Mode stability of a cylindrical flame front in an annular combustion chamber in the presence of entropy waves

The initial (linear) stage of the development of rotating transverse detonation waves in a flat-radial annular combustion chamber is determined and simulated. The problem of linear mode stability of the cylindrical front of Chapman–Jouguet deflagration combustion in a radially diverging subsonic flow with a small Mach number in the presence of perturbation waves of the flow entropy is solved. The steady flame front is described by discontinuity of the gas-dynamic parameters provided that the combustion products are in chemical equilibrium. It is revealed that the flame front is unstable for some types of small perturbations of the main flow of the combustible mixture and the flame front. Instability is determined under the condition of a constant flow rate in the mixture injection system. The spatial forms of oscillations and perturbation waves of the combustion front in the annular combustion chamber are obtained by numerical and analytical methods.