长圆柱结构绕流的数值模拟
Modelling of Flow Past Long Cylindrical Structures
摘要：
湍流在工程和环境中是基本的，但是它们的混沌和三维（3-D）性质使得它们的模拟在计算上昂贵。在这项工作中，降维技术进行了研究，以利用流呈现均匀的方向，如尾流挤压二维（2-D）的几何形状。首先，我们在$Re=10^4$上研究了均匀方向跨度对不可压缩圆柱绕流尾流湍流动力学的影响。据发现，固体壁的存在下诱导3-D结构，即使在高度收缩的域。如果圆柱体跨度为直径的50%或更小，由于跨度短于自然尾流模式B不稳定波长，则三维结构通过大尺度卡门涡快速二维化[.]。有了这个物理的理解，2-D数据驱动的模型，结合3-D的影响，发现在3-D尾流，提出。2-D模型是从一种基于局部展向平均流的新的流分解中推导出来的，产生展向平均纳维尔-斯托克斯（SANS）方程[...]。一个机器学习（ML）模型提供封闭的SANS方程。在先验框架中，ML模型产生了SSR项的准确预测，与完全无法捕获闭合项结构的标准涡粘性模型相反[...]。在后验分析中，虽然我们发现了动力系统长期ML预测的已知稳定性问题的证据，但封闭的SANS方程仍然能够预测尾流指标和诱导力，误差在1- 10%之间。这导致在大约一个数量级的改进，在标准的2-D模拟，同时减少了99.5%的3-D模拟的计算成本。
英文摘要：
Turbulent flows are fundamental in engineering and the environment, but their chaotic and three-dimensional (3-D) nature makes them computationally expensive to simulate. In this work, a dimensionality reduction technique is investigated to exploit flows presenting an homogeneous direction, such as wake flows of extruded two-dimensional (2-D) geometries. First, we examine the effect of the homogeneous direction span on the wake turbulence dynamics of incompressible flow past a circular cylinder at $Re=10^4$. It is found that the presence of a solid wall induces 3-D structures even in highly constricted domains. The 3-D structures are rapidly two-dimensionalised by the large-scale Kármán vortices if the cylinder span is 50\% of the diameter or less, as a result of the span being shorter than the natural wake Mode B instability wavelength[...]. With this physical understanding, a 2-D data-driven model that incorporates 3-D effects, as found in the 3-D wake flow, is presented. The 2-D model is derived from a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier-Stokes (SANS) equations[...]. A machine-learning (ML) model is employed to provide closure to the SANS equations. In the a-priori framework, the ML model yields accurate predictions of the SSR terms, in contrast to a standard eddy-viscosity model which completely fails to capture the closure term structures[...]. In the a-posteriori analysis, while we find evidence of known stability issues with long-time ML predictions for dynamical systems, the closed SANS equations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
