On the propagation of acceleration waves in vibrational and radiative nonequilibrium magnetogasdynamic flows

Abstract

The effect of magnetic field on the propagation of acceleration waves in vibrational and radiative nonequilibrium gas flows, which is induced by the motion of a piston advancing with finite acceleration into a constant state of rest, has been studied along with the characteristic path by using the characteristics of the governing quasilinear system of equations of motion as the reference coordinate system. A differential equation governing the growth and decay of an acceleration wave is derived and integrated. The discontinuity at the wave front is shown to satisfy a Bernoulli-type equation which occurs frequently in studies of acceleration waves in continuous media. It is shown that a linear solution in the characteristic plane can exhibit nonlinear behaviour in the physical plane. The critical time when the breakdown of the characteristic solution occurs in the neighbourhood of the leading frozen characteristic is obtained; that is, when all the characteristics will pile up at the wave front to form a shock wave. For the formation of shock waves the following flows; that is,

1. (i) Vibrational and radiative nonequilibrium gas dynamic flow;

2. (ii) Vibrational nonequilibrium magnetogasdynamic flow;

3. (iii) Radiative nonequilibrium magnetogasdynamic flow; and

4. (iv) Vibrational and radiative nonequilibrium magnetogasdynamic flow, have been studied in detail. It has been observed that in the absence of a magnetic field the effect of the coupling of vibrational and radiative nonequilibrium characters of the gas is to increase the decay rate of expansive waves, while on compressive waves the effect is to increase the motion of the breakdown point along the leading frozen characteristics, and thus to increase the shock formation time, whereas in the presence of the magnetic field, it has been shown that for the slow nonequilibrium processes the effect of the magnetic field is to slow down the motion of the breakdown point along the leading characteristics, and thus to increase the shock formation time while the effect on expansive waves is to enhance the decay rate. However, for the quick nonequilibrium processes the effect of the magnetic field on compressive waves is to cause an early shock formation while on expansive waves the effect is to decrease the decay rate.