Abstract
This paper investigates the critical plunger velocity in high-pressure die casting during the slow phase of the piston motion and how it can be determined with computational fluid dynamics (CFD) in open source software. The melt-air system is modelled via an Eulerian volume-of-fluid approach, treating the air as a compressible perfect gas. The turbulence is treated via a Reynolds-averaged Navier Stokes (RANS) approach that uses the Menter SST k-ω model. Two different strategies for mesh motion are presented and compared against each other. The solver is validated via analytical models and empirical data. A method is then presented to determine the optimal velocity using a two-dimensional (2D) mesh. As a second step, it is then discussed how the results are in line with those obtained for an actual, industrially relevant, three-dimensional (3D) geometry that also includes the ingate system of the die.
Highlights
As in our earlier computational fluid dynamics (CFD) modelling of high-pressure die casting [18,23,24], we model the two-phase flow of molten metal and air in the shot sleeve of a high-pressure die casting machine, as shown in Figure 1, by using the volume-of-fluid (VOF) method [26], wherein a transport equation for the VOF function, γ, of each phase is solved simultaneously with a single set of continuity and Navier-Stokes equations for the whole flow field; note that γ, which is advected by the fluids, can be interpreted as the liquid fraction
It is necessary to distinguish between the physics solver, that solves the partial differential equations (PDEs) given in Section 2, and how to handle the ever-shrinking computational domain
In [9], the solution to this problem was obtained in quasi-analytical form by formulating in terms of the shallow-water theory equations and using the method of characteristics until the wave hits and reflects from the wall at x = L, after which the problem must be solved numerically [12], and via CFD using the PHOENICS code [40]; subsequently, these results were used for CFD code validation in [13,14,15,35], and we will do likewise
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. There turns out to be exactly one critical constant speed that can be measured experimentally [5,6,7,8], or, under certain assumptions, determined analytically [9,10,11,12]; in particular, this requires: assuming a two-dimensional (2D) geometry, an isothermal flow and that the horizontal length scale is much greater than the vertical length scale; and neglecting the air flow, the effects of melt viscosity and turbulence Under these conditions, it is possible to derive the shallow-water equations and analytical, or at worst quasi-analytical, solutions can be obtained using the method of characteristics.
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