Experimental and theoretical estimation of acoustic energy source terms and instability growth rates in an annular combustor

Abstract

The determination of acoustic source terms and growth rates is of paramount importance in the thermoacoustic stability analysis of combustion systems. This article aims to experimentally quantify the acoustic energy source term in the laboratory-scale annular combustor MICCA-Spray and deduce growth rate estimates from these measurements. MICCA-Spray is equipped with sixteen modular injection units and an original method is used to vary the level of self-sustained pressure oscillations at limit cycle in the system by mixing injectors leading to different flame dynamics, characterized by their flame describing functions (FDFs). Various injectors’ arrangements are explored, and the Rayleigh source terms associated to the different flames are determined from the simultaneous recording of pressure and heat release rate fluctuations that are respectively detected by a set of microphones plugged on the chamber backplane and photomultipliers collecting the light emitted by OH* radicals. The contribution of the different flames to the total acoustic source term is quantified and shown to depend on the flame position with respect to the nodal line and the flame dynamical characteristics (FDF gain and phase). A theoretical expression of the growth rate, based on the FDF data collected in a single-injector test rig, is derived. The analytical results closely match the experimentally determined Rayleigh source terms and provide growth rates that exceed the damping rate, which is in agreement with experimental observations, thus validating the analytical framework and indicating that the model can be used for predictive purposes.