Highly elastic solutions for Oldroyd-B and Phan-Thien/Tanner fluids with a finite volume/element method: planar contraction flows

Aboubacar, M.; Matallah, H.; Webster, M.F.

doi:10.1016/s0377-0257(01)00164-1

Cited by 91 publications

(95 citation statements)

References 34 publications

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“…5b. Here, again, the choice of δ M DC is not critical for CT 3 , though the slight improvement brought about by δ M DC =1 on the boundary, is marginal in core flow. Finally, as anticipated, PSI with MDC, inherits the long-time behaviour of PSI without MDC.…”

Section: Pure Fd-schemes Less MDC (δ M Dc =0): A1 Shear Boundarymentioning

confidence: 87%

“…Moreover, incorporating mass-matrix iteration into [CT 3 -PSI], degrades solution quality at the boundary beyond peak-1 (which itself is remarkably good), with respect to pure [CT 3 -PSI], irrespective of number of iterations employed (see Fig. 5a versus Fig.…”

Section: Pure Fd-schemes Less MDC (δ M Dc =0): A1 Shear Boundarymentioning

confidence: 99%

“…In previous studies [1,2,3], we devised stable and accurate steady-state hybrid finite volume/finite element algorithms to simulate complex viscoelastic flows. These schemes were applied successfully to flow past cylinder [1], and to the benchmark flow of an Oldroyd-B fluid through a planar sharp 4:1 contraction [2].…”

Section: Introduction and Governing Equationsmentioning

confidence: 99%

“…These schemes were applied successfully to flow past cylinder [1], and to the benchmark flow of an Oldroyd-B fluid through a planar sharp 4:1 contraction [2]. Subsequently, application was extended to various Phan-Thien/Tanner model fluids, contrasting planar and axisymmetric flows through sharp and rounded-corner contractions [3,4]. Such advances were achieved by ensuring consistency in the treatment of flux and complex sourceterms (solution and velocity-gradient dependent), which arise in the constitutive equation.…”

Section: Introduction and Governing Equationsmentioning

confidence: 99%

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Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

Webster

Tamaddon-Jahromi

Aboubacar

2004

Numerical Methods Partial

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Hybrid finite volume/element methods are investigated within the context of transient viscoelastic flows. A finite volume algorithm is proposed for the hyperbolic constitutive equation, of Oldroyd-form, whilst the continuity/momentum balance is accommodated through a TaylorGalerkin finite element method. Various finite volume combinations are considered to derive accurate and stable implementations. Consistency of formulation is key, embracing fluctuation distribution and median-dual-cell constructs, within a cell-vertex discretisation on triangles. In addition, we investigate the effect of treating the time-term in a finite element fashion, using mass-matrix iteration instead of the standard finite volume mass-lumping approach. We devise an accurate transient scheme that captures the analytical solution at short and long time, both in core flow and near shear boundaries. In this respect, some difficulties are highlighted. A new method emerges, with the Low Diffusion B (LDB, with or without mass-matrix iteration) as the optimal choice. We progress to a complex flow application and demonstrate some provocative features due to the influence of true transient boundary conditions on evolutionary flow-structure in a 4:1 start-up rounded-corner contraction problem. c (Year) John Wiley & Sons, Inc.

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Section: Pure Fd-schemes Less MDC (δ M Dc =0): A1 Shear Boundarymentioning

confidence: 87%

Section: Pure Fd-schemes Less MDC (δ M Dc =0): A1 Shear Boundarymentioning

confidence: 99%

Section: Introduction and Governing Equationsmentioning

confidence: 99%

Section: Introduction and Governing Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

Webster

Tamaddon-Jahromi

Aboubacar

2004

Numerical Methods Partial

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“…For the full-developed steady Poiseuille flow, the inlet boundary condition is No-slip conditions are imposed on solid boundaries and symmetry conditions are specified on the symmetrical axis [9].…”

Section: Governing Equationsmentioning

confidence: 99%

Flow behavior of UCM viscoelastic fluid in sudden contraction channel

Chen¹,

Zhou²,

Yin³

et al. 2010

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A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential upper-convected Maxwell (UCM) fluid through a contraction channel has been chosen as a prototype example. The conservation and constitutive equations are solved using the finite volume method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.

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A finite piece method for simulating polymer melt flows in extrusion sheet dies

Zheng

Xia

et al. 2011

J of Applied Polymer Sci

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A finite piece method is proposed to simulate three-dimensional slit flows in extrusion sheet dies in this paper. The simulations concern incompressible fluids obeying different constitutive equations: generalized Newtonian (Carreau-Yasuda law), and viscoelastic Phan-Thien Tanner (PTT) models. Numerical simulations are carried out for the isothermal and nonisothermal flows of polymer melt through sheet dies. The Picard iteration method is utilized to solve nonlinear equations. The results of the finite piece method are compared with the three-dimensional (3D) finite element method (FEM) simulation and experiments. At the die exit, the relative error of the volumetric flow between the finite piece method and the 3D FEM is below 1.2%. The discrepancy of the pressure distributions does not exceed 6%. The Maximum error of the uniformity index between the simulations and experiments is about 2.3%. It shows that the solution accuracy of the finite piece method is excellent, and a substantial amount of computing time and memory requirement can be saved.

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Highly elastic solutions for Oldroyd-B and Phan-Thien/Tanner fluids with a finite volume/element method: planar contraction flows

Cited by 91 publications

References 34 publications

Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

Flow behavior of UCM viscoelastic fluid in sudden contraction channel

A finite piece method for simulating polymer melt flows in extrusion sheet dies

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