THE IMPACT OF ASPECT RATIO ON THE TRANSITIONS OF LID-DRIVEN CAVITY FLOW
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摘要:流场过渡流临界特性是指流场因流动分岔而引起的流动状态和流场物理特性变化. 它从根本上决定了流动演化模式和流场特性等物理规律, 对解释复杂流动现象意义重大. 文章针对不同深纵比($ R \in [0.1,2.0] $)的顶盖驱动方腔内流开展数值模拟和流场稳定性分析研究. 预测Hopf, Neimark-Sacker和period-doubling流动分岔及湍流始现的临界雷诺数; 分析流场演化模式, 发现对应不同的深纵比, 有些流动遵循经典的Ruelle-Takens模式, 有些流动则会由周期性流动跃变至湍流; 捕捉和分析各种流动现象, 如流场稳定性丧失、能量级串、流场拓扑结构变化规律等. 研究成果对于揭示深纵比这一几何参数对腔体内流过渡流临界特性的影响规律意义重大, 进一步完善了内流流场特性的研究. 研究发现, Moffatt效应不仅存在于拥有尖锐夹角的内部流动中, 也出现于挤压拉伸的狭长空间; 无论是深腔还是浅腔, 流场稳定性最初的破坏总是以Hopf流动分岔的出现而开始; 就浅腔($ R < {\text{1}}{\text{.0}} $)而言, 随着深纵比逐渐增加, Hopf流动分岔的临界雷诺数越来越小, 流动更容易变为非定常状态, 说明流场稳定性变得越来越容易被破坏; 就深腔($ R > {\text{1}}{\text{.0}} $)而言, 相较于经典方腔驱动内流($ R = {\text{1}}{\text{.0}} $), 流场稳定性更容易丧失; 沿纵向的几何外形拉伸并不是提升流场稳定性的强制约束.Abstract:The critical characteristics of flow transitions refer to the changes of flow state and physical characteristics caused by flow bifurcations. It fundamentally determines the physical laws of flow evolution mode and flow characteristics and is of great significance to reveal the formation mechanism of flow phenomena. In the present paper, the numerical simulations and stability analysis of the classic lid-driven cavity flow with multiple aspect ratios ($ R \in [0.1,2.0] $) were performed. We predicted the critical Reynolds numbers for Hopf, Neimark-Sacker and period-doubling bifurcations and the initiation of turbulence. We found that some flows followed the classical Ruelle-Takens model as a routine, while others jumped from periodic flow to turbulent flow due to the period-doubling bifurcation. The mechanism of various flow phenomena was revealed and discussed, such as the loss of stability of flow field, energy cascade and flow topology changing along with aspect ratio etc.. The results are of great significance to reveal the influence of the aspect ratio Ron the critical characteristics of the transitions in the cavities. It further improves the study of the internal flow. In the present study, some physical characteristics are found, for example, it is found that the Moffatt effect not only exists with sharp corners, but also in the elongated domain; Regardless of the value of R, the initial instability always starts with the appearance of Hopf bifurcation. For the shallow cavities ($ R < {\text{1}}{\text{.0}} $), as Rincreases, the critical Reynolds number of Hopf bifurcation decreases, indicating that the stability becomes more and more easily destroyed. For deep cavity ($ R > {\text{1}}{\text{.0}} $), compared with classical lid-driven square cavity flow ($ R = {\text{1}}{\text{.0}} $), the stability is more likely to be lost. Stretching along the longitudinal geometry is not a mandatory constraint to improve the stability of the flow field.
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图 15准周期性解不同庞加莱交叉点的流场变化
Figure 15.Quasi-periodic snapshots at different Poincaré crossings
表 1网格总量
Table 1.Total number of mesh cells
R Number of cells (n) 0.1 100000 0.3 300000 0.5 500000 0.75 750000 1.0 1000000 1.5 1500000 2.0 2000000 
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表 2算法验证
Table 2.Methodology validation
P Ref. [23] Ref. [24] This work LD X =0.0703
Y =0.1367
$ \psi $ = 0.001361
$ \omega $ = 1.5306X =0.0733
Y =0.1367
$ \psi $ = 0.001376
$ \omega $ = 1.5143X =0.0735
Y =0.1372
$ \psi $ = 0.001379
$ \omega $ = 1.512RD X =0.8086
Y =0.0742
$ \psi $ = 0.003084
$ \omega $ = 2.6635X =0.8050
Y =0.0733
$ \psi $ = 0.003073
$ \omega $ = 2.739X =0.8055
Y =0.0741
$ \psi $ = 0.003076
$ \omega $ = 2.743C X =0.5117
Y =0.5352
$ \psi $ = −0.1190
$ \omega $ = −1.8602X =0.5150
Y =0.5350
$ \psi $ = −0.1222
$ \omega $ = −1.9405X =0.5156
Y =0.5362
$ \psi $ = −0.1214
$ \omega $ = −1.922下载:
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