Dynamics of weak finite-amplitude perturbations in two-phase homogeneous medium (gas + solid particles) with non-equilibrium chemical reaction in gas is studied theoretically. Non-linear model of plane perturbation evolution is substantiated. The model takes into account wave-kinetic interaction and dissipation effects, including inter-phase heat and momentum transfer. Conditions for uniform state of the system are analyzed. Non-linear equation describing evolution of plane perturbation is derived under weak dispersion and dissipation effects.
The criterion for low-frequency perturbation amplification is substantiated. It is shown that instability has threshold character: perturbations increase when reaction heat release predominates over dissipative losses of energy. As a consequence the uniform reaction regime changes spontaneously. The role of non-linearity in perturbation spectrum stabilization is analyzed. As a result of instability and non-linearity self-sustained weak shock waves are generated in the system. Numerical simulation of evolution of gas-dynamic perturbations is carried out under different kinetic and dissipation parameters.
The obtained results demonstrate self-organization in the homogeneous system: steady-state periodic structure arises, its period, amplitude and velocity depends on the features of the medium. The dependencies of these parameters on dissipation and chemical kinetics are analyzed.
| Abstracts file: | Sharypov_Anufriev_abstract.pdf |
| Full text file: | Sharypov_Anufriev_paper.pdf |