Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Sharypov O.   Anufriev I.  

Dynamics of finite-amplitude perturbations in two-phase reacting system

Reporter: Sharypov O.

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

To reports list
© 1996-2019, Institute of computational technologies of SB RAS, Novosibirsk