A Theoretical Model for the Cavity Filling Process in Injection Molding

Broyer, E.; Gutfinger, C.; Tadmor, Z.

doi:10.1122/1.549379

Cited by 102 publications

(26 citation statements)

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“…A cell is considered to be on the free surface when the values of f lies between 0 and 1 (0¡f¡1). A similar concept of 'fractional uid volume' can be found in the ow analysis network (FAN) method [38,39]. The FAN-type method basically assumes a quasi-steady Hele-Shaw ow in a thin channel.…”

Section: Vof Methodsmentioning

confidence: 99%

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface‐tracking algorithm and its verification

Kim

Lee

2003

Numerical Methods in Fluids

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SUMMARYNumerical simulation of uid ow with moving free surface has been performed. For the free surface ow, a volume of uid (VOF)-based algorithm utilizing a ÿxed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a ÿxed grid system, a new free surface-tracking algorithm based on the donor-acceptor scheme has been proposed. Novel features of the proposed algorithm are characterized by two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the uid volume ux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems usually encountered in the ÿnite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3D free surface ow problems without additional e orts. For computation of unsteady incompressible ow, a ÿnite element approximation based on the explicit fractional step method has been adopted. In addition, the streamline upwind=Petrov-Galerkin (SUPG) method has been implemented to deal with convection dominated ows. Combination of the proposed free surfacetracking scheme and the explicit fractional step formulation resulted in an e cient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

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Section: Vof Methodsmentioning

confidence: 99%

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface‐tracking algorithm and its verification

Kim

Lee

2003

Numerical Methods in Fluids

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“…These assumptions are mainly of geometrical nature, namely related to cavity symmetry and thickness variation. For non-symmetric cavities, the formulation is generalized by taking a more general mapping than in Equation (13), and the pressure expansion (17) would have to include both cosine and sine terms. More general initial and conditions could easily accommodated including front shape and pressure variation and history.…”

Section: Resultsmentioning

confidence: 99%

A hybrid spectral/finite-difference to transient free-surface flow inside thin symmetric cavities of longitudinally varying thickness

Zhang

Khayat

2005

Int. J. Numer. Meth. Fluids

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SUMMARYThe lubrication theory is extended for transient free-surface ow of a viscous uid inside threedimensional symmetric thin cavities of thickness that varies in the ow direction. The problem is ÿrst formulated for a cavity of arbitrary shape. The moving domain is mapped onto a rectangular domain at each time step of the computation. The pressure, which in this case is governed by the modiÿed Laplace's equation, is expanded in a Fourier series in the spanwise direction. The expansion coe cients are obtained using the ÿnite-di erence method. Only a few modes are usually needed to secure convergence. The ow behaviour is strongly in uenced by the cavity thickness. The ows inside a straight, contracting, expanding, and modulated cavities are examined. It is found that while the evolution of the front is always monotonic with time, that of the velocity at the front can be oscillatory if the degree of contraction of the cavity (whether modulated or not) is signiÿcant. The velocity of the contact point along the lateral walls is usually larger than that at the front, leading to the straightening of the front. However, for modulated cavities, the front may advance at a faster rate, leading to its own undulation.

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“…Obviously, a truncation level will have to be imposed, leading to a ÿnite number of modes, N , in the expansion. If expression (17) is substituted into Equation (13), and the Galerkin projection method is used, then the following recursive relation is obtained for the pressure coe cients: …”

Section: Pressure Expansionmentioning

confidence: 99%

A low‐dimensional spectral approach for transient free‐surface flow inside thin cavities of symmetric shape

Zhang

Khayat

2002

Numerical Methods in Fluids

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SUMMARYThe lubrication theory is extended for transient free-surface ow of a viscous uid inside threedimensional cavities of general symmetric shape but of small thickness. The problem is closely related to the ÿlling stage during the injection molding process. The moving domain is mapped onto a rectangular domain at each time step of the computation. A modiÿed pressure is introduced, which in this case is governed by the Laplace's equation, and it is expanded in a Fourier series along the ow direction. The expansion coe cients are obtained using the ÿnite-di erence method. This approach is valid for simple and complex cavities as illustrated for the cases of a at plate and a curved plate. Only a few modes are needed to secure convergence in general. It is found that the ow behaviour is strongly in uenced by the shape of the initial uid domain, the shape of the cavity, cavity thickness, and the inlet ow.

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A Theoretical Model for the Cavity Filling Process in Injection Molding

Cited by 102 publications

References 0 publications

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface‐tracking algorithm and its verification

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface‐tracking algorithm and its verification

A hybrid spectral/finite-difference to transient free-surface flow inside thin symmetric cavities of longitudinally varying thickness

A low‐dimensional spectral approach for transient free‐surface flow inside thin cavities of symmetric shape

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