Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

Ng, Hoi Dick; Higgins, Andrew; Kiyanda, Charles B.; Radulescu, Matei I.; Lee, J.; Bates, Kevin R.; Nikiforakis, Nikolaos

doi:10.1080/13647830500098357

Cited by 97 publications

(93 citation statements)

References 23 publications

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“…1. This implies the onset of chaos [10]. The sequence of period doubling bifurcations and onset of chaos is very similar to the non-linear dynamics of chemical detonations [10] and many other non-linear systems.…”

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confidence: 76%

“…This implies the onset of chaos [10]. The sequence of period doubling bifurcations and onset of chaos is very similar to the non-linear dynamics of chemical detonations [10] and many other non-linear systems. The results thus clearly highlight that our simple detonation model captures this universality observed in non-linear dynamics of complex systems.…”

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confidence: 76%

“…In multiple dimensions, multiscale cellular patterns have been observed [1], while in a single space dimension, a pulsating instability has been observed [9]. Numerical simulations of the reactive Euler equations used to model one-dimensional pulsating detonations have shown the universality in the wave dynamics [10]. As the sensitivity of the reaction rates is increased, stable travelling waves become oscillatory, and subsequently develop a hierarchy of period doubling bifurcations appearing according to Feigenbaum's scaling [11], and eventually become chaotic.…”

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confidence: 99%

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Nonlinear Dynamics of Self-Sustained Supersonic Reaction Waves: Fickett’s Detonation Analogue

Radulescu

Tang

2011

Phys. Rev. Lett.

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The present study investigates the spatio-temporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.

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confidence: 76%

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confidence: 76%

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confidence: 99%

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Nonlinear Dynamics of Self-Sustained Supersonic Reaction Waves: Fickett’s Detonation Analogue

Radulescu

Tang

2011

Phys. Rev. Lett.

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“…Table 1 shows the thermophysical properties of the mixture considered in the present work also used in other investigations (e.g., [16,46,47] [15,[54][55][56]. The activation energy corresponds to the mixtures such as hydrogen-oxygen, acetylene-oxygen, and methane-oxygen at low pressures (see [7,10,15,54,[57][58][59]). …”

Section: Boundary and Initial Conditions And Grid Resolutionmentioning

confidence: 99%

Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

Mahmoudi

Karimi

Deiterding

et al. 2014

Journal of Propulsion and Power

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A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier-Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier-Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier-Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier-Stokes computations, which appear to be fully combusted when large-eddy simulation is employed.

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“…Simulations of one-dimensional detonation dynamics have been the subject of a significant number of studies [46,47,72]. Some interesting new work looks at the issue of bifurcation from pulsation and transition to chaos [73], and the issues associated with elimination of shock generated errors by computing in a shockattached frame [74,75]. There are numerous other papers not listed here that have computed the 1-D pulsation.…”

Section: Comparison With Numerics and Computational Requirementsmentioning

confidence: 99%

State of Detonation Stability Theory and Its Application to Propulsion

Stewart

Kasimov

2006

Journal of Propulsion and Power

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We present an overview of the current state of detonation stability theory and discuss its implications for propulsion. The emphasis of the review is on the exact or asymptotic treatments of detonations, including various asymptotic limits that appear in the literature. The role that instability plays in practical detonation-based propulsion is of primary importance and is largely unexplored, hence we point to possible areas of research both theoretical and numerical, that might help improve our understanding of detonation behavior in propulsion devices. We outline the basic formulation of detonation stability theory that starts from linearized Euler equations, describe the algorithm of solution, and present an example that illustrates typical results.shock velocity vector E = activation energy e = internal energy per unit mass including chemical energy f = degree of overdrive H = enthalpy flux across the shock k = transverse wave number k ! = reaction rate constant M = local Mach number relative to the shock M = mass flux across the shock n = shock-attached frame axial coordinate n = unit normal to the shock P = momentum flux across the shock p = pressure Q = heat release per unit mass q = state vector t = unit tangent vector to the shock U = x component of particle velocity in steady shock frame U 1 = x component of particle velocity in unsteady shock frame u = particle velocity vector in laboratory frame u 1 = x component of particle velocity in laboratory frame u 2 = y component of particle velocity v = specific volume x = laboratory frame axial coordinate y = transverse coordinate = perturbation growth rate = ratio of specific heats = reaction progress variable = density = thermicity = shock displacement from the steady position along x axis ! = reaction rate University. He has published extensively in the areas of combustion theory, asymptotic analysis, theory for multidimensional detonation, detonation stability, continuum mechanics of multiphase flows, phase transformations, modeling of energetic materials, solid rocket motor combustion, advanced level set methods, and computational modeling of reactive flow. He is a past associate editor for SIAM Journal of Applied Mathematics, and was a founding (and still serves as a) board member for Combustion Theory and Modelling. In 1987 he was a founder of the SIAM Conferences on Numerical Combustion that are still held worldwide. He was the concept originator and principal investigator for the University of Illinois Center for Advanced Rockets (CSAR).

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Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

Cited by 97 publications

References 23 publications

Nonlinear Dynamics of Self-Sustained Supersonic Reaction Waves: Fickett’s Detonation Analogue

Nonlinear Dynamics of Self-Sustained Supersonic Reaction Waves: Fickett’s Detonation Analogue

Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

State of Detonation Stability Theory and Its Application to Propulsion

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