Preferential diffusion plays an important role especially in hydrogen flames. Flame stretch significantly affects the flame structure and induces preferential diffusion. A problematic phenomenon occurring in real combustion devices is flashback, which is influenced by non-adiabatic effects, such as wall heat loss. In this paper, an extended flamelet-generated manifold (FGM) method that explicitly considers the preferential diffusion, flame stretch, and non-adiabatic effects is proposed. In this method, the diffusion terms in the transport equations of scalars, viz. the progress variable, mixture fraction, and enthalpy, are formulated employing non-unity Lewis numbers that are variable in space and different for each chemical species. The applicability of the extended FGM method to hydrogen flames is investigated using two- and three-dimensional numerical simulations of hydrogen-air flame flashback in channel flows. The results of the extended FGM method are compared with those of detailed calculations and other FGM methods. The two-dimensional numerical simulations show that considering both preferential diffusion and flame stretch improves the prediction accuracy of the mixture fraction distribution and flashback speed. The three-dimensional numerical simulations show that the prediction accuracy of the flashback speed, backflow region, and distributions of physical quantities near the flame front is improved by employing the extended FGM method, compared with the FGM method that considers only the heat loss effect. In particular, the extended FGM method successfully reproduced the relationship between the reaction rate and curvature. These results demonstrate the effectiveness of the extended FGM method. Novelty and Significance Statement The novelty of this research is the development of a flamelet-generated mani-fold (FGM) method that explicitly considers preferential diffusion, flame stretch, and non-adiabatic effects. To the best of the authors' knowledge, no studies have performed numerical simulations of pure hydrogen flames using such an FGM method. The developed FGM method was applied to numerical simula- tions of hydrogen-air premixed flame flashback at an equivalence ratio of 0.5 and reproduced the flashback speed of lean hydrogen-air premixed flame. The applicability of the FGM method to the numerical simulation of hydrogen-air flashback is reported first. This research is significant because the FGM method is one of the most widely used combustion models for premixed combustion, and the development of an accurate FGM method will contribute to the engineering field. The accurate prediction of the flame flashback attempted in this study is particularly important for the development of hydrogen-fueled combustion devices.
