Frequency analysis of macrosegregation measurements and simulations

Simple metrics for verification and validation of macrosegregation model predictions

“…In support of figure 1, table 1 shows the mean, standard deviation, and skewness change with grid size. Matching the findings in Voller and Vušanović [1] the main observation to take from figure 1b), is that as the grid is refined, the positive segregation region extends to the right and the predicted maximum truncation value of (M) increases. Essentially, a finer resolution, be it from simulation or experiments, will continue, up to some physical limit (e.g.…”

“…Even given the accuracy limitations of the grid size and the physical shortcomings in the mixture model, these statistical measures, in particular the Cumulative Distribution Function (CDF), provide two important insights. The first, supporting the initial work presented in Voller and Vušanović [1], is that the power-law tail in the CDF indicates why it is often so difficult to grid converge macrosegregation simulation. The second, is that the shape and spread of the CDF is extremely sensitive to change in the parameters that control the fluid flow in the mushy region.…”

“…Thus indicating that as numerical or measurement resolution is refined one will, up to the formation of a second phase, encounter higher and higher values of solute concentration. Here we will extend the use of the (CDF) recently proposed in [1] and demonstrate how it can also be used to evaluate changes in process and model conditions.…”

“…In recent work Voller and Vušanović [1] have proposed a simple way of constructing a so called Cumulative Distribution Function (CDF). This involves (i) listing the nodal values M i in descending order, (ii) assigning a rank number j = 1, 2,3, …, N to each item in the list, and then (iii) associating with each entry an inverse Weibul number…”

“…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.…”