航空学报 > 2009, Vol. 30 Issue (3): 385-390

二维抛物化稳定性方程的特征分析

涂国华1,2,3,袁湘江1,3,查俊1,3,陶建军4   

  1. 1.中国空气动力研究与发展中心 2.天津市现代工程力学重点实验室 3.北京航空航天大学 国家计算流体力学实验室 4.北京大学 力学与空间工程系和湍流与复杂系统国家重点实验室
  • 收稿日期:2007-09-21 修回日期:2008-12-19 出版日期:2009-03-25 发布日期:2009-03-25
  • 通讯作者: 袁湘江

Characteristics Analysis of Two-dimensional Parabolized Stability Equations

Tu Guohua1,2,3, Yuan Xiangjiang1,3, Zha Jun1,3, Tao Jianjun4   

  1. 1.China Aerodynamics Research and Development Center 2.Tianjin Key Laboratory of Modern Engineering Mechanics 3.National Laboratory for CFD, Beijing University of Aeronautics and Astronautics 4.LTCS and Department of Mechanics and Aerospace Engineering, Peking University
  • Received:2007-09-21 Revised:2008-12-19 Online:2009-03-25 Published:2009-03-25
  • Contact: Yuan Xiangjiang

摘要:

在对抛物化稳定性方程(PSE)的基本流场没有做任何近似假定的情况下,分析了PSE的特征性质。分析表明,当法向速度不为零时,PSE有一个非零主特征值,其余主特征值都为零。PSE的次特征值与扰动波的空间波数α有关,α的实部代表扰动波的波动情况,它可以直接导致复特征值出现;α的虚部表示扰动波的增长(衰减)情况,当它的绝对值超过一定范围时,也会在边界层内亚声速区的局部区域导致复特征值出现。增大求解PSE的空间推进步长,可以克服PSE的椭圆性。

关键词: 抛物化稳定性方程, 特征值, 次特征值, 可压流, 边界层

Abstract:

The characteristics of parabolized stability equations (PSE) are analyzed without any approximate hypothesis of base flows. The analysis indictes that there is a nonzero main characteristic due to the nonzero transverse velocity, and all the other main characteristics of PSE are zero. The sub-characteristics are related to the spacial wave number (α) of a disturbance. The real part of α denotes the wavelength of the disturbance, and a nonzero real part of α leads to complex sub-characteristics. The image part of α denotes the increase/decrease rate of the disturbance, and a nonzero image part of α would lead to complex sub-characteristics if the absolute value of the image part is large enough. The ellipticity of PSE tends to be alleviated by a large matching step size.

Key words: parabolized stability equation, characteristic, sub-characteristic, compressible flow, boundary layer

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