Theoretical Model for Electromagnetic Flowmeter with Conductive Pipe Wall Based on Weight Function Correlation of Fluid Domain

This paper investigates the weight function distribution in the electromagnetic flowmeter with conductive pipe wall by combining the virtual current density method and COMSOL Multiphysics simulation software. It was found that the average weight function values were identical in any arbitrarily small annular domain in the pipe wall or fluid. Additionally, the ratio of the average weight function of the fluid domain to the pipe wall domain was only related to the ratio of their conductivity. Then a correlation for the average weight function ratio of the fluid and pipe wall was derived for the first time. The weight function correlation of the fluid domain was subsequently obtained by combining the physical meaning of the weight function. Finally, a theoretical model was derived based on the weight function correlation and the control equation of the electromagnetic flowmeter. The deviation between this model and the calculation results of the electromagnetic flowmeter model established by COMSOL Multiphysics was less than 4%.