Abstract Insufficient dynamic information on helium piping systems limits our ability to understand and identify thermoacoustic oscillation (TAO) phenomena in these systems. In this study, we investigate the associated oscillation behaviours and the effects of the temperature distribution steepness, S, and the inflection point position, x0, on the TAO characteristics through numerical simulations. The results indicate that x0 has a greater impact on the oscillation behaviour and is a decisive factor for oscillation-free operation. It is found that oscillation-free operation can be achieved when x0 = 0.9 m. To identify the nonlinear dynamic characteristics related to TAO, the original pressure time series are unfolded in phase portraits and Poincare maps. In contrast to the period-1 and period-2 limit circle oscillations at other positions, the trajectory at x0 = 0.9 m displays a transition from limit circles to a fixed point (zero amplitude), corresponding to a series of points including the point (0,0) in the Poincare map. Therefore, an approach of adjusting the inflection point position can be used to control the state of the TAO, and the transition in the nonlinear dynamic characteristics can be identified, which can also provide guidelines for designers to mitigate unfavourable TAO.

中文翻译：

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氦气管道系统热声振荡非线性特性的识别

摘要 氦气管道系统的动态信息不足限制了我们理解和识别这些系统中的热声振荡 (TAO) 现象的能力。在这项研究中，我们通过数值模拟研究了相关的振荡行为以及温度分布陡度 S 和拐点位置 x0 对 TAO 特性的影响。结果表明，x0 对振荡行为的影响更大，是无振荡运行的决定性因素。发现当 x0 = 0.9 m 时可以实现无振荡操作。为了识别与 TAO 相关的非线性动态特性，原始压力时间序列在相图和 Poincare 图中展开。与在其他位置的周期 1 和周期 2 限制圆振荡相反，x0 = 0.9 m 处的轨迹显示了从极限圆到固定点（零振幅）的过渡，对应于一系列点，包括 Poincare 图中的点 (0,0)。因此，可以通过调整拐点位置的方法来控制TAO的状态，识别非线性动态特性的转变，也可以为设计者减轻不利的TAO提供指导。