Statistical method to calculate local interfacial variables in two-phase bubbly flows using intrusive crossing probes

This paper presents a statistical method to calculate local interfacial variables in two-phase gas–liquid bubbly flows from data taken with double-sensor intrusive probes. Firstly, one derives the geometrical relationship existing between the apparent and actual bubble velocity for a single spherical bubble flowing in a multidimensional flow field. The apparent variables are obtained from the experimental data when one assumes that the bubble trajectory is aligned with the probe axis. A similar relationship exists for the intersected chord length and bubble diameter. Then, the analysis is extended to a swarm of bubbles. The ratio between the apparent to the actual bubble velocity and the intersected chord length to the bubble diameter appear now as probability density functions. The experimental data were taken for air–water bubbly flow regime in a vertical round pipe with a double tip electrical probe. Processing the phase density function generated by the bubble events, one determines distribution function of the bubble velocity and intersected chord length, termed the apparent distributions. The variables of interest, actual bubble velocity and diameter, come out of the solution of a linear system of equations relating the probability function of the measured and estimated bubble velocity and bubble size ratio. The probability density function of the actual bubble velocity and bubble diameter, plus the bubble frequency, add up to various interfacial properties calculated with this technique: the void fraction, the bubble velocity, the bubble size, the interfacial area density and the interface velocity fluctuation intensity. To validate the method, the paper compares local and area averaged quantities with previously published results, volumetric measurements and extensively used correlation.