Polymer-induced drag reduction: Effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow

In this work we systematically investigate the effects of the flow elasticity and inertia in polymer-induced drag reduction through (pseudo)spectral simulations of a turbulent channel flow of a dilute polymer solution. Viscoelastic effects are modeled by the finite-extensibility nonlinear elastic dumbbell model with the Peterlin approximation. The present work updates the low Weissenberg results (We(tau0)less than or equal to50) reported in earlier works by Sureshkumar [Phys. Fluids 9, 743 (1997)] and Dimitropoulos [J. Non-Newtonian Fluid Mech. 79, 433 (1998)] for a zero shear rate friction Reynolds number, Re-tau0=125, by allowing for a lower value for the numerical diffusivity. In addition, we examine two effects on drag reduction: (A) high elasticity, by varying We(tau0) from 62.5 to 125 for a constant Re-tau0=125, (B) friction Reynolds number, Re-tau0=180, 395, and 590, for a constant We(tau0)=50. In the high elasticity region, the mean Reynolds, Re-mean, continues to increase with increasing We(tau0), albeit at a smaller rate. Thus, the drag reduction achieved at the highest We(tau0) number, We(tau0)=125, is about 37.5%, as compared to about 30% for We(tau0)=50. On the other hand, the percent drag reduction remains virtually unchanged as Re-tau0 is increased to 180, 395, and 590 for a constant We(tau0)=50. Increasing the friction Reynolds number while keeping the friction Weissenberg number constant, does affect the detailed turbulent statistics. However, the boundary and the buffer layers approach an asymptote at a friction Reynolds number of 395 as it has also been observed in the Newtonian limit. The effect of variations in the computational domain, mesh resolution and the numerical diffusivity on the turbulent statistics is also reported. (C) 2003 American Institute of Physics.