Executive Summary : | The positive feedback loop between the heat release rate fluctuations and the acoustic pressure fluctuations inside the combustion chambers of systems like gas turbine engines, domestic boilers, industrial burners etc. lead to thermoacoustic instabilities (high amplitude pressure fluctuations) that may be catastrophic to the combustor, if unchecked. One of the methods to mitigate these instabilities is through the use of secondary heat sources/sinks. In thermoacoustic modelling, heat sources/sinks are usually assumed to be infinitesimally thin and compact. In the proposed project, we aim to study the thermoacoustic behaviour of combustors in the presence of secondary heating/cooling through the combustor walls. However, for the spatially distributed heat transfer through the wall, we propose to treat it as a Rayleigh flow. To this end, an Eigenvalue analysis will be carried out on the combustor after modelling it in terms of a network of acoustic elements that are described through their respective Transfer Matrices. The transfer matrix for the secondary heating/cooling will be built by assuming the flow to be a Rayleigh flow; and the heat transfer process (at the walls) will be analysed through the thermal boundary layer formulation. Additionally, the time lag between the heat transfer (at the wall) fluctuations and acoustic fluctuations is a critical parameter which determines the establishment of a positive/negative feedback loop that enhances/mitigates instability; and for the heat transfer at the walls, this quantity will be determined through numerical simulations (since there is limited literature available). |