Direct Numerical Simulations (DNS) are performed to investigate the process of spontaneous ignition of hydrogen flames at laminar, turbulent, adiabatic and non-adiabatic conditions. Mixtures of hydrogen and vitiated air at temperatures representing gas-turbine reheat combustion are considered. Adiabatic spontaneous ignition processes are investigated first, providing a quantitative characterization of stable and unstable flames. Results indicate that, in hydrogen reheat combustion, compressibility effects play a key role in flame stability and that unstable ignition and combustion are consistently encountered for reactant temperatures close to the mixture’s characteristic crossover temperature. Furthermore, it is also found that the characterization of the adiabatic processes is also valid in the presence of non-adiabaticity due to wall heat-loss. Finally, a quantitative characterization of the instantaneous fuel consumption rate within the reaction front is obtained and of its ability, at auto-ignitive conditions, to advance against the approaching turbulent flow of the reactants, for a range of different turbulence intensities, temperatures and pressure levels. ©2021The Author(s).