Mitigation of Thermoacoustic Instability Through Amplitude Death: Model and Experiments

Abstract

The combustors used in practical devices such as rockets and gas turbine engines are in most cases prone to large amplitude pressure oscillations, known as thermoacoustic instability. Due to such high-amplitude pressure oscillations, the lifetime of the engines reduces, including structural damage and reduction in the performance of the engines. Hence, such oscillations need to be avoided, and therefore, many control techniques, both passive and active, have been implemented in the past to suppress these undesired oscillations. In the present chapter, we discuss an approach based on amplitude death (AD) phenomenon to mitigate thermoacoustic oscillations. AD is a general outcome in coupled oscillators, wherein individual oscillators cease to oscillate when coupled appropriately. We systematically investigate amplitude death (AD) phenomenon in a thermoacoustic system using a mathematical model of coupled prototypical thermoacoustic oscillators, the horizontal Rijke tubes. We particularly examine the effect of time-delay and dissipative couplings on a system of two Rijke tubes when they are symmetrically and asymmetrically coupled. The regions where appropriate combinations of delay time, detuning, and the strengths of time-delay and dissipative coupling lead to AD are identified. The relative ease of attaining AD when both the couplings are applied simultaneously is inferred from the model. In the presence of strong enough coupling, AD is observed even when the oscillators of dissimilar amplitudes are coupled, while a significant reduction in the amplitudes of both the oscillators is observed when the coupling strength is not enough to attain AD. We further focus on the possibility of amplitude death (AD) in a noisy system. In the stochastic case, AD or a complete cessation of oscillation is impossible. However, we observed a considerable amplitude reduction in the coupled limit cycle oscillations. We also substantiate our claim through experiments where two Rijke tubes are coupled through a coupling tube whose length and diameter are varied as coupling parameters. We show that the effectiveness of coupling is sensitive to the dimensions of the coupling tube which can be directly correlated with the time-delay and coupling strength of the system.