Interplay of Darrieus-Landau instability and weak turbulence in premixed flame propagation

Abstract

In this study we investigate, both numerically and experimentally, the interplay between the intrinsic Darrieus-Landau (DL) or hydrodynamic instability of a premixed flame and the moderately turbulent flow field in which the flame propagates. The objective is threefold: to establish, unambiguously, through a suitably defined marker, the presence or absence of DL-induced effects on the turbulent flame, to quantify the DL effects on the flame propagation and morphology and, finally, to asses whether such effects are mitigated or suppressed as the turbulence intensity is increased. The numerical simulations are based on a deficient reactant model which lends itself to a wealth of results from asymptotic theory, such as the determination of stability limits. The skewness of the flame curvature probability density function is identified as an unambiguous morphological marker for the presence or absence of DL effects in a turbulent environment. In addition, the turbulent propagation speed is shown to exhibit a distinct dual behavior whereby it is noticeably enhanced in the presence of DL instability while it is unchanged otherwise. Furthermore, increasing the turbulence intensity is found to be mitigating with respect to DL-induced effects such as the mentioned dual behavior which disappears at higher intensities. Experimental propane and/or air Bunsen flames are also investigated, utilizing two distinct diameters, respectively, above and below the estimated DL cutoff wavelength. Curvature skewness is still clearly observed to act as a marker for DL instability while the turbulent propagation speed is concurrently enhanced in the presence of the instability.

Analysis of flame curvature evolution in a turbulent premixed bluff body burner

“…Moreover, curvature contributions can dominate diffusion rates and displacement speed for ignition kernels of small radii [44,45] and determine their probability of survival. Furthermore, the flame curvature is intrinsically related to the analysis of hydrodynamic and thermos-diffusive instabilities in premixed flames [1][2][3][46][47][48], and the skewness of curvature probability density function can be related to the Darrieus-Landau instability in premixed turbulent flames [48]. been compared to 3D curvature PDFs using DNS data [27,55] and it has been found that 2D statistics compare well with results of planar experimental techniques, but while 2D PDFs are symmetric with nearly zero average mean curvature, 3D PDFs display positive skewness with negative average mean curvature.…”

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

“…The point is that the vast majority of models of the influence of turbulence on premixed combustion (i) deal with single-step chemistry and (ii) neglect density variations, with a few exceptions [13][14][15][16]. Accordingly, to explore foundations of such models, heavy DNS with complex chemistry are not necessary, but extension of the range of studied conditions appears to be of paramount importance.…”

Surface-averaged quantities in turbulent reacting flows and relevant evolution equations

“…Equation (6) shows that the difference in area-weighted and unweighted values can vanish either in an unlikely case of zero correlation between φ and |∇c| or in the trivial case of zero fluctuations, i.e., φ 2 1/2 Using these inequalities and applying Eq. (5) to φ = 1, we arrive at 1 |∇c|…”

“…A problem of the influence of turbulence on reaction waves is straightforwardly relevant to various phenomena ranging from reactions in aqueous solution [1], combustion [2][3][4][5][6], and deflagration-to-detonation transition [7,8] under terrestrial conditions to evolution of thermonuclear type Ia supernovae [9,10] in the Universe. This nonlinear and multiscale problem attracted much attention since the 1940's when significant acceleration of flame propagation by turbulence was found.…”