Sensitivity analysis of thermoacoustic instabilities

Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land-based gas turbines. The thermoacoustic oscillations of these systems are of significant importance as they can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. In this work we use a low-order network model representation of a combustor where linear acoustics are solved together with appropriate boundary conditions and flame jump conditions. Special emphasis is directed towards the interaction between instabilities associated with acoustic modes and flame-intrinsic modes. Adjoint methods are used to perform a receptivity and sensitivity analysis of the spectral properties of the system to changes in the parameters involved. To better analyse the extreme sensitivities that arise in the neighbourhood of a modal interaction, we compare the results with a time domain model that allows us to perform a pseudospectra analysis. The results provide key insights into the interplay between mode types.