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

Abstract

Flame surface density (FSD) based reaction rate closure is an important methodology of turbulent premixed flame modelling in the context of Large Eddy Simulations (LES). The transport equation for the Favre-filtered reaction progress variable needs closure of the filtered reaction diffusion imbalance (FRDI) term (i.e. filtered value of combined reaction rate and molecular diffusion rate) and the sub-grid scalar flux (SGSF). A-priori analysis of the FRDI and SGSF terms has in the past revealed advantages and disadvantages of the specific modelling attempts. However, it is important to understand the interaction of the FRDI and SGSF closures for a successful implementation of the FSD based closure. Furthermore, it is not known a-priori if the combination of the best SGSF model with the best FRDI model results in the most suitable overall modelling strategy. In order to address this question, a variety of SGSF models is analysed in this work together with one well established and one recent FRDI closure based on a-priori analysis. It is found that the success of the combined FRDI and SGSF closures depends on subtle details like the co-variances of the FRDI and SGSF terms. It is demonstrated that the gradient hypothesis model is not very successful in representing the SGSF term. However the gradient hypothesis provides satisfactory performance in combination of a recently proposed FRDI closure, whereas unsatisfactory results are obtained when used in combination with another existing closure, which was shown to predict the FRDI term satisfactorily in several previous analyses.

Effects of Reaction Progress Variable Definition on the Flame Surface Density Transport Statistics and Closure for Different Combustion Regimes

“…Case C nominally represents the broken reaction zones regime where energetic turbulent eddies penetrate into the flame structure and also in the reaction zone. This effect is particularly important for the H 2 mass fraction based RPV because the reaction zone (Boger et al, 1998;Cant and Bray, 1998;Charlette et al, 2002;Keppeler et al, 2014;Klein et al, 2016;Chakraborty and Klein., 2008a;Ma et al, 2013;Cant et al, 1990;Duclos et al, 1993;Hawkes and Cant 2001a;Chakraborty and Cant, 2007;Hernandez-Perez et al, 2011;Reddy and Abraham, 2012;Chakraborty and Cant, 2013;Ma et al, 2014 = 1 − ( ) ̅̅̅̅̅̅ ( ) ̅̅̅̅̅̅ , optimal, RPV dependent, 0 and provided in Table 2 ̅ ̅ = 0 Performance is the best for based RPV and the deviation from DNS data is the highest for 2 based RPV.…”

“…The generalised FSD is defined as (Boger et al, 1998): Σ = |∇ | ̅̅̅̅̅ where is the reaction progress variable (RPV) and the overbar indicates a Reynolds averaging or filtering operation in the context of Reynolds-averaged Navier-Stokes (RANS) or large eddy simulations (LES). A number of previous analyses focussed on both algebraic (Boger et al, 1998;Cant and Bray, 1998;Charlette et al, 2002;Knikker et al, 2002;Keppeler et al, 2014;Klein et al, 2016;Chakraborty and Klein., 2008a;Ma et al, 2013) and transport equation (Cant et al, 1990;Duclos et al, 1993;Veynante et al, 1996;Hawkes and Cant 2001a;Chakraborty and Cant, 2007;Hun and Huh, 2008;Katragadda et al, 2011;Chakraborty et al, 2011;Hernandez-Perez et al, 2011;Reddy and Abraham, 2012;Chakraborty and Cant, 2013;Ma et al, 2014;Sellman et al, 2017) based closures of FSD for turbulent premixed combustion. However, most of these analyses (Boger et al, 1998;Cant and Bray, 1998;Charlette et al, 2002;Keppeler et al, 2014;Klein et al, 2016;Chakraborty and Klein., 2008a;Ma et al, 2013;Cant et al, 1990;Duclos et al, 1993;Hawkes and Cant 2001a;Chakraborty and Cant, 2007;Hun and Huh, 2008;Katragadda et al, 2011;Chakraborty et al, 2011;…”

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.…”

Reynolds-Averaged, Scale-Adaptive and Large-Eddy Simulations of Premixed Bluff-Body Combustion Using the Eddy Dissipation Concept

“…Under certain assumptions it is possible to calculate the turbulence flame speed and the turbulence flame thickness using the sub-grid residence time and the reactive volume fraction, γ * , from the LES-EDC closure as The gradient hypothesis model (GHM) was used for the sub-grid flux closure in the present study. It worth noting that recent findings [1], [28], [36] showed that the accurate modeling of the sub-grid flux (SGSF) can be important and the interaction of chemical source term and the sub-grid flux modeling is of considerable importance for LES and should not be ignored. Klein et al [28] investigated several SGSF models and demonstrated that the gradient hypothesis model was not very successful in representing the SGSF term obtained by DNS, but provided satisfactory performance in combination of a recently proposed the filtered value of combined reaction rate and molecular diffusion rate closure.…”