Accurate and efficient numerical predictions of flutter is essential for the turbomachinery industry. The decoupled method has been the main workhorse of the industry for decades thanks to its low computational resources required. However, there arises the need for an innovative propulsion architecture and a lightweight material, which hinders the accuracy and effectiveness of the decoupled method. Hence, the use of fully-coupled methods for flutter predictions has been steadily increasing. Despite more demanding computational resources needed to perform the fully-coupled simulations, the large amount of data generated in the time-domain is not often used efficiently. Typically the aeroelastic stability is judged in a straightforward manner using the logarithmic decrement. Although this global parameter is useful to compare the aeroelastic stability among configurations, it yields almost no meaningful understanding of the physical vibration mechanisms. In the present paper, a spatial–temporal analysis approach based on the Hilbert transform is proposed. It can work well with the non-linear non-stationary data typically generated from the time-domain fully-coupled solutions. In addition, the Hilbert transform-based analysis approach is designed to be consistent with the conventional energy method when the newly developed method is applied to the decoupled simulation data. The Hilbert transform-based approach is applied to three computational examples, each with a particular aeroelastic flow mechanisms of interest (i.e. tip clearance, laminar separation bubble, stall). The new approach has been shown to effectively elucidate the associated vibration mechanisms using the decomposition method in space and time.

准确有效的颤振数值预测对于涡轮机械行业至关重要。由于所需的计算资源少，解耦方法几十年来一直是该行业的主要主力。然而，需要创新的推进结构和轻质材料，这阻碍了解耦方法的准确性和有效性。因此，用于颤振预测的全耦合方法的使用一直在稳步增加。尽管执行全耦合仿真需要更多的计算资源，但在时域中生成的大量数据通常没有得到有效利用。通常，气动弹性稳定性是使用对数减量以直接方式判断的。虽然这个全局参数对于比较配置之间的气动弹性稳定性很有用，但它几乎没有产生对物理振动机制的有意义的理解。在本文中，提出了一种基于希尔伯特变换的时空分析方法。它可以很好地处理通常由时域全耦合解决方案生成的非线性非平稳数据。此外，当新开发的方法应用于解耦模拟数据时，基于希尔伯特变换的分析方法被设计为与常规能量方法保持一致。基于希尔伯特变换的方法应用于三个计算示例，每个示例都具有特定的气动弹性流动机制（即叶尖间隙、层流分离气泡、失速）。