混沌声振荡的稳定性、灵敏度和优化
Stability, sensitivity and optimisation of chaotic acoustic oscillations
摘要：
在具有热源（例如燃气轮机中的火焰）的声腔中，热源的热能可转换成声能，声能可产生响亮的振荡。如果不受控制，这些非线性声振荡，也称为热声不稳定性，可能导致大的振动，直至结构失效。数值和实验研究表明，热声振荡可以是混沌的。然而，目前还不知道如何最小化这种混沌振荡。我们提出了一种策略，以分析和减少混沌声振荡，传统的稳定性和灵敏度的方法预锻打破。本文研究了声谐振器中非线性热源的声学特性。首先，我们提出协变李雅普诺夫分析作为一种工具来计算混沌声学的稳定性，使连接特征值和Floquet分析。我们表明，协变李雅普诺夫分析是最普遍的流动稳定性工具。其次，将协变李雅普诺夫向量分析应用于混沌系统。通过改变热源参数，研究了时均声能。热声系统可以表现出双曲和非双曲混沌，以及时间平均声能的不连续性。第三，我们在优化例程中嵌入时间平均声能的灵敏度。这个过程实现了显着减少声能，并确定混沌的分叉。提出的分析和方法，使减少混沌振荡的热声系统的最佳被动控制。所提出的技术可以用于其他非定常流体动力学问题，几乎没有修改。
英文摘要：
In an acoustic cavity with a heat source, such as a flame in a gas turbine, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these nonlinear acoustic oscillations, also known as thermoacoustic instabilities, can cause large vibrations up to structural failure. Numerical and experimental studies showed that thermoacoustic oscillations can be chaotic. It is not yet known, however, how to minimise such chaotic oscillations. We propose a strategy to analyse and minimise chaotic acoustic oscillations, for which traditional stability and sensitivity methods break down. We investigate the acoustics of a nonlinear heat source in an acoustic resonator. First, we propose covariant Lyapunov analysis as a tool to calculate the stability of chaotic acoustics making connections with eigenvalue and Floquet analyses. We show that covariant Lyapunov analysis is the most general flow stability tool. Second, covariant Lyapunov vector analysis is applied to a chaotic system. The time-averaged acoustic energy is investigated by varying the heat-source parameters. Thermoacoustic systems can display both hyperbolic and non-hyperbolic chaos, as well as discontinuities in the time-averaged acoustic energy. Third, we embed sensitivities of the time-averaged acoustic energy in an optimisation routine. This procedure achieves a significant reduction in acoustic energy and identifies the bifurcations to chaos. The analysis and methods proposed enable the reduction of chaotic oscillations in thermoacoustic systems by optimal passive control. The techniques presented can be used in other unsteady fluid-dynamics problems with virtually no modification.
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