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Specific objective functions and algorithms are presented, which by means of dedicated finite element simulation software, calculate optimized control variables for an industrial Bridgman casting furnace. A gradient method and an evolution strategy have been integrated into an efficient optimization tool in order to minimize an objective function which characterizes the quality of directional solidified (DS) or single crystal (SC) turbine blades. The goal is to minimize the manufacturing costs for a desired quality. For a dummy turbine blade geometry, the macrograin structures produced by the optimized withdrawal velocity profile and an equivalent constant velocity, which had the same total process time, are compared. This comparison shows that the developed optimization techniques are applicable to the casting of DS/SC turbine blades.

In this article, a numerical model is presented which predicts phase distributions and dendrite arm spacings for a realistic casting within suitable CPU time. Three software components are coupled to perform calculations: (1) an FEM simulation package for the macroscopic temperature field, (2) an FDM code for the microstructure parameters, and (3) a thermodynamic software package for equilibrium calculations at the interfaces. The macrosoftware provides the micromodule with the present temperature at each node of a finite-element grid. At each such node, the micromodule calculates the dendrite arm spacings, the phase amounts, and the diffusion-controlled segregation profiles for the current time-step using equilibrium information from the thermodynamic software. A change of solid fraction and of the phase concentrations results in the release of latent heat and in the change of the heat capacity. These values are used as input parameters in the macrosoftware for the temperature calculation in the next time-step. Simulations have been performed for the ternary alloy AlCu4Mg1 and the results have been compared to "traditional" temperature calculations and to experimentally determined phase fractions and dendrite arm spacings. Measurements have been done by means of an interactive image analysis system over the entire breadth of an ingot casting at four different heights as well as at three different longitudinal cuts.

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