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Effect of pressure gradient on viscous shear flow past an axisymmetric depression or protuberance on a plane wall

机译:压力梯度对粘性剪切流经过平面壁上的轴对称凹陷或凸起的影响

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摘要

The effect of pressure gradient on the structure of unidirectional viscous shear flow over an axisymmetric depression or protuberance on a plane wall, possibly in the presence of an upper parallel plane wall in the configuration of two-dimensional Hagen-Poiseuille flow, is considered. The problem is formulated in terms of a system of three coupled Fredholm integral equations of the first kind for the first-order Fourier coefficients of the boundary traction, and the solution is found using a boundary element method. The numerical results illustrate the effect of the pressure gradient on the streamline pattern and on the distribution of the shear stress along the plane wall and over the depression or protuberance. The topology of the streamline pattern in three-dimensional flow is found to be generally similar to that in two-dimensional flow, but important differences arise in the vicinity of stagnation points. The structure of semi-infinite parabolic flow is similar to that of the channel pressure-driven flow, when the distance between the channel walls is roughly larger than six times the characteristic size of the depression of protuberance. The force and torque exerted on a protuberance are evaluated for pure shear flow, pure parabolic flow, and pressure-driven channel flow, and a linear combination of the results for the first two cases is shown to accurately describe the results for the third case when the channel is moderately wide.
机译:考虑到压力梯度对平面壁上的轴对称凹陷或凸起上的单向粘性剪切流结构的影响,可能是在二维哈根-泊厄依流结构中存在平行的上部壁的情况下。根据边界牵引力的一阶傅立叶系数的第一类三个耦合的Fredholm积分方程的系统来表达该问题,并使用边界元方法找到解决方案。数值结果说明了压力梯度对流线型式和沿平面壁以及在凹陷或隆起上的切应力分布的影响。发现三维流中流线型态的拓扑通常与二维流中的流态型态相似,但是在停滞点附近会出现重要差异。当通道壁之间的距离大约大于突起凹陷特征尺寸的六倍时,半无限抛物线流动的结构类似于通道压力驱动的流动。对于纯剪切流,纯抛物线流和压力驱动的通道流,评估了施加在突起上的力和扭矩,并显示了前两种情况的结果的线性组合,可以准确地描述第三种情况的结果,当通道适中。

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