Abstract

The influences of characteristic Lewis number hbox{Le} on the statistics of density-weighted displacement speed and consumption speed in spherically expanding turbulent premixed flames have been analysed using three-dimensional direct numerical simulations data for hbox{Le} = 0.8 , 1.0 and 1.2 under statistically similar flow conditions. It has been found that the extents of flame wrinkling and burning increase with decreasing hbox{Le} , which is reflected in increasing trends of mean and most probable values of both density-weighted displacement and consumption speed. Moreover, in all cases the marginal probability density functions of density-weighted displacement speed show finite probabilities of obtaining negative values, whereas consumption speed remains deterministically positive. The strain rate and curvature dependences of scalar gradient and temperature have been found to be strongly dependent on hbox{Le} , and these statistics, along with the interrelation between strain rate and curvature, influence the local strain rate and curvature responses of consumption speed and both reaction and normal diffusion components of density-weighted displacement speed. Density-weighted displacement speed and curvature have been found to be negatively correlated, whereas positive correlations are obtained between density-weighted displacement speed and tangential strain rate for all flames considered here. The positive correlation between temperature and curvature arising from differential diffusion of heat and mass in the hbox{Le} = 0.8 case induces a positive correlation between consumption speed and curvature, whereas these correlations are negative in the hbox{Le} = 1.2 flame. The statistical behaviour of density-weighted displacement speed has been utilised to demonstrate that Damköhler’s first hypothesis does not strictly hold for spherically expanding turbulent premixed flames.

Highlights

  • The aforementioned analyses on spherically expanding flames have been conducted for unity Lewis number flames and this gap in the existing literature will be addressed in this paper by using three-dimensional simple chemistry direct numerical simulation (DNS) of spherically expanding turbulent premixed flames with Le = 0.8, 1.0 and 1.2 but the analysis of the effects of initial flame radius is kept beyond the scope of this paper

  • The main objective of the current analysis is to demonstrate and explain the influences of Le on both mean behaviours of consumption speed (CS) Sc and density-weighted displacement speed (DDS) Sd∗ and their local curvature and tangential strain rate dependences

  • The qualitative nature of the strain rate and curvature dependences of Sd∗ does not change for the range of Le considered here, the strain rate and curvature dependences of the reaction and normal diffusion components of Sd∗ have been found to be strongly dependent on Le

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Summary

Introduction

A number of experimental (Abdel-Gayed et al 1984; Renou et al 2000; Chaudhuri et al 2012; Gashi et al 2005; Poinsot et al 1995) and direct numerical simulation (DNS) (Thevenin 2005; Jenkins and Cant 2002; van Oijen et al 2005; Klein et al 2006, 2009; Chakraborty et al 2007; Dunstan and Jenkins 2009) investigations concentrated on the analysis of statistically spherical turbulent premixed flames because of their relevance to Spark Ignition (SI) engines and accidental explosions. Bechtold and Matalon (2001) proposed the characteristic value of Lewis number Le = 1.0 + LeF − 1 + LeO − 1 ALe ∕ 1 + ALe where ALe = 1 + (Φ − 1) with Φ = for fuel-rich mixtures, whereas Φ = 1∕ for fuel-lean mixtures with and being the equivalence ratio and Zel’dovich number, respectively and subscripts F and O are used for fuel and oxidiser, respectively It is well-known that the characteristic Lewis number Le ( referred to as Lewis number) significantly affects the flame wrinkling and burning rate (Williams 1985; Clavin and Joulin 1983; Ashurst et al 1987; Haworth and Poinsot 1992; Rutland and Trouvé 1993; Trouvé and Poinsot 1994; Chakraborty and Cant 2005a, 2006; Han and Huh 2008; Chakraborty and Klein 2008; Dopazo et al 2018). A summary of main findings is provided along with conclusions

Mathematical Background and Numerical Implementation
Results and Discussion
Conclusions
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