Three-dimensional Large Eddy Simulations (LES) are conducted on a non-premixed hydrogen-air annular rotating detonation combustor (RDC). A 22-step finite-rate chemistry reaction mechanism and a flow solver previously developed for high-speed reacting flow are used to perform the LES’. The selected case is an RDC designed by the US Air Force Research Laboratory and has been studied experimentally across various configurations and a variety of operating conditions. In this investigation, one RDC geometry has been chosen whereas the mass flow rate is varied. A stoichiometric equivalence ratio, ϕ, is maintained for all simulations. Three cases with mass flow rates between 0.144 kg/s and 0.628 kg/s are studied. Following initiation and an unsteady transition period, the detonation wave(s) settle into a stable mode of rotation. The cases exhibited either one, two, or four co-rotating waves, with more waves for higher flow rates. The model’s ability to reproduce key features of rotating detonation waves is demonstrated. Quantitative evaluation of the LES results is performed with the validation of some against available experimental data. The time-averaged chamber pressures are found to share similar values and trends as experimental data. The behaviour of the propagating wave and the effects on the surroundings are analysed. For instance, the time-varying LES data reveal how the waves interact with the instantaneous temperature, pressure, and reactant fields.