Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

Dutta, Anit; Ryan, Michael E.

doi:10.1002/aic.690280209

“…It can be seen that the swelling ratio increases from 1.110 to 1.165 as the mesh is refined. The results for the swelling ratio are considered to be in reasonable agreement with previous numerical predictions of Chang et al [31] and Dutta and Ryan [32]. From this same table, one may note that, using the implicit technique in the Freeflow code, it is possible to use a time step t greater than the explicit t visc , and as a consequence the CPU time was reduced.…”

Section: Die-swell Flowsupporting

confidence: 86%

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

Ferreira

¹

,

Oishi

²

,

Kurokawa

³

et al. 2006

Commun. Numer. Meth. Engng.

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SUMMARYThis paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions.

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“…In such a case, the normal component of the traction is vanishing at the exit plane. Similar assumptions for the velocity and the normal traction at the exit plane have been made in various theoretical and numerical studies of both the axisymmetric and planar extrudate swell problems under gravity and surface tension, and are valid when the exit plane is taken sufficiently far from the exit of the die [7][8][9][10][11]. In the numerical simulations, we use the finite element method (FEM) with the Newton-Raphson iterative scheme for the calculation of the unknown positions of the inner and outer free surfaces, i.e.…”

Section: Introductionmentioning

confidence: 91%

“…Hence, the simulation of the annular extrusion process has been the subject of quite a few publications in the past two decades [1 -6]. To our knowledge, in all two-dimensional studies of annular extrusion reported so far, gravity and surface tension are neglected, which is not the case in simulations of extrusion through slits and dies [7][8][9][10][11]. However, it is known from experimental observations that both gravity and surface tension push the annular film towards the axis of symmetry and have a dramatic effect on the shape of the extrudate.…”

Section: Introductionmentioning

confidence: 99%

The steady annular extrusion of a Newtonian liquid under gravity and surface tension

Housiadas

¹

,

Georgiou

²

,

Tsamopoulos

³

2000

Int. J. Numer. Meth. Fluids

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The steady extrusion of a Newtonian liquid through an annular die and its development outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surface profiles are calculated simultaneously with the other unknown fields, i.e. using the Newton–Raphson iterative scheme. The effects of three relevant parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on the shape of the annular film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin annular film respectively. A one‐dimensional model for the extrudate region, valid for thin annular films, is also presented, and its predictions are compared with the two‐dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one‐dimensional model predicts satisfactorily the effects of the Stokes and capillary numbers. Copyright © 2000 John Wiley & Sons, Ltd.

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“…Similar assumptions for the velocity and the normal traction at the exit plane have been made in various theoretical and numerical studies of both the axisymmetric and planar extrudate swell problems under gravity and surface tension, and are valid when the exit plane is taken sufficiently far from the exit of the die [7][8][9][10][11]. It is assumed that the closing length is large, i.e.…”

Section: Introductionmentioning

confidence: 93%

The steady annular extrusion of a Newtonian liquid under gravity and surface tension

Housiadas

¹

,

Georgiou

²

,

Tsamopoulos

³

2000

Int. J. Numer. Meth. Fluids

View full text Add to dashboard Cite

The steady extrusion of a Newtonian liquid through an annular die and its development outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surface profiles are calculated simultaneously with the other unknown fields, i.e. using the Newton–Raphson iterative scheme. The effects of three relevant parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on the shape of the annular film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin annular film respectively. A one‐dimensional model for the extrudate region, valid for thin annular films, is also presented, and its predictions are compared with the two‐dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one‐dimensional model predicts satisfactorily the effects of the Stokes and capillary numbers. Copyright © 2000 John Wiley & Sons, Ltd.

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Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

Cited by 30 publications

References 42 publications

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

The steady annular extrusion of a Newtonian liquid under gravity and surface tension

The steady annular extrusion of a Newtonian liquid under gravity and surface tension

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