Measurement of velocity profiles in multiphase flow using a multi-electrode electromagnetic flow meter

This paper describes an electromagnetic flow meter for velocity profile measurement in single phase and multiphase flows with non-uniform axial velocity profiles. A Helmholtz coil is used to produce a near-uniform magnetic field orthogonal to both the flow direction and the plane of an electrode array mounted on the internal surface of a non-conducting pipe wall. Induced voltages acquired from the electrode array are related to the flow velocity distribution via variables known as ‘weight values’ which are calculated using finite element software. Matrix inversion is used to calculate the velocity distribution in the flow cross section from the induced voltages measured at the electrode array. This paper presents simulations and experimental results including, firstly the effects of the velocity profile on the electrical potential distribution, secondly the induced voltage distribution at the electrode pair locations, and thirdly the reconstructed velocity profile calculated using the weight values and the matrix inversion method mentioned above. The flow pipe cross-section is divided into a number of pixels and, in the simulations, the mean flow velocity in each of the pixels in single phase flow is calculated from the measured induced voltages. Reference velocity profiles that have been investigated in the simulations include a uniform velocity profile and a linear velocity profile. The results show good agreement between the reconstructed and reference velocity profiles. Experimental results are also presented for the reconstructed velocity profile of the continuous water phase in an inclined solids-in-water multiphase flow for which the axial water velocity distribution is highly non-uniform. The results presented in this paper are most relevant to flows in which variations in the axial flow velocity occur principally in a single direction.