Physically based sub-grid scale modelling for large-eddy simulation to enhance turbulence noise prediction

本项目的重点是建立亚网格尺度（SGS）模型，用于湍流大涡模拟（LES），以增强宽带噪声预测。主要目标是研究和开发湍流的亚网格尺度模型，该模型允许捕获尽可能多的基本运动方程，欧拉和纳维-斯托克斯方程以及相应的统计方程的对称性。这种方法背后的道理是观察到，在上个世纪，只有在模型方程中实现了基本对称性和对称性破缺的情况下，湍流建模才能取得相当大的进步。这些发现既适用于雷诺平均模型，也适用于已显示的亚网格比例模型。具体来说，建议有三个方面：首先，现有的sgs模型将根据其对称性进行调查。一个已建立的模型将进一步发展，或者一个新的模型将沿着这些路线推导出来。其次，由于LES在很大程度上受到未解决的近壁问题的困扰，因此将调用对称性来利用思想减少墙附近的计算成本。第三，将研究sgs模型与声学类比（如Lighthill的类比）的兼容性。这些类比具有特定的对称性和相关的分析性质。由于sgs模型修改声学类比，因此必须确保闭合假设尽可能少地改变声场。sgs模型设计应符合这一要求。

This project is focused on the modelling of sub-grid scale (SGS) models for Large-Eddy Simulation (LES) of turbulence to enhance broad-band noise prediction. The primary objective is to investigate and develop sub-grid scale models for turbulence which allow to capture as many as possible symmetries of the fundamental equations of motion, the Euler and Navier-Stokes equations and the corresponding statistical equations. The rational behind this approach is the observation that in the last century considerable improvement in turbulence modelling has only been achieved if fundamental symmetries and symmetry breaking have been implemented into model equations. These findings apply both for Reynolds averaged as well as for sub-grid scale models as has been shown. Specifically the proposal is threefold: Firstly, the existing SGS-model will be investigated with respect to its symmetries. An established model will be developed further or a new model will be derived along these lines. Secondly, since LES largely suffers from the unsolved nearwall problem, symmetries will be invoked to reduce the computational cost in the vicinity of the wall employing ideas. Thirdly, SGS-models will be investigated with respect to their compatibility with acoustic analogies, such as the Lighthill´s analogy. These analogies have specific symmetries and related analytical properties. Since SGS-models modify acoustic analogies it has to be ensured that the closure assumptions alter the acoustic field as little as possible. SGS-model design should comply with this requirement.