Thermodiffusively-unstable lean premixed hydrogen flames: Phenomenology, empirical modelling, and thermal leading points

Abstract

Thermodiffusively-unstable lean premixed hydrogen flames are investigated using three-dimensional direct numerical simulation with finite-rate chemical kinetics. A large number of simulations have been performed to investigate the influence of reactant conditions (pressure, temperature, and equivalence ratio) on thermodiffusive response in freely-propagating and turbulent flames. Reactant conditions are characterised using an instability parameter ω2, which was recently shown to characterise freely-propagating flames well in 2D. Freely-propagating flame speeds and thicknesses are found to correlate with ω2 using the same functional form found in 2D (with larger model constants), and different correlations are required either side of the most-unstable surface in ω2-space. The freely-propagating values are demonstrated to be more appropriate for characterising turbulent flames than the corresponding 1D laminar flame values. Both turbulence and thermodiffusive instability bring about a similar flame response (increasing curvature, reaction rates and temperature), and so starting from strongly thermodiffusively-unstable conditions limits the potential turbulent response; an empirical model for local flame speed and thickness is provided incorporating this dependence. Joint probability density functions are used to correlate local consumption-based flame speed with curvature, strain-rate and stretch with single and independent Markstein numbers. A simple curvature-based model coupled with the empirical flame speed model is found to yield reasonable results. Principal curvatures are used to partition the flame surface into six classifications, allowing for conditional analysis in different parts of the flame surface. Fractional contributions show that the bulk of the fuel consumption occurs in flat regions and leading edges, shifting from the former to the latter with increasing instability and/or turbulence. Furthermore, the flat flame regions experience speeds in excess of the reference value despite the lack of focussing of fuel by preferential diffusion in these regions, contrary to the conventional expectations of thermodiffusive instability. We propose a thermal leading point interpretation of these phenomena: as expected, strong positive curvature in the leading points/edges result in diffusive focussing of fuel, increasing the reaction rates, resulting in superadiabatic temperatures; these high temperatures left behind the leading points/edges then support higher-than-expected reaction rates in regions where the flame surface is relatively-flat.