Numerical investigation of transitional supersonic axisymmetric wakes
Numerical investigation of transitional supersonic axisymmetric wakes
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DOI：
10.1017/s0022112006000899
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发表时间：
2006-09
影响因子：
3.7
通讯作者：
R. Sandberg;H. Fasel
中科院分区：
文献类型：
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作者：
R. Sandberg;H. Fasel
通过各种数值实验研究了超声速过渡轴对称尾迹。主要目标是确定在$M\,{=}\,2.46$的几个雷诺数下的流体动力学不稳定机制，并将这些机制与从各种可视化技术中发现的相干结构联系起来。这种方法的前提是假定流动不稳定性会导致相干结构的形成。为了这项工作，我们在柱坐标下开发了三个高阶精确可压缩代码：用于直接数值模拟（DNS）的空间Navier-Stokes （N-S）代码，用于使用轴对称基本状态进行线性稳定性研究的线性化N-S代码，以及用于执行局部稳定性分析的时间N-S代码。利用数值模拟故意排除物理效应的能力。这包括通过为不同的周向域大小使用DNS有意地消除某些方位/螺旋模式。通过这种方法，可以仔细检查与某些模式相关的结构对全球尾流行为的影响。进行了补充的空间和时间计算，以调查不稳定性是局部性质还是全局性质。间接证据表明，再环流区内绝对不稳定的全球模态与对流不稳定的剪切层模态共存。对于模态$k\,{>}\, $Re_D\,{>}\,5000$和轴对称模态$k\,{=}\,0$对于$Re_D\,{>}\,100\ 000$，流动是绝对不稳定的。得出的结论是，$k\,{=}\,2$和$k\,{=}\,4$的方位角模式是尾迹的主导模式，产生了“四瓣”尾迹模式。提出了两种可能的再环流区域纵向构造形成机制。
Transitional supersonic axisymmetric wakes are investigated by conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at $M\,{=}\,2.46$ for several Reynolds numbers, and to relate these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. Three high-order accurate compressible codes were developed in cylindrical coordinates for this work: a spatial Navier–Stokes (N-S) code to conduct direct numerical simulations (DNS), a linearized N-S code for linear stability investigations using axisymmetric basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to exclude physical effects deliberately is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain sizes. With this approach, the impact of structures associated with certain modes on the global wake-behaviour can be scrutinized. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region co-exist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes $k\,{>}\,0$ for $Re_D\,{>}\,5000$ and with respect to the axisymmetric mode $k\,{=}\,0$ for $Re_D\,{>}\,100\,000$. It is concluded that azimuthal modes $k\,{=}\,2$ and $k\,{=}\,4$ are the dominant modes in the trailing wake, producing a ‘four-lobe’ wake pattern. Two possible mechanisms responsible for the generation of longitudinal structures within the recirculation region are suggested.