Analytical investigation of an inductive flow sensor with arc-shaped electrodes for water velocity measurement in two-phase flows

• An inductive flow sensor with arc-shaped electrodes is proposed.
• Relationship between the voltage induced on electrodes and the water velocity is solved theoretically.
• Comparisons have been made for the analytical calculation.
• Experiments have been carried out to calibrate the proposed flow sensor.

An inductive flow sensor with spot-shaped electrodes (IFS-SE) is sensitive to the shape of the flow profile and is restricted to be used to measure the flow rate of axisymmetric single-phase flows in a circular pipe. In many cases of application, it is not possible to provide a fully developed flow profile. Therefore, the inductive flow sensor has to cope with flow profiles that are not fully developed. To improve the accuracy, an inductive flow sensor with a pair of arc-shaped electrodes flush-mounted on the internal surface of an insulating section of a pipe is proposed in this article to investigate the characteristics of vertical gas-water two-phase flows. The effect of the flow profile on the inductive flow sensor is analyzed. A key contribution of the present work is to estimate the relationship between the induced voltage and the velocity of the conductive phase in two-phase flows. The estimation is achieved by the analytical calculation of magnetic-inductive equations through the method of variables separation. The analytical solution is compared with the results from an ideal model and from numerical simulation. Experiments are conducted to calibrate the inductive flow sensor with arc-shaped electrodes (IFS-AE). It is noted that the proposed IFS-AE can be adopted to obtain the velocity of the conductive phase in two-phase flows by measuring the voltage induced on the arc-shaped electrodes.