<p>Turbulent hydrogen flames with varying operating conditions in the swirl-axial air injection AHEAD combustor were studied computationally with a multi-regime flame closure method, combustion LES / Stochastic fields. The method was validated by comparisons with measurements in isothermal and reacting flows. The velocity fields, flames, mixing fields and thermo-chemical states were analysed in detail. Further comparisons were carried out for different operating conditions to study the effect of global equivalence ratio and axial air injection ratio. On the one hand, it introduces higher axial momentum, which restricts flashback. On the other hand, increasing the global equivalence ratio or axial air injection ratio negatively affects the spatial mixing quality where the axial momentum flux plays an important role. The results also suggest that thermo-chemical states are dominantly controlled by the global equivalence ratio rather than the inlet reactant temperature or flow conditions. The effect of differential diffusion was also studied. Differential diffusion slightly increases the possibility of the upstream occurrence of the flame inner branch, which results in the inner flame branch brush becoming broader. This was found to be related to the changes of the upstream mixing field due to differential diffusion. Nevertheless, the global system is negligibly influenced by differential diffusion due to the high Reynolds number.</p>