Stress boundary layers in the viscoelastic flow past a cylinder in a channel: limiting solutions
Stress boundary layers in the viscoelastic flow past a cylinder in a channel: limiting solutions
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经过通道中圆柱体的粘弹性流中的应力边界层：极限解
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
R. Tanner
中科院分区：
文献类型：
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作者：
Yurun Fan;Huayong Yang;R. Tanner
采用Galerkin/Least-square有限元法和p-自适应加密算法，研究了上随体麦克斯韦（UCM）流体和Oldrophil-B流体（粘度比为0.59）在纵横比为2：1的通道中绕圆柱的流动。后验误差估计表明，应力梯度误差占主导地位的总误差。当Deborah数De分别接近0.8和0.9时，在后驻点附近形成了强的应力边界层，其特征是在圆柱壁面和对称面上的应力分布发生跳跃，应力梯度很大，且在很窄的厚度范围内应力梯度迅速衰减。巨大的应力梯度的起源可以追溯到后驻点后面的纯拉伸流动，当Deborah数接近临界值时，延伸率为1/2De的位置接近后驻点。这些观察结果意味着UCM和Oldrophil-B流体的圆柱体问题可能分别具有0.8和0.9的物理限制Deborah数。
The flow past a cylinder in a channel with the aspect ratio of 2:1 for the upper convected Maxwell (UCM) fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.