Analytical calculation of the measuring error of an electromagnetic velocity probe caused by a side channel wall

The distribution of virtual current around an electromagnetic velocity probe is distorted as the probe is installed too close to a wall and thus, an additional measuring error is caused. In this paper, an analytical calculation method is introduced to determine the distorted virtual current and the additional measuring error caused for a probe having two line electrodes on its side surface when installed close to the side wall of an open channel. Based on ignoring the end effect of the line electrodes, the problem is discussed in a horizontal section plane of the measuring system. Through conformal mapping of the irregular section plane to an annulus, Laplace’s equation of the virtual current’s potential is analytically solved using Neumann (as the wall is insulated) and Dirichlet–Neumann mixed boundary conditions (as the wall is conductive). The analytical solutions are verified by a comparison with numerically calculated data for a test case and used to calculate the distorted virtual currents for different ratios of the installing distance dd (between the probe and the wall) to the probe radius RR. The measuring error of an actual probe is calculated and compared with experimental data to validate the analytical calculation method. Possible reasons for the discrepancy between theory and experiment are discussed.