Modeling of Unstable Regimes in a Rijke Tube

In the ducts with mean flows and heat sources, excitation of acoustic eigen modes is possible when unsteady heat release is coupled with pressure perturbations. The simplest device for studying the fundamental principles of thermoacoustic instabilities in the presence of a mean flow is a Rijke tube. In this work a series of experiments was carried out to determine the conditions for the transition to instability and the non-linear characteristics of a Rijke tube, such as limit-cycle amplitudes and frequencies of the dominant mode. Sound, excited in the tube, affects the heat transfer process; that leads to modifications of the acoustic mode shapes and steady state properties. It was observed in the experiment that the thermoacoustic system possesses hysteresis. A mathematical model incorporating heat transfer, acoustics, and thermoacoustic interactions is developed for determining the transition to instability. The dominant nonlinear factor in the system, defining the limit-cycle characteristics, is the nonlinearity of the heater transfer function. Two approximate and generally applicable nonlinear models are considered, and results of the modeling are compared with the experimental data for one position of the heater. The influence of noise on the transitions between stable and unstable regimes is discussed.Copyright © 2002 by ASME