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Impact of inlet shear on unsteady boundary layer separation from two square cylinders in tandem arrangement
Journal of the Brazilian Society of Mechanical Sciences and Engineering ( IF 2.2 ) Pub Date : 2021-11-15 , DOI: 10.1007/s40430-021-03252-6
Atendra Kumar 1, 2, 3 , Souymendu Raha 2 , Rajendra K. Ray 3
Affiliation  

We know that boundary layer separation is essentially the structural bifurcation of the velocity field of fluid flows (Ma and Wang in Geometric theory of incompressible flows with applications to fluid dynamics. No. 119, American Mathematical Soc, 2005; Wang and Ma in Revista de la Real Academia de Ciencias Exactas 96(3):447–459, 2002; Ghil et al. in Phys D Nonlinear Phenom 197(1–2):149–173, 2004; Ghil et al. in SIAM J Appl Math 65(5):1576–1596, 2005). In this paper, the unsteady separation of two-dimensional shear flow having constant fluid properties from the surfaces of a pair of square cylinders in a tandem arrangement is analyzed numerically. The mechanism of separation has been characterized using the structural bifurcation concept developed by Ma and Wang (Disc Contin Dyn Syst A 10(1&2):459, 2004). The investigation is carried out by analyzing the solutions of Navier–Stokes equations on uniform Cartesian grids using a higher-order compact finite difference scheme. The numerical scheme is validated by comparing the results with the previous results in the literature. The effect of shear rate K and gap ratio s/d (where s is the distance between two cylinders, d is the side length of the cylinder) on the initial flow separation and fully developed vortex shedding structure are discussed. The results are presented for initial flow development with time and fully developed flow for the parameter range \(0.0\le K\le 0.4\), \(0.5\le s/d\le 6.0\) at Reynolds number (Re) 100. The details of the flow separation points (i.e., bifurcation points), time of their occurrences, saddle points, vorticity contours and streaklines pattern are presented. The centerline velocity profiles along \(x\)-axis and phase diagrams are also shown. The present study confirms the significant effect of the K value and s/d ratio on the exact location and time of flow separation and its connection to complex vortex shedding phenomena. It is observed that the downstream cylinder does not go through the process of structural bifurcation from its upper and lower surfaces at the present Re value. We say that the placement of the upstream cylinder suppresses the flow separation from the surface of the downstream cylinder. To the best of our knowledge, this is the first time, a topological aspect-based structural bifurcation analysis has been done to understand the vortex shedding phenomenon and flow separation for this problem.



中文翻译:

入口剪切对串联排列的两个方柱非定常边界层分离的影响

我们知道,边界层分离本质上是流体流动速度场的结构分岔(Ma and Wang in Geometric theory of incompressible flow with applications to fluid dynamics. No. 119, American Mathematical Soc, 2005; Wang and Ma in Revista de la Real Academia de Ciencias Exactas 96(3):447–459, 2002;Ghil 等人在 Phys D Nonlinear Phenom 197(1–2):149–173, 2004 年;Ghil 等人在 SIAM J Appl Math 65( 5):1576–1596, 2005)。本文对具有恒定流体特性的二维剪切流从串联排列的一对方柱表面的非定常分离进行了数值分析。分离机制已使用 Ma 和 Wang 开发的结构分叉概念进行了表征(Disc Contin Dyn Syst A 10(1&2):459, 2004)。研究是通过使用高阶紧致有限差分格式分析 Navier-Stokes 方程在均匀笛卡尔网格上的解来进行的。通过将结果与文献中的先前结果进行比较来验证数值方案。剪切速率的影响讨论了初始流动分离和充分发展的涡旋脱落结构上的K和间隙比s / d(其中s是两个圆柱体之间的距离,d是圆柱体的边长)。结果显示为初始流动随时间发展和完全发展的流动在参数范围\(0.0\le K\le 0.4\) , \(0.5\le s/d\le 6.0\)在雷诺数 ( Re ) 100 . 流动分离点(即分叉点)的细节、它们出现的时间、鞍点、涡度等值线和条纹图案被呈现。沿\(x\)的中心线速度分布还显示了 - 轴和相图。本研究证实了K值和s / d比对流动分离的确切位置和时间及其与复杂涡流脱落现象的联系的显着影响。观察到在当前Re值下,下游圆柱体从其上下表面没有经历结构分叉过程。我们说上游圆柱体的放置抑制了与下游圆柱体表面的流动分离。据我们所知,这是第一次进行基于拓扑方面的结构分岔分析,以了解该问题的涡旋脱落现象和流动分离。

更新日期:2021-11-15
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