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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 ( ω 2 ) 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 ω 2 attains a local peak, and different characteristic correlations are found either side of the surface. Specifically, the thermodiffusive response (over the range of ω 2 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 ω 2 , all of which can be evaluated based solely on inexpensive one-dimensional calculations. |
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