A numerical approach to the determination of electromagnetic flow meter weight functions

A new finite element procedure for the solution of the electromagnetic flow meter weight function is presented. The weight function represents the relative contribution of the fluid velocity at a particular spatial location in the flow cross section to the output signal from the flow meter. The solution of the weight function is important for inferring the velocity profile from measured potential differences within the electromagnetic flow meter. First, a numerical simulation model was constructed with COMSOL Mutiphysics [1]. Next, a study was undertaken to compare the numerical simulation model with Shercliff's [2] analytical solution for the weight function. The finite element methodology was found to be correct for solving the weight function. Based on this result, the numerical simulation model was used to compute the weight function for two flow meter geometries. For both cases the electrodes were located on the internal circumference of the flow pipe and the line joining the electrodes was normal to the imposed magnetic field. In the first case the separation of the electrodes was equal to one pipe diameter but in the second case the electrode separation was less than one pipe diameter. The methodology presented in this paper represents the first stage in the development of an image reconstruction technique which could be used to obtain the liquid velocity profile from boundary voltage measurements obtained in flows with highly skewed velocity distributions.