Predicting the amplitude of limit-cycle oscillations in thermoacoustic systems with vortex shedding

Thermoacoustic instability is a plaguing problem encountered in many combustion systems. The large-amplitude acoustic oscillations, which are a noted aspect of this instability, can have a detrimental effect on the performance of the system; and they sometimes even cause lasting damage to the system components. The aim of this study is to estimate the amplitude of the limit-cycle oscillations observed during thermoacoustic instability corresponding to the axial acoustic modes using pressure measurements acquired during stable combustion. First, an equation is derived that describes the slow-varying amplitude of oscillations in certain reduced-order models of combustion systems involving vortex shedding. Subsequently, a procedure is detailed, wherein this equation is used in conjunction with the measured pressure time series and some information about the system to predict the instability amplitude. The estimation capability of this technique is then tested using acoustic pressure data obtained from laboratory-scale bluff-body and swirl-stabilized combustors. It is observed that the estimated amplitudes are in good agreement with actual values.