Scaling Laws for Thermodiffusively Unstable Lean Premixed Turbulent Hydrogen-Air Flames

Lean premixed hydrogen-air flames are strongly affected by thermodiffusive (TD) instabilities, which can alter the flame structure and enhance the local reactivity many-fold. Two recent models (Howarth et al. (Combust.~Flame 253, 2023) and Rieth et al. (MSC 2023)) describe the scaling of the stretch factor in turbulent hydrogen flames with the Karlovitz number using different parameters, i.e., the $\omega_2$ parameter from linear stability theory and the ratio of the Zel'dovich to the Peclet number (${Ze}/{Pe}$). Using a comprehensive set of 91 direct numerical simulation (DNS) cases spanning a wide range of pressures, equivalence ratios, turbulence intensities, and flow configurations, both formulations are systematically evaluated and an adapted formulation is proposed. The analysis of the governing non-dimensional groups reveals a scaling behavior characterized by two distinct regimes. In the first regime, typically relevant for burner and gas turbine conditions, both models reduce to an identical form that depends solely on the Karlovitz number and the stretch factor of laminar flames, independent of $\omega_2$ or ${Ze}/{Pe}$. In the second regime, characterized by ultra-low flame speeds, the explicit consideration of $\omega_2$ or the ratio ${Ze}/{Pe}$ is required for accurate scaling. In both regimes, the two models predict the DNS data reasonably well and reduce to the same functional form of non-dimensional groups, indicating their physical equivalence.