Determination of local heat transfer coefficients in precision castings by genetic optimisation aided by numerical simulation

The heat transfer coefficient between casting and mould is the most crucial parameter in predicting the evolution of solidification and the resulting properties of the part. In numerical simulations setting, heat transfer coefficient value is considered an ill-posed, inverse problem that requires experimental data, whose solution, if at all possible to reach, is often numerically correct but physically meaningless. In this paper, it is proposed to use a Genetic Algorithm which stochastically explores alternative heat transfer coefficient values. These are evaluated by running a numerical simulation and comparing the resulting cooling curves at a number of nodes of interest to their experimentally measured counterparts until a close enough match is achieved. The combinatorial complexity of determining different heat transfer coefficients corresponding to different regions of complex castings, which are selected due to their differing casting moduli, is possible to tackle in this way with reasonable computational resources. Furthermore, different well-established forms of heat transfer coefficient function can be tried, notably heat transfer coefficient as a function of time (either stepwise or exponential) and as a stepwise function of temperature. Integer encoding in the Genetic Algorithm and a database of accumulating simulation results are features that were developed in order to reduce computational load. The approach is successfully demonstrated on a brass part produced by investment casting, exhibiting three sections of different casting moduli.