Multi-scale Physics of Rotating Detonation Engines: Autosolitons and Modulational Instabilities

We develop a theoretical framework that predicts and fully characterizes the diverse experimental observations of the nonlinear, combustion wave propagation in a rotating detonation engine (RDE), including the nucleation and formation of combustion pulses, the soliton-like interactions between these...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Koch, James, Kurosaka, Mitsuru, Knowlen, Carl, Kutz, J Nathan
Format: Article
Language:English
Subjects:
Balances (scales)
Combustion chambers
Detonation
Gain-Loss
Hopf bifurcation
Modulation
Nonlinearity
Nucleation
Numerical models
Parameters
Physics
Pulse propagation
Qualitative analysis
Rotation
Solitary waves
Wave propagation
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Summary:We develop a theoretical framework that predicts and fully characterizes the diverse experimental observations of the nonlinear, combustion wave propagation in a rotating detonation engine (RDE), including 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, dispersion, gain, and dissipation exactly balance. We find that the global dominant balance physics in the RDE combustion chamber are dissipative and multi-scale in nature, with local fast scale (nano- to microseconds) combustion balances generating the fundamental mode-locked autosoliton state, while slow scale (milliseconds) gain-loss balances determine the instabilities and structure of the total number of autosolitons. In this manner, the global multi-scale 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 with no parameter tuning. Moreover, numerical continuation (computational bifurcation tracking) of the RDE analog system establishes 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.
ISSN:2331-8422
DOI:10.48550/arxiv.2003.06655