A new method of relating a chord length distribution to a bubble size distribution for vertical bubbly flows

Measurements of a bubbly flow using an intrusive probe give a set of random chord length values whose distribution differs considerably from the actual bubble size distribution (BSD). Considering the interaction of bubbles in groups of different sizes and shapes with the probe, a new method of relating the measured chord length distribution (CLD) to the BSD is proposed. The CLD is decomposed into simple distributions, which are considered as the CLDs of individual bubble groups and translated into BSDs using a developed analytical transformation. Entire BSD is constructed statistically from the obtained BSDs. The new method is applied to analyzing the CLDs measured by a five-sensor conductivity probe for a vertical bubbly flow in a narrow rectangular channel at different flow conditions. The results show a good agreement between the predicted BSDs and the experimental distributions measured simultaneously by a high-speed video camera. Valuable information on the statistical characteristics estimated from the CLDs and BSDs, including the chord length, bubble size and shape, and bubble population fraction, are evaluated and discussed in detail.