Sensitivity study on double-sensor conductivity probe for the measurement of interfacial area concentration in bubbly flow

Abstract

The sensitivity study on a double-sensor conductivity probe for the measurement of local interfacial area concentration, has been carried out by considering the effects of bubble lateral motions and probe spacing. The measurable value was rigorously related to the local bubble interface velocity in the surface normal direction, and the probability density function of each individual variable was identified with proper coordinate transform. Three theoretical calibration factors were defined to bridge the mean measurable parameter to the interfacial area concentrations carried by the missed bubbles, measured bubbles and their combination. These calibration factors were obtained through numerical method. The results indicate that the total calibration factor is the best choice for practical applications, whereas the other two factors bring in profound understandings of the measuring mechanisms. With the probe spacing varying from about 36–86% of the mean bubble diameter, the total calibration factor is only determined by the bubble velocity fluctuation, almost independent of the probe spacing. The analysis also suggests that the missed bubbles contribute larger interfacial area concentration to the measuring point than that obtained from the measured bubbles. Moreover, for better statistic behaviors, the appropriate sample size was provided using a Monte Carlo approach.