Effect of choked outlet on transient energy growth analysis of a thermoacoustic system

Thermoacoustic instability occurs in many practical combustion systems. These systems are non-normal and associated with transient growth of acoustic disturbances. If the transient growth is large enough, then thermoacoustic instability may be triggered. In this work, transient energy growth analysis of a thermoacoustic system with a choked outlet is conducted. The effect of the choked boundary is studied by using an analytical and a linearized Euler equation (LEE) method. To quantify the transient growth, two energy measures are defined and calculated. One is associated with the acoustical energy. The other is the total energy of both entropy and acoustic fluctuations. Comparison is made between the transient growth results obtained from the analytical method and those from the LEE method. It is found that the transient growth analysis of the total energy by using the analytical model with the expression of the choked outlet is consistent with that by using the LEE method. However, when only acoustical energy is considered, the analytical model may leads to a wrong prediction of transient growth. The present work opens up new applicable way to predict transient stability behaviors of a practical engine system ended with a choked outlet.