Finite Element Simulation of the Directional Solidification Process for Cylinders (2D) and Rectangular Bars (3D)

"The directional solidification of complex advanced gas turbine airfoils must be carried out without the nucleation of undesirable grains and with minimal shrinkage. Such problems are typically eliminated by using a number of mold design and process iterations. A more efficient approach is envisioned where a solidification model is generated and utilized to accelerate process development. Towards this end, the directional solidification (DS) of simple geometrical shapes in a crystal grower apparatus has been simulated with MARC finite element nonlinear thermal analyses.The finite element models of cylindrical (2D) and rectangular (3D) cross-section bars in the DS environment are presented. Temperature dependent properties, the impact of latent heat of fusion and a time-dependent radiation boundary condition constitute the more salient features of the MARC models. Solidification zone thermal behavior is predicted during the withdrawal transient for the specific case of nickel based superalloys grown in ceramic shell molds. Comparisons of analytical results with experiments demonstrate notable prediction accuracy. INTRODUCTIONSingle crystal and uni-directional crystal turbine blades require tightly controlled conditions if metallurgically and mechanically acceptable parts are to be produced. Gated blade geometry and process parameters must be precisely determined if incorrect grain structure, orientation and shrinkage are to be avoided. Since purely experimental development programs designed to evaluate these parameters can be excessively costly and time-consuming, an effort combining engineering analysis and verification by experiment has been initiated at Pratt & Whitney. Comparison of analytical predictions and measured data for geometries simpler than a turbine blade, namely cylindrical and rectangular bars, comprised the initial stage of this effort. Subsequent tasks involve modeling geometries of increasing complexity and ultimately the simulation of the directional solidification of the turbine blade, shown schematically in Figure 1. This paper summarizes the results of the initial stage of the effort."