一类用于湍流粗粒化方法的动态RANS闭合模型的发展

中文摘要 AI 辅助

这项工作代表了Cimarelli等人[1]构思的一类新型湍流闭合模型发展中的关键进展。这类新型闭合模型基于时间滤波的Navier-Stokes方程所提供的理论框架。该框架为从统计到尺度分辨的湍流粗粒化方法提供了一个统一的 formalism，并提供了在不同粗粒化水平上关联湍流应力的精确方程。后者已在Cimarelli等人[1]中用作理论基础，以推导一类基于涡粘性定义中出现的模型系数动态计算的新型闭合模型。在此，我们通过推导基于k-ω模型的新公式来扩展这类动态RANS模型，包括一个替代版本，其中k和ω的输运方程所再现的自由流湍流的非物理衰减以优雅的方式得到解决。进行了一项尺度分辨模拟活动，结果分析揭示了有趣的特征。其中，新的动态k-ω模型对时间分辨率的粗粒化表现出强大的鲁棒性，并成功捕获了复杂的流动现象，包括层流向湍流的转捩以及边界层分离和再附着对边界处设定的自由流湍流水平的敏感性。

英文摘要

This work represents a crucial advancement in the development of a new class of turbulence closures conceived by Cimarelli et al. [1]. This new class of closures is based on the theoretical framework provided by the temporally filtered Navier-Stokes equations. This framework represents a unifying formalism for coarse-grained approaches to turbulence ranging from the statistical to the scale-resolving ones and provides exact equations relating turbulent stresses at different levels of coarsening. The latter have been used in Cimarelli et al. [1] as the theoretical foundation to derive a new class of closures based on the dynamic computation of the model coefficient appearing in the definition of eddy viscosity. Here, we extend this class of dynamic RANS models by deriving a new formulation based on the k-ω model including an alternative version where the non-physical decay of free-stream turbulence reproduced by the transport equations of k and ω is solved in an elegant way. A scale-resolving simulation campaign is performed and the analysis of the results reveals interesting features. Among others, the new dynamic k-ω model demonstrates strong robustness to a coarsening of the temporal resolution and successfully captures complex flow phenomena, including laminar-to-turbulent transition and the sensitivity of boundary-layer separation and reattachment to free-stream turbulence levels prescribed at the boundaries.

发表机构

• Department of engineering ”Enzo Ferrari”, University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学恩佐·费拉里工程学院）

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