Modal stability analysis of a helical vortex tube with axial flow
Modal stability analysis of a helical vortex tube with axial flow
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轴流螺旋涡流管模态稳定性分析
DOI：
10.1017/jfm.2013.591
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发表时间：
2014
影响因子：
3.7
通讯作者：
Yuji Hattori and Yasuhide Fukumoto
中科院分区：
文献类型：
--
作者：
渡辺真仁;三宅和正;Yuji Hattori and Yasuhide Fukumoto
采用模态稳定性分析的方法，研究了旋转机翼螺旋涡流模型--轴向流动螺旋涡管的线性稳定性。在前导阶处，基流被设置为沿螺旋管均匀速度的朗肯旋涡，其中心线是一个常曲率和常扭转的螺旋线。在无限区域中的螺旋涡管，其中自由边界条件施加在管的表面，是我们的主要目标，虽然也考虑了刚性边界条件的情况，以阐明扭转的影响以及扭转和轴向流动的联合影响。分析的基础是线性化的不可压缩欧拉方程，它不仅考虑了扭转的影响，而且还出现了扭转和轴向流动的联合影响，这一事实仅在短波极限下表现出来。具有正/负螺旋度的右旋/左旋螺旋的最大增长速率增大，其中扭转使粒子运动的周期增加。所有结果都收敛于以前的短波极限局部稳定性结果。不同边界条件下两种情况的差异是由于自由边界情况下的孤立模式，其色散曲线强烈依赖于轴向流动。
The linear stability of a helical vortex tube with axial flow, which is a model of helical vortices emanating from rotating wings, is studied by modal stability analysis. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube whose centreline is a helix of constant curvature and torsion. The helical vortex tube in an infinite domain, in which the free boundary condition is imposed at the surface of the tube, is our major target although the case of the rigid boundary condition is also considered in order to elucidate the effects of torsion and the combined effects of torsion and axial flow. The analysis is based on the linearized incompressible Euler equations expanded in not only the effects of torsion but also the combined effects of torsion and axial flow appear, a fact which has been shown only for the short-wave limit. The maximum growth rate increases for the right-handed/left-handed helix with positive/negative helicity, in which the torsion makes the period of particle motion increase. All results converge to the previous local stability results in the short-wave limit. The differences between the two cases of different boundary conditions are due to the isolated mode of the free boundary case, whose dispersion curve depends strongly on the axial flow.