Fig. 2. The thermal conductivity of the core/mold is graphed.
Fig. 3. The density-specific heat of the core/mold is graphed.
amount of liquid metal available in the cells from which the fluid is removed. Te top of a liquid region is defined by the direction of gravity. Te relevance of this approach is supported by the fact, that in many situations, fluid flow in the solidifying metal can be ignored. Porosity formation in that case is pri- marily governed by metal cooling and gravity. Feeding due to gravity often occurs on a time scale much shorter than the total solidification time.
Microshrinkage When the solid fraction reaches a
sufficiently high value for a dendritic structure to exist throughout the bulk of the metal, further liquid flow is impossible without extremely high pressure gradients. Te zero flow point is called the solid fraction for rigid- ity, or the critical solid fraction. For modelling microporosity, it is assumed this last stage of solidification accounts for microporosity. Microporosity can exist only in a
computational element containing a solid fraction exceeding the solid frac- tion for rigidity. Te volume shrinkage in an element is computed from the change in density using a conservation of mass relation. Te mixture density is assumed to be a linear function of solid fraction. According to the model, the
28 | MODERN CASTING September 2014
maximum shrinkage porosity (vol- ume fraction) possible is equal to the density at the solidus temperature minus the density at the liquidus temperature, divided by the density at the solidus temperature. However, the maximum microporosity is much less, because it is associated only with solidification occurring above the critical solid fraction.
Core Gas In computational fluid dynamics
software, gas is considered ideal and has a fixed composition with a specific gas constant. Te specific gas constant can be deduced from experiments in which the gas is collected in a fixed volume apparatus and the gas pressure is measured. Te specific gas constant can be computed from the total col- lected standard volume and the initial mass of the binder. Te density of the core gas simul-
taneously satisfies the mass transport equation and follows the ideal gas assumption. Because the core gas is compressible, thermal expansion can occur, increasing the flow of the initial gas in the core as the temperature increases, even in the absence of gas sources. Te temperature of the gas generated is assumed to be equal to the local core temperature. Tis is a good approximation because the heat
capacity of the solid core material is very large compared to that of the gas. Te exchange of gas at boundar- ies of the core material is treated as boundary conditions for the core gas model. For instance, if the core surface is exposed to air, then gas may flow across the boundary in either direction depending on the pressure difference. If there is liquid metal at the core surface, gas is allowed to pass out of the core when its pressure is greater than the pressure of the metal at that location, but no metal is allowed to enter the core. If the metal has already solidified at the surface of the core, no gas is allowed to flow across the boundary at that location. At core print surfaces, where a core surface is in contact with another solid part of the mold, gas does not normally flow unless channels have been cut into the mold to allow for venting. For this scenario, the core gas model has an option for allowing venting at the print surfaces.
Simulation Tests Te geometry of the casting/riser
assembly used in the simulation is shown in Fig. 1. Te steel casting was poured at a metal temperature of 1,853 K. Te metal was prefilled with a uniform pouring temperature to simplify the simulation. Te casting
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