Passive instability control by a heat exchanger in a combustor with nonuniform temperature

Thermoacoustic instabilities, caused by the feedback between unsteady heat release and acoustic pressure perturbations, are characterised by large-amplitude pressure oscillations. These oscillations, if uncontrolled, pose a threat to the integrity of combustion systems. One strategy to mitigate them is by installing cavity-backed perforated plates with bias flow into the combustion chamber. In this study, we consider a generic combustor configuration: a one-dimentional tube (with open and/or closed ends) containing a compact heat source and a heat exchanger tube row. The idea is to use the heat exchanger tube row as a device (analogously to a cavity-backed perforated plate) to manipulate the downstream end condition. We simulate the row of heat exchanger tubes by a slit-plate with bias flow. We derive the characteristic equation for the complex eigenfrequencies of this set-up. From the growth rates (imaginary parts of the eigenfrequencies), we construct stability maps for various system parameter combinations. The results, obtained for the first two modes of the system, show that by varying the cavity length or the bias flow velocity through the slits, we can stabilise a previously unstable combustion system.