Multiscale Modeling and Simulation of Directional Solidification Process of Turbine Blade Casting with MCA Method
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A directionally solidified gas turbine blade has been widely used in aeronautical and energy industries, which is mainly manufactured by the Bridgman process. The processing parameters in directional solidification, such as the withdrawal rate, temperature gradient, pouring temperature, and so on, have great influence on the size and morphology of columnar grains as well as the performance of the final casting. The withdrawal rate, which affects temperature distribution and determines the formation of casting defects and the final quality, has been paid much more attention.[1–3] If the withdrawal rate is too high, it would cause an extremely concave solid–liquid (S/L) interface and lead to declining grains, transverse grains, or other defects. However, too low withdrawal rate would result in coarse grain, crack in the shell, or other defects and, thus, low productivity. Both experimental[4,5] and numerical methods[6–10] are extensively studied to learn more about the Bridgman process in the past few decades. Many kinds of numerical methods and models are proposed to
QINGYAN XU, Associate Professor, HANG ZHANG, Ph.D. Candidate, XIANG QI, Master Student, and BAICHENG LIU, Professor, are with the School of Materials Science and Engineering, Key Lab for Advanced Materials Processing Technology of MOE, Tsinghua University, Beijing 100084, P.R. China. Contact e-mail: [email protected] Manuscript submitted January 27, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS B
simulate the directional solidification process and microstructure evolution in blade castings. In this article, an integrated macro and micro multiscale model based on the modified cellular automaton (CA)-finite difference (FD) method was employed for the three-dimensional simulation of the microstructure evolution in the directional solidification process of super-alloy blade casting. The model was used to investigate the temperature distribution and grain evolution of the casting during solidification, and to predict the final grain morphology. Validation experiments were carried out. The simulated microstructure was compared with the experimental. II.
MATHEMATICAL MODELS
The metal pouring and solidification processes of the turbine blade castings take place in vacuum environment during the directional solidification process. The schematic of the directional solidification process is shown in Figure 1. In this model, the inner geometry of the furnace, the pattern of the blades on the chill plate, and the withdrawal rate are most important. Macro heat transfer during the directional solidification process can be calculated by the transient nonlinear heat conduction equation as follows: 2 @T @ T @2T @2T @fS ¼k þ QR ½1 þ 2 þ 2 þ qL qc 2 @t @x @y @z @t where T represents the temperature; t is the time; q is the density; c is the specific heat; L is the latent heat; k is the
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9 Fig. 2—Schematic of grain competitive growth.
Fig. 1—Schematic of directional solidification process of superalloy turbine blade: 1—gating system, 2—ceramic mold shell
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