A Capacitance Sensor for Two-Phase Liquid Film Thickness Measurements in a Square Duct

Abstract

The use of capacitance sensors for measuring liquid film thickness or phase concentration in two-phase flow has gained popularity in recent years. In designing such sensors, there are many issues which must be considered in order to optimize performance: desired temporal and spatial resolution, two-phase flow regime, permittivity of the phases, duct geometry, electrical shielding, and temperature variation in the flow field. These issues are discussed, and the design of a 12.7 mm square cross section capacitance sensor which measures liquid film thickness in either stratified are annular two-phase flow is presented. Using a composite material analysis and an effective permittivity ratio, predictive relations for capacitance as a function of liquid film thickness have been derived for stratified and annular film patterns. The analysis eliminates the need for calibrating the sensor for stratified and annular flow regimes. Optical measurements of liquid film thickness using a high resolution CCD camera are compared against those using the capacitance sensor in conjunction with the predictive relations. The sensor was tested on a bench top for a stratified film pattern with no flow and two different electrode configurations (upwards and side configurations) using FC-87, a low-permittivity (εr = 1.72) dielectric fluid. The standard deviations between the film thicknesses measured optically and those predicted using the capacitance sensor and analysis are 0.014 and 0.019 mm for the respective upward and side electrode configurations. The sensor was also implemented in a vertical flow boiling facility, which uses FC-72 (εr = 1.75) as the working fluid. Time-averaged film thicknesses measured using the capacitance sensor are compared against ensemble-averaged measurements using the CCD camera for annular vertical upflow and downflow. The upflow and downflow standard deviations are 0.17 and 0.093 mm, respectively. As expected, the agreement for vertical flow is not as good as that for the horizontal no-flow case, because large fluctuations in film thickness are characteristic of annular two-phase flow, and the uncertainty of the photographic measurement is increased.