Abstract An extensive data set describing separated flows with different Reynolds numbers (Re), free-stream turbulence intensities (Tu) and adverse pressure gradients (APG) is used for the statistical characterization of laminar separation bubbles (LSBs). Measurements were performed by means of time-resolved particle image velocimetry along a flat plate installed between two adjustable endwalls, providing a test matrix of 3 Re, 4 Tu levels and 4 APGs. In this paper, 22 flow conditions are considered, which are related to the occurrence of boundary layer separation for each combination of the flow parameters. Boundary layer integral parameters, the root mean square of velocity fluctuations and the intermittency function distributions were computed for each condition. The connections between the main quantities that are commonly adopted for the statistical characterization of separated flows are clearly highlighted, thus providing the description of a LSB by means of a reduced set of these parameters. Empirical correlations predicting the transition onset location as well as the main dimensions (i.e., length and height) describing the geometry of a LSB are included in this work. Proper orthogonal decomposition is also adopted for the statistical characterization of the shedding process developing as a consequence of the Kelvin–Helmholtz instability. The frequency, wavelength and propagation velocity of the large-scale structures shed near the bubble maximum displacement are computed for each condition, showing the relation between the dominant shedding frequency and the average flow field at the separation position, and how these quantities are affected by Re, Tu and APG. Graphic abstract

中文翻译：

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平板层流分离气泡对雷诺数、自由流湍流和逆压力梯度变化的响应

摘要 描述具有不同雷诺数 (Re)、自由流湍流强度 (Tu) 和不利压力梯度 (APG) 的分离流的大量数据集用于层流分离气泡 (LSB) 的统计表征。测量是通过时间分辨粒子图像测速法沿着安装在两个可调端壁之间的平板进行的，提供 3 Re、4 Tu 水平和 4 APG 的测试矩阵。本文考虑了 22 种流动条件，它们与每种流动参数组合的边界层分离的发生有关。计算每个条件的边界层积分参数、速度波动的均方根和间歇函数分布。通常用于分离流的统计特征的主要量之间的联系被清楚地突出显示，从而通过这些参数的简化集来提供 LSB 的描述。这项工作包括预测过渡起始位置以及描述 LSB 几何形状的主要尺寸（即长度和高度）的经验相关性。由于开尔文-亥姆霍兹不稳定性而发展的脱落过程的统计表征也采用了适当的正交分解。计算每个条件下在气泡最大位移附近脱落的大型结构的频率、波长和传播速度，显示了主要脱落频率与分离位置的平均流场之间的关系，以及这些量如何受 Re、Tu 和 APG 的影响。图形摘要