A mathematical examination of the impact of mould transparency to infrared radiation on solidification during the investment casting process

Investment casting is a highly dynamic process during which multiple competing physical phenomena are at work. Those seeking to understand and simulate such processes computationally are confronted with a considerable task, balancing accuracy with efficiency. Approximations and models based on well-understood and documented fundamental physics are powerful tools in a modeller's arsenal. Driven by observed discrepancies between experimental thermocouple measurements and simulation predictions of casting temperatures, this work explores the additional alloy cooling mechanism of mould transparency to infrared radiation, targeting a new mathematical approximation applicable in such situations. Direct attenuation, scattering from coarse sand, sand distribution in the mould and material temperatures play a role in the extent of radiation transparency that must be considered. From this model, estimation of the additional cooling rate resulting from expected mould transparency can be determined and applied as a corrective measure to computation fluid dynamics (CFD) simulation results that do not capture this phenomenon.