Among factors affecting the accuracy of flow simulations with Reynolds-Averaged Navier-Stokes turbulence models is modeling turbulent diffusion processes. With the use of the Gram-Charlier series expansions, the turbulent diffusion in fourth-order one-point statistical closures of the Reynolds-Averaged Navier-Stokes equations can be modeled without introducing unknown model coefficients and without assuming turbulence being Gaussian. Terms representing turbulent diffusion processes in transport equations for second- and third-order velocity correlations do not require any modeling in such closures. In this regard, fourth-order closures are a more accurate alternative to lower-order closures where turbulent diffusion is modeled on semi-empirical or Gaussian turbulence assumptions. In the current paper, the accuracy of the closing procedure based on the Gram-Charlier series expansions is evaluated using data of direct numerical simulations in an incompressible zero-pressure-gradient turbulent boundary layer over a flat plate. One-point third-, fourth-, and fifth-order velocity moments were extracted for this purpose from the dataset collected by the Fluid Dynamics Group at the Universidad Politécnica de Madrid at two streamwise locations Reθ= 4101 and 5200 that correspond to channels and pipes at δ+= 1331 and 1626. Results demonstrate that the truncated Gram-Charlier series expansions are an accurate approximation of the fifth-order velocity moments in the considered flow.

中文翻译：

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在不可压缩的零压力梯度湍流边界层中使用 DNS 数据验证四阶 RANS 湍流模型的闭合程序

影响使用 Reynolds-Averaged Navier-Stokes 湍流模型进行流动模拟准确性的因素之一是模拟湍流扩散过程。通过使用 Gram-Charlier 级数展开式，可以对雷诺平均纳维-斯托克斯方程的四阶单点统计闭包中的湍流扩散进行建模，而无需引入未知的模型系数，也无需假设湍流为高斯。在二阶和三阶速度相关性的传输方程中表示湍流扩散过程的项不需要在此类闭包中进行任何建模。在这方面，四阶闭包比低阶闭包更准确，其中湍流扩散是基于半经验或高斯湍流假设建模的。在目前的论文中，使用平板上不可压缩的零压力梯度湍流边界层中的直接数值模拟数据评估基于 Gram-Charlier 级数展开的闭合程序的准确性。为此目的，从马德里理工大学流体动力学小组在两个流向位置 Reθ= 4101 和 5200（对应于通道和管道）收集的数据集中提取了一点三阶、四阶和五阶速度矩在 δ+= 1331 和 1626 处。结果表明截断的 Gram-Charlier 级数展开是所考虑流中五阶速度矩的准确近似。