Three‐dimensional extrudate swell of creeping Newtonian jets

Karagiannis, A.; Hrymak, Andrew N.; Vlachopoulos, J.

doi:10.1002/aic.690341222

Cited by 29 publications

(19 citation statements)

References 11 publications

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“…The 18-node elements are used to simplify the free-surface parametrization when complex geometries are present. More information on these types of elements is given elsewhere [9,10]. The field variables are approximated within each element by…”

Section: Galerkin Formulationmentioning

confidence: 99%

“…The free surface update scheme has an impact on the number of non-linear iterations required and in this work both the idea of spines [9,12], and the pathline approach [13,14] (and a hybrid of the two) were followed depending on the problem characteristics.…”

Section: Free Surface Updatementioning

confidence: 99%

“…[9,12] (see figure 2). The free surface node x~ is parametrized as the distance h i along the i-th spine ~, 17, ( is the local coordinate system of the parent element on which the 27-node element is isoparametrically mapped.…”

Section: = Xio + Hi E Imentioning

confidence: 99%

“…When material is extruded from geometries where sharp corners are present and there are no surface tension effects, the extrudate tends to form edges [9,13,14] corresponding to the die corners.…”

Section: = Xio + Hi E Imentioning

confidence: 99%

“…The corner point is not very clearly defined unless it lies on a spine [9]. The pathline method is capable of defining the corner point location since it follows the path of the corner material point but convergence is slow.…”

Section: = Xio + Hi E Imentioning

confidence: 99%

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Three-dimensional non-isothermal extrusion flows

1989

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A three-dimensional (3-D) non-isothermal study of viscous free-surface flows with exponential dependence of viscosity on temperature is presented. The effects of non-isothermal conditions and/or geometry on the extrudate shape are investigated with a fully three-dimensional finite element/Galerkin formulation. Apart from the well known thermally induced extrudate swelling phenomenon, bending and distortion of the extrudate may occur because of temperature differences and/or geometric asymmetries. A temperature difference across the die can be imposed by heating or cooling the die walls, but can also arise because of asymmetric viscous heat generation due to the die geometry. Temperature differences affect velocity profiles because of the temperature dependence of viscosity and lead to extrudate bending, an effect known as "kneeing" in the fiber spinning industry. It is also shown numerically and confirmed experimentally that the die geometry induces extrudate bending even in the case of isothermal Newtonian flows.

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Section: Galerkin Formulationmentioning

confidence: 99%

Section: Free Surface Updatementioning

confidence: 99%

Section: = Xio + Hi E Imentioning

confidence: 99%

Section: = Xio + Hi E Imentioning

confidence: 99%

Section: = Xio + Hi E Imentioning

confidence: 99%

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Three-dimensional non-isothermal extrusion flows

1989

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An Algorithm for Simulation of Steady Free Surface Flows

Ramanan¹,

Engelman²

1996

Int. J. Numer. Meth. Fluids

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An algorithm to simulate steady, viscous free surface flows is presented in this paper. A Picard‐type approach wherein the flow and free surface updates are performed alternately is utilized to iterate for a solution. The procedure is intended for large‐scale two‐ or three‐dimensional problems. A surface‐intrinsic co‐ordinate system which facilities representation of general free surface shapes is used. Using a Galerkin finite element method (GFEM), two free surface updates, namely kinematic and normal stress updates are formulated. It is shown that the effects of surface tension, surface tension gradients and imposition of contact angles can be simulated elegantly within the framework of the GFEM. A novel feature of the updates is that the deformations are sought in a direction normal to the current iterate free surface shape, with the result that the method is ideally suited when used in conjunction with an automatic mesh generator. With the normal stress update a volume constraint can also be imposed. A segregated method is utilized to solve iteratively one degree of freedom at a time for the solution of the flow variables. As a result, the memory and disc space requirements are minimal. Sample problems in extrusion, coating and crystal growth are presented to clearly illustrate the convergence behaviour and accuracy of the algorithm.

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Three-Dimensional Extrudate Swell: Formulation With the Stream Tube Method and Numerical Results for a Newtonian Fluid

Normandin

Clermont

1996

Int. J. Numer. Meth. Fluids

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Stream tube analysis, already applied to two‐dimensional extrudate swell problems involving rate and integral constitutive equations for incompressible fluids, is now considered in the problem of free surface determination in a three‐dimensional flow situation. The method allows computation of the unknown free surface by considering only a ‘peripheral stream tube’ limited by the wall and the jet surface and an inner stream surface. Those boundary surfaces are determined by considering the conservation equations together with boundary condition equations, solved by the Levenberg/Marquatdt optimization algorithm. The method leads to a considerable reduction in the number of degrees of freedom and the storage area. As in a previous study in the two‐dimensional case, singularity problems in the vicinity of the junction points between the wall and the free surface are avoided. However, the numerical method still allows evaluati on of stress peaks due to the singularity at the exit, as may be observed for results obtained with a Newtonian fluid in a duct of square cross‐section.

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Three‐dimensional extrudate swell of creeping Newtonian jets

Cited by 29 publications

References 11 publications

Three-dimensional non-isothermal extrusion flows

Three-dimensional non-isothermal extrusion flows

An Algorithm for Simulation of Steady Free Surface Flows

Three-Dimensional Extrudate Swell: Formulation With the Stream Tube Method and Numerical Results for a Newtonian Fluid

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