Viscoelastic shear flow over a wavy surface
Viscoelastic shear flow over a wavy surface
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DOI：
10.1017/jfm.2016.455
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发表时间：
2016-07
影响因子：
3.7
通讯作者：
Jacob Page;T. Zaki
中科院分区：
文献类型：
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作者：
Jacob Page;T. Zaki
库埃特流下壁面上的小振幅正弦表面起伏引起涡量扰动。使用线性分析，这个涡度场检查时，流体是粘弹性的，对比的牛顿配置。对于强弹性Oldrophil-B流体，诱导涡量渗透到体中可以使用两个无量纲量进行分类：（i）通道深度和（ii）剪切波的临界层深度与表面粗糙度波长的比值。在浅弹性制度，其中粗糙度波长大于通道深度和临界层是域外，批量流响应是一个扭曲的张紧流线，以匹配表面形貌，和一个恒定的扰动涡填充的通道。在上壁的薄溶剂边界层中，这种涡度被显著放大。在深弹性情况下，临界层远离壁面，扰动涡量随高度呈指数衰减。在第三，跨临界制度，临界层的高度是在下壁的波长和运动放大机制在其附近产生涡。分析扩展到本地化，高斯壁凸块使用傅立叶合成。牛顿流响应由凸起上方的单个涡流组成。在浅弹性流动中，在表面凸起的上游建立了具有相反环流的第二涡，该第二涡由上壁涡量层诱导。在深跨临界情况下，扰动场由一对以临界层周围的大涡量为中心的反向旋转涡组成。更现实的FENE-P模型，它占有限的可伸展性的聚合物链，表现出相同的定性行为。
A small-amplitude sinusoidal surface undulation on the lower wall of Couette flow induces a vorticity perturbation. Using linear analysis, this vorticity field is examined when the fluid is viscoelastic and contrasted to the Newtonian configuration. For strongly elastic Oldroyd-B fluids, the penetration of induced vorticity into the bulk can be classified using two dimensionless quantities: the ratios of (i) the channel depth and of (ii) the shear-waves’ critical layer depth to the wavelength of the surface roughness. In the shallow-elastic regime, where the roughness wavelength is larger than the channel depth and the critical layer is outside of the domain, the bulk flow response is a distortion of the tensioned streamlines to match the surface topography, and a constant perturbation vorticity fills the channel. This vorticity is significantly amplified in a thin solvent boundary layer at the upper wall. In the deep-elastic case, the critical layer is far from the wall and the perturbation vorticity decays exponentially with height. In the third, transcritical regime, the critical layer height is within a wavelength of the lower wall and a kinematic amplification mechanism generates vorticity in its vicinity. The analysis is extended to localized, Gaussian wall bumps using Fourier synthesis. The Newtonian flow response consists of a single vortex above the bump. In the shallow-elastic flow, a second vortex with opposite circulation is established upstream of the surface protrusion and is induced by the vorticity layer on the upper wall. In the deep transcritical case, the perturbation field consists of a pair of counter-rotating vortices centred on the large vorticity around the critical layer. The more realistic FENE-P model, which accounts for the finite extensibility of the polymer chains, shows the same qualitative behaviour.