Asymptotic laws of behavior of detonation waves

Левин, В. А.; Chernyi, G. G.

doi:10.1016/0021-8928(67)90026-3

Cited by 17 publications

(14 citation statements)

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“…It was demonstrated in [5] that the transition to the Chapman-Jouguet regime in flows with a cylindrical or spherical detonation wave occurs at a finite distance, in contrast to flows with plane waves. An overdriven wave passing to the Chapman-Jouguet regime has a third-order tangency.…”

Section: Vorticity Behind a Steady-state Detonation Wave For Flows Wimentioning

confidence: 97%

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

Левин

Skopina

2007

J Appl Mech Tech Phy

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The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented.Formulas for components of vorticity behind a steady-state shock wave for flows with constant parameters in the general case were obtained in [1] under the assumption of an infinite shock-wave intensity. Formulas for components of vorticity behind a shock wave of an arbitrary intensity for a uniform incoming flow were derived in [2,3]. The vorticity behind a curvilinear steady-state detonation wave in a supersonic vortex flow is obtained in the present paper. Calculation of Vorticity behind a Steady-State Detonation Wave.Let there be a detonation wave in a steady-state supersonic axisymmetric vortex flow of a combustible gas. The detonation wave is considered as a strong discontinuity surface on which combustion of a unit mass of the gas releases an amount of heat Q, which may be a variable function. For Q = 0, there is a usual shock wave. In this case, the gas motion is described by the following system of equations:Here u(x, r), v(x, r), and w(x, r) are the components of velocity V in a cylindrical coordinate system (x, r, ϕ) and ρ and p are the density and pressure of the gas, respectively. The vorticity 2ω = rot V has the components 2ω r = − ∂w ∂x , 2ω x = 1 r ∂rw ∂r , 2ω ϕ = ∂v ∂x − ∂u ∂r .(2)

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Section: Vorticity Behind a Steady-state Detonation Wave For Flows Wimentioning

confidence: 97%

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

Левин

Skopina

2007

J Appl Mech Tech Phy

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“…An energy efficiency is now defined as 1e = £o reg /£o calc (6) Here £ 0reg follows directly from a mathematical regression to experimental data; while £ 0calc is derived from knowledge of the detonator-Detasheet combination. Energy efficiencies have been determined for a range of energies for which experimental blast wave data was taken.…”

Section: Methodsmentioning

confidence: 99%

“…If Q is the combustion energy per unit mass of fuel oxidizer mixture, then r* = (v£oAr v ePi) 1/v (1) where v = 1, 2, 3 and a v -2, 2n, 4xc, for planar, cylindrical, and spherical waves; where this definition is strictly valid for the case of a negligibly small shock and reaction zone separation. When the blast radius r s <^ r*, the blast energy E 0 is dominant and asymptotic analysis 6 shows that the flow then can be described by the self-similar strong blast wave solution of Sedov 7 and Taylor. 8 When r s ^> r*, combustion dominates and the blast wave decays to a constant velocity Chapman-Jouguet (C-J) detonation, provided combustion is intantaneous at the shock front.…”

Section: Introductionmentioning

confidence: 97%

Blast Initiation and Propagation of Cylindrical Detonations in MAPP-Air Mixtures

Fry

Nicholls

1974

AIAA Journal

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An experimental investigation of the initiation, transition and quasi-steady propagation of blast initiated cylindrical detonations in Methyl Acetylene, Propane, Prodadiene (MAPP)-air mixtures is described. A sectored shock tube was employed which was originally designed to allow study of cylindrical shock, and homogeneous and heterogeneous detonation waves. Cylindrical blast waves were generated by firing of controlled amounts of a condensed explosive at the apex of the sector. Experimental data served to suggest the existence of three wave propagation regimes: subcritical energy regime, where decoupling of shock and reaction zone results in a reacting blast wave-type decay; the critical energy regime, where decoupling occurs but is followed by the re-establishment of a sub-Chapman-Jouguet condition, with an asymptotic strengthening to the C J state; and supercritical energy regime, where the initially overdriven detonation decays asymptotically to its CJ state. Threshold energy levels delineating the subcritical to critical energy regimes were established for a wide range of MAPP-air mixtures. Lean and rich limits for steady propagating detonation waves were also established. Comparisons made with the work of others reveal that these limits do not suffer from scale effects. The detonation velocity, when attained, displayed a definite dependence on blast wave energy with the higher energy runs giving reasonable agreement with theory. The measured transition distances from blast to detonation wave, nondimensionalized by the blast wave explosion length, compared satisfactorily with theoretical predictions.

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“…-{li = 0 at ~ = 1. Later studies by Levin and Cheryni (1967) and of the asymptotic decay of diverging detonation had revealed the possibility of the approach to the C-J condition occurring at a finite radius instead of at infinite radius. For planar waves where j = 0 the numerators vanishes and such a singularity does not exist.…”

Section: Nonmentioning

confidence: 99%

Combustion in High-Speed Flows

Buckmaster¹,

Jackson²,

Kumar³

1994

ICASE/LaRC Interdisciplinary Series in Science and Engineering

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The focus of the second workshop was directed towards the development, analysis, and application of basic models in high speed propulsion of particular interest to NASA. The exploration of a dual approach combining asymptotic and numerical methods for the analysis of the models was particularly encouraged. The objectives of this workshop were i) the genesis of models that would capture or reflect the basic pllysical phenomena in SCRAMJETs and/or oblique detonation-wave engines (ODWE), and ii) the stimulation of a greater interaction between NASA experimental research community and the academic community.The lead paper by D. Bushnell on the status and issues of high speed propulsion relevant to both the SCRAMJET and the ODWE parallels his keynote address which set the stage of the workshop. Following the lead paper were five technical sessions with titles and chairs: Experiments (C. Rogers), Reacting Free Shear Layers (C. E. Grosch), Detonations (A. K. Kapila), Ignition and Structure (J. Buckmaster), and Unsteady Behaviour ('1'. L. Jackson).The session chairs were responsible for the planning of their session. In each of the sessions formal discussion papers were given by experts followed by a general discussion involving the participants. This volume contains the manuscripts presented in each session. In addition, a panel discussion was held on the last day, chaired by J. Buckmaster. The panel members were

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Asymptotic laws of behavior of detonation waves

Cited by 17 publications

References 0 publications

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

Blast Initiation and Propagation of Cylindrical Detonations in MAPP-Air Mixtures

Combustion in High-Speed Flows

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