Effects of Lewis number on vorticity and enstrophy transport in turbulent premixed flames

Abstract

The effects of Lewis number Le on both vorticity and enstrophy transport within the flame brush have been analysed using direct numerical simulation data of freely propagating statistically planar turbulent premixed flames, representing the thin reaction zone regime of premixed turbulent combustion. In the simulations, Le was ranged from 0.34 to 1.2 by keeping the laminar flame speed, thermal thickness, Damköhler, Karlovitz, and Reynolds numbers unchanged. The enstrophy has been shown to decay significantly from the unburned to the burned gas side of the flame brush in the Le ≈ 1.0 flames. However, a considerable amount of enstrophy generation within the flame brush has been observed for the Le = 0.34 case and a similar qualitative behaviour has been observed in a much smaller extent for the Le = 0.6 case. The vorticity components have been shown to exhibit anisotropic behaviour within the flame brush, and the extent of anisotropy increases with decreasing Le. The baroclinic torque term has been shown to be principally responsible for this anisotropic behaviour. The vortex stretching and viscous dissipation terms have been found to be the leading order contributors to the enstrophy transport for all cases, but the baroclinic torque and the sink term due to dilatation play increasingly important role for flames with decreasing Le. Furthermore, the correlation between the fluctuations of enstrophy and dilatation rate has been shown to play an important role in determining the material derivative of enstrophy based on the mean flow in the case of a low Le.

Numerical investigation of the effect of pressure on heat release rate in iso-octane premixed turbulent flames under conditions relevant to SI engines

“…The assumption of constant TKE should be verified in future high-Re, high-Ka experimental or numerical work. Note that, independent of the forcing, baroclinic torque and dilatation where shown to have a negligible effect on enstrophy transport in similar Le F > 1, high-Ka flames [19,32].…”

Recent Advances in Understanding of Thermal Expansion Effects in Premixed Turbulent Flames

“…Even in sufficiently intense turbulence, a decrease in the Lewis number results in vorticity generation due to a significant increase in the local baroclinic torque (Chakraborty 2014, Chakraborty et al 2016) because faster (slower) diffusion of reactants (heat) into (from) thin, inherently laminar reaction zones stretched by turbulent eddies leads to a local increase in the burning rate, |∇p| and |∇ρ| (if the flamelet structure is resolved). Readers interested in Lewis number effects in premixed turbulent combustion are referred to a review by Lipatnikov & Chomiak (2005).…”

“…Moreover, if σ ≤ 2.5, enstrophy attenuates within a flame brush due to viscous dissipation (Treurniet et al 2006. Additionally, in small-scale intense turbulence, baroclinic torque and dilatation play a less important role when compared to vorticity generation due to vortex stretching and viscous dissipation, and vorticity attenuates within flames (Hamlington et al 2011, Chakraborty et al 2016, with the influence of combustion Surface strain rate (a t ): projection of the rate-of-strain tensor S i j on the plane tangential to the surface Principal strain rate (PSR): eigenvector of the rate-of-strain tensor on the vorticity field mitigated by u /S L (Hamlington et al 2011). Finally, in small-scale, highly intense turbulence, the influence of combustion on the vorticity field is reduced to an increase in ν in hot products (Bobbitt et al 2016).…”

Influence of the Lewis Number on Effective Strain Rates in Weakly Turbulent Premixed Combustion

“…A widely used DNS database (Chakraborty and Klein, 2008;Cant, 2009,2011;Chakraborty and Swaminathan, 2010;Chakraborty and Lipatnikov, 2013;Chakraborty et al, 2014;Gao et al, 2014;Gao et al, 2015;Klein et al, 2016;Chakraborty et al, 2016) of freely propagating statistically planar flames with global Lewis number = 0.34, 0.6, 0.8, 1.0 and 1.2 has been considered for this analysis so that the effects of global Lewis number on the statistical behaviours of the effective strain rates can be analysed in isolation. Several previous theoretical (Sivashinsky, 1977;Clavin and Williams, 1982) and numerical (Ashurst et al, 1988;Haworth and Poinsot, 1992;Rutland and Trouvé, 1993;Trouvé and Poinsot, 1994;Han and Huh, 2008) analyses used simple chemistry and modified Lewis number independently of other parameters in order to analyse the effects of differential diffusion arising from non-unity Lewis number in isolation; the same approach has been adopted in this analysis.…”