Uncertainty Quantification in Modeling Metal Alloy Solidification

Abstract

Numerical simulations of metal alloy solidification are used to gain insight into physical phenomena that cannot be observed experimentally. These models produce results that are used to draw conclusions about a process or alloy and often compared to experimental results. However, uncertainty in model inputs cause uncertainty in model results, which have the potential to significantly affect conclusions drawn from their predictions. As a step toward understanding the effect of uncertain inputs on solidification modeling, uncertainty quantification (UQ) and sensitivity analysis are performed on a transient model of solidification of Al–4.5 wt % Cu in a rectangular cavity. The binary alloy considered has columnar solidification morphology, and this model solves equations for momentum, temperature, and species conservation. UQ and sensitivity analysis are performed for the degree of macrosegregation and solidification time. A Smolyak sparse grid algorithm is used to select input values to construct a polynomial response surface fit to model outputs. This polynomial is then used as a surrogate for the complete solidification model to determine the sensitivities and probability density functions (PDFs) of the model outputs. Uncertain model inputs of interest include the secondary dendrite arm spacing (SDAS), heat transfer coefficient, and material properties. The most influential input parameter for predicting the macrosegregation level is the dendrite arm spacing, which also strongly depends on the choice of permeability model. Additionally, the degree of uncertainty required to produce accurate predictions depends on the outputs of interest from the model.