Closed‐form solution for the orientation field in a center‐gated disk

Altan, M. Cengiz; Rao, Binqi

doi:10.1122/1.550714

Cited by 28 publications

(14 citation statements)

References 46 publications

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“…The center-gated disc has been studied by other authors (3)(4)(5). Bay and Tucker (3) obtained good agreement for the fiber orientation in the flow direction by tuning the fiber interaction coefficient, and concluded that the closure approximation for & was the main source of error in the predictions.…”

Section: Introductionmentioning

confidence: 99%

“…In their case the part thickness was b = 3.18 mm and the average fiber length 1 = 0.21 mm. Altan and Rao (5) closed-form solution for the orientation field in a center-gated disc. Based on a study assuming steady, Newtonian flow, and comparing predictions with experimental results from (3), they concluded that both the quadratic and hybrid closure appraximations yielded significant errors in complex suspension flows.…”

Section: Introductionmentioning

confidence: 99%

“…We cut a section at an angle 45" to the flow plane, as depicted in Fig. 5. In the analysis we then neglect the possibility of having fibers oriented an angle exceeding 45" to the flow plane by constrain- ing the values of + based on the double value possibility.…”

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confidence: 99%

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Injectin molding of short fiber reinforced thermoplastics in a center‐gated mold

Larsen

2000

Polymer Composites

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We have studied injection molding of a rectangular box using short fiber reinforced polypropylene. The fiber orientation distribution and the local stiffness properties in radial and transverse directions have been measured in the bottom plane. The deduced orientation tensors are compared with predictions of a commercial computer code. Discrepancies are related to approximations made in the calculations and effects not accounted for by the present modeling approach. In the calculations the fiber interaction coefficient was varied seeking to fit experiments. We comment on the out-of-plane components of the orientation tensor, the relative thickness of skin and core layers, and the radial dependence of the fiber orientation in each layer. Values of the components of the 4'h-order orientation tensor calculated from the measured orientation distribution are used to compare different closure approximations referred in the literature. Anisotropy in the stiffness properties, calculated from the measured fiber orientation, agree well with measurements.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Injectin molding of short fiber reinforced thermoplastics in a center‐gated mold

Larsen

2000

Polymer Composites

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“…4 Similarly, to align particles across the streamlines, one expands the cross-section of the flow. 5 In a Brownian suspension, as we show, it is possible to align particles with the flow direction without any net contraction of the flow domain normal to the flow direction! Such a capability can improve industrial processes such as fiber spinning.…”

Section: B Closed Flowsmentioning

confidence: 76%

Exploitation of Brownian motions for the optimal control of fiber orientation distributions

Szeri

1996

Physics of Fluids

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An analogy of the charge distribution on Julia sets with the Brownian motion Comment on ''Photoselection in uniaxial liquid crystals: The effect of rotational Brownian motion on measurements of orientational distribution functions'' J. Chem. Phys. 73, 3021 (1980); 10.1063/1.440440 Photoselection in uniaxial liquid crystals: The effect of rotational Brownian motion on measurements of orientational distribution function J. Chem. Phys. 73, 3019 (1980); 10.1063/1.440439 Polarized fluorescent emission in uniaxial liquid crystals. The effect of intramolecular energy transfer and rotational Brownian motion on measurements of the orientational distribution functionThe dynamical behavior of suspensions of rod-like particles is explored in unsteady elementary flows characterized by the following special property: while there may be arbitrarily large excursions from an initial state by the carrier fluid, the fluid returns to the initial state at the end of the time interval. In such a closed flow, it is shown that the orientation distribution of a dilute non-Brownian suspension will also return to its initial state, after arbitrarily large excursions driven by the flow of the carrier fluid. In contrast, the orientation distribution in a Brownian suspension will not return to its initial state at the end of the interval in a closed flow. These effects are exploited in a constrained nonlinear optimal control problem for the orientation distribution of a Brownian suspension in an example closed flow. The result of the control problem is a family of protocols that are most effective at achieving various degrees of anisotropy of the suspension, within the class of flows under consideration.

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“…28 However, under some other specific flow conditions, the closure approximations give incorrect results. [29][30][31] Albeit the closure approximations generally have relatively higher computational efficiency than the distribution based method, yet the former has lower precision and narrower field of application compared with the latter.…”

Section: Introductionmentioning

confidence: 99%

Solution of three-dimensional fiber orientation in two-dimensional fiber suspension flows

2007

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Effects of bending and torsion rigidity on deformation and breakage of flexible fibers: A direct simulation study J. Chem. Phys. 136, 074903 (2012) Clouds of particles in a periodic shear flow Phys. Fluids 24, 021703 (2012) Steady-state hydrodynamics of a viscous incompressible fluid with spinning particles J. Chem. Phys. 135, 234901 (2011) Orientational order in concentrated suspensions of spherical microswimmers Phys. The orientation of fibers in simple two-dimensional flows is investigated. According to different ranges of the Péclet number, Pe, defined as the ratio of a characteristic rotational speed of fibers and the orientational diffusivity, three methods are developed: characteristic method for Pe= ϱ, regular perturbation method for Peӷ 1, and spectral method for everything else. All the methods subtly utilize the evolving solution of the rotational dynamics of fibers, which is also given in this paper. Especially, the adoption of spherical harmonics in the spectral method eliminates the singularity of the Fokker-Planck equation in spherical coordinates, and provides high precision and efficiency. The evolving solution of orientation distribution with Pe= ϱ is obtained through the solution of rotational dynamics. Using a regular perturbation method, the solution of orientation distribution with Pe= ϱ is extended for the condition of Peӷ 1. This paper provides systematical and high efficient techniques to deal with the fiber orientation.

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Closed‐form solution for the orientation field in a center‐gated disk

Cited by 28 publications

References 46 publications

Injectin molding of short fiber reinforced thermoplastics in a center‐gated mold

Injectin molding of short fiber reinforced thermoplastics in a center‐gated mold

Exploitation of Brownian motions for the optimal control of fiber orientation distributions

Solution of three-dimensional fiber orientation in two-dimensional fiber suspension flows

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