Effects of Lewis Number on Scalar Variance Transport in Premixed Flames

Abstract

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le = 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study.

Dynamic Closure of Scalar Dissipation Rate for Large Eddy Simulations of Turbulent Premixed Combustion: A Direct Numerical Simulations Analysis

“…Re t = ρ 0 u l/μ 0 , where ρ 0 and μ 0 are the unburned gas density and viscosity respectively) were not addressed. Chakraborty and Swaminathan [10] extended the RANS-K model [22] for non-unity Lewis number flames and obtained good agreement with DNS data even for small values of Damköhler number (i.e. Da < 1).…”

“…The relation <ẇ >= 2 < ρ>Ň c /(2c m − 1) (where < Q > andQ =< ρQ > / < ρ > are the Reynolds averaged and Favre averaged values of a general quantity Q respectively) can be derived based on the balance of the reaction rate and scalar dissipation rate contributions to the scalar variance transport in the context of RANS for Da >>1.0 flames where the pdf of c shows high probability of finding both unburned and completely burned gases, and small probability of finding burning mixtures [5]. Chakraborty and Cant [9] demonstrated based on scaling arguments [10] that <ẇ >= 2 < ρN c > /(2c m − 1) remains valid even for Da < 1 flames as long as the flamelet assumption holds. It has been demonstrated earlier [6][7][8] thatw = 2ρÑ c /(2c m −1) can be used for filtered reaction ratew closure for >> δ th .…”

“…Da < 1). This RANS SDR model by Chakraborty and Swaminathan [10] (henceforth referred to as the RANS-CS model) has recently been extended for LES in Ref. [7] including the influences of heat release parameter τ , global Lewis number Le and turbulent Reynolds number Re t .…”

“…The same approach has been adopted in the current analysis. In any case, dynamic evaluation of β c provides an alternative method of extending the RANS-CS model [10] in comparison to the methodology described by Gao et al [7]. Furthermore, this model parameter β c represents effects induced by flame curvature which may be scale-dependent and thus it is well suited for dynamic evaluation.…”

Large Eddy Simulation of Premixed Combustion: Sensitivity to Subgrid Scale Velocity Modeling

“…The direct relationship between averaged reaction rate and scalar dissipation rate in high Damköhler number flames was shown by Bray (1979Bray ( , 1980 for RANS methodology, which was also shown to hold for low Damköhler number combustion (Chakraborty and Cant, 2011;Chakraborty and Swaminathan, 2011). Dunstan et al (2013) demonstrated its applicability for LES, which is supported by subsequent analyses using DNS and LES (Butz et al, 2015;Ma et al, 2014).…”