On model evolution equations for the whole surface of three-dimensional expanding wrinkled premixed flames

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

“…higher order expansions in α for MS type equations [28,29,30], second order in time equations for transients or acoustics [31,32] non perturbative approaches [33,34], asymptotic expansion based on flame aspect ratio [35], 3D planar equations [36,37,38], equations dealing with non connected or non stellate front topology [39,40,41]. In the context of 3D expanding flames [13,42,43], many of the proposed equations can be seen as different extensions of Michelson-Sivashinsky equation. For reasons specified later on, the chosen asymptotic EE is the one proposed and analysed in [13].…”

“…In the context of 3D expanding flames [13,42,43], many of the proposed equations can be seen as different extensions of Michelson-Sivashinsky equation. For reasons specified later on, the chosen asymptotic EE is the one proposed and analysed in [13]. It reads…”

“…To mimic turbulent flow, and since the EEM (Evolution Equation Modeling) approach does not solve for the flow, a synthetic turbulent forcing u ′ must also be supplied. The aim of the paper is to tentatively assess a chosen EEM strategy for 3D expanding flames (from reference [13]) by comparing its results with present DNS (Direct Numerical Simulations) and available experimental data from the literature.…”

“…The numerical set-up for turbulent wrinkled flames computation is finally presented at the end of the section. The EEM approach, similar to the one from [13], is outlined section 4, as well as the adopted numerical strategy (Exponential Time Differencing Runge-Kutta method, or ETDRK, in the Fourier-Legendre basis) to solve it. The way to mimic external "turbulent" forcing by a Passot-Pouquet spectrum and a proposed equation for the mean flame radius can also be found there.…”

Premixed flames propagating freely in tubes

“…The theoretical analysis of these flames has been successful: nonlinear model equations have been derived, first by Sivashinsky in 1977 [7] and by Frankel in 1990 [8]. Simple solutions of the Sivashinsky equation have been obtained in 1985 by Thual Frisch and Henon [9], and building on this discovery G. Joulin has studied theoretically large scale flame fronts in a number of configurations, spherical flames, oblique flames or flames of overall parabolic shape [10][11][12][13]. Numerical simulations of the Sivashinsky equation have been performed in these configurations, as they are hundred times faster than direct numerical simulations, permitting the study of very large flames [14][15][16][17].…”