Low order modelling of thermoacoustic instabilities in aero-propulsion engines

In the present work, we investigate the thermoacoustic stability behaviour of a combustor-heat exchanger assembly pertinent to the Synergetic Air Breathing Rocket Engine (SABRE) of Reaction Engines Ltd. Since the thermoacoustic behaviour of heat exchangers is poorly understood, we have approximated it to a combination of heat transfer/heat sink and aeroacoustic scattering (dissipation) mechanisms. The ε-NTU method is used to characterise the low frequency, linearised unsteady heat transfer (heat exchanger transfer function) behaviour in compact heat exchangers. The aeroacoustic response of the tube row is evaluated from the linearised conservation equations, wherein the hydrodynamics of the bias flow in the tube row is described as being similar to that of an isentropic contraction followed by a sudden expansion. The stability predictions are carried out through low order modelling of the combustor and subsequent eigenvalue analysis. The flame dynamics is approximated using the n-τ law, with τ being a parameter. Stability predictions show that the thermoacoustic response of the heat exchanger was dominated by aeroacoustic dissipation. Only one mode was predicted to be unstable and can be stabilised by moving the heat exchanger upstream. Further work is required to better characterise the flame and the heat exchanger transfer functions.