A model for obtaining the velocity vectors of spherical droplets in multiphaseflows from measurements using an orthogonal four-sensor probe

Abstract

This paper presents a mathematical model which enables the velocity vectors anddiameters of spherical droplets (or bubbles) in bubbly two-phase flows to bedetermined from the outputs of a local four-sensor intrusive probe. Each of thefour sensors functions by measuring the fluid conductivity at its tip andso use of the probe is relevant to flows where there is a contrast in theelectrical conductivity of the continuous and dispersed phases. The motionof a non-conducting spherical droplet has been simulated as it movesacross a four-sensor probe, which has a leading sensor and three rearsensors in an orthogonal arrangement. The technique described in thispaper relies upon measuring the time intervals between the droplet surfacefirst contacting the leading sensor and then coming into contact witheach of the three rear sensors. Assuming that the surface of the dropletcomes into contact twice with each of the rear sensors, as the dropletmoves across the probe, there will be six such time intervals. It has beenshown that in order to obtain the droplet velocity components in thex,y andz directions with anaccuracy of ±2%, the six time delays must all be measured with an accuracy of ±10 µs. Ithas been shown that the probe dimensions are critical to the measurementtechnique and that the separation of the four sensors should be of theorder of 1 mm. It has also been shown that if the droplets are oblatespheroids rather than spheres then, provided their aspect ratio is greater than0.75, the magnitude of the additional error in the estimates of the dropletvelocity components is less than 10.5%. No account has been taken of theinfluence of the probe on either the shape or the motion of the droplet.