Transverse-jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio
Transverse-jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio
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DOI：
10.1017/s002211200800102x
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发表时间：
2008-04
影响因子：
3.7
通讯作者：
L. Alves;R. Kelly;A. Karagozian
中科院分区：
文献类型：
--
作者：
L. Alves;R. Kelly;A. Karagozian
在第1部分（Megerian et al.， J. Fluid Mech.）中，等密度横向射流的主要无量纲参数是平均射流与横向流的速度比r。， vol. 593, 2007, p. 93)，给出了横向射流近场剪切层不稳定性的实验结果，在速度比范围14范围内，使用两种不同的横向射流基流。第一种分析假设流场可以用Coelho & Hunt （J.流体力学）的势流解的修正版本来描述。， vol. 200, 1989, p. 95)，其中射流被旋涡片包围。第二种分析假设基于相同的无粘基流的连续速度模型；该分析适用于最不稳定扰动的典型的较大的斯特劳哈尔数值，并允许对扰动的最大空间增长率进行预测。在这两种方法中，结果都是通过对R的逆幂展开得到的，因此自由射流的结果是R→∞。两种方法的结果在中等低频状态下一致。第二种方法提取的最大空间生长率和相关Strouhal数均随着流速比R的减小而增大，在4<R≤10的范围内与第1部分的实验结果一致。在位核末端上游的横向射流剪切层近场区，名义轴对称模态是最不稳定的模态。理论与实验结果基本一致，表明当射流与横流速度比大于4时，横流剪切层发生对流不稳定性，且随着R的减小，对流不稳定性增强。
The dominant non-dimensional parameter for isodensity transverse jet flow is the mean jet-to-crossflow velocity ratio, R. In Part 1 (Megerian et al., J. Fluid Mech., vol. 593, 2007, p. 93), experimental results are presented for the behaviour of transverse-jet near-field shear-layer instabilities for velocity ratios in the range 1 4, using two different base flows for the transverse jet. The first analysis assumes the flow field to be described by a modified version of the potential flow solution of Coelho & Hunt (J. Fluid Mech., vol. 200, 1989, p. 95), in which the jet is enclosed by a vortex sheet. The second analysis assumes a continuous velocity model based on the same inviscid base flow; this analysis is valid for the larger values of Strouhal number expected to be typical of the most unstable disturbances, and allows prediction of a maximum spatial growth rate for the disturbances. In both approaches, results are obtained by expanding in inverse powers of R so that the free-jet results are obtained as R→∞. The results from both approaches agree in the moderately low-frequency regime. Maximum spatial growth rates and associated Strouhal numbers extracted from the second approach both increase with decreasing velocity ratio R, in agreement with the experimental results from Part 1 in the range 4<R≤10. The nominally axisymmetric mode is found to be the most unstable mode in the transverse-jet shear-layer near-field region, upstream of the end of the potential core. The overall agreement of theoretical and experimental results suggests that convective instability occurs in the transverse-jet shear layer for jet-to-crossflow velocity ratios above 4, and that the instability is strengthened as R is decreased.