Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames.

Daniel Wacks,Nilanjan Chakraborty,Ilias Konstantinou

doi:10.1098/rspa.2017.0706

Abstract

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

Highlights

Strict pollution control regulations have increased the need for low-emission premixed combustion, in which the reactants are homogeneously mixed prior to combustion
Temperature inhomogeneity is observed in the burned gas for non-unity Lewis number flames because of the inequality of the diffusion rates of species and heat, whereas the burned gas temperature remains equal to the adiabatic flame temperature for the unity Lewis number flames
The lowest Lewis number case exhibited strong signs of increased burning rates and flame-generated enstrophy. These were embodied by a larger magnitude of the dilatation rate, of the QW-component associated with vorticitydominated regions and of the PQW-component associated with both the dilatation rate and vorticity. This was apparent from the variation of the individual flow topologies across the flame, such that those flow topologies associated with a positive dilatation rate (S7 and S8) were more prominent further into the flame for low Lewis number cases

Summary

Introduction

Strict pollution control regulations have increased the need for low-emission premixed combustion, in which the reactants are homogeneously mixed prior to combustion. Hydrogen is often identified as a potential future fuel which would allow combustion with the complete elimination of greenhouse gas emission, but the chemistry of hydrogen is significantly different from that of hydrocarbon fuels [1], while the presence of lighter chemical species induces significant effects of the differential diffusion of heat and mass. It has been found that the rate of diffusion of fresh reactants into the reaction zone supersedes the rate at which heat is diffused out in the positively stretched zones for Le < 1.0 flames This gives rise to the simultaneous presence of high reactant concentration and high temperature, and the burning rate and flame area generation are greater in the Le < 1.0 flames than in the unity Lewis number flames with similar turbulent flow conditions in the unburned reactants. Just the opposite mechanism gives rise to a reduced burning rate in the Le > 1.0 flames, in comparison with the corresponding unity Lewis number flame

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