Stability of a cylindrical flame front in an annular combustion chamber

Within the framework of the phenomenological theory of combustion of mixtures, we investigate the stability of the cylindrical front of deflagration combustion in an annular combustion chamber with the use of small perturbations. The front of the flame is described by a discontinuity of the gas-dynamical parameters. We find that the flame front remains unstable for some types of small perturbations of the main flow of the fuel mixture and the flame front. Using numerical-analytical methods, we study the mechanics of instability. Some examples are given of the development of instabilities rotating in an annular channel.