Multiscale physics of rotating detonation waves: Autosolitons and modulational instabilities

Area of Science:

• Combustion science
• Nonlinear dynamics
• Fluid mechanics

Background:

• Rotating detonation engines (RDEs) exhibit complex nonlinear combustion wave propagation.
• Experimental observations include pulse nucleation, soliton-like interactions, and time-periodic wave modulation.
• Classical detonation theory alone does not fully capture RDE dynamics.

Purpose of the Study:

• To propose a phenomenological modeling framework for RDE combustion wave propagation.
• To classify mode-locked structures as autosolitons or nonlinear waves.
• To elucidate the role of multiscale physics and Hopf bifurcations in RDE stability.

Main Methods:

• Development of a phenomenological modeling framework.
• Classification of mode-locked structures based on local physics balance (nonlinearity, gain, dissipation).
• Analysis of global multiscale balance physics (fast combustion energy input, slow exhaust/propellant recovery).
• Numerical continuation (computational bifurcation tracking) of an RDE analog system.

Main Results:

• The framework reproduces diverse experimental observations of RDE combustion waves.
• Autosolitons are identified as stably propagating nonlinear waves where local physics balance.
• Global dissipative and multiscale physics, involving fast combustion and slow recovery, govern stable structures.
• A Hopf bifurcation is identified as the source of RDE instability and time-periodic wave modulation.
• Solitonic interactions of varying strength are observed along Hopf orbit branches.

Conclusions:

• The proposed framework successfully models RDE combustion wave phenomena, including autosoliton formation and interactions.
• Multiscale physics, not just frontal dynamics, are crucial for stable RDE structures.
• Hopf bifurcation analysis reveals the fundamental instability mechanism driving RDE wave modulation.
• The study provides a unified understanding of RDE nonlinear dynamics and wave behavior.