The flow past a flat plate of finite width
The flow past a flat plate of finite width
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DOI：
10.1017/s0022112060000979
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发表时间：
1960-09
影响因子：
3.7
通讯作者：
J. W. Elder
中科院分区：
文献类型：
--
作者：
J. W. Elder
本文报道了雷诺数为104 ~ 106时，有限平板在零攻角下侧边附近不可压缩流动的实验研究，但与已发表的数据比较表明，雷诺数不超过109时，所得结论在定量上是有效的。层流速度场处处是凸的，并且除了层的正常扩散生长的流之外不包含任何二次流，但是在应力由局部曲率半径控制的边缘处具有对数奇异性。由于边缘引起的多余表面摩擦力比基于瑞利近似的计算结果大得多，但与Varley（1958）最近的Pohlhausen计算结果一致。在边缘附近，高应力和易于动量扩散使得流动非常不稳定，并且在板中间的正常过渡区的上游出现湍流点。这些斑点起源于板边缘的一个近似点状的区域，并以与普通湍流斑点相同的速率随时间线性增长，以扫过边缘附近的湍流流体的窄舌，直到它们与正常过渡区合并。在这个舌头的普朗特的第二类，由各向异性雷诺应力驱动的弱二次流开始发展。在完全紊流中，当二次流主要局限于边缘的几个附面层厚度内时，二次流速度处处小于自由流速度的0.04。尽管如此，来自每个侧边的二次流相互作用，而不管板的宽度如何，总阻力系数增加0.0004，这与雷诺数和板的宽度无关，除非板很窄。这个简单的结果使有限平板阻力系数的各种公式之间的明显差异减小到± 1% S.D.以下。在这些公式中，舍恩赫尔（1932）的经验关系式与目前的数据最符合。
An experimental study of the incompressible flow near the side edge of a finite flat plate at zero incidence is reported for the Reynolds number range 104 to 106, but comparison with data already published shows that the conclusions are quantitatively valid for Reynolds numbers up to 109. The laminar velocity field is everywhere convex and does not contain any secondary flow other than that of the normal diffusive growth of the layer, but has a logarithmic singularity at the edge where the stress is controlled by the local radius of curvature. The excess skin friction due to the edge is considerably greater than that given by calculations based on the Rayleigh approximation but agrees with a recent Pohlhausen calculation by Varley (1958). Near the edge the high stress and ease of momentum diffusion makes the flow very unstable and turbulent spots occur well upstream of the normal transition zone in the middle of the plate. The spots originate from a nearly point-like region at the edge of the plate and grow linearly in time at the same rate as ordinary turbulent spots to sweep out a narrow tongue of turbulent fluid near the edge until they merge with the normal transition zone. Within this tongue a weak secondary flow of Prandtl's second kind, driven by the anisotropic Reynolds stresses, begins to develop. In fully turbulent flow when the secondary flow is largely localized to within a few boundary-layer thicknesses of the edge the secondary flow velocities are everywhere less than 0.04 of the free-stream velocity. Nevertheless, the secondary flows from each of the side edges interact, regardless of the width of the plate, to increase the total drag coefficient by an amount 0·0004 which is independent both of the Reynolds number and the width of the plate except when it is very narrow. This simple result allows apparent discrepancies between various formulations of the drag coefficient of a finite plate to be reduced to less than ± 1% S.D. Of these formulations Schoenherr's (1932) empirical relation agrees best with the present data.