A correlation to compute the thermo-diffusive instability effect of lean hydrogen flames at engine-like conditions

Lean hydrogen mixtures are a valid alternative to conventional fuels for internal combustion engine. Lean hydrogen flames are characterised by a low effective Lewis number, which triggers flame instabilities. Therefore, being able to correctly quantify the effect of such phenomenon on the flame propagation is important. However, the computation of the flame instability second order growth rate (ω2), which is widely used to model the laminar flame speed increase due to instabilities, is not straightforward, as chemical kinetics must be considered. In this work, a comprehensive correlation for modelling thermo-diffusive instabilities at engine-like conditions is presented, and an easy-to-implement correlation for the enhancement of the flame speed is proposed. As a first step, one-dimensional freely propagating flame simulations are used to compute the thermal expansion parameter σ of lean hydrogen flames. Secondly, by imposing the Sutherland’s Law to describe the mixture thermal conductivity, the terms that include the stabilising (or destabilising) effects of heat diffusion (B1), molecular diffusion (B2), and viscous diffusion (B3) are computed, and a fitting function is found for each of them. Thirdly, the computation of the Zel’dovich number β is performed, and a fitting procedure carried out. Finally, by the resulting fitting functions, an ω2 correlation dependent only on the local thermodynamic conditions of the mixture is developed within pressure, unburnt temperature and equivalence ratio ranges of 10–50 bar, 500–900 K and 0.2–0.7, respectively. Furthermore, reasonable results can be found through extrapolation up to 100 bar and 1100 K. The flame speed enhancement values obtained with the developed correlation differ by less than 6% from those reported in literature at relevant light-duty engine-like conditions. Larger discrepancies are observed only at low unburnt gas temperatures (300 K) or for very lean mixtures (Φ = 0.2).