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Global transition dynamics of flow in a lid-driven cubical cavity
Theoretical and Computational Fluid Dynamics ( IF 3.4 ) Pub Date : 2021-03-19 , DOI: 10.1007/s00162-021-00565-z
Rajesh Ranjan , S. Unnikrishnan , J.-C. Robinet , Datta Gaitonde

The dynamics of a fully three-dimensional lid-driven cubical cavity (3D-LDC) flow at several post-critical conditions, i.e., beyond the first bifurcation, are elucidated using both linear and nonlinear analyses. When the Reynolds number is increased beyond the critical value, symmetry breaks down intermittently with subsequent gradual growth in spanwise inhomogeneity. This results in crossflow as well as pronounced secondary flow due to enhanced imbalance between centrifugal and pressure forces. Thus, while a stable solution is obtained at \(\hbox {Re}=1900\) (Reynolds number based on lid velocity and cavity side length), nonlinear analysis identifies intermittent and nearly saturated regimes at \(\hbox {Re}=2100\) and \(\hbox {Re}=3000\), respectively. These changes in the regime are examined by considering five basic states at different Reynolds numbers starting from \(\hbox {Re}=1900\). At the lowest Reynolds number, linear analysis yields only symmetric modes, characterized by Taylor–Görtler-like (TGL) vortices. However, at \(\hbox {Re}=2100\), the intermittent breakdown of symmetry results in the emergence of an antisymmetric low-frequency mode apart from primary high-frequency mode. The frequencies of both these modes are numerically close to those obtained from corresponding nonlinear simulations. When the Reynolds number is increased even further, the TGL structures drift under the influence of the crossflow to occupy the previously structureless region near the wall. The frequency of each mode decreases with increase in \(\hbox {Re}\); between 1900 and 3000, the frequency of the primary mode changes by more than 20%. Furthermore, the spatial support of each mode becomes larger within the cavity. Both primary and secondary modes are increasingly destabilized with \(\hbox {Re}\); however, the secondary antisymmetric mode is destabilized at a higher rate. The current study thus provides a comprehensive picture of the overall dynamics of 3D-LDC flows in pre- and post-bifurcation regimes in an extended \(\hbox {Re}\) range not considered hitherto.



中文翻译:

盖子驱动的立方腔中流动的整体跃迁动力学

使用线性和非线性分析阐明了在几个后临界条件下(即,超出第一个分叉点)的全三维盖驱动立方腔(3D-LDC)流动的动力学。当雷诺数增加到超过临界值时,对称性会间歇性地破坏,随后跨度不均匀性会逐渐增大。由于离心力和压力之间的不平衡增强,导致横流以及明显的二次流。因此,尽管在\(\ hbox {Re} = 1900 \)(基于盖速度和腔侧面长度的雷诺数处获得了稳定的解,但非线性分析确定了\(\ hbox {Re} = 2100 \)\(\ hbox {Re} = 3000 \), 分别。通过考虑从\(\ hbox {Re} = 1900 \)开始的不同雷诺数下的五个基本状态,检查了体制的这些变化。在最低雷诺数下,线性分析仅产生对称模式,其特征为泰勒-戈特勒式(TGL)涡旋。但是,在\(\ hbox {Re} = 2100 \),对称性的间歇性破坏导致出现了与主要高频模式不同的反对称低频模式。这两种模式的频率在数值上都接近于从相应的非线性模拟获得的频率。当雷诺数进一步增加时,TGL结构在横流的影响下漂移,从而占据了壁附近的先前无结构的区域。每个模式的频率随着\(\ hbox {Re} \)的增加而降低;在1900到3000之间,主模式的频率变化超过20%。此外,每个模式的空间支撑在腔体内变得更大。\(\ hbox {Re} \)使主要和次要模式都变得越来越不稳定; 但是,次级反对称模式会以较高的速率不稳定。因此,当前的研究提供了迄今为止尚未考虑的扩展\(\ hbox {Re} \)范围内分叉前后的3D-LDC流动的整体动力学的全面情况。

更新日期:2021-03-19
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