New variants of the terms involved in the transport equations of Laminar Kinetic Energy (LKE) transition schemes are proposed. The model here proposed was tuned by means of a big experimental data set describing transitional separated flows. Data were acquired by means of time-resolved Particle Image Velocimetry (TR-PIV) measurements above a flat plate centered in a variable area opening channel. Tests were carried out for different free-stream turbulence intensities, Reynolds numbers and adverse pressure gradients. The large amount of test conditions provides the statistical response of the separated flow transition process to the parameter variation. For each condition, Proper Orthogonal Decomposition (POD) was applied to the ensemble of snapshots. Analysis of POD modes and spectra of related temporal coefficients allows us to define a scale separation criterion, and thus construct reduced order models of laminar and turbulent terms appearing in LKE schemes. Combinations of the POD modes of the two velocity components, their gradients and mixed terms involving velocity scales and mean flow strain rates are used to compute the targeting function vectors for the learning of the models. The role played by normal and shear stress-strain mechanisms in the different parts of the separated flow region was addressed for a fine tuning of both the laminar and the turbulent kinetic energy production terms. Additionally, a new definition of the energy transfer rate between the laminar and the turbulent scales is educated, using ingredients representing the work done by the finer scale on the larger one, inspired by the exact definition of the transfer rate appearing in the transport equations of coherent and incoherent fluctuations. An elastic-net technique was used to identify the best predictors, thus the model learning. The ability of the proposed model is verified by using it to predict results obtained in a different experimental database that did not participate to the education of the model.

中文翻译：

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大的分离流实验数据库的弹性网改进层流动能转换模型的公式

提出了层流动能 (LKE) 转换方案的传输方程中涉及的项的新变体。这里提出的模型是通过描述过渡分离流的大型实验数据集来调整的。数据是通过时间分辨粒子图像测速 (TR-PIV) 测量在以可变面积开口通道为中心的平板上方获得的。对不同的自由流湍流强度、雷诺数和不利压力梯度进行了测试。大量的测试条件提供了分离流转变过程对参数变化的统计响应。对于每个条件，将适当的正交分解 (POD) 应用于快照集合。对 POD 模式和相关时间系数谱的分析使我们能够定义尺度分离标准，从而构建 LKE 方案中出现的层流和湍流项的降阶模型。两个速度分量的 POD 模式、它们的梯度和涉及速度尺度和平均流动应变率的混合项的组合用于计算模型学习的目标函数向量。法向和剪切应力应变机制在分离的流动区域的不同部分所起的作用得到了解决，以对层流和湍流动能产生项进行微调。此外，还对层流尺度和湍流尺度之间的能量传递率进行了新的定义，使用代表较大尺度上较细尺度所做工作的成分，受到相干和非相干波动的传输方程中出现的传输速率的精确定义的启发。弹性网技术用于识别最佳预测因子，从而进行模型学习。通过使用它来预测在未参与模型教育的不同实验数据库中获得的结果，验证了所提出模型的能力。