Outer Free Surface Research Articles

Finite Element Simulation of Thick Tube Expansions

Abstract We consider the numerical simulation of the combined drawing and radial expansion of a thick tube, which is a possible model for continuous tube-making. Both Newtonian and visco-elastic cases are considered. Mesh refinement studies show convergence; to stabilize the computations we have introduced relaxation factors. The main difficulty here is in finding the region of contact with the sizing die, as well as the form of the free surface. It was found that the extra stress component, τθθ, is most helpful in considering the characteristics of tube expansion. The maximum value of τθθ occurs near the outer wall of the exit of the annular die for Newtonian flow and near the interface for K-BKZ liquids. Both for Newtonian and K-BKZ liquids the extra stress component τθθ in the expansion region, not including the vicinity of the exit of the die, develops from the inner free surface toward the outer free surface. The pressure value needed for tube expansion increases and then decreases as the expansion ratio R0/RW increases.

A Comparative Analysis of Finite Element and Finite Difference Methods for Free Surface Transport

The present work consists of the comparative evaluation of the finite element method (FEM) and the finite difference method (FDM) for the analysis of free surface transport within a hollow ampule. The phenomenon of motion reversal of the five surfaces obtained earlier by the FDM is also analyzed by the FEM. It is found that the times at which the motion reversal occurs are independent of the applied pressure difference for any fixed dimension of the hollow ampule. Furthermore, it appears that the displacement of the inner and outer free surfaces varies linearly with the magnitude of the applied pressure difference. Finally, detailed comparative discussion is presented on the differences between the results obtained by FDM and FEM.

Thermo-Stress Analysis of a Plated-Through-Hole in a Composite Printed Wiring Board

A stress analysis model for determining the thermal stresses in the vicinity of a plated-through-hole in a printed wiring board is presented. The model is based on axi symmetnc deformation and the superposition of an exact elasticity solution for far field stresses (away from the outer free surfaces) and an approximate near field solution (near the outer free surfaces). The approximate solution exactly satisfies point-by-point equilib rium, but violates compatibility.

ANALYSIS OF FREE SURFACE TRANSPORT WITHIN A HOLLOW GLASS AMPULE

ABSTRACT The formulation and numerical investigation of free surface transport within a hollow glass ampule art presented. The glass ampule is treated as a vertical film with a finite pressure difference across the film. A modified form of the marker and cell method within a semi-implicit algorithm is used to deal with the free surface problem, and full consideration of surface tension and viscosity effects is taken into account. It is found that the viscous effects on the free surface pressure conditions can be neglected because of the dominance of the surface tension effects. Furthermore, it is found that the convective terms have less than 1% effect on either the pressure or the velocity fields. The results clearly show the effects of a pressure differential across the glass ampule. The movements of the inner and outer free surfaces and the corresponding pressure distributions at these surfaces are analyzed. An interesting phenomenon corresponding to the reversal of direction of the movement of the fre...

Analysis of extrudate swell from an annular die

An isothermal annular jet swell problem has been analyzed using a control volume based finite difference scheme. This numerical scheme has been previously used for the analysis of the jet swell problem in capillary and slit dies, and is also shown to be applicable to annular geometries as well. In the absence of gravity and surface tension, the thickness swell ratio reaches 15.88%, which is in reasonable agreement with values reported in the literature. A relatively long jet was employed in this study and the effect of gravity on the jet shape appeared to be significant. In accordance with other calculations in the literature, the surface tension was found to have a more pronounced effect on the inner free surface compared with the outer free surface. The effects of the power-law index and die gap size were also investigated, and a suggestion for improvement of the numerical approach is briefly described.

Study of electron traps in the thin interfacial oxide layer of Al-, Au- and [formula omitted] GaAs Schottky barriers by detrapping experiments : R. L. Van Meirhaeghe, W. H. Laflere and F. Cardon. Solid-St. Electron.25 (11), 1089 (1982)

In this paper, a procedure for the determination of the angles α̃e(re,h;pe)(α̃i(ri,h;pi)) between the tangent line to the outer free surface (inner free surface) of the meniscus at the three-phase point, of coordinates (re,h)((ri,h)) and the horizontal axis ‘Or’ is presented. These functions appear in the system of differential equations which describe the evolution of the outer radius re (inner radius ri) of a tube grown from the melt by the edge-defined film-fed growth (EFG) technique. These angles can fluctuate during the growth. The deviation of the tangent to the crystal outer (inner) free surface at the triple point from the vertical is the difference α̃e(re,h;pe)−(π2−αg), (α̃i(ri,h;pi)−(π2−αg)), where αg is the growth angle. The deviation can also fluctuate, and the outer (inner) radius re(ri) is constant when the deviation is constant equal to zero.The knowledge of α̃e(re,h;pe), α̃i(ri,h;pi) is necessary for the analysis of the nonlinear system of differential equations describing the dynamics of the tube growth and for the determination of the interface height h and of the outer and the inner radii re, ri, respectively, of the tube to be grown with a given pulling rate v in specified thermal and pressure conditions pe, pi. These kinds of result are useful in experiment planning and manufacturing technology design. Numerical results are given for a silicon tube.

