An Experimental Derivation of Transient Nonuniform External Boundary Conditions for the Solidification Process Modeling of Equiaxed Investment Castings

The external heat transfer mechanisms acting on the external mold surfaces for equiaxed casting processes are very complex. The mechanisms are multi-mode, transient, and nonuniform, consisting of very complex radiative and convective definitions. In this work, a real-life mold, SGT6-5000 FD 3/4 Blade 4 cast in Alloy-247, was instrumented with thermocouples and temperature readings were recorded throughout the entire casting sequence of events. Analytical models based on the first law of thermodynamics, Fourier’s law, Newton’s Law of Cooling, and diffuse gray radiation for an N-sided enclosure were developed to use the thermocouple data as input to back calculate the emissivity of the mold, as well as the spatially varying heat transfer coefficients for a number of local regions. The derived external heat transfer mechanisms are presented as transient Biot numbers. The derived emissivity and nonuniform heat transfer coefficients for these surfaces were then validated in ProCAST numerical simulation by comparing the external mold temperature profiles. An extensive iterative, curve fitting, extrapolating, and averaging procedure was exercised to derive an expression for emissivity across the entire temperature range associated with the casting process. The predicted temperatures on the nodes corresponding to the thermocouple locations agree within reasonable error with the experimental data. The model also qualitatively predicted the shrinkage porosity detected via x-ray imaging for this casting. The current study confirms the hypothesis of previous work by the current authors with respect to the transient nonuniform boundary condition concept. Unique values of heat transfer coefficients were observed at different vertical positions along the airfoil. The analytical models were also able to capture phenomena associated with specific sequences of the casting process. This work provides the analytical models, and procedure, needed to derive these spatially varying conditions. The current authors contribute to the intellectual know-how of the large gas turbine casting industry which by other foundries is considered highly proprietary and strictly confidential. This paper should be used to set the precedence for how foundries derive and validate the external boundary conditions used in solidification process modeling.