Simulation of Fiber Suspensions—A Multiscale Approach

[+] Author and Article Information
Krista Mäkipere

Laboratory of Computational Fluid & BioFluid Dynamics, Lappeenranta University of Technology, Lappeenranta, Finland

Piroz Zamankhan

School of Energy Engineering, Power and Water University of Technology, P.O. Box 16765-1719, Tehran, Iran

J. Fluids Eng 129(4), 446-456 (Aug 18, 2006) (11 pages) doi:10.1115/1.2567952 History: Received August 17, 2006; Revised August 18, 2006

The present effort is the development of a multiscale modeling, simulation methodology for investigating complex phenomena arising from flowing fiber suspensions. The present approach is capable of coupling behaviors from the Kolmogorov turbulence scale through the full-scale system in which a fiber suspension is flowing. Here the key aspect is adaptive hierarchical modeling. Numerical results are presented for which focus is on fiber floc formation and destruction by hydrodynamic forces in turbulent flows. Specific consideration was given to dynamic simulations of viscoelastic fibers in which the fluid flow is predicted by a method that is a hybrid between direct numerical simulations and large eddy simulation techniques and fluid fibrous structure interactions will be taken into account. Dynamics of simple fiber networks in a shearing flow of water in a channel flow illustrate that the shear-induced bending of the fiber network is enhanced near the walls. Fiber-fiber interaction in straight ducts is also investigated and results show that deformations would be expected during the collision when the surfaces of flocs will be at contact. Smaller velocity magnitudes of the separated fibers compare to the velocity before collision implies the occurrence of an inelastic collision. In addition because of separation of vortices, interference flows around two flocs become very complicated. The results obtained may elucidate the physics behind the breakup of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow at the continuum level where an Eulerian multiphase flow model can be developed for industrial use.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A schematic of a group of fibers clumped together.

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Figure 2

(a) The original shape of the fiber network whose fibers are bonded together due to colloidal forces of attraction, (bj) Deformed shape of the fibrous network under different shearing motion. In (f), the contact of middle fiber with its right-hand side neighbor is frictional. The material properties and the dimensions of the fibers are given in Sec. 3.

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Figure 3

Interaction regions between resolved and subgrid scales

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Figure 4

Instantaneous vector plot of the velocity field in the vicinity of a point of contact between two fibers in an accelerating fiber network whose schematic is illustrated in Fig. 5. An observer moving with the fibrous system makes the realization.

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Figure 5

(a) Schematic of a fiber-water suspension flow in a channel. The dimensions of the channel are L=5cm and H=w=1cm, (b) the original shape of the fiber network. The dimensions of a single fiber are l=3mm and d=0.1mm. (c) Á sample of the mesh used in the fiber-water system. (df) Temporal evolution of the fiber network. Note that fluid-fiber interaction caused the fibers to bend and the network to deform. The pressure at the outlet of the channel is assumed to be atmospheric.

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Figure 6

Vector plot of a velocity field in a moderately dense fiber suspension of thirty multisized fiber assembly. To improve the visualization of the vector field, a low-resolution grid is used. The dimensions and the material properties of the fibers are given in the text. Water flows from the left to the right in a parallelepiped duct with rectangular cross section cubic duct with dimensions of 4×3.5cm2, and the length of channel is only 4cm. (Inset) Fluid pressure distribution around the fibrous assembly. Also shown is the fluid pressure distribution on two perpendicular plane, xy plane and xz plane located at Z=−5.4mm and Y=−8.5mm, respectively, with respect to the origin located at the center of the inlet.

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Figure 7

(a) Flocculated suspension observed in the extrusion of an ultra-high consistency fiber suspension. (b) Schematics of fiber aggregates. (c) Schematic of the pipe whose dimensions are D=2cm and L=35cm. In addition, samples of triangular meshes used to discretize the inlet, outlet, and wall faces of the pipe are shown. The number of elements used for the aforementioned faces are 12,994, 12,933, and 168,285, respectively. The boundary condition at the outlet is pressure constant and is set to the atmospheric pressure. The dimensions of aggregates initially located at y0≈20mm, are as follows: l1=l2=8mm, and d1=d2=0.75mm, and the triangular finite element meshes used are 22,772, and 20,054. The total tetrahedral elements used to discretize the grid is 3,311,197.

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Figure 8

(a) Initial configuration of the two aggregates. The arrows represent their initial velocity vectors. (b) Configuration of aggregates after 3×10−3s. (c) Configuration of aggregates after 5×10−4s from that shown in (b). (d) and (e) are vector plots of the velocity field around the aggregates whose arrangements are illustrated in (a) and (b), respectively. The simulations are unsteady and the time step for the liquid phase equals 5×10−6. (f) The magnified velocity vector field for the configuration as illustrated in (c) when the aggregates are very close to each other. The velocity magnitudes are dimensionless defines as Vs*=Vs∕Vinlet, where the average velocity of water at the inlet, Vinlet, is set to 0.5m∕s.

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Figure 9

Solid-body collision of aggregates: (a) the instant of contact and (bd) three instantaneous configurations of the aggregates in contact each separated by 3×10−7s. The configurations in (bc) represent the approach and the restitution periods, respectively. The configuration in (d) represents the instant of separation. The simulations are unsteady and the time step for the aggregate-aggregate contact equals 4×10−10. The surface elements are color coded using the magnitude of the dimensionless velocity of the aggregates. Here, the velocities are normalized using the magnitude of the inlet velocity of water. Physical properties used in solid body collision of the aggregates are listed in Table 1.

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Figure 10

(a) Initial configuration of two aggregates at the instant of contact. The simulations are unsteady and the time step for the aggregate-aggregate contact equals 4×10−10. (b) The separation of configuration of the aggregates at the instant of separation (at the end of restitution period). Here, no adhesive force is taken into account. (c) Final configuration of aggregates for which a Lenard-Jones–type potential for attraction is considered. (d) The force separation relationship for contact surfaces. In the present attempt a suitable value for s0 is set to in order to finalize the collision at the end of approaching period. Here, dad represents the separation of the aggregates in cohesive zone. The surface elements are color coded using the effective stress defined as seff=sxx2+syy2+szz2−(sxxsyy+sxxszz+syyszz)+3(txy2+txz2+tyz2).

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Figure 11

(a) Grid for the deformed aggregates whose configuration is shown in Fig. 9 whose location from the inlet is L1⪢25mm. The number of cells used are nearly the same as those reported in Fig. 7. The geometries of one of the aggregates before and after the collision. Here, slide bending occurred during the collision in the aggregate. (c) Velocity vector field around the aggregates 5×10−5s, after the separation. The simulations are unsteady and the time step for the liquid phase equals 5×10−6. The arrows represent their initial velocity vectors. The surface of the aggregates is color coded using the magnitude of their normal stresses. (d) Iso surface of the liquid velocity magnitude of 0.6m∕s color coded using subgrid kinetic energy of turbulence. The boundary condition at the outlet is pressure constant and it is set to the atmospheric pressure.



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