Flow topology distribution in head-on quenching of turbulent premixed flame: A Direct Numerical Simulation analysis

Jiawei Lai,Daniel H Wacks,Nilanjan Chakraborty

doi:10.1016/j.fuel.2018.03.021

Abstract

The distribution of flow topologies within the flame, and their evolution with flame quenching have been analysed using a Direct Numerical Simulation (DNS) database of head-on quenching of statistically planar turbulent premixed flames by isothermal inert walls for different values of turbulence intensity and global Lewis number. It has been found that dilatation rate plays a key role in determining the flow topology distribution within the flame and this dilatation rate field is significantly affected by the flame quenching in the vicinity of the wall. The influence of the wall on the dilatation rate field in turn affects the statistical behaviour of all three invariants of the velocity gradient tensor and the distribution of flow topologies. The effects of heat release and thermal expansion strengthen with decreasing Lewis number which give rise to an increase in the probability of obtaining topologies which are specific to high positive values of dilatation rate. As the magnitude of positive dilatation rate and the likelihood of obtaining it decrease with flame quenching, the probability of finding the topologies, which are obtained only for positive values of dilatation rate, decreases close to the wall. The interrelation between the flow and flame topologies has been analysed in terms of Gaussian flame curvature and mean of principal flame curvatures. The contributions of individual flow topologies on the mean behaviour of wall heat flux magnitude, and the scalar-turbulence interaction and vortex-stretching terms in the scalar dissipation rate and enstrophy transport equations, respectively have been analysed in detail and dominant flow topologies which dictate the mean behaviours of these quantities have been identified. Detailed physical explanations have been provided for the observed flow topology distribution and its contribution to the scalar-turbulence and vortex-stretching terms. The nodal flow topologies have been found to be the significant contributors to the wall heat flux magnitude during head-on quenching of turbulent premixed flames irrespective of the value of global Lewis number.

Highlights

Flow topologies are often characterised in terms of a three-dimensional space made up of the three invariants of the velocity gradient tensor ∂ui/∂xj [1,2], where ui is the ith component of the velocity vector
Considerable effort has been made to analyse flame-wall interaction based on numerical investigations [22,23,24,25,26,27,28,29,30,31,32,33,34,35], but none of these analyses focussed on the flow topology distribution in the near-wall region during unsteady wall-induced flame quenching
The flow topology distribution and statistical behaviours of the invariants of velocity gradient tensor P,Q and R have been analysed for head-on quenching of statistically planar turbulent premixed flames by isothermal inert walls using three-dimensional Direct Numerical Simulation (DNS) data for different values of Lewis numbers at different turbulence intensities u′/SL and integral length scale to flame thickness ratios l/δth.The flow topologies have been characterised by the first, second and third invariants (i.e. P,Q and R) of the velocity gradient ∂ui/∂xj tensor

Summary

Introduction

Flow topologies are often characterised in terms of a three-dimensional space made up of the three invariants (i.e. first P, second Q and third R) of the velocity gradient tensor ∂ui/∂xj [1,2], where ui is the ith component of the velocity vector. Considerable effort has been made to analyse flame-wall interaction based on numerical investigations [22,23,24,25,26,27,28,29,30,31,32,33,34,35], but none of these analyses focussed on the flow topology distribution in the near-wall region during unsteady wall-induced flame quenching This gap in the existing literature is addressed here by analysing the statistical behaviours of the invariants of the velocity gradient tensor ∂ui/∂xj and flow topology distributions at different instants of time as the flame approaches the isothermal wall in the case of head-on quenching of statistically planar turbulent flames with different values of global Lewis number Le (i.e. Le = 0.8−1.2). The conclusions will be drawn and main findings will be summarised in the final section of this paper

Mathematical background

Numerical implementation

Results & discussion

Conclusions