In this work, a theoretical-experimental study on the drag reduction phenomenon by the addition of macromollecules in turbulent pipes flows is carried out. The reduction of the friction factor is obtained when low concentrations of high mollecular weigth polymers are added on the flow. In order to investigate the mean effect of the macromollecules, a constitutive non-linear model for the extensional viscosity is proposed. The friction factor of the flow in the presence of additives is determined theoretically as a function of the aspect ratio and the concentration of the macromollecules, and of the Reynolds number of the flow. The present theory is based on an extention of the universal Prandtl theory for turbulent flows in smooth pipes. The experimental friction factor was determined by pressure drop and flow rates measurements. The velocity profiles of the flow were obtained by the laser doppler anemometry (LDV). Velocity signals acquired in three different stations along the tube radius were formally treated from a statistical point of view. LDV experiments were carried out for both pure water and 120 ppm polymer solution, keeping the same Reynolds number based on the friction velocity of the flow in both cases. The theory and the exper- iments show that the reduction of friction factor in turbulent flows with macromollecules can be understood in terms of the ratio between the relaxation time of the polymer and the characteristic time scale of the flow. A comparison between the friction factor correlation that was predicted by the theory and the experimental results reveal a good agreement when appropriate values of the constants of the model are used. A reduction of about 65% on the friction factor of the flow is verified for a 350 ppm concentration of polyacrilamide. |