Flow of a real gas in annular channels with curvilinear walls, with high parameters of the magnetohydrodynamic interaction

A. I. Bertinov - L. K. Kovalev - S. M. Koneev - Yu. M. Nikitin

Abstract
This paper discusses the statement and solution of some two-dimensional problems involving the flow of a nonviscous and nonthermally conducting gas in annular magnetohydrodynamic channels, when the parameter of the magnetohydrodynamic interaction and the Euler number are much greater than unity, while the magnetic Reynolds number and the Hall parameter are small. An external plane-meridional magnetic field is given. The conductivity and the density are assumed to be functions of the enthalpy and the pressure. It is shown that, in the absence of an electrical field in the channel, and with certain limitations on the distribution of the enthalpy at the entrance to the channel, the question comes down to the problem of the flow of an incompressible liquid. An approximate solution is obtained to the problem of the flow of a gas in an annular channel with curvilinear walls, when there are no nonconducting meridional partitions in the cross section of the channel. The conditions for the development of stagnant zones in such a channel are elucidated. With the suppression of end effects, and with a constant enthalpy of the gas over the cross section at the inlet, the system of equations of magnetogasdynamics describing the flow of a gas in an annular channel with curvilinear walls and flat meridional electrodes, in a constant magnetic field, reduces to a system of ordinary differential equations. The results obtained are illustrated by the examples of the calculation of two channels: an annular channel without meridional nonconducting partitions, and a channel with meridional electrodes. The calculations presented demonstrate a substantial effect of the compressibility of the gas at large parameters of the magnetohydrodynamic interaction on the flow of a gas in channels.