DECAY OF A SAW-TOOTH PROFILE IN CHEMICALLY REACTING GASES

A progressive wave approach is used to obtain an asymptotic solution o f the non-linear system of partial differential equations governing an unsteady axisymmetric flow of a chemically reacting gas. A Burgers-ty pe evolution equation has been derived for the wave amplitude g(p, s, xi), which leads to the Bernoulli-type evolution equation governing th e growth and decay of an acceleration wavefront. It is concluded that all expansion wavefronts decay with time but all compressive wavefront s will not decay out. There exists a critical value of the magnitude o f the initial wave amplitude such that all compressive waves with magn itude of the initial wave amplitude exceeding this critical value will grow into a shock wave within a finite time. When a piston suddenly m oves from rest with an acceleration into a chemically reacting gas and then decelerates to a zero velocity, it gives rise to a shock front m oving ahead of the disturbance and an expansive wavefront following it . This physical situation of a flow pattern can be described as a saw- tooth profile with an expansive wavefront on the left and a shock wave on the right. The main object of the present communication is to stud y the decay of a saw-tooth profile due to diffusion of disturbances. I t is found that the relaxation effects of the chemically reacting gas flow will accelerate diffusion and cause early decay of the saw-tooth profile.