Impedance void meters are frequently used to measure the area-averaged void fraction in pipes. This is primarily for two reasons: firstly, this method is non-intrusive since the measurement can be made by electrodes flush mounted in the walls, and secondly, the signal processing equipment is simple. Impedance probes may be calibrated by using a pressure drop measurement or a quick closing valve system. In general, little attention is paid to void distribution effects. It can be proved that in annular flow, the departure from radial symmetry has a strong influence on the measured mean film thickness. This can be easily demonstrated by solving the Laplace equation for the electrical potential by simple analytical methods. When some spatial symmetry conditions are encountered, it is possible to calculate directly the conductance of the two-phase medium without a complete calculation of the potential. A solution of this problem by using the separation of variables technique is also presented. The main difficulty with this technique is the mixed nature of the boundary condition is both of Neumann and of Dirichlet type on the same coordinate curve. This formulation leads to a non-separable problem, which is solved by truncating an infinite algebraic set of linear equations. The results, although strictly valid in annular flow, may give the correct trends when applied to bubbly flow. Finally, the theory provides an error estimate and a design criterion to improve the probe reliability.
