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

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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.