The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes fk which denotes the ratio of modeled to total kinetic energy. In RANS, fk=1 while in DNS it tends to zero. In the present study we propose an improved formulation for fk based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of fk is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) “detect” laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.

中文翻译：

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一种能够模仿 IDDES 的 PANS 公式

Girimaji (2006) 提出的部分平均 Navier-Stokes (PANS) 模型允许模拟 RANS、LES 或 DNS 模式下的湍流。PANS 模型包括 fk，它表示建模的动能与总动能的比率。在 RANS 中，fk=1 而在 DNS 中它趋于零。在本研究中，我们基于 Friess 等人引入的 H 等价提出了一种改进的 fk 公式。(2015)。在这个公式中，fk 的表达式被推导出来模拟改进的延迟分离涡流模拟 (IDDES)。这种新公式的行为方式与 IDDES 非常相似，尽管这两种公式使用不同的机制来分离建模和解析的尺度。它们在分离流和附着边界层中表现出非常相似的性能。特别是，新公式能够 (i) 像 IDDES 一样正确处理附着的边界层，以及 (ii) “检测”层流初始/边界条件，在这种情况下，它会强制执行 RANS 模式。此外，发现新公式在数值上比 IDDES 更稳定。