Theory analysis for the virtual current distribution in an electromagnetic flowmeter with one bubble

On the theory of electromagnetic flow meter, the effect of bubbles on the virtual current distribution was studied by using two-dimensional (2D) and three-dimensional (3D) analysis. To solve this problem, it was to establish the physical equation and boundary conditions used for the virtual current distribution of the flow meter. The method of separating variables was used to solve the physical equation to obtain a semi-analytical solution, and then the method of alternating iteration was used to work out the unknown coefficients in the semi-analytical solution. The solution analyzes the virtual current distribution with one bubble at radial position, at radial position in 2D coordinates, and at random position in 3D coordinates. The bubble has some effects on the distribution of the virtual current distribution. The greater the bubble, the greater the effects; the closer the bubble from the electrodes, the greater the effects.