Monte-Carlo calculation of the calibration factors for the interfacial area concentration and the velocity of the bubbles for double sensor conductivity probe

This paper presents a study of the estimation of the correction factors for the interfacial area concentration and the bubble velocity in two phase flow measurements using the double sensor conductivity probe. Monte-Carlo calculations of these correction factors have been performed for different values of the relative distance (ΔS/D) between the tips of the conductivity probe and different values of the relative bubble velocity fluctuation parameter. Also this paper presents the Monte-Carlo calculation of the expected value of the calibration factors for bubbly flow assuming a log-normal distribution of the bubble sizes. We have computed the variation of the expected values of the calibration factors with the relative distance (ΔS/D) between the tips and the velocity fluctuation parameter. Finally, we have performed a sensitivity study of the variation of the average values of the calibration factors for bubbly flow with the geometrical standard deviation of the log-normal distribution of bubble sizes. The results of these calculations show that the total interfacial area correction factor is very close to 2, and depends very weakly on the velocity fluctuation, and the relative distance between tips. For the velocity calibration factor, the Monte-Carlo results show that for moderate values of the relative bubble velocity fluctuation parameter (Hmax ≤ 0.3) and values of the relative distance between tips not too small (ΔS/D ≥ 0.2), the correction velocity factor for the bubble sensor conductivity probe is close to unity, ranging from 0.96 to 1.