Remarkable drag reduction in non-affine viscoelastic turbulent flows

Abstract

We carry out a direct numerical simulation (DNS) study which aims to reveal the mechanism of turbulence drag reduction (DR) in polymer diluted flows. The polymer chains are modeled as elastic dumbbells. This paper focuses on elucidation of effect of introduction of non-affinity to describe the motions of the dumbbells on DR. We consider the cases in which the motions do not precisely correspond to macroscopically-imposed deformation. The Johnson-Segalman (JS) model is adopted to express the polymer stress. Assessment is done in forced homogeneous isotropic turbulence and pipe flow. In both flows, DR exhibits non-monotonous dependence on the strength of non-affinity. DR is maximal when non-affinity is either minimum (slip parameter α = 0.0) or maximum (α = 1.0) and almost no DR is obtained when α = 0.5. Remarkable enhancement of DR is achieved when α = 1.0 in both flows. In pipe flow, the mean velocity profile surpasses the Virk's maximum DR limit and nearly complete relaminarization occurs. This marked DR is not established when α ≠ 1.0. Mechanism of DR applied commonly to both flows is identified. A method to evaluate the normal-stress difference (NSD) and elongation viscosity is proposed using new eigenvector basis which span the isosurface of vortex tube and sheet. It is shown that the first NSD is predominantly positive, while the second NSD is negative along the sheets and tubes in both α = 0.0 and 1.0, implying that the polymer molecules exhibit alignment in a preferential direction in both cases. Mechanism in α = 1.0, however, is distinctively different from that in α = 0.0. When α = 0.0, the connector vector of dumbbell is convected as a contravariant vector representing material line element and elasticity is incurred primarily on filament-like element or the vortex tube. As shown in previous studies, the force exerted by the polymer stress such as the torque force reduces the vortex strength by opposing the vortical motions. When α = 1.0, the connector vector is convected as a covariant vector representing material surface element, and directs outward perpendicularly on the vortex sheet and exert an extra tension on the sheet. Creation of tubes due to rolling-up of the sheet is attenuated by this tensile force and energy cascade is annihilated. In high-DR cases, the elongation viscosity increases and stretching of the sheet and tube is hindered. Consistency of the results obtained in the DNS data with those predicted using an explicit expression of the polymer stress in the JS model is shown. Analogy of DR in α = 1.0 with DR occurring in the fluid diluted with high-concentration cationic surfactant and the fibers is presented. Limitation of the JS model in the intermediate range of 0.0 < α < 1.0 is discussed.