Abstract
Lean premixed hydrogen flames are thermodiffusively unstable due to the high mobility of the fuel, which leads to localised acceleration and thinning of the flame. Consequently, the one-dimensional steady unstretched laminar flame speed and thermal thickness are not representative of multi-dimensional flames, and the extent of the disparity is strongly dependent on reactant conditions. This paper presents an empirical model to predict local as well as characteristic freely-propagating values of flame speeds and thicknesses that can be evaluated from one-dimensional simulations (in Cantera for example). It was found that the thermodiffusive response was well characterised in terms of the second-order instability parameter (ω2) that arises from classical linear stability analysis. This instability parameter depends strongly on Zel’dovich number, and presents non-monotonic behaviour in pressure/temperature/equivalence-ratio space. In particular, there is a surface where ω2 attains a local peak, and different characteristic correlations are found either side of the surface. Specifically, the thermodiffusive response (over the range of ω2 considered) is stronger and more unpredictable (greater uncertainties) on the higher-pressure side of this peak surface. The empirical model is inferred from a large dataset of two-dimensional freely-propagating flames over a broad range of reactant conditions. PDFs of local flame speed and thickness are used to define freely-propagating characteristic values as the corresponding mean surface value, implicitly supplying a mean local burning enhancement factor I¯0. Local flame speeds are then correlated with curvature and strain rate through JPDFs to identify an appropriate Markstein number. The resulting model consists of expressions for characteristic flame speeds, thicknesses and Markstein numbers in terms of the instability parameter ω2, all of which can be evaluated based solely on inexpensive one-dimensional calculations.
Highlights
Interest in hydrogen combustion has greatly increased in recent years due to the desire to move away from carbon-based fossil fuel energy sources
Lean premixed hydrogen flames can suffer from intrinsic instabilities, the study of which is important for understanding the mechanisms involved in flame propagation and more complex flame-flow interactions
Neglecting turbulent, acoustic and buoyancy effects, lean premixed hydrogen flames are susceptible to two kinds of instability; the Darrieus-Landau instability and the thermodiffusive instability
Summary
Interest in hydrogen combustion has greatly increased in recent years due to the desire to move away from carbon-based fossil fuel energy sources. The Darrieus-Landau instability is a consequence of the density drop due to heat release occurring across the flame, whereas thermodiffusive instability originates in an imbalance of thermal and molecular diffusion across the flame Both kinds of instability have been observed experimentally, for example Markstein [1], Groff [2], Bradley et al [3,4], and Law et al [5], as well as numerically, for example Baum & Poinsot [6], Trouvé & Poinsot [7], Aspden et al [8], Creta et al [9,10], Altantzis et al [11], and Frouzakis et al [12]
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