The two‐dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time‐step method, were used to investigate separation due to the application of an adverse pressure gradient to a low‐Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP 4, 813 (1966)] was applied in the present computations to study the development of a laminar separation bubble. In all cases studied, periodic vortex shedding occurred from the primary separation region. The shed vortices initially lifted from the boundary layer and then returned towards the surface downstream. The shedding frequency nondimensionalized by the momentum thickness was found to be independent of Reynolds number. The value of the nondimensional Strouhal number, however, was found to differ from the results of Pauley et al. [J. Fluid Mech. 220, 397 (1990)], indicating that the shedding frequency varies with the nondimensional pressure distribution, C_p. The computational results were time averaged over several shedding cycles and the results were compared with Gaster. The numerical study accurately reproduced the major characteristics of the separation found in Gaster’s study such as the separation point, the pressure plateau within the upstream portion of the separation bubble, and the reattachment point. The similarity between the experimental results and the time‐averaged two‐dimensional computational results indicates that the low‐frequency velocity fluctuations detected by Gaster are primarily due to the motion of large vortex structures. This suggests that large‐scale two‐dimensional structures control bubble reattachment and small‐scale turbulence contributes a secondary role.

中文翻译：

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二维稳态层流分离的非定常结构

通过分数时间步法求解的二维非定常不可压缩Navier-Stokes方程用于研究由于施加不利条件而引起的分离 压力 降低到低雷诺数 边界层 流。 无形 压力法莫替丁[AGARD CP的分布4，813（1966）]在本计算被应用于研究层流分离气泡的发展。在所有研究的案例中，定期涡流从主要分离区域脱落。庇护所旋涡 最初从 边界层然后返回到下游表面。发现由动量厚度无量纲的脱落频率独立于雷诺数。但是，发现无量纲Strouhal数的值与Pauley等 人的结果不同。[J. 流体机械。220，397（1990）]，表明脱落频率与无量纲变化压力分布，C _p。将计算结果在几个排放周期内进行时间平均，并将结果与​​Gaster进行比较。的数值研究 准确地再现了Gaster研究中发现的分离的主要特征，例如分离点， 压力分离气泡上游部分中的平稳期和重新连接点。实验结果与时间平均二维计算结果之间的相似性表明，Gaster检测到的低频速度波动主要归因于运动 大 涡流结构。这表明，大型二维结构控制气泡的重新附着，而小型则控制气泡的重新附着。湍流 发挥次要作用。