Wall-normal Rotating channel flow: Direct Numerical Simulation, Modeling and Lie Group Analysis

壁法向旋转对槽道湍流流动的影响具有重要的应用价值。壁法向旋转导致沿跨向x3方向的横流，破坏了最初的单向平均流动方向。还没有对所考虑的流动进行模拟或实验。该项目的第一个目标是对旋转槽道流动进行直接数值模拟。计划研究旋转诱导和修正的共格结构。详细的雷诺平均统计数据及其分析是域名系统的第二个重要主题。在过去的十年中，当实验难以或不可能进行时，域名系统统计已被确立为分析和验证壁面边界流动中的湍流模型的主要来源。由于已知任意转速下层流情况的一个相当复杂的解析解，我们可以直接比较层流和湍流的结果。Lie群分析已被证明是寻找流体运动方程的对称性和推导新的标度律(不变解)的有力工具。对于本流动情况，可望得到新的非平凡标度律。研究非线性两方程模型、显式代数雷诺应力模型(EARSM)和全雷诺应力输运模型与从李群分析得到的新标度律的兼容性，并在必要时进行修正是该项目的下一个主要目标。由于从李群分析得到的标度律完全基于流体运动方程的基本对称性，所以任何湍流模型都必须与之一致。由于湍流标度律的适用范围有限，我们还将比较最后的湍流模型，特别是那些遵守适当标度律的湍流模型，并将其与DNS数据进行比较。这使我们能够研究湍流模型的整体性能，如有必要，还可以调整模型常数。

The influence of wall-normal rotation on turbulent channel flows is of great significance for a variety of applications. Wall-normal rotation induces a cross-flow in spanwise x3-direction, which destroys the initially unidirectional mean flow direction. No simulations or experiments have been conducted for the flow under consideration. The first aim of the project is to perform a direct numerical simulation (DNS) of the rotating channel flow. It is planned to study coherent structure induced and modified by rotation. Detailed Reynolds averaged statistics and their analysis is the second important subject of the DNS. In the last decade DNS statistics has established as the main source to analyse and validate turbulent models in wall-bounded flows when experiments are difficult or impossible to perform. Since a rather complicated analytical solution for the laminar case for arbitrary rotation rate is known we may directly compare laminar and turbulent flow results.Lie group analysis has proven to be a powerful tool to find symmetries of the equations of fluid motion and to derive new scaling laws (invariant solutions). It is expected to obtain new non-trivial scaling laws for the present flow case. Studying and if necessary revision of non-linear two-equation models, Explicit Algebraic Reynolds Stress Model (EARSM) and full Reynolds stress transport models on their compatibility with the new scaling laws obtained from Lie group analysis is the next major aim of the project. Because of the fact that scaling laws obtained from Lie group analysis are solely based on the fundamental symmetries of the equations of fluid motion, any turbulent model has to be consistent with them. Since turbulent scaling laws only have a limited range of applicability we will also compare the last turbulence models, particularly those who observe the proper scaling laws, with the DNS data. This allows us to investigate the overall performance of turbulence models and if necessary a model constants adjustment.