This paper examines the role of induction coil design on stirring of molten metal in electromagnetic (EM) solidification processes. A model is presented to describe the EM, heat transfer, and fluid flow phenomena in these processes. It is based on a dual-zone description of the mushy region, and accounts for damping of turbulence by the solidified crystallites. The electromagnetic field equations were solved using the mutual inductance technique, while the temperature and turbulent flow fields were calculated using the control volume method. Calculations were performed for solidification of an Al-Cu alloy placed in a stationary magnetic field generated by an induction coil. The effect of coil design on the flow structure was investigated for three different coil positions. It was found that changing the coil position significantly alters the flow pattern from four recirculating loops when the coil is above the midsection of the melt to two loops, typical of a travelling magnetic field, when the coil is at the base of the melt. This significantly modifies the rate of solidification across the ingot, as well as the temperature gradient, in the mushy region. The decay of the velocity and turbulent fields in the mushy region was found to be exponential, with the maximum rate of decay at the solidification front. These results indicate that through changes in coil design, it is possible to control the flow characteristics and solidification behavior in the molten metal.
While numerical models are often used in industry to evaluate the transport phenomena in solidification processes, the uncertainty in the results propagated from uncertain input parameters is rarely considered. In this work, in order to investigate the effects of input uncertainty on the outputs of high pressure die casting (HPDC) simulations, the Center for Prediction of Reliability, Integrity, and Survivability of Microsystems (PRISM) uncertainty quantification (PUQ) framework was applied. Three uncertainty propagation trials investigate the impact of uncertainty in metal material properties, thermal boundary conditions, and a modeling parameter on outputs of interest, such as fraction liquid at different times in the process cycle and shrinkage porosity volume, in an industrial A380 aluminum alloy HPDC process. This quantification of the output uncertainty establishes the reliability of the simulation results and can inform process design choices, such as the determination of the part ejection time. The results are most sensitive to the uncertainty in the interfacial heat transfer (for both outputs of interest) and the feeding effectivity (FE) (a model parameter controlling porosity formation determination), while the other heat transfer boundary conditions, model parameters, and all the properties play a secondary role in output uncertainty.
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