Development of empirical correlation to predict droplet size of oil-in-water flows using a multi-scale Poincaré plot

Oil-water two-phase flow phenomena are frequently encountered in many industrial processes. Droplet size and its distribution are important characteristics of oil-in-water flows and have a significant effect on the interfacial heat and mass transfers. In this study, we conduct an experiment on vertical oil-water two-phase flows with high water volume fraction and low mixture velocity. The information of droplet sizes is collected using a double-ring conductance probe during this experiment. We propose a multi-scale mean distance (MS-MD) and a multi-scale short-term distribution entropy (MS-STDE) based on a multi-scale Poincaré plot to characterize the short-term fluctuations of the probe signals. An empirical correlation is constructed based on the MS-MD to accurately predict the mean droplet size of oil-in-water flows. Meanwhile, the MS-STDE enables to correlate the short-term variability of collected probe signals to the complexity of the droplet sizes, and serves as a useful indicator of the droplet size instability.