Multiscale physics of rotating detonation waves: Autosolitons and modulational instabilities

Proposed is a phenomenological modeling framework that is capable of reproducing the diverse experimental observations of the nonlinear, combustion wave propagation in a rotating detonation engine (RDE), specifically the nucleation and formation of combustion pulses, the soliton-like interactions between these combustion fronts, and the fundamental, underlying Hopf bifurcation to time-periodic modulation of the waves. In this framework, the mode-locked structures are classified as autosolitons or stably propagating nonlinear waves where the local physics of nonlinearity, gain, and dissipation exactly balance. We find that the global dominant balance physics in the RDE combustion chamber are dissipative and multiscale in nature: The fast combustion physics provide the energy input to form the fundamental mode-locked autosoliton state, while the slow physics of exhaust and propellant recovery shape the waveform and dictate the number of autosolitons. In this manner, the global multiscale balance physics give rise to the stable structures-not exclusively the frontal dynamics prescribed by classical detonation theory. Experimental observations and numerical models of the RDE combustion chamber are in strong qualitative agreement. Moreover, numerical continuation (computational bifurcation tracking) of the RDE analog system indicates that a Hopf bifurcation of the steadily propagating pulse train leads to the fundamental instability of the RDE, or time-periodic modulation of the waves. Along branches of Hopf orbits in parameter space exist a continuum of wave-pair interactions that exhibit solitonic interactions of varying strength.