The flow in the injection chamber of pressure die casting machines is analyzed using a model based on the shallow-water approximation which takes into account the effects of wave reflection against the end wall of the chamber. The governing equations are solved numerically using the method of characteristics and a finite difference grid based on the inverse marching method. The results of the model for wave profiles, volume of air remaining in the injection chamber at the instant at which the molten metal reaches the gate to the die cavity, and optimum values of the parameters characterizing the law of plunger motion, are compared with the numerical results obtained from a finite element code, which solves the two-dimensional momentum and mass conservation equations, taking into account nonhydrostatic and viscous effects. We found that, although the shallow-water model does not provide a very accurate estimation of the mass of entrapped air in the injection chamber for certain ranges of working conditions, it does describe reasonably well the influence of the acceleration parameters and the initial filling fraction on the entrapped air mass, and can be of help in selecting operating conditions that reduce air entrapment while keeping the injection chamber filling time as low as possible.
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