A direct numerical simulation study of a turbulent non-premixed lifted flame

Abstract

A turbulent lifted slot-jet flame is studied using direct numerical simulation (DNS). A one- step chemistry model is employed with a mixture-fraction dependent activation energy which can reproduce qualitatively the dependence of laminar burning rate on equivalence ratio that is typical of hydrocarbon fuels.

The qualitative structure of the flame is first examined, confirming some features that have previously been observed in experimental measurements as well as some which have not been previously discussed. Significant differences are observed comparing the present DNS representing a hydrocarbon fuel, and previous DNS representing hydrogen fuel. The statistics of flow and relative edge-flame propagation velocity components conditioned on the leading edge-flame locations are then examined. The results show that on average, the streamwise flame propagation and streamwise flow balance, thus demonstrating that edge-flame propagation is the basic stabilisation mechanism. Fluctuations of the edge locations and velocities are, however, significant. It is demonstrated that the edges tend to move in an essentially two-dimensional elliptical pattern (laterally outwards towards the oxidiser, then upstream, then inwards towards the fuel, then downstream again). It is proposed that this is due to the passage of large eddies, as outlined in Su et al. [1]. However, the mechanism is not entirely two-dimensional, and out-of-plane motion is needed to explain how flames escape the high velocity inner region of the jet.

Next, the time-averaged structure is examined. The entrainment flow is shown to be diverted around the flame base causing locally upstream streamwise velocities. A budget of terms in the transport equation for product mass fraction is used to understand the stabilisation from a time-averaged perspective. It is found to be consistent with the instantaneous perspective, featuring a fundamentally two-dimensional structure involving upstream trans- port of products on the lean side balanced by entrainment into richer conditions, while on the rich side, upstream turbulent transport and entrainment from leaner conditions balance the streamwise convection.

A complete analysis of the reasons behind the observed trends in the flame relative propagation velocity has been performed. The mean normalised edge-flame speed is less than laminar flame speed (at around 0.6 of laminar flame speed) and the edge-flame velocity fluctuations are mainly connected with strain rates, scalar dissipation rate, mixture-fraction curvature, product mass fraction curvature and the inner product . These quantities as well as the average normal orientations and nature of the flame in terms of categorisation of the edge as premixed or non-premixed go through cyclic fluctuations which appear to be connected with the passage of large eddies and the elliptical pattern of the on-average motion.

Overall the results provide strong support for the edge-flame theory of flame stabilisation, but point to significant roles played by large, coherent eddies in determining fluctuations of both the flow velocities and edge-flame relative propagation velocities, and thus the lifted height.