【作者】 熊俊；

【导师】 朱克勤； 凌国灿；

【作者基本信息】 清华大学 ， 流体力学， 2003， 博士

【摘要】 本文以三维不可压缩粘性流体的Navier-Stokes方程为数学模型对圆柱绕流问题作直接数值模拟，研究圆柱尾迹三维转捩区间转捩特征和动力学过程。Navier-Stokes方程的时间离散采用基于混合刚性稳定格式的三阶分裂算法，空间离散采用Fourier谱－谱元法。文中对GLL配置点下的求导误差进行了分析，提出的双精度方法可以将求导误差从O((N4)减小到O((N2)，其中(为机器精度，N为单元内插值多项式阶数。利用N-S方程的精确解，以及前人研究二维静止圆柱绕流、旋转圆柱绕流等问题的实验和计算结果的比较，对算法和程序作了严格的校验。在此基础上对Re = 200、250和300下的流动进行了三维数值模拟。Re = 200是刚超过模式A的临界雷诺数，计算结果表明，此时近尾迹流场处于三维准周期层流状态。占优展向模态的波长及流场的整体特性均受计算域的展向特征长度的影响。尤其值得注意的是发现在特定的展向特征长度下线性稳定的展向模态会取代模式A而在尾迹中占优并决定卡门涡脱落的展向相位差。Re = 250时模式B处于亚临界状态。在本文的计算中，模式A首先在流场中自发地发展起来，并通过各展向模态间的相互作用激发了模式B的出现，使得尾迹中模式A和B共存，这与前人的结果是一致的。研究进一步发现流向涡结构在下游尾迹中演化为新的模式-“双涡对模式”，以及导致时间信号不规则性的独立低频fm的出现。Re = 300时模式A和B均线性不稳定，模式B由于增长率较高，首先取代二维尾迹，而后随着模式A的增长尾迹中模式A和B共存。从圆柱表面到旋涡形成区、到近尾迹再到下游尾迹流向涡结构从模式A转换到模式B、双涡对模式、再恢复为模式A。本文初步研究了三角波形的展向非均匀来流速度剖面对圆柱尾迹三维转捩的影响，考察不同雷诺数下不同波长和幅值的情况。结果表明，在流动发展相当长的一段时间内，非均匀来流速度剖面的波长起主导作用，尾迹中相同波长及其谐波的展向模态受到激发，而其他模态则被抑制。尾迹中流向涡结构与模式A的相似性支持了模式A的产生源于来流绕过圆柱时三维性的观点。更多还原

【Abstract】 The flow past a uniform circular cylinder is studied in detail by direct numerical simulations of three-dimensional incompressible Navier-Stokes equations. The features and dynamics for various Reynolds numbers in the three-dimensional transition regime of the cylinder wake are investigated. The 3rd-order splitting algorithm based on the mixed stiffly stable scheme is employed in the temporal discretization of the N-S equations and the mixed Fourier-spectral-spectral-element method in the spatial discretization.The errors in calculating derivatives for the GLL collocation points are evaluated, which can be alleviated from O((N4) to O((N2) by the double-precision method proposed in the present paper, where ( denotes the machine precision and N the order of the interpolation polynomials in the elements. The exact solutions of the N-S equations are employed to verify the algorithm and the program. The two-dimensional flows past both a still cylinder and a rotating cylinder are computed. Our numerical results show good conformance with that from the previous experimental and numerical studies. After the verification, the three-dimensional numerical simulations of the cylinder wake for Re = 200, 250 and 300 are performed.Re = 200 is just beyond the critical Reynolds number of mode A. The numerical results of the present paper indicate that the near wake at this supercritical Reynolds number is in three-dimensional quasi-periodic laminar state with transitional behaviors. The spanwise characteristic length determines the transition features and global properties of the wake. Especially for the specific spanwise characteristic length linear stable mode can dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding.At Re = 250, mode B is subcritical. The present studies suggest that mode A spontaneously emerges in the wake preceding all the other spanwise modes. Then it excites the linear stable mode B through the nonlinear interactions among the various spanwise modes. Eventually mode A and B coexist in the wake, which confirms the previous studies. Besides, the present paper finds that downstream the streamwise<WP=7>vortices evolve into a new type of mode - "dual vortex pair mode". An independent low frequency fm, which result in the irregularity of the temporal signals, other than the vortex shedding frequency is also identified.When Re = 300, mode A and B are both unstable. Due to its higher growth rate mode B replaces the 2-D wake first. Then with the growth of mode A, the two modes coexist in the wake. From the surface of the cylinder to the formation region of the vortices then to the wake downstream, the structure of the streamwise vortices change from mode A to mode B, dual vortex pair mode then mode A again.Preliminary studies are performed on the effect of the non-uniform stream with cosine form velocity profile in spanwise direction on the three-dimensional transition of the cylinder wake. The parameters taken into consideration include the Reynolds number, the wavelength and the amplitude of the stream profile. The numerical results indicate that in a quite long period of evolution the wavelength of the stream profile determines the flow. In the wake the spanwise modes with the identical wavelength and the harmonic waves are excited, while the other modes are strongly suppressed. The similarity between the streamwise vortex structure in the wake and mode A for the uniform stream supports the opinion that mode A derives from the three-dimensionality in the bypassing process of the flow around the cylinder.更多还原