Theoretical Description of Direct Initiation of Detonation for One-Step Chemistry

Dold, John W.; Kapila, A. K.; Short, Mark

doi:10.1007/978-94-011-3548-1_5

Cited by 12 publications

(18 citation statements)

References 8 publications

(18 reference statements)

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“…Indeed, if at the initial time, there are no gas-dynamic perturbations in the medium, then z (1) = 0, z (1) ξ = 0, and c 0 p 0ξ > 0 (is determined only by the initial conditions) and the last term on the left side of the third equation (11) far exceeds the remaining terms related to the spatial derivatives. Conversely, once the moment of shock-wave formation is approached, the gradient of the gas-dynamic perturbations tends to infinity and the quantity c 0 p 0ξ > 0 is bounded (determined only by the initial conditions) and gas-dynamic nonlinearity plays the major role.…”

Section: Equations Of Gas Dynamics For Quantities Of the First Order mentioning

confidence: 99%

“…Differentiating the last equation of system (11) with respect to ξ, substituting p (1) ξ from the second equation of system (11), ignoring terms of the form ∂ ∂ξ ∂z 0 ∂p p (1) by virtue of (12) and the term u τ compared to u ξτ , because u ξτ → ∞ as the moment of shockwave formation is approached, we obtain…”

Section: Transport Equation For Gas-dynamic Perturbations Behind Zel'mentioning

confidence: 99%

“…Soft detonation initiation has been the subject of many experimental [5][6][7] and theoretical [4,[8][9][10][11][12][13][14] studies. In the papers cited, it has been shown that soft detonation initiation is a complex process including several stages [14]: the propagation of a supersonic attenuating combustion front without shock waves, the forma- 1 Kurchatov Institute, Moscow 123182; zaev@8ka.mipt.ru.…”

Section: Introductionmentioning

confidence: 99%

“…In most previous theoretical studies, the main method of research was numerical solution of the complete system of Eulerian equations of gas dynamics for a simple one-stage reaction [4,9,10,14] or a combination of asymptotic and numerical methods for the same model of reactive gas dynamics [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…Theoretical studies [11][12][13][14] have employed an asymptotic approach to solve simplified equations of gas dynamics, with the reciprocal of the dimensionless activation energy being the small parameter. It has been assumed that the gas-dynamic part of the equations is linear (acoustic approximation) and that nonlinearity is related to chemical reactions whose rate is exponentially dependent on temperature.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Transport equation for gas-dynamic perturbations in a spatially nonuniform self-igniting medium

Zaev

Kirillov

2008

Combust Explos Shock Waves

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An approach is developed to describe the formation and propagation of small gasdynamic perturbations in a spatially nonuniform self-igniting medium for arbitrary chemical-reaction kinetics. An asymptotic equation describing the variation in the amplitude of the gas-dynamic perturbation along the characteristic is derived, and the conditions of its applicability are defined. Zel'dovich's spontaneous flame wave is shown to be a natural zeroth approximation to the solution of the equations of gas dynamics. A method is proposed to determine the point in space at which a shock wave is formed.

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Section: Equations Of Gas Dynamics For Quantities Of the First Order mentioning

confidence: 99%

Section: Transport Equation For Gas-dynamic Perturbations Behind Zel'mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Transport equation for gas-dynamic perturbations in a spatially nonuniform self-igniting medium

Zaev

Kirillov

2008

Combust Explos Shock Waves

View full text Add to dashboard Buy / Rent full text

show abstract

Theoretical Description of Direct Initiation of Detonation for One-Step Chemistry

Cited by 12 publications

References 8 publications

Transport equation for gas-dynamic perturbations in a spatially nonuniform self-igniting medium

Transport equation for gas-dynamic perturbations in a spatially nonuniform self-igniting medium

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