Magnetogasdynamic channel flows

Abstract

The asymptotic behavior of small unsteady perturbations that are superposed on an equilibrium magnetogasdynamic channel flow is considered. Only those channels with slowly varying cross-sectional area and small characteristic width-to-length ratio are allowed, so that variations along the channel are typically much smaller than are those across the channel. Under these conditions and the provision that the current density inside the duct is small, a set of quasi-one-dimensional equations is obtained. From the resulting set of hyperbolic equations, the theory of characteristics provides certain compatibility relations that describe the behavior of small disturbances of the steady channel flow, which are caused by some local pressure fluctuation. Two distinct wave motions are present within the channel, and the asymptotic behaviors of both are examined with the use of the aforementioned compatibility relations. It is shown that, under certain conditions on the magnetic-field distribution, wave motions that lead to shock formation in ordinary gasdynamic flow will attenuate because of the action of the magnetic field. Therefore, an instability is no longer predicted, and the possibility of a stable or shockless flow, due to the action of a suitably placed magnetic field, is revealed. a A B c d E H h 3 Mc p p