General method for the transformation of chord-length data to a local bubble-size distribution



Bubble-size distributions influence the behavior of multiphase systems, but are not readily measured directly using probes. The chord lengths may be transformed into bubble sizes by modeling the bubble shapes as ellipsoids. Previous research on the transformation of chord-length data into bubble-size distributions using a numerical backward transformation revealed an instability problem. This problem was overcome by transforming the chord-length data to a local bubble-size distribution directly by using a Parzen window function and summing to yield the whole distribution. The best estimate of the local bubble-size density distribution depends on the Parzen window width that was chosen by proposing a measure of performance. An empirical relationship was also offered to determine the best Parzen window width. Chord lengths were generated using the example of a Rayleigh bubble-size distribution and Monte-Carlo simulation. The window approach transformed the chord lengths back into the bubble-size distribution with good agreement.