A Role of Elastic Energy in Turbulent Drag Reduction by Polymer Additives

In the present study, the mechanism of turbulent drag reduction by polymer additives in a fully developed channel ow is investigated using direct numerical simulation. In order to see the elastic e ect on turbulent drag reduction, the dilute polymer solution is expressed with an Oldroyd-B model which shows a linear elastic behavior. Simulations are carried out by changing the Weissenberg number at the Reynolds numbers of 3000 and 15000. The onset criterion for drag reduction predicted in the present study shows good agreement with previous theoretical and experimental studies. In addition, the turbulence statistics such as the mean streamwise velocity and rms velocity uctuations are also in good agreements with previous experimental observations. The kinetic and elastic energy transport equations are derived to investigate the e ect of elasticity on drag reduction. It is shown that the polymer stores the elastic energy from the ow in the sublayer and then releases again in the sublayer when the relaxation time is short (no drag reduction). However, when the relaxation time is long enough (drag reduction), the elastic energy is transported to and released in the bu er layer. Therefore, drag reduction occurs when the turbulent velocity scale is larger than the characteristic velocity scale of the polymer solution.