Instability threshold of gaseous detonations

Daou, Rémi; Clavin, Paul

doi:10.1017/s0022112003004038

Cited by 24 publications

(23 citation statements)

References 14 publications

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“…The critical heat release is much smaller in the latter case than in the former, for which the density jump across the lead shock may be as large as in ordinary detonations. The perturbation analyses in both cases are quite different from that of Short & Stewart [37], who do not include the Newtonian approximation, this approximation being essential to reveal in a clear manner the main physical mechanisms of real detonations within the context of small heat release; see [8,36] for more detailed discussions.…”

Section: (A) Methodsmentioning

confidence: 83%

“…Two opposite limits are of particular interest in this regard, namely strongly overdriven regimes and near-CJ regimes. For strongly overdriven regimes, the instability threshold appears for small heat release compared with the thermal enthalpy of the gas at the Neumann state (post-shock gas) [35,36]. In near-CJ regimes, the bifurcation appears for small heat release compared with the thermal enthalpy of the initial state [8].…”

Section: (A) Methodsmentioning

confidence: 99%

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Analytical studies of the dynamics of gaseous detonations

Clavin

Williams

2012

Phil. Trans. R. Soc. A.

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The dynamics of gaseous detonation is revisited on the basis of analytical studies. Problems of initiation, quenching, pulsation and cellular structures are addressed. The objective is to improve our physical understanding of the development, stability and structure of gaseous detonations. New insights that have been gained from analytical investigations are emphasized. Specific problems discussed are the direct initiation of detonations in spherical geometry, the spontaneous soft initiation and quenching of detonations in a temperature gradient, the stability threshold and dynamics of galloping detonations, and the multi-dimensional instability threshold and cellular structures of both overdriven and near-Chapman-Jouguet detonations. It will be seen that, although there have been many accomplishments, some outstanding questions remain.

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Section: (A) Methodsmentioning

confidence: 83%

Section: (A) Methodsmentioning

confidence: 99%

Analytical studies of the dynamics of gaseous detonations

Clavin

Williams

2012

Phil. Trans. R. Soc. A.

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“…Fluids 25, 076105 (2013) shock-wave propagation in ideal gases, but common planar detonations, however, are known to be strongly unstable, [21][22][23][24][25] so that steady planar fronts are seldom observed in practice. [26][27][28] A notable exception occurs for sufficiently overdriven detonations with propagation Mach numbers M much larger than the Chapman-Jouguet value M cj (i.e., at large overdrive factors (M/M cj ) 2 1).…”

Section: -3mentioning

confidence: 99%

“…Different distinguished limits involving different combinations of the controlling parameters have been considered in previous stability analyses. 23,24 The quantitative information on stability boundaries obtained in these analyses for a one-step Arrhenius reaction 23,24 is however specific to the chemistry model and, as such, cannot be used to assess in general the stability of a planar detonation for a given set of values of γ , M, and q (e.g., the results can be expected to be different when the heat release is controlled instead by a chain-branching/chain-terminating reaction mechanism). Nevertheless, the general conclusion that larger values of M and smaller values of q, both resulting in larger overdrives, always tend to favor stability is applicable regardless of the chemistry model.…”

Section: Formulation Of the Perturbation Problem For Interactionsmentioning

confidence: 99%

Theory of interactions of thin strong detonations with turbulent gases

2013

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We present the exact small-amplitude linear Laplace-transform theory describing the propagation of an initially planar detonation front through a gaseous mixture with nonuniform density perturbations, complementing earlier normal-mode results for nonuniform velocity perturbations. The investigation considers the fast-reaction limit in which the detonation thickness is much smaller than the size of the density perturbations, so that the detonation can be treated as an infinitesimally thin front with associated jump conditions given by the Rankine-Hugoniot equations. The analytical development gives the exact transient evolution of the detonation front and the associated disturbance patterns generated behind for a single-mode density field, including explicit expressions for the distributions of density, pressure, and velocity. The results are then used in a Fourier analysis of the detonation interaction with two-dimensional and three-dimensional isotropic density fields to provide integral formulas for the kinetic energy, enstrophy, and density amplification. Dependencies of the solution on the heat-release parameter and propagation Mach number are discussed, along with differences and similarities with results of previous analyses for non-reacting shock waves.

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“…Asymptotic analyses by Clavin and He and coworkers [66][67][68][69][70][71] mainly deal with combined limits of large overdrive, weak heat release, the Newtonian limit, and strong rate sensitivity (these authors argue against studying the basic one-step Arrhenius model and instead consider general forms). For the Newtonian limit, the acoustics is simplified and the pressure is nearly constant, hence the limit is also known as the isobaric limit.…”

Section: Large Activation Energy Asymptoticsmentioning

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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Instability threshold of gaseous detonations

Cited by 24 publications

References 14 publications

Analytical studies of the dynamics of gaseous detonations

Analytical studies of the dynamics of gaseous detonations

Theory of interactions of thin strong detonations with turbulent gases

State of Detonation Stability Theory and Its Application to Propulsion

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