ABSTRACT A linear stability analysis is performed to explain the formation of coherent structures in the narrow regions of a rectangular channel containing a cylindrical rod and a channel formed by two rectangular ducts connected through a narrow slot. This stability analysis introduces small perturbations of the velocity and the pressure in the governing equations. The linearised equations are transformed into a generalised eigenvalue problem solved using the spectral Tau-Chebyshev collocation method. The obtained critical Reynolds number variations with gap size are in qualitative agreement with published experimental data. The iso-contours of the streamwise and transverse velocities, obtained from the preferred modes solution, confirm the presence, in the narrow regions, of counter-rotating vortices, generated by the flow instability and resulting from the velocity profile in the middle of the gap. The vortices’ spatial arrangement, convective speed, spacing and Strouhal number for both configurations have qualitatively similar variations with relative gap sizes.

中文翻译：

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复合通道狭窄间隙中的流动结构：线性稳定性分析

摘要 进行线性稳定性分析以解释在包含圆柱形杆的矩形通道和由两个矩形管道通过窄槽连接形成的通道的狭窄区域中连贯结构的形成。这种稳定性分析在控制方程中引入了速度和压力的小扰动。线性化方程被转换为使用谱 Tau-Chebyshev 搭配方法求解的广义特征值问题。获得的临界雷诺数随间隙大小的变化与已发表的实验数据定性一致。从优选模式解中获得的流向和横向速度的等值线证实了在狭窄区域中存在反向旋转的涡流，由流动不稳定性和间隙中间的速度分布产生。两种配置的涡旋空间排列、对流速度、间距和 Strouhal 数在相对间隙大小的性质上具有相似的变化。