Second harmonic nonlinear resonance in propellant combustion

The paper discusses nonlinear oscillatory phenomena in propellant combustion which have a distinctive features as compared to similar phenomena in systems with a finite number of freedom degrees. As an example, nonlinear resonance phenomena in burning rate at oscillatory pressure is considered at frequencies about twice as high as the natural propellant frequency. The study is based on the approximation which takes into account thermal relaxation of the solid phase only. A nonlinear heat conduction equation for non-very-high amplitudes of oscillations is solved by the method of successive approximations. A quantitative study shows that, near the stability boundary of steady-state wave propagation, the corrections to the natural frequency and damping decrement are quadratic with respect to the burning rate amplitude. Various types of resonance curves at oscillatory pressure and a selfsustained oscillatory regime at constant pressure are studied. In conclusion some future research directions are discussed. The results presented can be useful in considering the operation of solid-propellant rocket engines.