Uncertainty Quantification of Modelling of Equiaxed Solidification

Abstract

Numerical simulations of metal alloy solidification are used to gain insight into physical phenomena that cannot be observed experimentally. Often validation of such models has been done through comparison to sparse experimental data, to which agreement can be misinterpreted due to both model and experimental uncertainty. Uncertainty quantification (UQ) and sensitivity analysis are performed on a transient model of solidification of Al-4.5 wt.% Cu in a rectangular cavity, with equiaxed (grain refined) solidification morphology. This model solves equations for momentum, temperature, and species conservation; UQ and sensitivity analysis are performed for the degree of macrosegregation. A Smolyak sparse grid algorithm is used to select input values to construct a response surface fit to model outputs. The response surface is then used as a surrogate for the solidification model to determine the sensitivities and probability density functions of the model outputs. Uncertain model inputs of interest include the secondary dendrite arm spacing, equiaxed particle size, and fraction solid at which the rigid mushy zone forms. Similar analysis was also performed on a transient model of direct chill casting of the same alloy.