Probe measurements in gas-liquid systems

Abstract

Resistance probes measure the presence or absence of a conducting fluid at a point in multiphase flows. Although resistance probes are often used to determine local gas hold-up in gas-liquid, gas-slurry and gas-liquid-solid flows, they are seldom used to find the bubble size distribution in the flow. This is because the distribution of time intervals measured by the probe due to the passage of bubbles is not readily translated into a bubble size distribution. Even if a bubble rise velocity is known, the resultidng distribution of bubble chord lengths cut by the probe has a lower mean and wider range than the size distribution. However, with enough data and a knowledge of the bubble shape, it is possible to back-transform to a size distribution. The current work deals with the case when the bubble shape is not a constant but changes with bubble size. Shape descriptors have been obtained from photographs of bubbles in water. By using these descriptors and probability density functions, a forward transform is developed to yield an expected chord length distribution for a given distribution of bubble sizes. The more important backward transform is accomplished numerically through a triangular matrix solution. Monte-Carlo simulations demonstrate the correctness of this approach and are also used to show that the back-transform can be unstable if too few data or too many size divisions in the matrix are used.