Energy consideration of the nonlinear effects in a Rijke tube

The goal of this work is to characterize the excited states of a thermoacoustic system with mean flow. The properties of excited regimes are determined by the balance between thermoacoustic energy transformation and acoustic losses. In many systems, the sound intensity is not sufficient for nonlinear acoustic losses to be a major factor in defining nonlinear saturation of thermoacoustic instability. It is the nonlinearity of the heat transfer process that is responsible for limit-cycle stabilization of linearly unstable acoustic modes and for the appearance of higher harmonics. In the present study, both a nonlinear theory based on energy consideration and a model for the nonlinear convective heat transfer in unsteady flow are developed. Experimental data are obtained for the excited regimes of operation of an electric Rijke tube. Model results for hysteresis in the transition between stable and excited states and for limit-cycle parameters are compared with test data.