Role of acoustic waves and acoustic feedback in instability and aeroacoustics of shear flows

研究背景自然界和工程中大多数流体流动都是以剪切流动的形式进行的。此外，它们经历了从具有简单时空格局的层流态到具有高度复杂和明显随机时空波动特征的湍流态的过渡。剪切-层过渡的内在原因是层流状态的不稳定，但环境扰动等外部因素也起着重要作用。过渡涉及一系列的物理过程，从激发小振幅不稳定波开始。接下来是线性阶段，在这个阶段中，受激的不稳定波呈指数增长，导致非线性状态，其中不稳定波之间或不稳定波与外部扰动的非模态响应之间发生相互作用。跃迁是具有重大基础科学意义的突出的非线性现象之一。理解和预测过渡也具有至关重要的实际意义，因为它会影响临界阻力、高速空气动力学加热、混合以及噪声的产生。目的与目的剪切流的过渡容易受到外界干扰。在超音速状态下，环境声波是特别重要的。在实验室条件下，声波来自沿隧道壁的边界层，而在空气动力学应用中，声波可能由流动的其他部分产生。在这两种情况下，声波冲击剪切流改变其不稳定性，从而发生过渡。另一方面，超音速剪切流可能支持所谓的辐射不稳定性。入射和自发辐射声波可以形成一个声反馈回路，从而完全改变不稳定和过渡情景。博士项目研究声波和声反馈回路在不稳定和过渡中的作用。本文首先研究了入射声波与超声速边界层的相互作用，计算了入射声波在超声速边界层中的反射系数和强迫响应特征。接下来，我们分析了强迫响应与不稳定波的相互作用，并监测了它对后者发展的影响。将特别注意可能出现的辐射不稳定性，这种不稳定性表现为共振过反射。声学反馈回路的形成将在与风洞实验相关的双边界层模型中进行研究。这项工作将扩展到双喷气机。随着入射声波对不稳定性的影响被量化，理论结果将有助于将风洞数据“外推”到飞行条件。所获得的更好的理解将有助于开发利用声波驱动的流量控制技术。该研究将有助于更好地描述双射流的不稳定性和声辐射。研究方法的新颖性研究结合了详细的渐近分析和精确的数值计算来探讨物理机制，允许基于第一性原理构建相关的理论描述。

Context of the researchMost fluid flows in nature and engineering are in the form of shear flows. Moreover, they undergo transition from laminar states, which exhibit simple temporal and spatial patterns, to turbulent states, which are characterized by highly complex and apparently stochastic fluctuations in both time and space. The intrinsic reason of shear-layer transition is instability of the laminar state, but external factors such as ambient disturbances also play an important role. Transition involves a sequence of physical processes, starting with excitation of small-amplitude instability waves. This is followed by the linear stage, in which the excited instability waves grow exponentially, leading to the nonlinear regime, where mutual interactions take place between instability waves, or between instability waves and the non-modal response to the external disturbances. Transition is one of the outstanding nonlinear phenomena of great fundamental scientific significance. Understanding and predicting transition are also of crucial practical importance because it affects critically drag, aerodynamics heating at high speeds, mixing as well as noise generation.Aims and objectivesTransition in shear flows is prone to external disturbances. In the supersonic regime, ambient acoustic waves are of particular importance. In laboratory conditions, acoustic waves come from the boundary layers along the tunnel walls, whereas in aerodynamical applications sound waves may be generated by other parts of the flow. In either case, acoustic waves impinge on the shear flow to change its instability and hence transition. On the other hand, supersonic shear flows may support the so-called radiating instabilities. The incident and spontaneously radiated sound waves may form an acoustic feedback loop thereby changing completely the instability and transition scenarios. The PhD project investigates the role of acoustic waves and acoustic feedback loop in instability and transition. We start with studying the interaction of an incident acoustic wave with a supersonic boundary layer and calculating the reflection coefficient as well as the signature of the forced response in the boundary layer. Next, we analyze the interaction of the forced response with instability waves and monitor its impact on the development of the latter. Particular attention will be directed to possible radiating instabilities, which manifest as resonant over-reflection. Formation of an acoustic feedback loop will be investigated in a twin-boundary-layer model pertaining to the wind tunnel experiments. The work will then be extended to twin jets.Potential applications and benefitsWith the effect of the incident sound waves on instability being quantified, the theoretical results will help 'extrapolate' wind tunnel data to the flight condition. The improved understanding gained will help develop flow control technique using acoustic actuation. The proposed research will lead to a better description of instability and acoustic radiation of twin jets.Novelty of the research methodologyThe research combines detailed asymptotic analysis and accurate numerical computations to probe into physical mechanisms, allowing for construction of relevant theoretical descriptions based on first principles.