On the Extension of Polymer Molecules in Turbulent Viscoelastic Flows: Statistical and Tensor Investigation

In the present work, direct numerical simulations of turbulent channel flow of a viscoelastic FENE-P fluid, at zero-shear friction Reynolds number equal to 180, are used to analyze the polymer extension mechanism. As a primary focus, the relative polymer stretch and the probability distribution function of the alignment between the conformation tensor and other relevant entities are investigated. In near-wall regions, polymers present a strong tendency to orient along the streamwise direction of the flow. Furthermore, the polymer extension seems to be strongly correlated to the alignment between both conformation tensor and the velocity fluctuations product tensor, \(\mathbf { {\tau }^{\prime } }\) (defined as \({{u^{\prime }}_i}{{u^{\prime }}_j}\)). Joint probability density functions show that large positive polymer work fluctuations, \({{E^{\prime }}_x}\), are closely related to the positive growth rate of the product of streamwise velocity fluctuations, \({\partial _{t} {u^{\prime }}^2_x}\). In contrast, small negative fluctuations of polymer work are observed in the regions of negative rate of \({u^{\prime }}^2_x\). However, in both cases, polymers are predominantly oriented along the principal direction of \(\mathbf { {\tau }^{\prime } }\), which indicates the relevance of this tensor for the polymer-turbulence interaction mechanism.