Development of Second-Moment Closure of High Performance

这个项目的目的是通过测试和改进一个低雷诺数第二弯矩闭包，该闭包没有壁面反射再分布项，从而开发一个湍流模型，该模型再现了大范围的湍流流动，该闭包由项目的首席研究员Shima于1997年提出。二次弯矩闭合（模型97）已在跨向、顺向和壁向旋转、非定常管道流动、通过同心环空的流动和周期性蒸发的通道流动中进行了试验。本文还对系统旋转流动和通过同心环空的流动进行了直接数值模拟，并建立了这些流动的数据库。模型97较好地再现了同心环空流动，在周期性蒸腾的通道流动中也表现出明显的涡流-黏度模型的优越性。然而，在非定常管道流动中，该模型给出的湍流对流速变化的响应不如Shima先前包含壁面反射项的模型准确。在弱旋流情况下，预测的速度剖面与DNS数据基本一致。然而，在高旋转速率下，剪切应力分量的预测符号与DNS的不一致，导致速度剖面的预测不佳。当转速变大时，壁向旋转导致了流动的再分层。该模型对弱旋转的预测效果较好，但在较低的旋转次数下给出了再分层。正如我们所看到的，模型97显示出几个弱点，尽管它在许多流中作为低雷诺数第二弯矩闭包是有用的，没有壁反射重分布项。基于这些结果，我们正在开发一种性能更高的新模型。

The purpose of this project is to develop a turbulence model which reproduces a wide range of turbulent flows by testing and refining a low-Reynolds-number second-moment closure without wall-reflection redistribution terms proposed by Shima, the head investigator of the project, in 1997.The second-moment closure (Model 97) has been tested in channel flows with spanwise, streamwise and wall-normal rotations, unsteady pipe flows, flows through concentric annuli, and periodically transpired channel flows. Direct numerical simulations (DNS) of the flows with system rotations and flows through concentric annuli have also been performed, and databases of these flows have been constructed. The model 97 reproduces the concentric annulus flows well, and also shows a clear superiority to eddy-viscosity models in the periodically transpired channel flows. In the unsteady pipe flows, however, the model gives less accurate response of turbulence to flow-rate variation than a Shima's previous model which includes wall-reflection terms. In the case of weak streamwise rotation, the predicted velocity profiles are in reasonable agreement with DNS data. At high rotation rates, however, the predicted sign of a shear stress component disagrees with that of DNS, leading to poor predictions of the velocity profiles. The wall-normal rotation leads to relaminarization of the flow when the rotation rate becomes high. Good predictions are obtained for weak rotation but the model gives relaminarization at a lower rotation number than DNS. As we have seen, the model 97 shows several weaknesses, though it is useful in many flows as a low-Reynolds-number second-moment closure without wall-reflection redistribution terms. Based on these results, we are developing a new model for higher performance.