Tandon Shruti, Pawar Samadhan A, Banerjee Subham, Varghese Alan J, Durairaj Premraj, Sujith R I
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2020 Oct;30(10):103112. doi: 10.1063/5.0005379.
Intermittency observed prior to thermoacoustic instability is characterized by the occurrence of bursts of high-amplitude periodic oscillations (active state) amidst epochs of low-amplitude aperiodic fluctuations (rest state). Several model-based studies conjectured that bursting arises due to the underlying turbulence in the system. However, such intermittent bursts occur even in laminar and low-turbulence combustors, which cannot be explained by models based on turbulence. We assert that bursting in such combustors may arise due to the existence of subsystems with varying timescales of oscillations, thus forming slow-fast systems. Experiments were performed on a horizontal Rijke tube and the effect of slow-fast oscillations was studied by externally introducing low-frequency sinusoidal modulations in the control parameter. The induced bursts display an abrupt transition between the rest and the active states. The growth and decay patterns of such bursts show asymmetry due to delayed bifurcation caused by slow oscillations of the control parameter about the Hopf bifurcation point. Further, we develop a phenomenological model for the interaction between different subsystems of a thermoacoustic system by either coupling the slow and fast subsystems or by introducing noise in the absence of slow oscillations of the control parameter. We show that interaction between subsystems with different timescales leads to regular amplitude modulated bursting, while the presence of noise induces irregular amplitude modulations in the bursts. Thus, we speculate that bursting in laminar and low-turbulence systems occurs predominantly due to the interdependence between slow and fast oscillations, while bursting in high-turbulence systems is predominantly influenced by the underlying turbulence.
在热声不稳定性出现之前观察到的间歇性特征是，在低振幅非周期性波动（静止状态）的时期中出现高振幅周期性振荡的突发（活跃状态）。一些基于模型的研究推测，突发是由于系统中潜在的湍流引起的。然而，这种间歇性突发甚至在层流和低湍流燃烧器中也会发生，而基于湍流的模型无法对此进行解释。我们断言，此类燃烧器中的突发可能是由于存在具有不同振荡时间尺度的子系统，从而形成了快慢系统。在水平瑞利管上进行了实验，并通过在控制参数中外部引入低频正弦调制来研究快慢振荡的影响。诱导的突发显示出静止状态和活跃状态之间的突然转变。由于控制参数围绕霍普夫分岔点的缓慢振荡导致延迟分岔，此类突发的增长和衰减模式表现出不对称性。此外，我们通过耦合快慢子系统或在控制参数不存在缓慢振荡的情况下引入噪声，开发了一种热声系统不同子系统之间相互作用的唯象模型。我们表明，具有不同时间尺度的子系统之间的相互作用会导致规则的振幅调制突发，而噪声的存在会在突发中诱导不规则的振幅调制。因此，我们推测，层流和低湍流系统中的突发主要是由于快慢振荡之间的相互依存关系，而高湍流系统中的突发主要受潜在湍流影响。
