Applying nonlinear dynamic theory to one-dimensional pulsating detonations

Abderrahmane, Hamid Ait; Paquet, Frederick; Ng, Hoi Dick

doi:10.1080/13647830.2010.535566

Cited by 11 publications

(10 citation statements)

References 25 publications

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“…Limit cycle: the shock front dynamics In order to study the shock dynamics, it is useful to plot the phase plane d(p s /p N )/dt s versus p s /p N , as in Ng et al (2005) and Abderrahmane et al (2011). The numerical results shown in figure 7 reveal that, for large tube diameters and with E a = 22 RT 0 , the mean post-shock pressure stabilizes to a constant value after an initial transient.…”

Section: Detonation-velocity Deficitmentioning

confidence: 93%

“…Following previous studies (see for example Zhang & Lee 1994, Ng et al 2005and Abderrahmane et al 2011, the dimensionless parameters are taken as γ = 1.2 and q/RT 0 = 50 so that comparisons can be made with the previously published results. Three test cases are considered with different E a .…”

Section: Problem Setupmentioning

confidence: 99%

“…As E a increases, several modes of instabilities appear. Since the dynamics of such unstable detonations cannot be completely described by the linear analysis, Ng et al (2005) and Abderrahmane, Paquet & Ng (2011) have shown that nonlinear concepts, such as limit cycles, the power spectral density and the bifurcation diagram can help to assess the main properties of the shock dynamics of gaseous detonations. A coarse bifurcation diagram can be developed, based on the local maximum oscillation amplitude of the detonation velocity as a function of E a .…”

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confidence: 99%

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Mean structure of one-dimensional unstable detonations with friction

2014

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WOS:000332844200022International audienceThis investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge-Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies

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Section: Detonation-velocity Deficitmentioning

confidence: 93%

Section: Problem Setupmentioning

confidence: 99%

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confidence: 99%

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Mean structure of one-dimensional unstable detonations with friction

2014

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“…In the past, several authors have studied the dynamics of ideal one-dimensional detonations using a single-step Arrhenius model [3][4][5][6] by numerical means. These studies indicated that the activation energy (E a ) is the main parameter which controls the onset of the longitudinal instability for constant heat of reaction and specific heat ratio.…”

Section: Introductionmentioning

confidence: 99%

Computational study of non-ideal and mildly-unstable detonation waves

2015

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“…In recent years, it has been applied to the temporal behavior of the unstable combustion state observed not only in experiments (e.g., a thermal pulse combustor, 10 a ducted premixed combustor, [11][12][13] a spark ignition engine, 14,15 and swirling premixed flames 16 ) but also in the numerical solutions of sets of nonlinear differential equations derived from first principles (e.g., a thermal pulse combustor, 17 detonation, 18,19 and a spark ignition engine 20 ). In previous studies 6,[11][12][13] relevant to thermoacoustic combustion oscillations, the Grassberger-Procaccia (GP) algorithm, 21 used to obtain the correlation dimension as a class of the fractal dimension from an observational time series, was used to characterize the nonlinear nature.…”

Section: Introductionmentioning

confidence: 99%

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor

Gotoda

Amano

Miyano

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

110

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Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy J. Chem. Phys. 137, 22A550 (2012) Rectified Brownian transport in corrugated channels: Fractional Brownian motion and Lévy flights J. Chem. Phys. 137, 174101 (2012) Brownian dynamics simulations with hard-body interactions: Spherical particles J. Chem. Phys. 137, 164108 (2012) Noncolliding Brownian motion with drift and time-dependent Stieltjes-Wigert determinantal point process J. Math. Phys. 53, 103305 (2012) Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation J. Chem. Phys. 137, 144107 (2012) Additional information on Chaos We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout. An understanding of the physical process underlying combustion instability leading to lean blowout is of current interest in modern combustion physics as well as in nonlinear science. In this study, the characterization of complexities in combustion instability in a lean premixed gas-turbine combustor, which is of fundamental and practical importance for combustion systems, has been carried out from the viewpoint of nonlinear dynamics, focusing on characterizing the dynamic behavior of combustion instability close to lean blowout. The use of nonlinear time series analysis involving permutation entropy in combination with a surrogate data method, multifractal analysis, and nonlinear forecasting based on a radial basis function network allows us to capture the signature of self-affine structures and chaotic oscillations in combustion instability. Our results have not been reported in previous papers on combustion phenomena, in particular, thermoacoustic combustion oscillations.

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Applying nonlinear dynamic theory to one-dimensional pulsating detonations

Cited by 11 publications

References 25 publications

Mean structure of one-dimensional unstable detonations with friction

Mean structure of one-dimensional unstable detonations with friction

Computational study of non-ideal and mildly-unstable detonation waves

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor

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