Theoretical model of the two-chamber pressure casting process

This article develops a theoretical model of the two-chamber pressure casting process. In this process, a molten metal drop, formed by arc melting a solid ingot, falls into a conical crucible attached to a gas-filled, porous cast mold. An energy-based formulation of the mold-filling process is developed which focuses on the drop’s motion within the crucible and mold cavity and on pressure evolution within the mold cavity. The model shows that drop acceleration into the mold depends on three dimensionless parameters, the Euler number, Eu, the Froude number, Fr, and the pressure loss coefficient, K, across the crucible exit. These parameters are in turn determined by the mold’s permeability to the process gas, the characteristic initial pressure difference between the interior and exterior of the mold, the mold thickness, the process gas viscosity, and the metal density. Drop acceleration into the mold compresses trapped gas within the mold cavity; under most conditions, pressure decay due to leakage of the trapped gas through the mold occurs at a faster rate than inertial compression. Under these circumstances, a downward acting pressure force, having a magnitude determined by the Euler number, acts on the drop. At low Froude numbers, however, gas compression occurs at a faster rate than leakage-induced decay and the pressure force acts upward, again with a magnitude determined by Eu. Scaling arguments show that friction and evaporation recoil forces are negligible in determining drop motion, while surface tension, pressure, drop inertia, and gravity are dominant. In addition, solidification effects are shown to be negligible.