Correlation of turbulent drag reduction in dilute polymer solutions with rheological properties by an energy dissipation model

Abstract

Both fresh and sheared dilute polymer solutions of Separan AP-30 (100, 250, 500 ppm by weight) were used to establish a correlation between rheological properties and turbulent drag reduction in tube flow. The viscosities of the dilute polymer solutions were measured in tubular, concentric and cone-and-plate viscometers with consistent results over a shear rate range from 0.01 to 20,000 1/s. The first normal stress difference was also measured in the cone-and-plate rheometry, and was found in good agreement with the predicted values based upon the method of Abdel-Khalid et al. The rheological model proposed by Tsai was modified to fit both the viscosity data as well as the normal stress difference data. Turbulent flow data in three tubes of different diameters (0.178, 0.406, and 0.460 cm) were obtained in a turbulent rheometer. The solvent Reynolds number ranged from 2,000 to 100,000. Five different horizontal tubes with diameters from 0.216 cm to 1.021 cm were used to observe the diameter effect in the 100 ppm fresh solution. An energy dissipation model was constructed to describe the mechanism of drag reduction in turbulent pipe flow. A shear rate dependent relaxation time was used in the data correlation. The dimensionless frequency (Deborah number) for the polymer solution was expressed in terms of the solvent Reynolds number, the zero shear rate viscosity, and the dimensionless relaxation time. The final correlation in the form of a generalized viscoelastic friction factor as a function of the solvent Reynolds number was capable of correlating all of the turbulent flow data, and reduces to the usual correlation for inelastic Newtonian fluids. This correlation was also applied to other data in the literature for similar polymer solutions, with good agreement.