慢扩张旋转流的稳定性分析(Ⅰ)——理论研究*
Stability Analysis of Slowly Divergent Swirling Flow(Ⅰ)——Theory
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摘要: 本文研究了无粘不可压慢扩张旋转流的稳定性问题,采用多重尺度展开法对有慢扩张的旋转流的非对称扰动进行浅化稳定性研究,导出了零阶及一阶扰动模所应满足的微分方程及由于慢扩张引起振幅变化的控制方程,将Plaschko关于慢扩张喷流的结果推广到具有慢扩张的旋转流情况.Abstract: The stability of inviscid incompressible swirling flow with slowly divergence is investigated.A multiple scale expansion is used to develop a linear stability study of slowly divergent swirling flow with non-axisymmetric disturbances.The differental equations of zero-order and first-order disturbance module and governing equation of amplitude variation due to slowly divergent flow are derved.The plaschko s equation for slowly divergent swirl-free jet has been extended to slowly divergent flow with swirlin the present study.
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Key words:
- stabilty /
- swirling flow /
- vortex flow /
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[1] M.Lesson and F.Paillet.The stability of a trailing line vortex.Part I.Inviscid theory,J.Fluid Mech.,62(1974).753-763. [2] P.W.Duck and M.R.Foster,The inviscid stability of a trailing line vortex.ZAMP,31(1988),524-532. [3] Yin Xieyuan and Xia Nan,The investigation of spatial instability of swirling flow Advances in Applied Math.and Mech,in China,3(1991),75-85. [4] S.Leibovich and K.Stewartson.A sufficient condition for instability of columnar vortices,J.Fluid Mech.126(1983).335-356. [5] H.Ludwieg,Stabilitat der stromung in einem zylindrischeo Ringraum,ZGW,9(1961),53-361. [6] L.N.Howard and A.S.Gupta,On the hydrodynamic and hydromagnetic stability of swirling flow,J.Fluid Mech.,14(1962),463-47 [7] J.H.Faler and S.Leibovich,Disrupted states of vortex flow and vortex breakdown,The Physics of Fluids,2(9)(177),1385-14 [8] C.Y.Tsai and S.E.Widnall,Examination of group-elocity criterion for breakdown of vortex flow in a divergent duct,Phys.Fluids,23(5)(195),54-87 [9] M.Bouthier,J.Mec.,11(1972),599. [10] D.G.Crighton and M.Gaster,Stability of slowly diverging jet flow,J.Fluid Mech.,77(1976),397-413. [11] P.Plaschko,Helical instability of slowly divergent jet J.Fluid Mech.,92(1979),29-215.
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