Statistics and tensor analysis of polymer coil–stretch mechanism in turbulent drag reducing channel flow

Abstract

The polymer coil–stretch mechanism in turbulent drag reducing flows is analysed using direct numerical simulations of viscoelastic finitely extensible nonlinear elastic fluids with the Peterlin approximation. The study is carried out taking into account low and high drag reduction regimes. The polymer stretching and the alignment between the conformation tensor and other relevant entities are investigated using statistical and tensor analysis. The significant alignment between the former and the velocity fluctuations product tensor indicates that the initial polymer stretching due to the mean shear is increased by the flow stress fluctuations, providing a supplementary polymer extension. In addition, interactions between the turbulence and the polymer are evaluated from an instantaneous turbulent energy exchange perspective by considering streamwise work fluctuating terms in elliptical and hyperbolic flow regions separately. Near the wall, polymers not only release energy to the streaks, but also to the elliptical (or vortical) and hyperbolic (or extensional) structures. However, polymers can also be dragged around near-wall vortices, passing through hyperbolic regions and experiencing a significant straining within both these turbulent structures and storing their energy. Hence, polymers weaken elliptical and hyperbolic structures leading to a tendency toward relaminarization of the flow. Polymer release of energy occurs primarily in the streamwise direction, which is in agreement with the enhanced streamwise velocity fluctuation observed in drag reducing flows. A detailed polymer coil–stretch mechanism is provided.