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

Abstract

Dynamic algebraic closure of scalar dissipation rate (SDR) of reaction progress variable in the context of Large Eddy Simulations (LES) of turbulent premixed combustion has been addressed here using a power-law based expression and a model, which was originally proposed for Reynolds Averaged Navier Stokes (RANS) simulations, but has recently been extended for LES. The performances of these models have been assessed based on a-priori analysis of a Direct Numerical Simulations (DNS) database of statistically planar turbulent premixed flames with a range of different values of heat release parameter τ , turbulent Reynolds number Re t and global Lewis number Le. It has been found that the power-law model with a single constant exponent α D does not adequately capture the volume-averaged behaviour of density-weighted SDR and this problem is particularly severe especially for Le << 1 flames. The deficiency of the power-law model with a single power-law exponent arises due to multi-fractal nature of SDR. The dynamic evaluation of the model parameter for the algebraic model, which was originally proposed in the context of RANS and has been extended here for LES, has been shown to capture the local behaviour of SDR better than the power-law model. It has been demonstrated that the empirical parameterisation of a model parameter for the static version of the RANS-extended SDR model can be avoided using a dynamic formulation which captures the local behaviour of SDR either comparably or better than the static formulation for a range of different values of τ, Le and Re t , without sacrificing the prediction of the volume-averaged SDR. Keywords

Analysis of the Combined Modelling of Sub-grid Transport and Filtered Flame Propagation for Premixed Turbulent Combustion

“…Furthermore, FSD and SDR models proposed based on a-priori DNS analyses using this database [28][29][30] have been found to be in good agreement with a-posteriori assessments based on actual LES simulations [16,[31][32][33]. The aforementioned facts provide the confidence in the findings of the present analysis.…”

A Priori Direct Numerical Simulation Modeling of Scalar Dissipation Rate Transport in Head-On Quenching of Turbulent Premixed Flames

“…In the context of Reynolds averaged Navier-Stokes (RANS) and large eddy simulations (LES), the SDR is closed using either an algebraic expression in terms of known quantities (Dunstan et al, 2013;Gao et al, 2014Gao et al, , 2015aKolla et al, 2009;Mura and Borghi, 2003;Swaminathan and Bray, 2005) or by solving a transport equation (Chakraborty et al, 2008aGao et al, 2015bGao et al, , 2015cMantel and Borghi, 1994;Mura et al, 2008Mura et al, , 2009). Some of the aforementioned closures (e.g., Dunstan et al, 2013;Gao et al, 2014Gao et al, , 2015aKolla et al, 2009) have already been implemented in RANS and LES of a range of laboratory-scale (Ahmed and Swaminathan, 2014;Butz et al, 2015;Dong et al, 2013;Kolla and Swaminathan, 2010;Langella et al, 2015;Ma et al, 2014;Robin et al, 2010) and industrial (Sadasivuni et al, 2012) configurations, and satisfactory results have been obtained. However, all of the aforementioned modeling of SDR has been carried out for flows away from the wall and the effects of flame quenching by the wall on SDR transport and its modeling are yet to be analyzed in detail.…”

Large Eddy Simulation of a Bluff Body Stabilised Premixed Flame Using Flamelets

“…The sub-grid dissipation rate, which is the fourth term in Eq. 5, is modelled using an algebraic closure [23], which has been tested thoroughly in past studies [11, 24, 35]. This expression is where the function ensures that the SGS dissipation rate goes to zero when the filter width approaches zero.…”

“…The term is related to the influence of flame curvature, which is induced by wrinkling. The parameter β c is therefore scale dependent, which is evaluated using a dynamic approach described in [25, 35]. Thus, there is no adjustable parameter in this modelling approach, but for the sake of comparison, a static value of β c = 0.4 is also used for this study.…”