Effect of combined liners on controlling thermoacoustic instability in a Rijke tube

In present paper, theoretical investigation on the effect of combined liners of a drum-like liner and a perforated liner with bias flow on controlling thermoacoustic instability in a Rijke tube is carried out by transfer element method (TEM). TEM is used to consider the interactions between the acoustic waves and the soft boundary of the drum-like liner or perforated liner with bias flow. The respective effect of the drum-like liner and perforated liner with bias flow on changing the frequency and growth rate of the first two planar modes are investigated. In addition, effects of main features of the combined liners on the growth rate and natural frequency of the thermoacoustic system are explored by calculating the complex resonance frequency in some representative configurations. It is found that the frequency decrease induced by the usage of the liners can lead to increase of the phase difference between unsteady heat release and pressure oscillation, which is helpful for controlling thermoacoustic instability. Besides, the change of frequency may result in the jump of the phase difference between heat and pressure oscillations at some fixed point in the tube, the potential positive side of which can be utilized to make the unsteady release stabilized. It is found that the damping effect of the perforated liner, which is manifested by attenuation of the sound pressure, is maximized when the perforated liner is placed close to the downstream end of the Rijke tube. At this “optimal” position for the perforated liner with bias flow, the inclusion of the drum-like liner will deteriorate control effect by decreasing the natural frequency. Nevertheless, when the perforated liner is located near the heat source, the damping effect of the perforated liner is weakened, and at this “non-ideal” position, the incorporation of the drum-like liner will help control thermoacoustic instability. It brings out an inspiration that the thermoacoustic instability can be controlled more effective when the main damping source is not at the “optimal” position with this technique without bringing in any aerodynamic loss.