Rotating finite liquid systems under zero-gravity

The coupled natural frequency equation for rotating cylindrical liquid bridges of finite length consisting of one liquid or two immiscible liquids are presented. Various important cases such as a single liquid around a center core, two immiscible liquids in a completely filled circular cylindrical container, two immiscible liquids exhibiting besides the interface also an outer free surface have been treated. Natural frequencies and surface- and interface elevations have been treated numerically.

Coupled oscillations of a solidly rotating liquid bridge

The coupled natural frequency equations for rotating and non-rotating cylindrical liquid bridges of finite and infinite length consisting of one liquid or two immiscible liquids are presented. Various important cases such as a single liquid with a free surface, two immiscible liquids in a completely filled circular cylindrical container, two immiscible liquids exhibiting besides the interface also an outer free surface and one liquid around a rigid cylindrical core are treated. Special cases such as infinite liquid columns or infinite media are presented for rotating and non-rotating systems. Some of the cases have been treated numerically, and for some of them the stability of the system has been determined.

Localization of phosphatase activities on mouse teratocarcinoma embryoid bodies

Non-specific alkaline phosphatase and Mg 2+-dependent adenosine triphosphatase activities were ultracytochemically investigated on embryoid bodies of murine teratocarcinomas, in order to find markers of endodermal cell differentiation of early embryonic cells. The former was localized mainly on the cell surface of inner embryonal carcinoma cells, as already shown by other workers, and weakly on the bound surface of outer endodermal cells of embryoid bodies. The latter, however, was found only on the outer free surface of endodermal cells and never on the surface of embryonal carcinoma cells. It suggests that Mg 2+-dependent ATP activity might become the marker for early differentiation of embryonal carcinoma cells.

Pressure Wave Propagation in an Imploding Liquid Metal Liner

The propagation of a pressure wave through an imploding liquid metal liner near turnaround, due to the compression of magnetic flux and plasma is considered, based on which the pressure distribution near turnaround is derived analytically under the assumption of a small Mach number M (defined by the ratio between characteristic radial velocity of liner and the velocity of sound through the medium). It is shown that under certain conditions, the rarefaction wave from the outer (free) surface causes the apparition of a negative pressure in the imploding liner, with consequent liability of cavitation. The criterion for the generation of the negative pressure is found to be MΛ0.6~0.7 for the range of parameters considered (A: liner thickness at turnaround normalized by the inner radius).

Pressure wave propagation in an imploding liquid metal liner.

The propagation of a pressure wave through an imploding liquid metal liner near turnaround, due to the compression of magnetic flux and plasma is considered, based on which the pressure distribution near turnaround is derived analytically under the assumption of a small Mach number M (defined by the ratio between characteristic radial velocity of liner and the velocity of sound through the medium). It is shown that under certain conditions, the rarefaction wave from the outer (free) surface causes the apparition of a negative pressure in the imploding liner, with consequent liability of cavitation. The criterion for the generation of the negative pressure is found to be MΛ0.6~0.7 for the range of parameters considered (A: liner thickness at turnaround normalized by the inner radius).

Ultrastructural studies of normal skin and epidermal papillomas of the flathead sole, Hippoglossoides elassodon.

Epidermal cells of normal fin web and of the epidermal papilloma of the flathead sole, Hippoglossoides elassodon, were compared by light and electron microscopy. The predominant cells of normal epidermis are squamous and are characterized by complex microvillous interdigitations between adjacent cells, numerous desmosome-like structures, terminal bars, prominent cytoplasmic filaments, and blunt, broad-based microvilli on the outer (free) surfaces of the superficial cells. The less numerous mucous cells of normal epidermis possess abundant ergastoplasm and mucus-filled vacuoles, but lack desmosome-like structures and cytoplasmic filaments.

An investigation of the transition from a continuous to a discontinuous chip in orthogonal machining

Various depths of cut were taken with all other cutting conditions constant and within this range continuous and discontinuous chips were obtained. Ciné pictures of the deformation were taken through a microscope and an analysis made using strain-hardening slip-line theory. The hydrostatic stress-distribution in the plastic zone was shown to vary from compression at the outer free surface to tension near the cutting edge, and the magnitude of the tensile stress was shown to be important in determining whether or not the chip became discontinuous.