Calculation of the virtual current in an electromagnetic flow meter with one bubble using 3D model

Based on the theory of electromagnetic induction flow measurement, the Laplace equation in a complicated three-dimensional (3D) domain is solved by an alternating method. Virtual current potentials are obtained for an electromagnetic flow meter with one spherical bubble inside. The solutions are used to investigate the effects of bubble size and bubble position on the virtual current. Comparisons are done among the cases of 2D and 3D models, and of point electrode and large electrode. The results show that the 2D model overestimates the effect, while large electrodes are least sensitive to the bubble. This paper offers fundamentals for the study of the behavior of an electromagnetic flow meter in multiphase flow. For application, the results provide a possible way to estimate errors of the flow meter caused by multiphase flow.