The goal of this study is to present a first step towards establishing criteria aimed at assessing whether a particular adverse-pressure-gradient (APG) turbulent boundary layer (TBL) can be considered well-behaved, i.e., whether it is independent of the inflow conditions and is exempt of numerical or experimental artifacts. To this end, we analyzed several high-quality datasets, including in-house numerical databases of APG TBLs developing over flat-plates and the suction side of a wing section, and five studies available in the literature. Due to the impact of the flow history on the particular state of the boundary layer, we developed three criteria of convergence to well-behaved conditions, to be used depending on the particular case under study. (i) In the first criterion, we develop empirical correlations defining the Re𝜃-evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter β = 1 and 2 (note that β = δ∗/τwdPe/dx, where δ∗ is the displacement thickness, τw the wall-shear stress and dPe/dx the streamwise pressure gradient). (ii) In the second one, we propose a predictive method to obtain the skin-friction curve corresponding to an APG TBL subjected to any streamwise evolution of β, based only on data from zero-pressure-gradient TBLs. (iii) The third method relies on the diagnostic-plot concept modified with the shape factor, which scales APG TBLs subjected to a wide range of pressure-gradient conditions. These three criteria allow to ensure the correct flow development of a particular TBL, and thus to separate history and pressure-gradient effects in the analysis.

中文翻译：

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重温逆压力梯度湍流边界层中的历史效应

本研究的目的是提出建立标准的第一步，该标准旨在评估特定的逆压力梯度 (APG) 湍流边界层 (TBL) 是否可以被认为是行为良好的，即它是否独立于流入条件和免除数值或实验工件。为此，我们分析了几个高质量的数据集，包括在平板和机翼部分的吸力侧上发展的 APG TBL 的内部数值数据库，以及文献中的五项研究。由于流动历史对边界层的特定状态的影响，我们开发了三个收敛到良好条件的标准，根据所研究的特定情况使用。(i) 在第一个标准中，我们开发了经验相关性，定义了皮肤摩擦系数的 Re𝜃 演化和 APG TBL 中的形状因子，其中 Clauser 压力梯度参数 β = 1 和 2 的恒定值（注意 β = δ∗/τwdPe/dx，其中δ∗ 是位移厚度，τw 是壁面剪切应力，dPe/dx 是流向压力梯度）。(ii) 在第二个中，我们提出了一种预测方法来获得对应于经受 β 的任何流向演化的 APG TBL 的皮肤摩擦曲线，仅基于来自零压力梯度 TBL 的数据。(iii) 第三种方法依赖于用形状因子修改的诊断图概念，该概念可缩放 APG TBLs 在各种压力梯度条件下。这三个标准可以确保特定 TBL 的正确流动发展，