Square cavity flow driven by two mutually facing sliding walls

Abstract

We investigate the flow inside a 2D square cavity driven by the motion of two mutually facing walls independently sliding at different speeds. The exploration, which employs the lattice Boltzmann method (LBM), extends on previous studies that had the two lids moving with the exact same speed in opposite directions. Unlike there, here the flow is governed by two Reynolds numbers (Re_T, Re_B) associated to the velocities of the two moving walls. For convenience, we define a bulk Reynolds number Re and quantify the driving velocity asymmetry by a parameter α. Parameter α has been defined in the range α∈[−π/4, 0] and a systematic sweep in Reynolds numbers has been undertaken to unfold the transitional dynamics path of the two-sided wall-driven cavity flow. In particular, the critical Reynolds numbers for Hopf and Neimark-Sacker bifurcations have been determined as a function of α. The eventual advent of chaotic dynamics and the symmetry properties of the intervening solutions are also analyzed and discussed. The study unfolds for the first time the full bifurcation scenario as a function of the two Reynolds numbers, and reveals the different flow topologies found along the transitional path.

目的

探究双边驱动方腔内流流场的过渡流临界特性,捕捉各种流动分岔点,分析其对流场特性带来的改变。确定流场演化模式,解释流动现象后的流动机理。通过流场拓扑结构和涡系演化分析流场稳定性与对称性的关系。

创新点

1. 首次揭示驱动速度比对该流场过渡流临界特性的影响规律;2. 从物理层面上阐明流动本质。

方法

1. 以均匀直角网格构建计算域,通过基于格子玻尔兹曼方法的数值模拟方法,计算各流动状态发生变化时的临界雷诺数。根据不同驱动速度比,绘制Hopf和Neimark-Sacker流动分岔点以及湍流临界点随速度比的函数图像(图9);2. 通过扰动衰减系数、速度相图、速度频谱分析来判断流动是否由定常变为非定常周期性流动,再由周期性流动变为准周期性流动直至演化为湍流;3. 通过流场拓扑结构分析流场对称性的破坏与不稳定性的关系;4. 通过能量频谱图像分析流动的能量级串现象(图11)。

结论

1. 跟预期一样,该流场的稳定性丧失总是伴随着Hopf流动分岔点的出现;2. 相较于顶盖驱动内流流场,双边驱动内流流场的稳定性较强,说明第二条边的驱动条件可以有效提高流场的稳定性;3. 当 时,流场稳定性最强,同时当双边驱动条件相同时可以更好的提高流场稳定性;4.不管驱动速度比如何变,流场始终展现了经典的Ruelle-Takens模式,从定常流动演化至非定常周期性流动,再由周期性流动演化至准周期性流动,最终演化为湍流;5.180度的旋转对称性对于推迟湍流的出现有很大作用。