Numerical Simulation Of Temperature Field During Directional Solidification Based On Finite Element Method

The directional solidification(DS) craft is applied to produce turbine blades mostly in aviation and space, and the lack of high-performance blades is always the biggest obstacle of the “Big Airplane Dream”. Numerous complex reaction processes are included in the actual DS process, especially the effect of radiation. The evolution of temperature filed and the possible defects can be analyzed efficiently by the technology of temperature field simulation, so the DS craft can be optimized. All aspects of the simulation of temperature field during DS process by Finite Element Method(FEM) have been intense researched in the paper, including the mathematic model, the numerical solving by FEM, the boundary dispose of the cooling liquid, the criterion of the analysis of DS temperature filed and so on, at the end, the simulation system of DS temperature field has been developed.Firstly, because of the vital effect of radiation, the governing equation of radiation heat transfer is obtained by ray tracing method and computer graphics. The mathematic model of DS process has been gotten with several relatively reasonable hypotheses, and, by combining the numerical theory of FEM with the governing formulas and boundary conditions, the FEM discrete process and solving method have been deduced in detail.Secondly, in order to meet the law of conservation energy, the latent heat has been handled becomingly with the equivalent specific heat method and the rectification of temperature. In allusion to the irregular shuttering of DS craft, an arithmetic which can distinguish the inner and outer surfaces intelligently is adopted to avoid the tedious work by manual operation. And the convective heat transfer boundaries of whole contact surfaces are been disposed exactly with the box-tree method, even on the condition of coarse mesh. As the shuttering is immersed into the cooling liquid gradually in LMC(Liquid Metal Cooling) craft, the problem of grid re-mesh will arise if we solve it directly, and a temperature- and time-dependent heat-transfer coefficient is used to represent the heat convection between the shuttering and the cooling liquid. In the analysis of HRS(High Rate Solidification) and LMC temperature fields, the criterion G/L has been used for forecasting the possible mixed crystal. At the same time, for the sake of guaranteeing the computational efficiency, the concept of mixed-matrix has been proposed, which means assembling each material's matrix separately. Then, the temperature-field simulation system of HRS and LMC DS process has been developed in the paper.In the end, the temperature field of a typical I-shaped specimen during air cooling is calculated by the self-developed program, which matches well with the result calculated by ANSYS, so the correctness of the FEM algorithm in the temperature program has been verified. The temperature fields of a pair of investment casting techniques are also calculated by the self-developed program. The simulated results of the initial project predict the shrinkage porosity in the center of the cover piece, which matches well with the actual product. The improved technique which quickens the center 's cooling rate eliminates the defects in both the simulated result and actual product, so the feasibility of the temperature program has been verified. Then a turbine blade's temperature fields of HRS and LMC processes with different draw speeds are calculated, which accord real process. The reliability of the DS temperature-field system has been verified, and it can provide guidance for the actual production of DS.