ANALYTICAL MODELLING OF FLAME-DYNAMICS WITHIN AUTO-IGNITION HYDROGEN AND METHANE FLAMES IN MACH STABILIZED COMBUSTION

The sequential combustion concept is characterized by two combustor stages. In the first stage a fraction of the fuel is premixed into the air flow before burning in a standard lean premixed flame. In the second stage, which is the focus of the present contribution, the remaining part of the fuel is injected into the hot products arriving from the first stage and combustion takes place in an autoignition-dominated flame. We analyse here a situation where auto-ignition in the second stage takes place in a flow subject to a positive static temperature gradient. This concept allows very short combustor residence times ans is well suited for incorporation into an integrated combustor-nozzle guide vane. In order to set up the static temperature gradient, the mixture of reactants flows through a converging-diverging channel, first accelerated to a relatively high Mach number, ca. M = 0.6, and then decelerated in the diffusing section where the flame is located. A fully analytical model describing the thermoacoustics behaviour of the converging-diverging combustor is developed. The critical part of this exercise is given by modelling the frequency response of the heat release rate concentrated at the position of the auto-igniting flame. It is shown here how this is closely related to the response of the displacement of the flame for which a novel analytical model, free from empirical assumptions, is provided. The model is finally applied to compare hydrogen and methane flames in terms of their thermo-acoustic behaviour.