Development of generalized correlations for two-phase flow velocity measurements obtained from impedance probes in rod bundle

A flag type electrical impedance probe has been developed at the Oak Ridge National Laboratory (ORNL) to measure liquid and vapor phase velocities in steam-water mixtures flowing through rod bundles. Such velocity measurements may be made by utilizing the probes in pairs, installed in line, parallel to the flow direction, and extending out into the flow channel.

Indications of the velocities of the phases are obtained by correlating the signals that are produced by the sensors as a result of the random fluctuations of the two-phase flow in the channel. Initial studies by McGill have yielded velocity correlations in dimensional form as functions of the void fraction and a quantity V_noise generated from a Fourier transform analysis of the flag probe signals. The correlations were successful in terms of reproducing corresponding liquid and vapor velocities as calculated by the two-phase separated flow model (±30%). However, these correlations do not work well when used with air-water data. Furthermore, their general applicability may be questioned since they were essentially derived from test data alone.

The present study addresses both of the foregoing difficulties by examining from a fundamental point of view the two-phase flow system in which the impedance probes typically operate. Specifically, the governing equations (continuity, momentum, energy) were formulated for both air-water and steam-water systems, and then subjected to a scaling analysis. The scaling analysis yielded the appropriate dimensionless parameters of significance in both kinds of systems. Additionally, with the aid of experimental data obtained at ORNL, those parameters of significant magnitude were established. As a result, generalized correlations were developed for test pressures ranging from 0 psig to 90 psig and void fractions ranging from 0.55 to 0.99. Values of liquid phase velocities ranged from about 1 to 60 ft/sec, while for the vapor phase, velocities ranged from about 10 to 110 ft/sec for steam-water flows and about 10 to 180 ft/sec for air-water flows. Beyond these experimental ranges the correlations may be used as references or as guidelines for j phase velocity calculations in two-phase flow systems. Also, it should be noted that the governing equations derived herein were simplified since the experimental conditions upon which the correlations were based i were those of steady flow, equilibrium conditions. The necessity of including a surface tension ratio in the correlation appears to indicate a deficiency in the governing momentum equations, which do not consider any surface tension effects.

The correlations were observed to successfully predict the liquid and vapor phase velocities for over 230 different test conditions from the AIRS (Advanced Instrumentation for Reflood Studies) at the Oak Ridge National Laboratory, for both air-water and steam-water systems. The prediction was consistently within ±25% for the liquid phase velocity and ±30% for the vapor phase velocity. Results of an uncertainty analysis further indicated that the magnitude of the scatter of data associated with the correlations was consistent with propagation of the uncertainties in the measurements of the pertinent system variables.