Thermodiffusively-unstable lean premixed hydrogen–methane blends: Phenomenology and empirical modelling

This paper considers direct numerical simulation of hydrogen–methane blends in three-dimensional freely-propagating and turbulent flames using the canonical flame-in-a-box configuration. Previous work has developed empirical models for mean local flame speed and thickness in two- and three-dimensional freely-propagating flames, as well as a Karlovitz-dependent modification to capture the exaggeration of thermodiffusive response by turbulence; more recently, a modification to the instability parameter was demonstrated for hydrogen–methane blends two-dimensional freely-propagating flames. The present paper first considers phenomenology of premixed flames of fuel blends where one component is thermodiffusively unstable, and shows that there are effectively two flames, correlated with local curvature. In regions of positive curvature (centre of curvature in the products), the usual thermodiffusive response is observed; diffusive focussing of hydrogen results in flames locally thinner and faster. For the fuel blend, the other component (in this case methane) is left behind, and burns more slowly in the negatively-curved regions (where extinction channels would be found in unblended hydrogen flames). The dual-flame nature of the burning means that the choice of progress variable becomes more important; the selected isosurfaces based on hydrogen and temperature did not correlate well with the negatively-curved heat release associated with methane consumption, and so a blend-based progress variable was required. Consequently, the blend-based flame surface area was up to 50% higher than the other surfaces, resulting in lower mean local flame speeds. Joint probability density functions of local flame speed and curvature highlight the dual-flame nature, with high flame speeds correlating positively with curvature and a second region of low level burning at negative curvatures. The empirical models are shown to work well in three dimensions; the modification to the instability parameter for blends is independent of dimension. An additional factor was required in the turbulent flame speed model to reduce the turbulent contribution to local flame speed as the hydrogen content goes to zero. The resulting empirical model is shown to work remarkably well, and provides a prediction of mean local flame speed for turbulent thermodiffusively-unstable lean premixed hydrogen–methane blends, which can be evaluated simply from one-dimensional flame simulations alone. Novelty and Significance The novelty of the paper is firstly in the phenomenological description of flames with fuel blends where one is thermodiffusively-unstable, specifically the dual-flame nature of the burning, correlated with flame surface curvature, and secondly in the extension of the empirical models for thermodiffusively-unstable blends in three-dimensional freely-propagating and turbulent flames. This is significant as it advances fundamental understanding of thermodiffusively-unstable blends, which are likely to be important for the transition to carbon-free power and propulsion, as well as for turbulent flame models suitable for thermodiffusively-unstable blends.