Analysis and Application of Ellipticity of Stability Equations on Fluid Mechanics
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摘要: 利用抛物化稳定方程(PSE)特征分析得知,原始扰动量的线性和非线性PSE整体来说为抛物型.利用PSE的次特征分析证明,对速度U,在亚音速和跨音速区,线性PSE分别为椭圆型和双曲-抛物型;对速度U+u,在亚音速和跨音速区,非线性PSE分别为椭圆型和双曲-抛物型(其中,U和u分别为主流方向的扰动和未扰流速度分量).结论表明,流体运动稳定性方程组的"抛物化"简化,仅把信息的对流扩散传播抛物化,而保留了信息的对流扰动传播特性,PSE实质上是扩散抛物化稳定性方程组.根据特征次特征理论提出了消除PSE剩余椭圆特性的方法,所得结论对线性PSE已有结论一致,并给出了Mach数的影响.同时,进一步给出了消除非线性PSE的剩余椭圆特性的方法.Abstract: By using characteristic analysis of the linear and nonlinear parabolic stability equations(PSE), PSE of primitive disturbance variables are prored to be parabolic in total. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic, for velocity U, in subsonic and supersonic:respectively U+u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.
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Key words:
- compressible fluid /
- parabolic stability equations /
- characteristic /
- sub-characteristic
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