Theoretical analysis of gas dynamic disturbances in an explosive atmosphere
Various problems, which examine the propagation of gas dynamic disturbances, through an explosive atmosphere, are considered. The first set studies a model relaxing gas, and asymptotic methods are employed. A high frequency expansion is used to investigate piston oscillations in an infinite half space. The first two terms in the velocity perturbation are found in the acoustic case. The amplitude and frequency change on a wavelet are given; the wave number alters from wavelet to wavelet. For an enclosed volume the multi-time method is employed. When a standing wave exists in the vessel the frequency changes: when the vessel oscillates the wave number changes. The situation when forced oscillations at a natural frequency of the container is discussed. Also finite amplitude oscillations in a vessel are considered by using the multi-time method. An integral equation for the amplitude growth is found. A numerical solution of outward wave propagation, in spherical and cylindrical coordinates until shock formation, is given. The second group of problems considers a multi-component gas which can be analysed numerically. The effect of the homogeneous explosion in amplifying or damping a weak ii discontinuity is simulated. Thus proposals for reaction schemes can be analysed. It is found there is a relation- ship between amplification/damping and strong/weak ignition, in a mixture of hydrogen and oxygen in a shock tube. The reactions liberating a significant amount of energy in the chemical reaction, are the reactions causing greatest amplification.