What is it about?

Using images, we present and assess an advanced method to obtain local probability density functions (PDF) of properties related to the gaseous phase. For that purpose, we assign a volume to each bubble (using the Voronoi diagram) and group them in clusters (using the constrained K-Means algorithm). This simple trick allows a consistent and robust derivation of probability distributions. The method is applied to synthetic and experimental snapshots. We show the applicability and advantages, discuss errors, and provide practical guidelines.

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Why is it important?

Information about the probability distribution of, for example, the bubble radius is important to improve and validate simulation methods. In simulations of bubbly flows, these probability distributions can be used instead of pure mean values to improve accuracy. In addition, the probability density functions depend on the location in the flow, which introduces difficulties for the evaluation. The presented method shows advantages for flows featuring low bubble densities or bubble density gradients.


This general-purpose method can be applied to an abundance of flows to shed more light on the probability distribution of bubble properties. Furthermore, numerical methods using such PDFs could benefit from the results of this method. Thus, this study can be viewed as a starting point for further investigations in that field.

Lorenz Weber
Karlsruher Institut fur Technologie

Read the Original

This page is a summary of: On the statistical evaluation of bubbly flows using Voronoi cells grouped in clusters with fixed cell count, Physics of Fluids, May 2023, American Institute of Physics, DOI: 10.1063/5.0145551.
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