Controlling secondary flows in Taylor–Couette flow using stress-free boundary conditions
Controlling secondary flows in Taylor–Couette flow using stress-free boundary conditions
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DOI：
10.1017/jfm.2021.534
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发表时间：
2020-10
影响因子：
3.7
通讯作者：
Vignesh Jeganathan;K. Alba;Rodolfo Ostilla-Mónico
中科院分区：
文献类型：
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作者：
Vignesh Jeganathan;K. Alba;Rodolfo Ostilla-Mónico
摘要Taylor-Couette(TC)流是两个独立旋转的同轴圆柱之间的流动，通常被用作剪切流动的正则模型。与平面Couette流不同，TC流中存在钉扎二次流。它们被称为泰勒辊，极大地影响了流动行为。我们研究了在内筒上使用无应力和无滑移边界条件模式来修改这些二级结构的可能性。为此，我们对具有纯内柱旋转的窄间隙TC流动进行了直接的数值模拟，在四个不同的剪切雷诺数下，最高可达$Re_S=3\x 10^4$。我们发现一维方位角方向图对流动拓扑没有显著影响，并且在完全无滑移的情况下，所产生的扭矩是扭矩的一大部分($SIM$80%-90%)。一维轴向模式进一步降低了扭矩，并且对于某些模式频率，通过干扰产生二次结构的现有雷诺应力来扰乱轧辊。对于$Re\geq 10^4$，这种破坏导致的扭矩小于简单边界层效应所预期的扭矩，以及由此产生的有效滑移长度和滑移速度。我们发现，二维棋盘花样具有与方位花样相似的行为，对流动或扭矩没有实质影响，但二维螺旋不均匀可以在钉扎的二次流周围移动，因为它们诱导了持续的轴向速度。我们量化了不同角度和螺旋图案宽度下轧辊的运动，发现了作为图案角度和图案频率的函数的非单调行为。
Abstract Taylor–Couette (TC) flow, the flow between two independently rotating and co-axial cylinders, is commonly used as a canonical model for shear flows. Unlike plane Couette flow, pinned secondary flows can be found in TC flow. These are known as Taylor rolls and drastically affect the flow behaviour. We study the possibility of modifying these secondary structures using patterns of stress-free and no-slip boundary conditions on the inner cylinder. For this, we perform direct numerical simulations of narrow-gap TC flow with pure inner-cylinder rotation at four different shear Reynolds numbers up to $Re_s=3\times 10^4$. We find that one-dimensional azimuthal patterns do not have a significant effect on the flow topology, and that the resulting torque is a large fraction ($\sim$80 %–90 %) of torque in the fully no-slip case. One-dimensional axial patterns decrease the torque more, and for certain pattern frequency disrupt the rolls by interfering with the existing Reynolds stresses that generate secondary structures. For $Re\geq 10^4$, this disruption leads to a smaller torque than what would be expected from simple boundary layer effects and the resulting effective slip length and slip velocity. We find that two-dimensional checkerboard patterns have similar behaviour to azimuthal patterns and do not affect the flow or the torque substantially, but two-dimensional spiral inhomogeneities can move around the pinned secondary flows as they induce persistent axial velocities. We quantify the roll's movement for various angles and the widths of the spiral pattern, and find a non-monotonic behaviour as a function of pattern angle and pattern frequency.