Numerical fluid-structure coupling schemes for high-frequency surface motion

这个项目的中心目标是数值模拟表面结构(沟槽)和/或横向横波对可压缩湍流的表面激励对宏观尺度的影响，以预测局部壁面摩擦分布。由于对于感兴趣的流型，表面结构和激励频率都不能直接通过总计算域的离散化来求解，因此我们希望发展基于均匀化或多尺度模拟的向上尺度方法。这些方法将被用来将那些确实能减少摩擦阻力的肋片结构和驱动参数转换成使宏观分析成为可能的边界公式。第一个供资期间的一个主要贡献是制定了一个适当的扰动分析框架，与已知的方法不同，该框架适用于相关的几何和湍流长度尺度。在微观尺度上识别合适的单元问题起着关键作用，其解被用来在宏观尺度上形成新的有效边界条件。虽然这些概念是以层流最透明的方式表述的，但当使用适当的湍流模型时，它们会延续到湍流区域，而湍流模型总是可以解释为正则化的Navier-Stokes方程。鉴于所设想的相关几何和湍流长度尺度，我们认为，除了低参数湍流模型之外，投影模型，如变分多尺度方法，最终最适合于正确地捕捉流动和几何结构/驱动的相互作用。在第一个资助期，重点是制定一项针对稳态问题的升级战略。除了进一步发展动荡制度的概念外，将其扩展到不稳定问题是第二个供资期间的中心目标。

The central objective of this project is the numerical simulation of effects on the macroscale that are caused by surface structures (riblets) and/or surface actuation by transversal waves in the spanwise direction on a compressible turbulent flow to predict the local skin friction distribution. Since for the flow regime of interest neither the surface structures nor the actuation frequency can be resolved directly by a discretization of the total computational domain we wish to develop upscaling methods based on homogenization or multiscale modelling. These methods are to be used to transfer those riblet structures and actuation parameters that indeed reduce friction drag into boundary formulations that make macroscopic analyses possible. A central contribution during the first funding period was the development of an appropriate framework for a perturbation analysis that, in contrast to the known methods applies to the relevant geometric and turbulent length scales. A pivotal role is played by the identification of suitable cell problems on the microscale whose solution is used to formulate new effective boundary conditions on the macroscale. While these concepts are formulated in the most transparent way for laminar flows they carry over to turbulent regimes when using appropriate turbulence models which can always be interpreted as regularized Navier Stokes equations. In view of the envisaged relevant geometric and turbulent length scales we believe that, beyond low parameter turbulence models, projection models such as the Variational Multiscale Method are ultimately best suited to correctly capture the interaction of flow and geometric structure/actuation. In the first funding period, the focus was on the development of an upscaling strategy for steady state problems. In addition to the further development of the concepts for turbulent regimes their extension to unsteady problems is the central goal in the second funding period.