Direct simulation of non-premixed flame extinction in a methane–air jet with reduced chemistry

Abstract

A three-dimensional direct numerical simulation (DNS) study of a spatially evolving planar turbulent reacting jet is reported. Combustion of methane with air is modelled using a four-step reduced mechanism in the non-premixed regime. A total of eight chemical species are integrated in time along with the fluid mechanical fields. The solution of the compressible Navier-Stokes equations is obtained numerically for moderately low Mach number. A large computational grid, with 100 million grid points, is required in order to resolve the flame. The cold flow Reynolds number is 3000. The focus of the study is to investigate the dynamics of extinction fronts in threedimensional turbulent flows. A novel data reduction and identification algorithm was developed to postprocess the large DNS database and extract the shape of the evolving flame surface including its edges and their propagation velocity. The joint probability density function (p.d.f.) of edge velocity and scalar dissipation was obtained and the results indicate that the three-dimensional flame edges propagate with a velocity that is largely controlled by the local rate of scalar dissipation, or equivalently in terms of the local Damköhler number at the flame edge, as predicted by theory. Naturally, the effects of unsteadiness in this flow produce a broad joint p.d.f. The statistics collected also suggest that the mean value of the hydrogen radical reaction rate are very small in the turbulent regions of the flow owing to the functional form of the hydrogen radical reaction rate itself. The consequence of these results in the context of turbulent combustion modelling is discussed. Additional statistical and morphological information of the flame is provided.

On the dynamics of flame edges in diffusion-flame/vortex interactions

“…It is important to note that the order of magnitude estimates presented in this section, leading to conditions (25), (27), and (28), could be used to extend existing diagrams of diffusion-flame/vortex interaction regimes [21] in the limit of strong vortices considered here.…”

“…7?./3 2 r => Dap r P (28) According to this, for nontrivial quasi-steadyextinction/reignition dynamics to occur, all three conditions, (25), (27), and (28), must be simultaneously satisfied.…”

“…There is also strong evidence from theoretical [23,24], numerical [25][26][27][28], and experimental [29][30][31][32][33][34][35] work that triple flames, or the more general flame edges, play an important role in the dynamics of locally extinguished regions in turbulent diffusion flames [36]. Local flame extinction leads to the formation of flame holes (chemically frozen regions of low temperature where the reactants mix without chemical reaction) which are separated by flame edges, typically in the form of thin premixed flames, with rich and lean branches, from regions of near equilibrium flow, where the reactants only coexist in a thin diffusion flame.…”

“…But as soon as the strain rate decreases below the critical value in the vicinity of these holes, they may be reignited by the surrounding flame elements, which may propagate toward the fresh mixture in the form of triple or edge flames [37]. In this context, flame/vortex interactions constitute a well-defined system of intermediate complexity between steady laminar flames and turbulent ones, appropriate to investigate unsteady and curvature effects [38], as well as local flame extinction and reignition phenomena [27,39]. Such investigations appear as a necessary step toward the extension of the classical isolated flamelet models, which regard the turbulent diffusion flame locally as a steady, onedimensional, laminar flame [1], into more involved interacting flamelet models accounting for local extinction/reignition events [40,41].…”

Influence of Strouhal number on pulsating methane–air coflow jet diffusion flames

“…In writing the energy equation, we have neglected the Dufour effect and have assumed a Fickian diffusion law, so that Y"V" = -D"VY" for n ^ N2, where V" is the diffusion velocity of the «th species and D" is the diffusion coefficient of the «th species. Similar to what has been done previously [26][27][28], we impose a constant Prandtl number, Pr = IJ,C P /X, where X denotes the thermal conductivity. The approximate value for air, Pr = 0.7, is employed throughout the study.…”