ACOUSTIC END EFFECTS IN MAGNETOHYDRODYNAMIC SUBMERGED VEHICULAR PROPULSORS .2. SOLITARY WAVES

In a magnetohydrodynamic (MHD) seawater propulsion system for a submer ged vehicle, a region of high-uniform magnetic induction (magnetic flu x density) inside the MHD propulsion channel is separated from the reg ion of essentially zero magnetic induction outside the channel in the seaway by a region of nonuniform, fringing magnetic induction at each end of the channel. This paper treats the propagation of an aperiodic fluid transient (solitary wave) which is produced by an arbitrary unit impulse in velocity or pressure at any cross section in the uniform-f ield region and which propagates through either fringing-field region and into the zero-field region outside the channel. The time scale for the transients is sufficiently short that compressive effects are imp ortant, so that the fluid transients are acoustic waves. The channel i s a straight, rectangular duct with electrically insulating walls and highly conducting walls perpendicular and parallel to the magnetic ind uction, respectively. The linearized acoustic equations are averaged o ver each cross section of the channel to obtain a pair of coupled equa tions governing the average pressure and average axial velocity as fun ctions of the axial coordinate and time. Together these equations repr esent a simple wave equation with a retarding force which is proportio nal to the square of the local magnetic flux density. Results are pres ented for three values of the acoustic interaction parameter N, which is the characteristic ratio of the electromagnetic body force opposing motions across magnetic-induction lines to the inertial ''force'' in the fluid transients. An abrupt change in velocity produces a wave fro nt which travels at the speed of sound. Without MHD effects, the entir e change in velocity or pressure occurs suddenly as the wave front pas ses. With MHD effects, only part of each change occurs suddenly as the wave front passes, followed by a gradual evolution to reach the entir e change. The split between the abrupt and gradual fractions of the en tire change depends on N. In previous work, the authors treated the fu ndamentally different MHD acoustic problem of the transmission of peri odic waves from the channel and the previous paper (Walker et al 1992) is Part 1 of the present work.