Geometric decomposition of the conformation tensor in viscoelastic turbulence

• Published in: arXiv.org 2018-03
• Main Authors: Ismail Hameduddin, Meneveau, Charles, Zaki, Tamer A, Gayme, Dennice F
• Format: Article
• Language: English
• Subjects: Channel flow; Computational fluid dynamics; Computer simulation; Decomposition; Deformation; Drag reduction; Euclidean geometry; Mathematical analysis; Polymers; Tensors; Turbulence; Turbulent flow; Variation; Viscoelasticity
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1803.07619

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.