Uncertainty Quantification in Solidification Modelling

Abstract

Numerical models have been used to simulate solidification processes, to gain insight into physical phenomena that cannot be observed experimentally. Often validation of such models has been done through comparison to a few or single experiments, in which agreement is dependent on both model and experimental uncertainty. As a first step to quantifying the uncertainty in the models, sensitivity and uncertainty analysis were performed on a simple steady state 1D solidification model of continuous casting of weld filler rod. This model includes conduction, advection, and release of latent heat was developed for use in uncertainty quantification in the calculation of the position of the liquidus and solidus and the solidification time. Using this model, a Smolyak sparse grid algorithm constructed a response surface that fit model outputs based on the range of uncertainty in the inputs to the model. The response surface was then used to determine the probability density functions (PDF's) of the model outputs and sensitivities of the inputs. This process was done for a linear fraction solid and temperature relationship, for which there is an analytical solution, and a Scheil relationship. Similar analysis was also performed on a transient 2D model of solidification in a rectangular domain.