Geometric decomposition of the conformation tensor in viscoelastic turbulence
Geometric decomposition of the conformation tensor in viscoelastic turbulence
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DOI：
10.1017/jfm.2018.118
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发表时间：
2018-03
影响因子：
3.7
通讯作者：
I. Hameduddin;C. Meneveau;T. Zaki;D. Gayme
中科院分区：
文献类型：
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作者：
I. Hameduddin;C. Meneveau;T. Zaki;D. Gayme
这项工作介绍了一种数学方法来分析的聚合物动力学在湍流粘弹性流动，使用一个新的几何分解的构象张量，沿着与相关的标量测量的聚合物波动。该方法避免了传统的构象张量的雷诺分解的固有困难：波动张量场不是正定的，因此不保留张量的物理意义。构象张量的几何分解产生正定的平均和波动张量场。在本分解的波动张量有一个明确的物理解释为相对于平均配置的聚合物变形。这个波动的构象张量的标量措施开发的基础上的非欧几何的正定张量。减阻粘弹性湍流槽道流，然后使用一个例子的情况下研究。构象张量场，使用直接的数值模拟，分析使用所提出的框架。
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.