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.
Highlights
The statistical behaviour of the transport of vorticity and enstrophy is of fundamental importance in the analysis of turbulent fluid motion.[1,2,3] The presence of heat release, density variation, and flame normal acceleration in turbulent flames significantly affects the underlying turbulent flow structure and is manifested in flame-generated turbulence[4] and counter-gradient scalar transport[5,6] to name a few
It was further shown by Hamlington et al.[11] that vorticity magnitude decays significantly in the burned gas across the flame brush, whereas Treurniet et al.[12] demonstrated that vorticity magnitude increases in the burned gas for the flames with high density ratio
As the current analysis focuses on the effects of characteristic Lewis number Le on vorticity and enstrophy transport in isolation, a simple one-step chemistry has been used for the purpose of computational economy following several previous analyses.[44,45,46,47,48,49,50,51,52]
Summary
The statistical behaviour of the transport of vorticity and enstrophy is of fundamental importance in the analysis of turbulent fluid motion.[1,2,3] The presence of heat release, density variation, and flame normal acceleration in turbulent flames significantly affects the underlying turbulent flow structure and is manifested in flame-generated turbulence[4] and counter-gradient scalar transport[5,6] to name a few. The significant effects of characteristic Lewis number Le on various aspects of premixed combustion (e.g., thermo-diffusive instability of laminar flames, burning rate, scalar gradient statistics, and combustion modelling) have been addressed analytically,[33,34,35,36] experimentally,[37,38,39,40,41,42,43] and numerically.[18,44,45,46,47,48,49,50,51,52,53] Various concepts, which have been developed in order to explain such effects in turbulent flames, are reviewed elsewhere.[54,55] the influences of Le on vorticity ω⃗ and enstrophy Ω transport are yet to be analysed in detail in the existing literature In this respect, the main objectives of the present analysis are as follows.
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