Viscous linear stability analysis of rectangular duct and cavity flows
Viscous linear stability analysis of rectangular duct and cavity flows
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矩形风道和空腔流的粘性线性稳定性分析
DOI：
10.1017/s002211200400850x
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发表时间：
2004
影响因子：
3.7
通讯作者：
J. Owen
中科院分区：
文献类型：
--
作者：
V. Theofilis;P. Duck;J. Owen
对矩形容器内四类不可压缩流动的粘性线性稳定性进行了数值研究。在第一类中，研究了矩形管道中流动的不稳定性，它是由沿管道轴线的恒定压力梯度(实质上是平面Poiseuille流-PPF的二维对应)驱动的。所考察的其他类型的流动是由一个壁面的切向运动产生的，其中一个壁面沿管道的轴向运动，另一个壁面垂直于该方向，分别对应于平面Couette流(PCF)和经典的盖子驱动空腔(LDC)流动的二维对应，在第四种情况下是先前两种切向壁面运动的组合。偏导数本征值问题在每种情况下都控制着全球三维小幅度扰动的时间发展，该问题被数值求解。验证了TatSumi&Yoshimura(1990)关于矩形管道内压力梯度驱动流动的结果，研究了PPF的特征值谱与矩形管道的特征值谱之间的关系。尽管进行了大量的数值实验，但在壁面边界的Couette流中没有发现不稳定的模，这种构型比它的一维极限更稳定。在正方形LDC流动中，所得结果与Ding&Kawahara(1998B)、Theofilis(2000)和Albensoeder等人的预测一致。(2001b)，就一种行进不稳定模而言。然而，与后两部著作的预测一致，而与以前发表的所有结果相反，从不稳定性分析的角度来看，该模式是第三个有意义的模式。在Ding&Kawahara(1998B)未探索的参数范围内以及所有以前的研究中，存在两个额外的本征模，它们都比这些作者发现的模更不稳定。第一个新的模式是静止的(因此不可能用实验数据的幂序列分析来检测)，而第二个模式是移动的，并且在实验观察到的支架内有一个临界雷诺数和频率。文中还考虑了腔体[0.5，4]中的可变纵横比对最不稳定本征模的影响，发现纵横比的增大会导致流动的总体失稳。最后，当雷诺数大于800美元(基于盖子速度和管道长度/高度)时，在方形管道中，当雷诺数大于800美元(基于盖子速度和管道长度/高度)时，当雷诺数大于800美元(基于盖子速度和管道长度/高度)时，由盖子沿(0，{\pi}/{2})角运动产生的壁面Couette流和LDC流的组合是线性不稳定的。因此，在LDC流动中与实验的良好一致性和对壁面边界Couette流稳定性的错误预测的缓解归因于面内基本流速分量的存在。
The viscous linear stability of four classes of incompressible flows inside rectangular containers is studied numerically. In the first class the instability of flow through a rectangular duct, driven by a constant pressure gradient along the axis of the duct (essentially a two-dimensional counterpart to plane Poiseuille flow – PPF), is addressed. The other classes of flow examined are generated by tangential motion of one wall, in one case in the axial direction of the duct, in another perpendicular to this direction, corresponding respectively to the two-dimensional counterpart to plane Couette flow (PCF) and the classic lid-driven cavity (LDC) flow, and in the fourth case a combination of both the previous tangential wall motions. The partial-derivative eigenvalue problem which in each case governs the temporal development of global three-dimensional small-amplitude disturbances is solved numerically. The results of Tatsumi & Yoshimura (1990) for pressure-gradient-driven flow in a rectangular duct have been confirmed; the relationship between the eigenvalue spectrum of PPF and that of the rectangular duct has been investigated. Despite extensive numerical experimentation no unstable modes have been found in the wall-bounded Couette flow, this configuration found here to be more stable than its one-dimensional limit. In the square LDC flow results obtained are in line with the predictions of Ding & Kawahara (1998b), Theofilis (2000) and Albensoeder et al. (2001b) as far as one travelling unstable mode is concerned. However, in line with the predictions of the latter two works and contrary to all previously published results it is found that this mode is the third in significance from an instability analysis point of view. In a parameter range unexplored by Ding & Kawahara (1998b) and all prior investigations two additional eigenmodes exist, which are both more unstable than the mode that these authors discovered. The first of the new modes is stationary (and would consequently be impossible to detect using power-series analysis of experimental data), whilst the second is travelling, and has a critical Reynolds number and frequency well inside the experimentally observed bracket. The effect of variable aspect ratio $A\in[0.5,4]$ of the cavity on the most unstable eigenmodes is also considered, and it is found that an increase in aspect ratio results in general destabilization of the flow. Finally, a combination of wall-bounded Couette and LDC flow, generated in a square duct by lid motion at an angle $\phi\in(0,{\pi}/{2})$ with the homogeneous duct direction, is shown to be linearly unstable above a Reynolds number $\Rey\,{=}\,800$ (based on the lid velocity and the duct length/height) at all $\phi$ parameter values examined. The excellent agreement with experiment in LDC flow and the alleviation of the erroneous prediction of stability of wall-bounded Couette flow is thus attributed to the presence of in-plane basic flow velocity components.