Mode-locked rotating detonation waves: Experiments and a model equation

Koch, James; Kurosaka, M.; Knowlen, C.; Kutz, J. Nathan

doi:10.1103/physreve.101.013106

Cited by 39 publications

(31 citation statements)

References 35 publications

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“…The nonlinear dynamics of the annular RDE can be approximated with a surrogate Burgers-Majda model 35,36 . This detonation analog models the evolution of a quantity u(x, t) which is understood to be an abstract representation of an intensive property of the medium such as specific internal energy.…”

Section: Resultsmentioning

confidence: 99%

Learning dominant physical processes with data-driven balance models

et al. 2021

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Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only applies in asymptotic regimes where there is a strict separation of scales in the physics. Here, we automate and generalize this approach to non-asymptotic regimes by introducing the idea of an equation space, in which different local balances appear as distinct subspace clusters. Unsupervised learning can then automatically identify regions where groups of terms may be neglected. We show that our data-driven balance models successfully delineate dominant balance physics in a much richer class of systems. In particular, this approach uncovers key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

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Section: Resultsmentioning

confidence: 99%

Learning dominant physical processes with data-driven balance models

et al. 2021

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“…Figure 2 shows an example of a DMT from three to two waves captured from the RDRE exhaust plane during an experimental run [13]. Additionally, theoretical studies by Koch et al [14], numerical simulations by Lietz et al [8], and wave stability investigations by Anand et al [15], have encountered modal transitions while examining RDE/RDRE nonlinear physics. As such, modal transitions are not isolated incidents.…”

Section: Introductionmentioning

confidence: 99%

Descending Modal Transition Dynamics in a Large Eddy Simulation of a Rotating Detonation Rocket Engine

et al. 2021

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Rotating detonation rocket engines (RDREs) exhibit various unsteady phenomena, including modal transitions, that significantly affect their operation, performance and stability. The dynamics of the detonation waves are studied during a descending modal transition (DMT) where four co-rotating detonations waves decrease to three in a gaseous methane-oxygen RDRE. Detonation wave tracking is applied to capture, visualize and analyze unsteady, 3D detonation wave dynamics data within the combustion chamber of the RDRE. The mechanism of a descending modal transition is the failure of a detonation wave in the RDRE, and in this study, the failing wave is identified along with its failure time. The regions upstream of each relative detonation show the mixture and flow-field parameters that drive detonation failure. Additionally, it is shown that descending modal transitions encompass multiple phases of detonation decay and recovery with respect to RDREs. The results show high upstream pressure, heat release and temperature, coupled with insufficient propellants, lead to detonation wave failure and non-recovery of the trailing detonation wave during a descending modal transition. Finally, the Wolanski wave stability criterion regarding detonation critical reactant mixing height provides insight into detonation failure or sustainment.

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“…Consequently, the physics exploration of these nonlinearities is often constrained to hardware-specific studies. For the Rotating Detonation Engine (RDE), Koch et al [37] recently proposed a mathematical model capable of reproducing the diverse, experimentally observed mode-locking dynamics of the RDE. Here, we build on this model and characterize the fundamental dominant, multiscale balances which drive the instabilities and bifurcation structure in the RDE, showing that the mode-locked states, or autosolitons, are solitonic in how they interact and that the Hopf bifurcation is the fundamental, canonical instability driving bifurcations in the combustion chamber.…”

Section: Introductionmentioning

confidence: 99%

“…Likewise, at a particular point in the annulus, the reactant mixture is regenerated within the transit time of a wave. This balance of heat release (gain), exhaust processes (dissipation), propellant injection (gain recovery), and nonlinearity of the medium governs the pulse shape, number, and behavior [37]. Should these physical processes be unbalanced, spatially or temporally, a wide array of spatiotemporal dynamics are known to exist and persist, as observed in experiments and detailed computational studies.…”

Section: Introductionmentioning

confidence: 99%

“…Should these physical processes be unbalanced, spatially or temporally, a wide array of spatiotemporal dynamics are known to exist and persist, as observed in experiments and detailed computational studies. Such dynamics include mode-locking of pulses [37], modulation of the pulse train [5,37], and bifurcations to different numbers of pulses [5,9,27,37]. The physical mechanisms and engineering implications of these transients and instabilities are not well understood, especially with regard to operational stability and performance.…”

Section: Introductionmentioning

confidence: 99%

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

Koch,

Kurosaka,

Knowlen

et al. 2020

Preprint

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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 structuresnot 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.

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Mode-locked rotating detonation waves: Experiments and a model equation

Cited by 39 publications

References 35 publications

Learning dominant physical processes with data-driven balance models

Learning dominant physical processes with data-driven balance models

Descending Modal Transition Dynamics in a Large Eddy Simulation of a Rotating Detonation Rocket Engine

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

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