Global instability of laminar separation bubbles
Global instability of laminar separation bubbles
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层流分离气泡的整体不稳定性
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发表时间：
2010
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通讯作者：
Daniel Álvarez
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作者：
Daniel Álvarez
流动分离与流过或穿过具有工程意义的结构的各种流动的内在拓扑变化密切相关。不可避免地，对提升面性能的不利影响与流动分离有关，这为半个多世纪以来不可压缩和可压缩分离流动的研究提供了动力。然而，尽管研究不断，但有关分离气泡的外观、结构和行为的许多问题仍未解决。虽然在大量的实验和数值研究中已经证实了与流动分离形成的剪切层相关的开尔文-亥姆霍兹不稳定性的优势，但它不足以解释呼吸或拍打气泡行为的发生，即分离气泡区域的振荡频率大大低于开尔文-亥姆霍兹不稳定性的预测频率。这种频率在控制分离气泡大小方面的有效性，以及气泡持续分解成完全三维模式的有效性。另一方面，考虑到分离气泡本质上的非平行、非局域性，全局不稳定性分析能够预测不同于开尔文-亥姆霍兹不稳定性的全局不稳定性机制。本文采用全局不稳定性分析方法研究了层流分离气泡的全局不稳定性。由于直接求解相关的基于偏导数的特征值问题需要大量的计算资源，这种方法一直局限于简单的几何形状和低分辨率。在当前工作过程中取得的最新进展导致了问题解决中使用的算法的并行化，显着放松了与串行解决方案相关的约束，达到了最先进的分布式内存超级计算机的可能性。两种配置包括分离气泡已经考虑在这里：一系列模型层流分离气泡在一个菲亚特piate，和周围的流动停滞NACA 0015翼型。本研究的第一部分涉及层流分离气泡模型的全局不稳定性分析。描述可能的分离状态所涉及的许多参数，以及它们对不稳定性的潜在决定性影响，表明需要寻找适当的层流分离气泡模型，在这些模型中可以独立分析参数的影响。基于Orr-Sommerfeld方程的解，与已建立的时空局部稳定性理论的结果进行比较，作为bigglobal分析恢复的模态失稳机制的识别和分类的基础。特别地，一个不稳定的，静止的和三维的全局模式是发现在平面和失速翼型；对其性能进行了详细分析。在论文的第二部分，为了揭示二维基本态和三维全局模态线性叠加所导致的不同拓扑分岔，我们使用了临界点的概念。特别注意表面流线或皮肤摩擦线，以便将目前的重建与实验油条纹拓扑进行直接比较。此外，还分析了与层流分离相关的三维场流线拓扑结构。由此产生的流动的拓扑描述，除了与理论的u型分离拓扑一致外，在质量上与实验中恢复的失速单元等效：跨展周期性结构，其中分离的流动区域围绕两个反向旋转的漩涡组织，由完全连接的带分开。此外，不稳定性分析预测的周期长度与实验观测到的特征长度吻合较好。本研究结果与文献实验结果的比较表明，层状分离气泡的整体模式的放大可能是失速细胞的来源。本文的主要结论是，层流分离泡的经典图像，由于受扰动波的弯曲不稳定性支配，既不能代表所有可能的分离泡，也不足以解释分离流的完整动力学。自激的、暂时放大的全局模态的存在不仅解释了名义上二维气泡的三维起源，而且还可能作为触发不稳定机制，导致不稳定的三维状态，在这些情况下，经典的（弯曲的）瑞利情景单独可以预测稳定的二维流动。
Flow separation is intimately related with intrinsic topological changes in a variety of flows over or through configurations of engineering signincance. Invariably, adverse effects on the performance of lifting surfaces are associated with flow separation, which has provided motivation for research efforts into both incompressible and compressible separated flows, spanning over half a century. However, and despite the continuous research, many questions related to the appearance, structure and behaviour of separation bubbles remain open. While predominance of the Kelvin-Helmholtz instability associated with the shear-layer formed on account of flow separation has been confirmed in a multitude of experimental and numerical investigations, it does not suffice to explain neither the occurrence of breathing or flapping bubble behavior, i.e. oscillations of the separation bubble region at frequencies substantially lower than those predicted for the Kelvin-Helmholtz instability, nor the effectiveness of such frequencies in controlling the size of separation bubbles, nor the time-persisting breakdown of bubbles into fully three-dimensional patterns. On the other hand, global instability analysis considering the essentially non-parallel, non-local nature of separation bubbles, are able to predict global instability mechanisms diiferent from the Kelvin-Helmholtz instability. The BiGlobal instability analysis has been used in this thesis to investigate the global instability of laminar separation bubbles. This approach has been historically confined to simple geometries and low resolutions because of the large computational resources required for the direct solution of the associated partial-derivative-based eigenvalue problems. Recent developments achieved in the course of the present work have resulted into the parallelization of the algorithms used in the solution of the problem, significantly relaxing the constrains related to the serial solution, up to the possibilities of state-of-art distributed memory supercomputers. Two kinds of configurations comprising separation bubbles have been considered herein: a series of model laminar separation bubbles on a fiat piate, and the flow around a stalled NACA 0015 airfoil. The first part of the present investigation is concerned with the BiGlobal instability analysis of the laminar separation bubble models. The many parameters involved in the description of possible separated states, and their potentially decisive effect on the instability properties suggests the search for adequate models of laminar separation bubbles in which the influence of the parameters could be analyzed independently. Comparisons with well-established results of both temporal and spatial local stability theories, based on the solution of the Orr-Sommerfeld equation, are used as a basis for the identification and classification of the modal instability mechanisms recovered by BiGlobal analysis. In particular, an unstable, stationary and three-dimensional global mode is found both in the flat piate and the stalled airfoil; its properties have been analyzed in detail. In the second part of the thesis, critical-point concepts have been employed in order to unveil the diiferent topological bifurcations resulting from the linear superposition of the two-dimensional basic states and the three-dimensional global mode. Special attention has been paid to the surface streamlines or skin-friction lines, in order to make direct comparisons between the present reconstructions and the experimental oil-streak topologies. In addition, three-dimensional field streamline topologies associated with laminar separation have been analyzed. The topological de-scription of the resulting flows, besides been in agreement with the theoretical U-shaped separation topology, is qualitatively equivalent to the stall cells recovered experimentally: spanwise periodic structures in which the separated flow regions are organized around two counter-rotating vortices, separated by fully attached bands. In addition, the periodicity length predicted by the instability analysis is in good agreement with the characteristic length observed in experiments. Comparison of the present results and experiments in the literature shows that the amplification of the global mode of laminar separation bubbles is a plausible origin of the stall cells. The main conclusion of this thesis is that the classic picture of laminar separation bubbles, as dominated by the inflectional instability of disturbance waves, is neither necessarily representative of all the possible separation bubbles, nor sufficient to explain the complete dynamics of the separated flow. The presence of the self-excited, temporally amplified global mode not only explains the origin of three-dimensionality in nominally two-dimensional bubbles, but may also serve as the triggering instability mechanism leading to unsteady three-dimensional states, in those cases in which the classic (inflectional) Rayleigh scenario alone would predict stable two-dimensional flow.