENT CFD Package

Zheng

Yang

2013

Advances in Mechanical Engineering

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Through embedding an in-house subroutine into FLUENT code by utilizing the functionalization of user-defined function provided by the software, a new numerical simulation methodology on viscoelastic fluid flows has been established. In order to benchmark this methodology, numerical simulations under different viscoelastic fluid solution concentrations (with solvent viscosity ratio varied from 0.2 to 0.9), extensibility parameters (100 ≤ 2 ≤ 500), Reynolds numbers (0.1 ≤ Re ≤ 100), and Weissenberg numbers (0 ≤ Wi ≤ 20) are conducted on unsteady laminar flows through a symmetric planar sudden expansion with expansion ratio of 1 : 3 for viscoelastic fluid flows. The constitutive model used to describe the viscoelastic effect of viscoelastic fluid flow is FENE-P (finitely extensive nonlinear elastic-Peterlin) model. The numerical simulation results show that the influences of elasticity, inertia, and concentration on the flow bifurcation characteristics are more significant than those of extensibility. The present simulation results including the critical Reynolds number for which the flow becomes asymmetric, vortex size, bifurcation diagram, velocity distribution, streamline, and pressure loss show good agreements with some published results. That means the newly established method based on FLUENT software platform for simulating peculiar flow behaviors of viscoelastic fluid is credible and suitable for the study of viscoelastic fluid flows.

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“…Straightforward centered differencing then places the required derivatives in the correct locations. This layout was initially proposed in computational physics [Darwish et al 1992;Mompean and Deville 1997], and first used in graphics by Goktekin et al [2004] for viscoelastic fluids.…”

Section: Discretizationmentioning

confidence: 99%

Variational stokes

2017

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Fig. 1. By carefully treating coupling between viscosity and pressure forces, our unified Stokes-based fluid solver can reproduce the classic liquid rope coiling instability of viscous liquids like honey, while prior grid-based methods cannot.We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.

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Numerical modelling of viscoelastic liquids using a finite-volume method

Cited by 53 publications

References 14 publications

Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries

Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries

Modeling Asymmetric Flow of Viscoelastic Fluid in Symmetric Planar Sudden Expansion Geometry Based on User-Defined Function in FLUENT CFD Package

Variational stokes

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