Instability modes on a solid-body-rotation flow in a finite-length pipe
Instability modes on a solid-body-rotation flow in a finite-length pipe
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DOI：
10.1063/1.4993643
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发表时间：
2017-09
期刊：
影响因子：
1.6
通讯作者：
Chunjuan Feng;Feng Liu;Z. Rusak;Shixiao Wang
中科院分区：
文献类型：
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作者：
Chunjuan Feng;Feng Liu;Z. Rusak;Shixiao Wang
数值求解了不可压Navier-Stokes方程，研究了在有限长管道中，在管道进出口处施加非周期边界条件时，轴对称和三维扰动对底部固体旋转流动的时间演化。结果发现，对于一个给定的雷诺数存在一个临界旋流数超过初始扰动增长，在对比的固体旋转流在一个无限长的管道或一个有限长的管道周期性的入口和出口的边界条件，经典的开尔文分析和瑞利稳定性准则确认中性稳定的各级漩涡。本文首次揭示了轴对称和三维情况下扰动的详细演化。计算揭示了一个线性增长阶段的扰动与一个恒定的增长率后，一个简短的初始期的衰减所施加的初始扰动。增长最快的轴对称和三维不稳定模式和相关的增长率的数值识别的第一次。计算结果表明，在相同旋流数下，随着雷诺数的减小，临界旋流数增大，不稳定性增长率减小。在高雷诺数的轴对称模式的增长率同意与以前的无粘流的稳定性理论。更重要的是，三维模拟发现，最不稳定的模式是螺旋型m = 1模式，它出现在一个较低的临界涡流数比轴对称模式的发病。在相同的涡流条件下，这种螺旋模态比不稳定的轴对称模态增长得快。此外，委员会认为，计算结果表明，扰动线性增长阶段后，流动继续非线性发展到饱和轴对称涡破裂状态.数值求解不可压Navier-Stokes方程，研究了有限长管道中非线性扰动下的轴对称和三维扰动对底部固体旋转流动的时间演化.在管道入口和出口处施加的周期性边界条件。结果发现，对于一个给定的雷诺数存在一个临界旋流数超过初始扰动增长，在对比的固体旋转流在一个无限长的管道或一个有限长的管道周期性的入口和出口的边界条件，经典的开尔文分析和瑞利稳定性准则确认中性稳定的各级漩涡。本文首次揭示了轴对称和三维情况下扰动的详细演化。计算揭示了一个线性增长阶段的扰动与一个恒定的增长率后，一个简短的初始期的衰减所施加的初始扰动。最快的成长…
Numerical solutions of the incompressible Navier-Stokes equations are obtained to study the time evolution of both axisymmetric and three-dimensional perturbations to a base solid-body-rotation flow in a finite-length pipe with non-periodic boundary conditions imposed at the pipe inlet and outlet. It is found that for a given Reynolds number there exists a critical swirl number beyond which the initial perturbations grow, in contrast to the solid-body rotation flow in an infinitely-long pipe or a finite-length pipe with periodic inlet and exit boundary conditions for which the classical Kelvin analysis and Rayleigh stability criterion affirm neutrally stable for all levels of swirl. This paper uncovers for the first time the detailed evolution of the perturbations in both the axisymmetric and three-dimensional situations. The computations reveal a linear growth stage of the perturbations with a constant growth rate after a brief initial period of decay of the imposed initial perturbations. The fastest growing axisymmetric and three-dimensional instability modes and the associated growth rates are identified numerically for the first time. The computations show that the critical swirl number increases and the growth rate of instability decreases at the same swirl number with decreasing Reynolds number. The growth rate of the axisymmetric mode at high Reynolds number agrees well with previous stability theory for inviscid flow. More importantly, three-dimensional simulations uncover that the most unstable mode is the spiral type m = 1 mode, which appears at a lower critical swirl number than that for the onset of the axisymmetric mode. This spiral mode grows faster than the unstable axisymmetric mode at the same swirl. Moreover, the computations reveal that after the linear growing stage of the perturbation the flow continues to evolve nonlinearly to a saturated axisymmetric vortex breakdown state.Numerical solutions of the incompressible Navier-Stokes equations are obtained to study the time evolution of both axisymmetric and three-dimensional perturbations to a base solid-body-rotation flow in a finite-length pipe with non-periodic boundary conditions imposed at the pipe inlet and outlet. It is found that for a given Reynolds number there exists a critical swirl number beyond which the initial perturbations grow, in contrast to the solid-body rotation flow in an infinitely-long pipe or a finite-length pipe with periodic inlet and exit boundary conditions for which the classical Kelvin analysis and Rayleigh stability criterion affirm neutrally stable for all levels of swirl. This paper uncovers for the first time the detailed evolution of the perturbations in both the axisymmetric and three-dimensional situations. The computations reveal a linear growth stage of the perturbations with a constant growth rate after a brief initial period of decay of the imposed initial perturbations. The fastest gro...