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.

A slug length is widely used to describe additional mass inertia at low frequencies in duct acoustics. It is often used in acoustic energy analysis, e.g. as one of the inputs for semi-analytical or empirical models to obtain the acoustic reflection and transmission coefficients. However, the calculation of slug length is usually empirical and limited to many conditions, such as simple geometric configurations, low frequencies, no mean flow, etc. In this paper, the slug length at a contraction with mean flow between two half cylinders is calculated by different methods: solving the Laplace's equation both analytically and numerically, solving the Helmholtz equation, and using the Cummings - Fant equation based on the numerical results of frequency-domain linearized Navier-Stokes equations. Both the frequency-dependence and the mean flow effect are discussed. The calculated slug lengths are then used in the semi-analytical model to predict the acoustic scattering at tube rows in the presence of a cross mean flow.

Cylindrical tubes in cross-flow, like the ones found in heat exchangers, are excellent acoustic dampers and as such have the potential to mitigate thermoacoustic instabilities. Flow separation and vortex shedding downstream of the tube row are key to significantly enhancing sound attenuation. However, constructing an analytical solution for the aeroacoustic response of tube rows in cross-flow is very challenging owing to the complex flow structure, vortex shedding and coupling with acoustics. To overcome this, we propose the adaptation of a slit model for tube row acoustic scattering (aeroacoustic response) predictions at low Strouhal numbers. The slit model was modified such that the loss coefficients across the slit and the tube row matches. The model is then validated against numerical predictions using Linearised Navier Stokes Equations and experimental measurements. The predictions for both magnitude and phase for transmission and reflection coefficients agree well with the simulations and experiments.