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EN
The equiaxed investment casting process is a multi-physics problem which requires knowledge from engineers who have expertise in materials, metallurgy, fluid dynamics, thermodynamics, and heat transfer. Process modeling is a tool used by foundries to help predict casting defects such as shrinkage porosity, hot tears, and poor grain structure. The reliability of these predictions is strongly dependent on the accuracy of the thermal boundary conditions set in the model. In this work, a SGT5-2000E Vane 4 cast in Rene 80 nickel-based superalloy was modeled, using the FEA simulation package ProCAST, with two different methodologies. One methodology had very little effort invested into defining the thermal domain. The other methodology involved a thorough consideration of all heat transfer mechanisms acting on the mold. An extensive literature search was performed to define a unique natural convection heat transfer coefficient for each set of surfaces on the mold. The transient boundary layer development was also captured in the definition of the heat conditions. The shrinkage porosity predictions of the models were compared to real-world x-ray data and the transient nonuniform methodology predictions were much more representative than the low fidelity heat transfer methodology predictions. The low fidelity heat transfer model did predict some shrinkage, but not where it appeared in reality. The process modeler will be misdirected by the model results when deriving a solution to the casting process if the real-world physics are not appropriately accounted for in the model. This will be very counterproductive when the foundry is using the model to reduce developmental trials by running trials in model space. References and derived parameters are provided for material properties, emissivity of shell and insulation wraps, and external mold spatially varying heat transfer coefficients.
EN
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.
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