Dynamic Parameters of Gaseous Detonations

Lee, J H S

doi:10.1146/annurev.fl.16.010184.001523

Cited by 462 publications

(99 citation statements)

References 25 publications

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“…Nevertheless, the concept of a cell size characteristic to a given mixture (and initial state) is a very useful one, due to several empirical observations of phenomena which appear to scale with this characteristic size. These correlations include the minimum values of (i) the tube diameter in which the detonation can propagate in narrow, smooth walled tubes, (ii) the critical tube diameter for a detonation to survive diffraction out of the end of the tube into open space, (iii) the critical tube diameter for propagation in porous walled tubes, and (iv) the source energy required for the establishment of a detonation from direct (blast) initiation (see [2,[4][5][6] for reviews). The correlations obtained differ between regular and irregular mixtures.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear cellular dynamics of the idealized detonation model: Regular cells

Sharpe

Quirk

2007

Combustion Theory and Modelling

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High-resolution numerical simulations of cellular detonations are performed using a parallelized adaptive grid solver, in the case where the channel width is very wide. In particular, the nonlinear response of a weakly unstable ZND detonation to two-dimensional perturbations is studied in the context of the idealized one-step chemistry model. For random perturbations, cells appear with a characteristic size in good agreement with that corresponding to the maximum growth rate from a linear stability analysis. However, the cells then grow and equilibrate at a larger size. It is also shown that the linear analysis predicts well the ratio of cell lengths to cell widths of the fully developed cells. The evolutionary dynamics of the growth are nonetheless quite slow, in that the detonation needs to run of the order of 1000 reaction lengths before the final size and equilibrium state is reached. For sinusoidal perturbations, it is found that there is a large band of wavelengths/cell sizes which can propagate over very long distances (∼1000 reaction lengths). By perturbing the fully developed cells of each wavelength, it is found that smaller cells in this range are unstable to symmetry breaking, which again results in cellular growth to a larger final size. However, a range of larger cell sizes appear to be nonlinearly stable. As a result it is found that the final cell size of the model is non-unique, even for such a weakly unstable, regular cell case. Indeed, in the case studied, the equilibrium cell size varies by 100% with different initial conditions. Numerical dependencies of the cellular dynamics are also examined.

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Section: Introductionmentioning

confidence: 99%

Nonlinear cellular dynamics of the idealized detonation model: Regular cells

Sharpe

Quirk

2007

Combustion Theory and Modelling

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“…In experiments carried out at McGill with very lean mixtures near the flammability limit, flames were observed to propagate for some distance and then self-extinguish (Lee et al, 1984). This type of behavior was found to be typical for mixtures with very low burning velocities, such as methane-air.…”

Section: Resultsmentioning

confidence: 90%

“…( 1 988) and Desbordes et al ( 1 993) demonstrated that heavy diluting of an acetylene-oxygen mixture with a monatomic inert gas, such as argon or helium, resulted in the failure of the classical dynamic detonation parameters linking the critical tube and critical energy with the detonation cell size (Lee, 1984). These types of mixtures are said to produce more stable detonation waves.…”

Section: Influence Of Detonation Stabilitymentioning

confidence: 99%

The effect of initial temperature on flame acceleration and deflagration-to-detonation transition phenomenon

Ciccarelli¹,

Boccio²,

Ginsberg³

et al. 1998

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“…The intersection points between the transverse waves and the leading shock are called triple points. The tracks of these triple points that are regions of high vorticity, generate diamond shaped cellular regions on a channel wall coated with soot, that are called detonation cells (Strehlow, 1969 and1970;Lee, 1984;Austin, 2003). The size and degree of regularity of these cellular structures depend on the composition of the gaseous mixture and its initial conditions (Shepherd, 1986).…”

Section: Introductionmentioning

confidence: 99%

“…Also, the acoustic chemically reacting field behind the leading shock of a weakly unstable detonation front is more amenable to linear analysis. There are several empirical observations that appear to scale with the detonation cell sizes (Lee, 1984;Gamezo et al, 1999), making it an important feature of detonation waves. This has made understanding the cellular formation dynamics and prediction of the cell size dependence on the fuel mixture and initial conditions a major objective of theoretical and numerical studies.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Cellular Structure of Weak Detonation and Evaluation of Linear Stability Analysis Predictions

Barkhordari

Farshchi

2013

Engineering Applications of Computational Fluid Mechanics

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This paper investigates the development of cellular structures created by the propagation of a detonation wave in a gaseous mixture. Two dimensional reactive Euler equations with an idealized one-step Arrhenius type reaction model are solved using the PPM scheme coupled with the exact Riemann solver. The numerical flow solver simulates the evolution process of regular cellular structures of a weakly unstable detonation wave. The cellular structures are generated by two-dimensional sinusoidal perturbations imposed on a ZND detonation wave. The initial sinusoidal perturbation wavelengths are predicted from linear stability analysis. The objective of these calculations is to examine the validity of the linear stability analysis predictions on the final cell sizes of a weakly unstable detonation. We found that for a given mixture, there is not just a single detonation cell size related to the wavelength with maximum growth rate. Instead, depending on the initial perturbation wavelength, the cellular dynamics reaches a final equilibrium state with the corresponding final cell size that belongs to a specific band of unstable wavelengths predicted by the linear stability analysis. Indeed, it is not the magnitude of the perturbation growth rate, but the magnitude of its rate of change with respect to the wavelength that predicts the domain of this specific band and corresponding final cell sizes.

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Dynamic Parameters of Gaseous Detonations

Cited by 462 publications

References 25 publications

Nonlinear cellular dynamics of the idealized detonation model: Regular cells

Nonlinear cellular dynamics of the idealized detonation model: Regular cells

The effect of initial temperature on flame acceleration and deflagration-to-detonation transition phenomenon

Numerical Simulation of Cellular Structure of Weak Detonation and Evaluation of Linear Stability Analysis Predictions

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