Sensitivity of macroscopic transport calculations to uncertain microscale relationships during metal alloy solidification

Abstract

The formation of grains during metallic solidification results in a multiphase system consisting of many moving interfaces. Models have been formulated in terms of variables describing the microscopic details of interface motion during solidification, but the computational cost prohibits their extension to the length scale of industrial castings. For this reason, macroscopic transport equations are mathematically formulated using averaging methods to replace the instantaneous description of interfaces. The most common approach is the volume-averaged, Eulerian approach relying on both the proper derivation of macroscopic field equations as well as uncertain interfacial conditions used to account for the average behavior of the interphase transfer occurring on the sub-grid length scale. In this work, common models used to describe the microsegregation occurring during solidification are evaluated in terms of the uncertainty of parametric inputs invoked in each model and their effect on macroscale predictions. We show that the qualitative macroscale predictions are not significantly changed by using more sophisticated microsegregation models, however significant uncertainty in input parameters used to describe the unresolved sub-grid interface is accumulated. Therefore, the use of simplified models is preferred until the uncertainty in model inputs can be reduced.