Methodology for statistical evaluation of bubbly flows using grouped bubble cells

The present study aims to introduce an improved evaluation method of the statistical properties of bubbly two-phase flow for situations where bubble count density may exhibit low and/or strongly varying values. In these cases (sheet cavitation, boiling flows, etc.), accurate statistical descriptions are challenging at every location in the flow field (particularly in areas with a low bubble count density). As a result, methods of evaluating closure terms for pdf-transport models, such as the stochastic field method, are deemed to uncertainty. In the proposed methodology, bubbles are clustered to form groups of a fixed size. The volume associated with each of the grouped bubble clusters is dynamically calculated by a Voronoi tessellation, based on a prior Delaunay triangulation. We found that the proposed methodology is useful for evaluating statistical terms in pdf-transport models, as the effects of bubble number density versus those of bubble size growth are properly separated. Significant improvements in the statistical accuracy are observed in comparison to traditional evaluation techniques. In the study, we apply the method in two different examples: (i) a synthetic bubble distribution with predefined analytical field values, and (ii) experimental data captured from a plunging jet. We discuss the assessment of inherent systematic errors and the resulting achieved statistical accuracy. The objective of the study is to share our experiences and provide a best practice recommendation.