Study on Process Tomography through Electro-Magnetic Induction for Nonsteady Flow

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Electromagnetic flowmeters using Faraday's law have been one of the standard meters to measure liquid flowrate in industry. A conventional electromagnetic flowmeter has a uniform magnetic field and point electrodes in a circular pipe. Such a flowmeter has a flow signal which is proportional to the flowrate when the velocity profile in the liquid is axisymmetric. The ideal field which induces the flow signal proportional to the flowrate free from velocity profile does not exist. Conversely, it is possible to evaluate velocity profiles through the proper design of the magnetic field.In previous study 2-dimensional tomography system with eight magnetic poles and eight signal pickup electrodes was reported. It was reported that when the flow was conditioned to be fully developed and axially symmetric, the reconstruction of 2-dimensional velocity distribution could be achieved from induced signals. In this paper, the author proposes a new design of the 3-D field excitation with two sets of eight magnetic poles and of eight signal pickup electrodes. This research aims at the estimation of 3-dimensional velocity distribution in the pipe. For numerical simulation the laminar swirling flow was supposed. The axial component is the same as Poiseuille flow. The tangential velocity components represent a swirl. In order to reconstruct the tangential velocity, the constraints of non-slipness at the pipe wall, equation of continuity, and tangential velocity near the wall were effective. A new method for reguralization parameters is proposed. The proposed method applies to L-curved one. When there are two reguralization parameters, the parameter surface is described in 3-D space. The reguralization parameters were determined by the proposed method. It is concluded that the reconstruction of 3-D velocity distribution can be achieved from induced signals. Numerical simulation study showed the feasibility of the 3-D flow velocity tomography.