Magnetic field estimation in measurement dead domain for dry calibration of electromagnetic flowmeter

Advances in computing technology enable dry calibration of large-diameter electromagnetic (EM) flowmeters at low cost, which has been recognized as an effective alternative to traditional flow rigs. Dry calibration requiring no actual liquid in the measuring pipe utilizes the magnetic field distribution reconstructed from measured boundary conditions to determine the sensitivity of the EM flowmeter. However, because sensors have finite sizes, and the fact that inner linings of the measuring pipe deform due to mechanical stresses, a measurement dead domain (MDD) exists between the measured boundary surface and the pipe wall. As the MDD is often close to the magnetic exciting unit, neglecting it results in significant errors in dry calibration. This paper offers a practical method combining iterative optimization and reconstruction to estimate the magnetic field in the MDD from the field data on the measured boundary surface. The method has been validated on an off-the-shelf industrial EM flowmeter by comparing the estimated field in the MDD with experimental measurements. It has been demonstrated that accurately accounting for the immeasurable field in the MDD eliminates more than two-thirds of the dry calibration errors. The estimation method illustrated here can also be extended to measure other physical fields which obey similar governing equations.