On the statistical evaluation of bubbly flows using Voronoi cells grouped in clusters with fixed cell count

Abstract

The extraction of statistical information from bubbly flow experiments is crucial for numerical studies. Knowledge regarding probability distributions is particularly relevant in cases where a model relying solely on the use of mean values would lead to inaccurate results. As such, existing studies have focused on evaluating spatial distributions and local histograms for the void fraction, bubble density, and bubble size. However, the traditional box-counting method, employed by various studies, results in inconsistencies when deriving these quantities, especially when the respective two-phase flow features regions with low bubble densities or density gradients. This study demonstrates the application and benefits of combining Voronoi diagrams with a constrained K-Means clustering algorithm as a method for analyzing bubbly flows. We conduct three test cases: The first two cases use synthetic snapshots with prescribed characteristics to show the influence of evaluation settings and to critically quantify the errors, and the last test uses snapshot data of a plunging-jet experiment with air entrainment. We, then, compare the identified entrainment rate and the mean void-fraction distribution with empirical values from the literature. All three test cases show good agreement with the prescribed field characteristics (synthetic snapshots) and the data from the literature (experiment). Beyond demonstrating its applicability, we also show how this method can derive local histograms more consistently. The derivation is robust throughout the domain in comparison with traditional methods. For these reasons, we conclude that this method provides good estimates of spatial distributions.