Divisionally analytical solutions of Laplace’s equations for dry calibration of electromagnetic velocity probes

Abstract

The potentials of weight function W → and magnetic flux density B → both obey Laplace’s equations in the measuring volume around an electromagnetic velocity probe. Analytical solutions of the Laplace’s equations are pre-requisite for the dry calibration of the probe, in which the sensitivity of the probe is calculated according to a mathematical model. However, the complexity of calculation geometry hindered the directly analytical solution of the equations, and there are still no effective analytical solutions applicable for the dry calibration at present. A method proposed in the paper is dividing the complex calculation geometry into two simple ones by an auxiliary surface, and thus the Laplace’s equations can be analytically solved in the each generated geometry separately. Specifically, two ways of division which can be effectively applied in the dry calibration, and the corresponding analytical solutions of the Laplace’s equations accessed using the method of separation of variables, are represented. Approaches to determine the additionally required boundary conditions on the auxiliary surfaces in dry calibration are also introduced. Finally, the study is validated on a numerical electromagnetic velocity probe.