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

壁面法向旋转对湍流通道流动的影响在各种应用中具有重要意义。壁面法向旋转引起沿展向x3方向的横流，破坏了初始的单向平均流动方向。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通道流动进行直接数值模拟（DNS）。计划研究由旋转诱导和修饰的相干结构。详细的雷诺平均统计及其分析是DNS的第二个重要课题。在过去的十年中，当实验很难或不可能进行时，DNS统计已成为分析和验证壁面有界流动中湍流模型的主要来源。由于已知任意旋转速率下层流情况的相当复杂的解析解，我们可以直接比较层流和湍流的结果。李群分析已被证明是发现流体运动方程对称性和推导新的标度定律（不变解）的有力工具。期望在当前流动情况下得到新的非平凡标度定律。研究非线性双方程模型、显式代数雷诺应力模型（EARSM）和全雷诺应力输运模型与李群分析得到的新标度律的相容性，并在必要时进行修正，是该项目的下一个主要目标。由于由李群分析得出的标度定律仅仅基于流体运动方程的基本对称性，因此任何湍流模型都必须与之一致。由于湍流标度定律的适用范围有限，我们还将最后的湍流模型，特别是那些遵循适当标度定律的模型，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，并在必要时调整模型常数。

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.