Simulating drag reduction phenomenon in turbulent pipe flows

Abstract

Drag reduction using polymeric additives is an interesting phenomenon in turbulent pipe flows which was first discovered by Toms [Toms, B.A., 1948. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. First Int. Cong. Rheol. 2, 135–141]. Due to its industrial importance, the phenomenon has been the subject of much study in the past, in both theoretical and experimental domains alike. As to the mechanisms involved, it has been argued that polymeric additives act through affecting the structure of turbulent bursts near the wall by boosting the extensional viscosity of the base fluid (see [Lumley, J.L., Blossey, P., 1998. Control of turbulence. Ann. Rev. Fluid Mech. 30, 311–327]). In practice, drag reduction as large as 90% has been achieved with concentration as low as 20 ppm of certain high-molecular-weight flexible polymers. Prediction of such huge drag reductions obtained using polymeric additives has not been possible in the past partly, because of the limitations of the computational facilities and also because of the inadequacies of the constitutive equations used for the simulations. Recently, Pinho [Pinho, F.T., 2003. A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k– ε type closure. J. Non-Newtonian Fluid Mech. 114, 149–184] modified the generalized Newtonian fluid (GNF) model in such a way that it could take into account the extensional viscosity (a measure of the elastic behavior of a fluid) in addition to the shear viscosity (a measure of the viscous behavior of a fluid). Based on this idea, Pinho (2003) derived the first time-averaged turbulent flow formulations for viscoelastic fluids. These formulations were used by Cruz and Pinho [Cruz, D.O.A., Pinho, F.T., 2003. Turbulent pipe flow predictions with a low-Reynolds number k– ε model for drag reducing fluids. J. Non-Newtonian Fluid Mech. 114, 109–148] and Cruz et al. [Cruz, D.O.A., Pinho, F.T., Resende, P.R., 2004. Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J. Non-Newtonian Fluid Mech. 121, 127–141] by embedding the low-Reynolds turbulence model of Nagano–Hishida [Nagano, Y., Hishida, M., 1987. Improved form of the k– ε model for wall turbulent shear flows. J. Fluid Eng. 109–156]. They performed several simulations using this well-known turbulence model and showed that it can well predict the large drag reduction observed in practice for some polymeric additives. But for certain other polymers the prediction were found not to be so great. In this work, it will be shown that better predictions can be obtained for these polymers if use is made of another low-Reynolds number k– ε turbulence model called Launder–Sharma model [Launder, B.E., Sharma, B.I., 1974. Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1, 131–138] for the simulations.