Subgrid-Scale Modeling of Reaction-Diffusion and Scalar Transport in Turbulent Premixed Flames

Abstract

A numerical study of premixed flame-turbulence interaction is performed to investigate the effects of turbulence on the structural features of the flame and the subgrid-scale (SGS) effects on vorticity dynamics, energy transfer mechanism, and turbulent transport across the flame. We consider a freely propagating methane-air turbulent premixed flame interacting with a decaying isotropic turbulence under three different initial conditions corresponding to the corrugated flamelet (CF), the thin reaction zone (TRZ), and the broken/ distributed reaction zone (B/DRZ) regimes. We employ the wellestablished linear eddy mixing (LEM) model in large-eddy simulation (LEMLES), a new subgrid closure for reaction-diffusion occurring in the small-scales based on LEM (RRLES), and a quasi-laminar chemistry based closure in large-eddy simulation (QLLES) to simulate flameturbulence interactions and to compare predictions with direct numerical simulation (DNS). We assess the accuracy and robustness of the closures by comparing statistical features to highlight their abilities and limitations. The newly proposed RRLES subgrid closure uses a dual-resolution grid for solving the species transport equations. Such an approach is shown to improve the existing LEMLES subgrid model especially at low Reynolds numbers. All SGS closures reveals good agreement, although there are some differences due to the closure used for convective transport of the scalar field and the reaction rate. Further analysis of the DNS dataset shows that there is a significant contribution by dilatation and baroclinic torque terms across the flame. In particular, at higher Karlovitz number, there is an abrupt change in the sign of the dilatation term, which is related to the competing effects of thermal expansion due to heat release and enhanced molecular mixing by the turbulence across the flame brush region. The enhanced mixing leads to localized pockets of cold reactants surrounded by hot products, which is only partly captured by the employed closures. The analysis of SGS kinetic energy and scalar dissipation rates indicates the presence of back-scatter of turbulent kinetic energy, and we also observe counter-gradient transport across the flame. The results suggest that further improvement of the traditional closures is needed to accurately capture the dynamics of flame-turbulence interaction.ARTICLE HISTORY

Sub-grid Reaction Progress Variable Variance Closure in Turbulent Premixed Flames

“…The closure of sub-grid scalar variance plays a crucial role in the modelling of micro-mixing in the context of large eddy simulations (LES) (Pierce and Moin 1998;Jimenez et al 2001). The knowledge of sub-grid scale (SGS) variance of reaction progress is often necessary to construct the sub-grid probability density function (PDF) of reaction progress variable c in the context of flamelet and Linear Eddy Modelling (Ranjan et al 2016) based modelling methodologies. The SGS variance of reaction progress variable c is defined as (Pierce and Moin 1998;Jimenez et al 2001;Ranjan et al 2016): where q = q∕̄ and q are the Favre-filtered and LES-filtered values of a general variable q , respectively and is the gas density.…”

“…The knowledge of sub-grid scale (SGS) variance of reaction progress is often necessary to construct the sub-grid probability density function (PDF) of reaction progress variable c in the context of flamelet and Linear Eddy Modelling (Ranjan et al 2016) based modelling methodologies. The SGS variance of reaction progress variable c is defined as (Pierce and Moin 1998;Jimenez et al 2001;Ranjan et al 2016): where q = q∕̄ and q are the Favre-filtered and LES-filtered values of a general variable q , respectively and is the gas density. Based on a presumed bi-modal PDF of c with peaks at 0.0 and 1.0, the SGS variance of reaction progress variable c can be expressed as (Bray et al 1985): 2 v =c(1 −c) but the sub-grid PDF of c is unlikely to be bi-modal in practice Cant 2007, 2009;Dunstan et al 2013;Gao et al 2014;Ma et al 2014).…”

“…Based on a presumed bi-modal PDF of c with peaks at 0.0 and 1.0, the SGS variance of reaction progress variable c can be expressed as (Bray et al 1985): 2 v =c(1 −c) but the sub-grid PDF of c is unlikely to be bi-modal in practice Cant 2007, 2009;Dunstan et al 2013;Gao et al 2014;Ma et al 2014). An alternative algebraic expression is often used for the evaluation of SGS variance of passive scalars in the following manner (Pierce and Moin 1998;Jimenez et al 2001;Ranjan et al 2016):…”

“…where C = 0.5 is the model constant (Ranjan et al 2016) and Δ is the LES filter width. It is worth noting that the evolution of SGS variance is expected to be influenced by both chemical and turbulent processes (Chakraborty and Swaminathan 2011;Lai and Chakraborty 2016) but this is not explicitly accounted for in Eq.…”

Subgrid Reaction-Diffusion Closure for Large Eddy Simulations Using the Linear-Eddy Model

“…The primitive-variable approach is standard for previous LES-LEM implementation so it is valuable then to explore how well a new LEM closure with the reaction-rate approach performs. Therefore, the present work and a parallel one [49] use LEM following the reaction-rate approach. The present work differs from this previous one in that it uses a significantly different code framework, and it retains the splicing algorithm instead of getting rid of it.…”