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

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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.