ABSTRACT

Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a theoretical justification for this unsteady RANS (URANS) approach. Here, we extend the dynamical system fixed point analysis to create a theoretical model for URANS dynamics. The results are compared to URANS simulations for homogeneous isotropic decaying turbulence. The model shows that URANS can predict incorrect decay rates and that the solution tends towards steady RANS over time. Similar analysis for forced turbulence shows a fixed modelled energy of about 30% of total energy, regardless of the model parameters. The same analysis can be used to show how hybrid type models can begin to address these issues.

摘要

自 20 世纪 90 年代以来，RANS 实践者在 RANS 模拟中观察到自发的不稳定现象。一些人建议故意使用这种方法来解决大型湍流结构。然而，迄今为止，还没有人为这种不稳定的 RANS (URANS) 方法提供理论依据。在这里，我们扩展动力系统定点分析来创建 URANS 动力学的理论模型。将结果与均匀各向同性衰减湍流的 URANS 模拟进行比较。该模型表明 URANS 可以预测不正确的衰减率，并且随着时间的推移，解决方案趋向于稳定的 RANS。对受迫湍流的类似分析显示，无论模型参数如何，固定模型能量约占总能量的 30%。相同的分析可用于展示混合型模型如何开始解决这些问题。