Nonlinear Dynamics of Wrinkled Premixed Flames and Related Statistical Problems

Joulin, Guy; Boury, Gaël; Cambray, Pierre; D'Angelo, Yves; Joulain, Karl

doi:10.1007/3-540-44698-2_9

Cited by 3 publications

(5 citation statements)

References 42 publications

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“…Joulin et al (2001) also claim very good agreement with cell shapes from direct numerical simulations, even for realistic O(1) thermal expansions. Bychkov, Kovalev & Liberman (1999) also give a version of the Michelson-Sivashinsky equation valid for O(1) thermal expansions, although Joulin et al (2001) argue that this equation is inadmissible due to missing 'counter'-terms. Bychkov et al (2001) report good agreements with cellular flame speeds from direct numerical simulations, but not with the cell shapes.…”

Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 97%

“…Joulin et al (2001) found that these higher order evolution equations predict that the average cell size grows linearly with time, but that any level of noise in the system (as will be present in any real experiment) cause the average cell size to eventually level off. Joulin et al (2001) also claim very good agreement with cell shapes from direct numerical simulations, even for realistic O(1) thermal expansions. Bychkov, Kovalev & Liberman (1999) also give a version of the Michelson-Sivashinsky equation valid for O(1) thermal expansions, although Joulin et al (2001) argue that this equation is inadmissible due to missing 'counter'-terms.…”

Section: Introductionmentioning

confidence: 97%

“…The Michelson-Sivashinsky equation has been extended to higher (second and third) order in the asymptotic expansion of the thermal expansion (Joulin et al 2001). Joulin et al (2001) found that these higher order evolution equations predict that the average cell size grows linearly with time, but that any level of noise in the system (as will be present in any real experiment) cause the average cell size to eventually level off.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Sharpe

Falle

2006

Combustion Theory and Modelling

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Abstract. Two-dimensional compressible Reactive Navier-Stokes numerical simulations of intrinsic planar, premixed flame instabilities are performed. The initial growth of a sinusoidally perturbed planar flame is first compared with the predictions of a recent exact linear stability analysis, and it is shown the analysis provides a necessary but not sufficient test problem for validating numerical schemes intended for flame simulations. The long-time nonlinear evolution up to the final nonlinear stationary cellular flame is then examined for numerical domains of increasing width. It is shown that for routinely computationally affordable domain widths, the evolution and final state is, in general, entirely dependent on the width of the domain and choice of numerical boundary conditions. It is also shown that the linear analysis has no relevance to the final nonlinear cell size. When both hydrodynamic and thermal-diffusive effects are important, the evolution consists of a number of symmetry breaking cell splitting and re-merging processes which results in a stationary state of a single very asymmetric cell in the domain, a flame shape which is not predicted by weakly nonlinear evolution equations. Resolution studies are performed and it is found that lower numerical resolutions, typical of those used in previous works, do not give even the qualitatively correct solution in wide domains. We also show that the long-time evolution, including whether or not a stationary state is ever achieved, depends on the choice of the numerical boundary conditions at the inflow and outflow boundaries, and on the numerical domain length and flame Mach number for the types of boundary conditions used in some previous works.

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Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Sharpe

Falle

2006

Combustion Theory and Modelling

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“…Since for weak turbulence, the flame acts as a band-pass filter for wave numbers (around K = K n ), a simple uncorrelated white noise would do the job [13,45,46,36]. However, a more realistic turbulent forcing would be both correlated in space and time [29].…”

Section: External Forcingmentioning

confidence: 99%

Assessment of the Evolution Equation Modelling approach for three-dimensional expanding wrinkled premixed flames

Albin

D'Angelo

2012

Combustion and Flame

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. Assessment of the Evolution Equation Modelling approach for threedimensional expanding wrinkled premixed flames. Combustion and Flame, Elsevier, 2012, 159 (5), pp.1932-1948. <10.1016/j.combustflame.2011 AbstractDirect Numerical Simulations (DNS), Evolution Equation Modelling (EEM) and Experimental results from the literature (EXP) are presented and analyzed for an expanding propane/air flame. DNS results are obtained thanks to the in-house finite-difference code HAllegro. Computed (DNS/EEM) and measured (EXP) equivalent radii R P and R S , mean stretch k and consumption velocity S C , as well as sample front shapes, are compared using to the same post-processing methodology. Small perturbations in the EEM input parameters induce comparatively small shifts in the compared results, showing the robustness of the approach. When slightly adapting only one O(1) parameter for the EEM strategy (the effective turbulent forcing amplitude felt by the flame), DNS and EEM show quite fair agreement one with the other and also with EXP, except for one of the experiments at early times. In the context of expanding flames, this validated EEM methodology can constitute a reliable tool to compute realisticly large sized flames.

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Mean cell wavelengths of wrinkled premixed flames in weak gravity fields: Spontaneous evolutions

Boury

Cambray

Joulin

2004

Combustion Theory and Modelling

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Nonlinear Dynamics of Wrinkled Premixed Flames and Related Statistical Problems

Cited by 3 publications

References 42 publications

Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Assessment of the Evolution Equation Modelling approach for three-dimensional expanding wrinkled premixed flames

Mean cell wavelengths of wrinkled premixed flames in weak gravity fields: Spontaneous evolutions

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