Lagrangian simulations of turbulent drag reduction by a dilute solution of polymers in a channel flow

Much progress in understanding the phenomenon of turbulent drag reduction by polymer additives has been made since its first experimental observation. While the use of direct numerical simulations has achieved significant success and dramatically improved our understanding of the mechanisms associated with polymer drag reduction, a conclusive explanation of the physics associated with the phenomenon is still lacking. In particular, the stretching and relaxation mechanisms of individual polymer molecules are still unclear since the numerical simulations have relied on a continuum approach to compute the polymer quantities, i.e., solving a constitutive equation in an Eulerian frame of reference. Moreover, the accuracy of these simulations is limited by their need for artificial dissipation to stabilize the simulations. To overcome these difficulties, one can simulate the polymer phase in a Lagrangian framework, which is well suited for solving the hyperbolic polymer equations. The Lagrangian approach is characterized by tracking a large number of polymer molecules in the turbulent flow and computing the polymer stresses along their trajectories. This allows an exact description of the dynamics of single molecules and avoids any explicit artificial diffusion—a great advantage over the previous techniques. As a first step, this work attempts to uncover the mechanisms of polymer stretching in turbulent flows using various polymer models with realistic parameters. A topological methodology is applied to characterize the ability of the flow to stretch the polymers. It is found, using conditional statistics, that highly stretched polymer molecules have experienced a strong biaxial extensional flow between quasi-streamwise vortices in the near-wall regions. The extended polymers then relax in regions where the flow is mainly rotational located in and around the quasi-streamwise vortices. In the second step, a novel numerical method is developed based on a Lagrangian approach to simulate drag reduction. This new method reproduces well all the characteristic features of drag-reduced flows. However, a large discrepancy between Eulerian and Lagrangian calculations is found in flows with limited drag reduction. The Eulerian simulations show a much larger mean extension and damp the small scales. However, when the amount of drag reduction is increased, this discrepancy reduces.