An extended <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg" display="inline" id="d1e310"> <mml:mi>G</mml:mi> </mml:math> -equation formulation for simulating thermodiffusively unstable hydrogen flames

Hydrogen flames featuring thermodiffusive instabilities are challenging to model in large eddy simulations (LES) and Reynolds-averaged Navier–Stokes (RANS) simulations, where the relevant scales of the instability are typically not resolved. Approaches for modeling thermodiffusively unstable flames have mostly been formulated and validated for laminar flames, where interactions with turbulence are not considered. This study aims to extend the G -equation model for turbulent thermodiffusively unstable hydrogen flames in the context of RANS simulations. Despite the rise of the available computational resources and the development in high-fidelity LES and direct numerical simulations (DNS), RANS simulations are still the most employed approach in industrial applications, especially for design and operation optimization. In this study, the formulation of the turbulent flame speed as part of the G -equation combustion model was modified by coupling the empirical scaling relations for flame speed and thickness, which were derived from DNS of turbulent hydrogen flames and consider the effects of thermodiffusive instabilities and their interactions with turbulence. Here, a new relation is proposed to account for cases with high Karlovitz numbers, where increasing turbulence intensity leads to suppression of thermodiffusive instabilities. The derived model was applied to RANS simulations of two hydrogen flame configurations. The first configuration corresponds to a DNS database of two premixed turbulent jet flames. One accounts for thermodiffusive instabilities, while the other disables them by setting the Lewis numbers of all species to unity. The second configuration is performed for a research hydrogen engine, where two operating conditions were considered: one with a stoichiometric mixture and the other with a lean mixture representing conditions without and with strong thermodiffusive instabilities, respectively. Significant improvement in the prediction of the flame length of the jet flame and the in-cylinder pressure of the research engine was achieved with the extended model. The super-adiabatic temperatures due to thermodiffusive instabilities cannot be captured by the extended model, indicating a potential for further improvement for cases where the temperature distribution is of interest.