On the mechanisms for drag reduction: A viscoelastic evaluation based on a bead‐spring model

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Abstract
Two possible drag reduction mechanisms were examined by studying the viscoelastic effects of polymer solutions for the separate cases of oscillatory shear flow and elongational flow. The constitutive equation used was based on a modified dumbbell molecular model which predicts non‐Newtonian viscosity and both the primary and the secondary normal stress differences. It can be shown that when this constitutive equation is arranged in the form of the Oldroyd model, the latter becomes a special case of this more general equation. The present results show that viscoelastic effects on the mean local rate of energy dissipation of a fluid element in an oscillatory motion are negligibly small. However, such effects introduce very large increases in the elongational viscosity as the stretching rate exceeds a certain limiting value and the flow time exceeds the terminal relaxation time of the fluid. The relative merits of these findings as possible explanations of turbulent drag reduction are briefly discussed.

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