A method for estimating the noise level of unstable combustion based on the flame describing function

Practical combustion is often coupled by the system acoustics and under some conditions the process may become unstable giving rise to oscillations of finite amplitude and to discrete tone noise radiation. The objective of this investigation is to model the nonlinear features of unstable combustion to predict limit cycle amplitudes and thus get an estimation of the radiated noise level under such regimes of operation. The present study is based on an analysis derived in a companion paper (Noiray et al. (2008)) which contains a complete nonlinear description of the thermo-acoustic coupling encountered in an unconfined reaction zone layout. Theoretical predictions are successfully compared with a set of measurements. It is shown that nonlinear phenomena such as frequency shifts, triggering or hysteresis may be suitably predicted by an analytical model based on the flame describing function (FDF). The objective of the present paper is to make use of this method to investigate nonlinear acoustic-combustion dy...