Decay of a saw-tooth profile in chemically reacting gases

Abstract

A progressive wave approach is used to obtain an asymptotic solution of the non-linear system of partial differential equations governing an unsteady axisymmetric flow of a chemically reacting gas. A Burgers-type evolution equation has been derived for the wave amplitude g(p, s, ξ), which leads to the Bernoulli-type evolution equation governing the growth and decay of an acceleration wavefront. It is concluded that all expansion wavefronts decay with time but all compressive wavefronts will not decay out. There exists a critical value of the magnitude of the initial wave amplitude such that all compressive waves with magnitude of the initial wave amplitude exceeding this critical value will grow into a shock wave within a finite time. When a piston suddenly moves from rest with an acceleration into a chemically reacting gas and then decelerates to a zero velocity, it gives rise to a shock front moving 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 study the decay of a saw-tooth profile due to diffusion of disturbances. It is found that the relaxation effects of the chemically reacting gas flow will accelerate diffusion and cause early decay of the saw-tooth profile. © 1994.