A PrioriAssessment of Algebraic Flame Surface Density Models in the Context of Large Eddy Simulation for Nonunity Lewis Number Flames in the Thin Reaction Zones Regime

Abstract

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimensionDand inner cut-off scaleηihave been studied in detail. It has been found thatDis strongly affected by Lewis number and increases significantly with decreasing Le. By contrast,ηiremains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation ofDis proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD.

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

“…A-priori DNS analyses [6,7] suggested that η iD scales with thermal flame thickness δ th = (T ad − T 0 )/Max |∇T | L (where T is the instantaneous dimensional temperature and the subscript L refers to the unstrained premixed laminar flame condition), which is consistent with the behaviour of η i obtained previously based on experimental [31,35] and DNS [29,[32][33][34] [6,7]. The predictions of Eq.…”

“…The DNS datasets have been explicitly filtered using the integral Q( x) = Q( x − r)G( r)d r for ranging from ≈ 0.4δ th to ≈ 2.8δ th where G( r) = (6/π 2 ) 3/2 exp(−6 r. r/ 2 ). This range of filter widths is comparable to the range of used in several previous a-priori DNS analyses [6,7,29,31,32,34,56], and span a useful range of length scales from comparable to 0.4δ th ≈ 0.71δ z (δ z = α T 0 /S L is the Zel'dovich flame thickness with α T 0 being the unburned gas thermal diffusivity) where the flame is partially resolved, up to 2.8δ th ≈ 5δ z where the flame becomes fully unresolved and is comparable to the integral length scale l.…”

“…where η i is the inner cut-off scale and D f is the fractal dimension of the flame surface [29][30][31][32][33][34]. Due to the close relation between gen = (N c /D) 1/2 and SDR, the analogy of power-law closure for FSD has been extended in previous analyses [6,7] for possible modelling of SDRÑ c :…”

“…ε ∼ u 3 / where ε is the sub-grid dissipation rate of turbulent kinetic energy) and μ ∼ ρS L δ th [33,34,37], C * 3 , C * 4 and β c are the model parameters, S L is the unstrained laminar burning velocity, f = exp[−0.7( /δ th ) 1.7 ] is a bridging function [7], u = [(ρu i u i /ρ − u iũi )/3] 1/2 = (2k sgs /3) 1/2 is the sub-grid turbulent velocity fluctuation with u i and k sgs being the i th component of fluid velocity and the sub-grid turbulent kinetic energy respectively. In Eq.…”

“…SDR and Flame FSD) is debatable but the assumption of scale-similarity was successfully used in the past for the closure of FSD [29][30][31]34]. However, the results in Figs.…”