Cylindrical conduction-type magnetohydrodynamic channel

Yu. K. Zanders

Institute of Physics, Latvian Academy of Sciences, Salaspils-1, LV-2169, Latvia

Abstract
The article presents an analysis of the operation of a magnetohydrodynamic channel of round cross section, with an arbitrary number of pairs of poles and electrodes, disposed on the surface of the cylinder with respect to the angular coordinate in the sequence N, ϕ₊, S, ϕ₋, N,ϕ₊, S,ϕ₋, etc. It is assumed that the conducting medium is incompressible, homogeneous, and isotropic, and that it moves with a constant velocity over the cross section of the channel, while the magnetic field of the currents flowing in the channel is compensated for by return current-conducting busbars. The method of separation of variables was used to find the distribution of the external magnetic field and of the density of the electric current in the channel, when, at the poles and electrodes of the cylindrical surfaces, the magnetic induction and the current density are assumed to be constant. For the operating conditions of a generator and a pump, the integral electrical characteristics of the magnetohydrodynamic channel were determined (the efficiency, and the useful electrical and hydraulic powers). Flow-meter conditions were used to study the values of the induced potential (sensitivity) and of the hydraulic power dissipated in Joule heat. A comparison shows that the characteristics of a round channel are, in practice, not worse than those of a channel with a square cross section, if constant velocities, mass flow rates, and electrical and magnetic energies are maintained in the models being compared.