The paper focuses on a study of turbulence decay in flow with streamwise gradient. For the first time, an analytical solution of this problem was obtained based on the k‐ε model of turbulence in one‐dimensional (1D) approximation, as well as on the symmetry properties of the system of differential equations. Lie group technique enabled reducing the problem to a linear differential equation. The analytical solution enabled parametric studies, which are computationally cheap in comparison to CFD based simulations. The lattice Boltzmann method (LBM) in two‐dimensional approximation (2D) was used to validate the analytical results. Large eddy simulation (LES) Smagorinsky approach was used to close the LBM model. Computations revealed that the rate of turbulence decay is significantly different for the cases of positive and negative streamwise pressure gradient. The further comparisons showed that the analytical solution underpredicts the predictions by the numerical methodology, which can be attributed to the simplified problem statement used to derive the closed‐form analytical solution. Comparisons of calculations with experiments revealed that the theoretical models used in the study underpredict the measurements for flows with a positive pressure gradient. Hence it can be concluded that the LBM technique combined with the LES Smagorinsky model requires the further modification.

中文翻译：

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解析和格子玻尔兹曼方法在汇流和扩散流中湍流衰减模拟的比较分析

本文着重研究了具有顺流梯度的流动湍流衰减。首次基于一维（1D）近似的湍流k-ε模型以及微分方程组的对称性质，获得了该问题的解析解。借助李群技术，可以将问题简化为线性微分方程。解析解决方案支持参数研究，与基于CFD的仿真相比，该方法在计算上便宜。使用二维近似（2D）的格子Boltzmann方法（LBM）来验证分析结果。大涡模拟（LES）Smagorinsky方法用于关闭LBM模型。计算表明，在正负流向压力梯度情况下，湍流衰减率显着不同。进一步的比较表明，解析解对数值方法的预测不足，这可以归因于用于导出封闭形式解析解的简化问题陈述。与实验的计算比较表明，研究中使用的理论模型对压力梯度为正的流量的测量结果预测不足。因此可以得出结论，LBM技术与LES Smagorinsky模型相结合需要进一步的修改。这可以归因于用于导出封闭形式分析解决方案的简化问题陈述。与实验的计算比较表明，研究中使用的理论模型对压力梯度为正的流量的测量结果预测不足。因此可以得出结论，LBM技术与LES Smagorinsky模型相结合需要进一步的修改。这可以归因于用于导出封闭形式分析解决方案的简化问题陈述。与实验的计算比较表明，研究中使用的理论模型对压力梯度为正的流量的测量结果预测不足。因此可以得出结论，LBM技术与LES Smagorinsky模型相结合需要进一步的修改。