A Direct Numerical Simulation analysis of pressure variation in turbulent premixed Bunsen burner flames-part 2: Surface Density Function transport statistics

Abstract

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Effects of Lewis Number on the Evolution of Curvature in Spherically Expanding Turbulent Premixed Flames

“…Using (x T1 , x T2 ) as the local principal axes along the tangential directions on a given c isosurface, the curvature flow stretching term can be expressed as T 3 = −(S 11 κ 1 + S 22 κ 2 ), where S 11 and S 22 are the tangential strain rates along axes x T1 and x T2 , respectively. The mean tangential strain rate a T = S 11 + S 22 assumes positive values throughout the flame front for all flames considered here [43][44][45][46][47][48][49]. A positive magnitude of T 3 is obtained for a combination of cup and saddle concave iso-scalar topologies.…”

“…where v c j = u j + S d n j is the jth component of local propagation velocity of a given c isosurface. The quantity n i v c j,i n j = n i S c ij n j = a c N = a N + ∂S d /∂x N is often referred to as the total or effective normal strain rate [46,48,49,53,56,57], whereas a N = n i S ij n j is the fluid-dynamic normal strain rate and ∂S d /∂x N is an added normal strain rate induced by flame propagation [46,48,49,53,60,61]. The gradient of the flame propagation velocity v c j takes the following form [52,53]: [52,53].…”

“…The role of mean flame curvature [20][21][22]26] on Flame Surface Density (FSD) [20,25] and Scalar Dissipation Rate (SDR) [25,27], which are central to determine the fuel burning rate, has been demonstrated in several previous DNS studies on ignition kernels [11,22] and spherically expanding flames [15,[17][18][19][20][21][22][23][24][25][26][27]. Moreover, LES of spherical flames using the flame wrinkling factor [14,16], FSD [27,29] and κ m is also known to affect the curvature and propagation terms in the Surface Density Function (SDF = |∇c| with c being the reaction progress variable) transport equation [43][44][45][46][47][48][49][50], which in turn influence the evolutions of FSD and SDR [27,[29][30][31]50]. It has been demonstrated in several previous analyses [27,39,44,47] that the curvature dependences of displacement speed, temperature and SDF are influenced by the characteristic Lewis number Le, and thus it is expected that the curvature evolution ...…”

Evolution of Flame Curvature in Turbulent Premixed Bunsen Flames at Different Pressure Levels

“…Analytical studies [4][5][6][7][8] indicate that flame curvature significantly affects flame propagation in perturbed laminar premixed flames and plays a key role in thermo-diffusive and hydrodynamic instabilities. The flame curvature has been shown to affect local displacement speed and the magnitude of reactive scalar gradient [19,24,[31][32][33][34][35] in turbulent premixed flames. Moreover, the differential diffusion of heat and species, arising from non-unity Lewis number, has been found to affect the curvature dependences of displacement speed [18,25,31], consumption speed [36,37] and reactive scalar gradient [24].…”

“…Previous analyses [34,35] indicate that the mean behaviours of dilatation rate and tangential strain rate in Bunsen flames are affected by the occurrence of the DL instability at high pressure, and these strain rate statistics may have a significant role in the curvature evolution at elevated pressure. A DNS database of five different methane-air turbulent premixed Bunsen burner flames has been considered to analyse these issues.…”