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Contravariant and covariant polymer dumbbells in non-affine viscoelastic turbulence

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We carry out numerical study to reveal the mechanism of drag reduction (DR) in polymer-diluted flows. The polymer chains are modeled as elastic dumbbells. Primary purpose of this study is to elucidate the effect of introduction of non-affinity in the motion of dumbbells on DR. We consider the cases in which their motions do not precisely correspond to macroscopically-imposed deformation. We conduct analysis by connecting a macroscopic description for the Newtonian turbulent flow whose evolution is pursued using DNS to the mesoscopic description of an ensemble of dumbbells which are advected using the Brownian dynamics simulation (BDS) in forced homogeneous isotropic turbulence. The polymer stresses incurred by the dumbbells are fed back into the Navier-Stokes equation. Compared with the complete affine case (alpha = 0.0), more drastic DR is achieved when non-affinity is maximum (alpha = 1.0). When alpha = 0.0, the connector vector of dumbbell is convected as a contravariant vector representing material line element and elasticity is caused on the tubular structures. When alpha = 1.0, the connector vector is convected as a covariant vector representing material surface element, and directs outward perpendicularly on the planar structures and exert an extra tension on vortex sheet, which leads to attenuation of energy cascade, causing larger DR.

Author(s):

Kiyosi Horiuti    
Tokyo Institute of Technology
Japan

Shohei Takeu    
Tokyo Institute of Technology
Japan