On the Hydrodynamic Stability of Flat-burner Flames

Joulin, Guy

doi:10.1080/00102208708947035

Cited by 21 publications

(10 citation statements)

References 22 publications

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“…ensues; notice that it was obtained without having to solve (8). Actually (39) can be shown from (3) to hold whatever N and ν [16], again without solving the pole-equations themselves.…”

Section: Flame Speed From Continuous Pole-densitymentioning

confidence: 93%

“…pertaining to isolated crests via adequate changes of independent variable. Whereas(16) itself basically follows from standard Fourier analysis combined with a lucky re-summation of the series thus obtained(15), it would be interesting to understand why the changes of variable (27) then (56) work so well. Admittedly the integral equation (26) bears some formal resemblance with(7), which guided us to propose the new variable (27); but that introduced in (56) looks more strange to us, and was actually discovered by trial-and-error after the 'resolvent' integral equation(55)is obtained.…”

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confidence: 99%

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Sivashinsky equation for corrugated flames in the large-wrinkle limit

Joulin

Denet

2008

Phys. Rev. E

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Sivashinsky's [Acta Astron. 4, 1177 (1977)] nonlinear integrodifferential equation for the shape of corrugated one-dimensional flames is ultimately reducible to a 2N -body problem, involving the 2N complex poles of the flame slope. Thual, Frisch, and Hénon [J. Phys. (France) 46, 1485 (1985)] derived singular linear integral equations for the pole density in the limit of large steady wrinkles (N>>1) , which they solved exactly for monocoalesced periodic fronts of highest amplitude of wrinkling and approximately otherwise. Here we solve those analytically for isolated crests, next for monocoalesced, then bicoalesced periodic flame patterns, whatever the (large) amplitudes involved. We compare the analytically predicted pole densities and flame shapes to numerical results deduced from the pole-decomposition approach. Good agreement is obtained, even for moderately large Ns . The results are extended to give hints as to the dynamics of supplementary poles. Open problems are evoked.

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“…ensues; notice that it was obtained without having to solve (8). Actually (39) can be shown from (3) to hold whatever N and ν [16], again without solving the pole-equations themselves.…”

Section: Flame Speed From Continuous Pole-densitymentioning

confidence: 93%

mentioning

confidence: 99%

Sivashinsky equation for corrugated flames in the large-wrinkle limit

Joulin

Denet

2008

Phys. Rev. E

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“…(I) which represent steadily propagating, 2n/lkl-periodic cellular flame patterns, including that previously found numerically by McConnaughey (1982) in the limiting case Ikl/l = O. The corresponding values of the instability-induced increase in flame-speed can be found as a function of Iklll in Joulin (1987a). By using the analytical properties of Eq.…”

Section: The Homogeneous Ms Equationmentioning

confidence: 97%

On a Model for the Response of Unstable Premixed Flames to Turbulence

Lin

1988

Combustion Science and Technology

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“…Over the last decades, several seminal studies carrying asymptotic analysis have provided a good understanding of flame instabilities in the linear regime. In particular, the specific role played by each effect has been identified: Darrieus-Landau (DL) [1,2], molecular and mass diffusion [3][4][5][6][7], gravity [3,5,8], viscosity of the gases [5,6], thermal losses [9] and regularization of the flow at finite distance [10].…”

Section: Introductionmentioning

confidence: 99%