Structural sensitivity of spiral vortex breakdown
Structural sensitivity of spiral vortex breakdown
复制标题
螺旋涡破裂的结构敏感性
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
M. Juniper
中科院分区：
文献类型：
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作者：
U. Qadri;Dhiren Mistry;M. Juniper
摘要以往的数值模拟表明，涡破裂开始于一个稳定的轴对称气泡的形成，然后在此之上发展一个非定常的螺旋模式。我们研究了这种螺旋模式与线性的整体稳定性分析周围的稳定气泡及其尾迹。我们得到的线性化的Navier-Stokes方程的线性直接和伴随的全球模式，并重叠这些螺旋模式，识别造波区域的结构灵敏度。我们还确定区域的绝对不稳定的局部稳定性分析。在中等旋度下，我们发现$m= - 1$方位角模是最不稳定的，而$m= - 1$方位角模的造波区位于气泡周围，这是绝对不稳定的。该模式是最敏感的反馈涉及的径向和方位角分量的动量在该区域的上游的气泡。在较小的程度上，该模式也是敏感的反馈，涉及在气泡周围的高剪切区域的动量的轴向分量。在中等旋涡中，气泡和尾流具有相似的绝对增长率，其他研究者发现非线性整体模式的造波源存在于尾流中。我们同意他们的分析，但发现在决定线性全局模式的增长率和频率方面，气泡周围的区域比尾流更有影响力。本文的研究结果为螺旋涡破裂的被动控制策略提供了初步的思路。
Abstract Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier–Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the $m= - 1$ azimuthal mode is the most unstable and that the wavemaker regions of the $m= - 1$ mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown.