Simple metrics for verification and validation of macrosegregation model predictions

Abstract

Abstract. While the numerical simulation of macrosegregation is now a common place activity efforts can still be enhanced by developing quantitative measures of the results. Here, on treating the nodal field of concentration predictions from a macrosegregation simulation as a sample from a statistical distribution, we demonstrate how statistical measures can be used in verification and validation. The first set of such measures is simply the central moments of the distribution, i.e., the mean, the standard deviation, and the skewness; measurements that provide quantitative checks of mass balance and grid convergence. In addition, building on recently reported work [1], we also demonstrate how to construct and use a cumulative distribution function (CDF) of the nodal concentration field; a measure that can be used to determine the fraction of the casting volume concentrations less than a specified value. We show how the CDF can be used to compare the influence of various process conditions and phenomena related to domain size, cooling rate, permeability, and micro-segregation. IntroductionCurrent macrosegregation simulations are advanced and when coupled with sophisticated graphical outputs lead to detailed predictions of the distribution of solute in cast products. Ultimately our objective with these simulations is twofold. In the first place we might like to compare differences in process settings such as cooling conditions, and geometry. Secondly, we may be interested in understanding the basic phenomena underlying the simulations, e.g., microsegregation, and mushy region flow behavior. Clearly, graphical output provides an immediate qualitative evaluation of changing process settings or model phenomena. But this powerful tool is lacking in obvious quantitative measures that can be used in case to case comparisons. One way of obtaining quantitative measures is to treat the predicted nodal values of solute concentrations from a macrosegregation calculation as a statistical distribution. In this way measures of central moments and derived distribution functions [1] can be used as quantitative representations of macrosegregation behavior. The objective of this paper is to introduce these measures and, through a number of example macrosegregation simulations, show how they can be used to evaluate process settings and phenomenological models.

Best practice for measuring grid convergence in numerical models of alloy solidification

“…The above well illustrates the utility of the CDF. But as elaborated by Vušanović and Voller (2015), the CDF will work best when the data are arranged on a uniform grid.…”