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

利用法拉第定律的电磁流量计已成为工业上测量液体流量的标准仪表之一。传统的电磁流量计具有均匀的磁场和圆形管道中的点电极。当液体中的速度分布为轴对称时，这种流量计的流量信号与流量成正比。不存在不受速度分布影响而产生与流量成正比的流量信号的理想场。相反，通过适当的磁场设计，可以评估速度分布。在以往的研究中，曾报道过由8个磁极和8个信号采集电极组成的二维断层成像系统。研究结果表明，当流动条件为充分发展和轴对称时，可以利用诱导信号重建二维速度分布。本文提出了一种由两组8个磁极和8个信号采集电极组成的三维磁场激励的新设计。本研究旨在估算管道内的三维速度分布。数值模拟假设层流旋流。轴向分量与泊泽维尔流相同。切向速度分量表示一个漩涡。为了重建切向速度，管壁不滑脱约束、连续方程约束和管壁附近切向速度约束是有效的。提出了一种正则化参数的新方法。所提出的方法适用于l型曲线。当有两个正则化参数时，参数面在三维空间中描述。利用该方法确定了正则化参数。结果表明，利用感应信号可以实现三维速度分布的重建。数值模拟研究表明了三维流速层析成像的可行性。

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.