Vorticity budgets in premixed combusting turbulent flows at different Lewis numbers

Abstract

A direct numerical simulations database of statistically planar turbulent premixed flames using a simple Arrhenius type irreversible chemistry for different values of global Lewis numbers, Le, (0.34, 0.60, 0.80, 1.00, 1.20) has been examined to analyze the effects of Le on vorticity transport within the flame. To meet this objective, a general enstrophy conservation equation has been considered, which distinctly describes contributions from vortex-stretching, destruction by volumetric dilatation rates, baroclinic and viscous force torques, viscous transport, and dissipation. The average statistical behavior of the various contributions conditioned upon the value of the reaction progress variable, c, has been analyzed in the preheat and reacting regions of the flame. The mean values of enstrophy monotonically decays with c from fresh reactants toward hot products for Le equal to 0.8, 1.0, and 1.2; vortex-stretching and viscous dissipation are the leading contributors, while the remaining contributions are slightly smaller although non-negligible. By contrast, the mean value of enstrophy decreases from the leading edge before increasing up to the trailing edge of the flame; in these cases, the mean value of baroclinic torque is significantly greater than the other contributions in most of the preheat and reacting regions; vortex-stretching, destruction by volumetric dilatation rates and viscous transport, and dissipation remain comparable over most of the flame. An explanation for the significant qualitative and quantitative differences in the enstrophy transport, taking place for Le between 0.6 and 0.8 for the given turbulence intensity, is sought in terms of the alignments of vorticity and the gradients of density, pressure, temperature, and reaction progress variable. The transport statistics of the enstrophies of the vorticity vector components tangential and normal to iso-scalar surfaces, c(x, t) = constant, provide further insight into the mechanisms of the differences in the enstrophy transport in response to the changes in the global Lewis number.

Statistical behaviors of conditioned two-point second-order structure functions in turbulent premixed flames in different combustion regimes

“…cases D-F) is governed by vortexstretching, dilatation and molecular dissipation terms. [14][15][16][17]74,75 In these cases, enstrophy drops monotonically from the leading edge and the components 1 , 2 and 3 behave in a similar manner within the flame. [14][15][16] This further suggests that the effects of anisotropy can be significant for flames in the wrinkled flamelets and corrugated flamelets regime but these effects progressively weaken in the thin reaction zones regime with increasing Karlovitz number.…”

“…(∇ × ∇ )/ 2 ) plays a key role in the vorticity ⃗ ⃗⃗ = ∇ × ⃗⃗ transport and enhances 2 and 3 . [13][14][15][16][17]74,75 By contrast, the vorticity transport in cases with ′ ⁄ ≫ 1 (e.g. cases D-F) is governed by vortexstretching, dilatation and molecular dissipation terms.…”

“…[1][2][3][4] To date, limited investigations have been directed to the analysis of correlation functions and spectra [5][6][7][8] or structure functions [9][10][11] in turbulent reacting flows. It is well-known that the effects of heat release on turbulent fluid motion significantly modify both the vorticity or/and enstrophy [12][13][14][15][16][17][18][19] and turbulent kinetic energy [20][21][22][23][24] transports in premixed turbulent flames, e.g. through the baroclinic torque and dilatation rate arising from thermal expansion.…”

“…through the baroclinic torque and dilatation rate arising from thermal expansion. Furthermore, it has been argued [25][26][27][28] and shown both experimentally [29][30][31][32] and computationally [12][13][14][15][16][17][18][19][20][21][22][23][24] that significant amplification of velocity fluctuations known as flame-generated turbulence 25,28 can occur in flames under certain conditions. There are other manifestations of the heatrelease effects [32][33][34] and interested readers are referred to Refs.…”

Transport equations for reaction rate in laminar and turbulent premixed flames characterized by non-unity Lewis number

“…Because DNS data analyzed in the following were discussed in details in various papers, e.g., see Refs. [29][30][31][32][33] and references quoted therein, we will restrict ourselves to a brief summary of the simulations.…”