The growth and decay of nonlinear wave in polytropic reacting gas with small solid dust particles

Abstract

The aim of this study is to examine the evolutionary process of shock waves along the characteristic path under the effect of dust particles in a polytropic reacting gas. Testing the nature of the governing quasilinear of this system as a coordinate, we reconstruct the governing equations as Bernoulli’s differential equation and obtain the results. The results in the characteristic plane can display a non-linear behavior in the physical plane. It is shown how the reacting gas parameter influences the evolutionary process of the compressive and expansive waves, respectively, in reacting gas flows. Also, it is shown how the existence of dust in reacting gas influences the growth and decay of the compressive and expansive waves. The transport equation leading to the evolution of shock waves is determined and used to derive the condition for the shock formation. The comparative study of the effect of reacting gas parameters and dust particles on the flow patterning and distorting of shock waves for planar, cylindrically and spherically symmetric flows is also performed.