Resistance coefficients for Stokes flow around a disk with a Navier slip condition
Resistance coefficients for Stokes flow around a disk with a Navier slip condition
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具有纳维滑移条件的圆盘周围斯托克斯流的阻力系数
DOI：
10.1063/1.4754869
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
J. Sherwood
中科院分区：
文献类型：
--
作者：
J. Sherwood
本文研究了零厚度圆盘在牛顿流体中运动时的Stokes阻力和力偶，并讨论了圆盘表面可能发生滑移的情况。结果表明，当磁盘平行于其轴平移，众所周知的速度场无滑移边界条件施加零剪应力的磁盘的表面上。因此，如果将圆盘上的边界条件修改为无应力边界条件或Navier滑移边界条件，则流动不变。这个不变性也适用于绕直径旋转的圆盘。然而，当无滑移边界条件变为Navier滑移条件时，绕着绕其轴旋转或在其自身平面内平移（沿边）的圆盘的流动被修改。流体速度可以用汉克尔变换表示，并对所得的对偶积分方程进行数值求解。在Navier边界条件下，圆盘上的扭矩和阻力的结果作为滑移长度的函数。
The Stokes drag and couple acting on a disk of zero thickness as it moves through Newtonian fluid are investigated for the case when slip can occur at the surface of the disk. It is shown that when the disk translates parallel to its axis, the well-known velocity field for a no-slip boundary condition exerts zero shear stress on the surface of the disk. The flow is therefore unchanged if the boundary condition on the disk is modified to a stress-free or to a Navier slip boundary condition. This invariance also holds for a disk that rotates about a diameter. However, flow around a disk that rotates about its axis, or that translates in its own plane (edgewise), is modified when the no-slip boundary condition is changed to a Navier slip condition. The fluid velocity can be expressed in terms of Hankel transforms, and the resulting dual integral equations are solved numerically. Results for the torque and drag on the disk are presented as functions of the slip length in the Navier boundary condition.