Numerical solution of fiber suspension flow through a complex channel

Chiba, Kazuhiro; Nakamura, Kiyoji

doi:10.1016/s0377-0257(98)00067-6

Cited by 58 publications

(46 citation statements)

References 31 publications

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“…However, the discretization of the advection equation is more complex. It can be carried out either integrating its Lagrangian description by means of the method of characteristics [5][6][7][8][9][10], or using the Eulerian discretization of its variational formulation: Streamline Upwind (SU) or Streamline Upwind Petrov-Galerkin (SUPG) finite elements [11][12][13][14][15], discontinuous finite elements [16] or discontinuous finite volumes [15]. However, for the orientation equations as encountered in short fiber suspensions models, the interpolation of the orientation tensors (which is required if standard Eulerian discretization techniques are used) introduces non-physical orientation effects [17].…”

Section: Numerical Treatment Of Models Involving Advection Equationsmentioning

confidence: 99%

On the solution of Fokker–Planck equations in steady recirculating flows involving short fiber suspensions

Chinesta

Chaidron

Poitou

2003

Journal of Non-Newtonian Fluid Mechanics

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Numerical modeling of non-Newtonian flows typically involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which is an advection equation linked to the fluid history. Thus, the numerical modeling of short fiber suspensions flows requires a description of the microstructural evolution (fiber orientation) which affects the flow kinematics and that is itself governed by this kinematics. There are different ways to describe the microstructural state. The use of orientation tensors, whose evolution is governed by advection equations, is widely considered. Other possibility is to describe the fiber orientation state from its probability density whose evolution is described by the Fokker-Planck equation (which does not involve any closure relation). The numerical treatment of advection problems is not a simple matter. Moreover, many industrial flows show often steady recirculating areas which introduce some additional difficulties, because in these flows neither boundary conditions nor initial conditions are known. In some of our former papers, we have proposed accurate techniques to solve the linear and non-linear advection equations governing the evolution of the second-order orientation tensor, in steady recirculating flows. These techniques combine a standard treatment of the non-linearity with a more original treatment of the associated linear problems imposing the periodicity condition. In this paper, we generalize those numerical strategies to compute the steady solution of the Fokker-Planck equation (which governs the evolution of the fiber orientation probability distribution) in steady recirculating flows.

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Section: Numerical Treatment Of Models Involving Advection Equationsmentioning

confidence: 99%

On the solution of Fokker–Planck equations in steady recirculating flows involving short fiber suspensions

Chinesta

Chaidron

Poitou

2003

Journal of Non-Newtonian Fluid Mechanics

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“…In spite of its low numerical diffusion and accuracy, this technique remains very time-consuming. Thus, in the original version of the method of characteristics, widely used in the context of non-Newtonian fluid flows simulation [7][8][9][10][11][12][13], for each point P where the solution is searched, we must reconstruct the upstream path until reaching the inflow boundary (where a boundary condition is imposed) at point Q, and from the solution known at point Q the equation can be integrated, using first or higher order finite differences, along the streamline until returning to the departure point P .…”

Section: Trðaþmentioning

confidence: 99%

“…Other possibility is the evaluation of the fiber orientation at the mesh nodes, using the same strategy, from which the orientation at the integration points can be interpolated [7,8,10,12]. A last possibility is based on the computation of the solution along a certain number of characteristics, from which the solution can be interpolated anywhere [11,13]. The strategy described in this paper can be applied to compute the solution of the orientation equation at the nodes, at the integration points or along certain characteristics, in general flows containing recirculating zones.…”

Section: Aðx; Y ¼ 8þmentioning

confidence: 99%

A characteristics strategy for solving advection equations in 2D steady flows containing recirculating areas

Chinesta

Chaidron

2003

Computer Methods in Applied Mechanics and Engineering

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Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion charac-terized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic character of advection equations. In non-recirculating flows, Eulerian discretisations can give an accurate mesh size dependent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In a former paper we have proved that in such flows Eulerian techniques lead to solutions with significant deviations from the exact one. These deviations obviously de-crease as the mesh density increases. In other paper, the authors have proved that some linear advection equations modelling non-Newtonian fluid behaviors have only one solution in steady recirculating flows. This solution is found imposing the solution periodicity along the closed streamlines, where the equation is integrated by the method of characteristics. In this paper we propose a characteristics algorithm for solving advection equations in general steady flows, which may contain recirculating areas.

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“…It is well known that, even at a low volume fraction in a Newtonian medium, a fiber suspension has non-Newtonian flow properties [1,2]. Lipscomb et al [1] found that the secondary vortex in a re-entrant corner at a contraction becomes larger for the flow of a dilute fiber suspension through an axisymmetric channel than that for a Newtonian fluid.…”

Section: Introductionmentioning

confidence: 99%

Velocity Profiles of Suspension Flows through an Abrupt Contraction Measured by Magnetic Resonance Imaging

2007

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Velocity profiles in steady flows of fluid/particle mixtures through a duct with an abrupt contraction were measured by magnetic resonance imaging. Aqueous solutions of carboxymethyl cellulose containing particles, including spheres, disklike particles, and short fibers, at high volume fractions were used. As a result, a plug-like velocity profile was observed in a straight duct flow for every suspension, but the velocity profile depends on the particle shape at contraction. Disklike particles caused an unsteady flow, and short fibers caused a concave shape in the velocity profile near the centerline upstream of the contraction. Spheres did not affect the flow field. The concave profile became obvious with increased volume fraction of fiber. This result is caused by the larger elongational viscosity of the fiber suspension near the centerline of the channel, as compared with that of the sphere suspension.

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Numerical solution of fiber suspension flow through a complex channel

Cited by 58 publications

References 31 publications

On the solution of Fokker–Planck equations in steady recirculating flows involving short fiber suspensions

On the solution of Fokker–Planck equations in steady recirculating flows involving short fiber suspensions

A characteristics strategy for solving advection equations in 2D steady flows containing recirculating areas

Velocity Profiles of Suspension Flows through an Abrupt Contraction Measured by Magnetic Resonance Imaging

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