Analytical and Numerical Solutions for Casting Processes with Initial Superheat and Natural Boundary Conditions

"Analytical solutions for investigating the solidification of casting problems with initial superheat and natural boundary conditions have been derived using an integral method. There are two moving interfaces in the solution field, one for the phase change line and the other for the superheat line. Two coupled nonlinear differential equations, representing two moving layers, were calculated by the Runge-Kutta numerical integration scheme. The solutions are in terms of six dimensionless parameters: phase change number, two Biot numbers for interfaces, diffusivity ratio, and dimensionless superheat temperature and time. Parametric studies on these parameters have been conducted to provide generic information about this phase change problem. This analytical information is extremely useful for validating numerical solutions. A simplified I-D finite element model was constructed for the purpose of comparison. The excellent agreement between the analytical and finite element solutions has proven that they are mutually validated.This validated finite element modeling tool was then used for modeling an investment casting process of a super-alloy with a simple geometry: a two-step plate. The nonlinear latent heat release, a common property of alloy materials, was approximated by several piecewise linear segments. The transient temperature response of this 2-D finite element solution, including a metal/mold gap resistance, shows excellent agreement with experimental data.This fundamental work provides a solid basis for further work on the development of a process modeling tool for the complex investment casting process.IntroductionAt present, the investment casting process is used in a variety of industries. In the aircraft engine industry, in particular, investment casting is used to produce parts ranging from turbine blades to engine frames. Because a large single casting can replace many component parts that require machining, fabrication, and assembly, this one-piece casting approach becomes a very cost-effective manufacturing process.The main constraint in using this process for mass production is the long design-to-production lead time. The standard rigging design is still an art, based on the experience of casting experts, rather than on scientific methods. Many trials are often required before making a sound final casting. In order to .reduce the number of expensive casting trials, the development of computer-aided tooling technology is needed.The fundamental physics describing this manufacturing process can be simply described. They reduce to a solid/liquid phase change problem, with two parts - first, the thermal balance of the initial superheat temperature of the molten metal and the preheat temperature of the ceramic shell through heat conduction, and second, the energy release from the mold surface to the ambient by radiation."