Onset mechanism of turbulent drag reduction in viscoelastic channel flow of dilute polymer solutions

The effects of fluid elasticity on the onset of drag reduction (DR) in turbulent channel flow of dilute polymer solutions are studied by direct numerical simulations. The fluid elasticity is measured by the elasticity number El in the range 0.002≤El≤0.010, which covers an inertial-driven turbulence but a wide range of drag reduction, up to intermediate DR regimes. Different DR regimes are characterized using flow and polymer dynamics for various El. Using the Prandtl–von Kármán coordinates, the onset Reynolds number Reonset and the onset Weissenberg number Wionset are computed as a function of El. In particular, Reonset decreases rapidly with elasticity, followed by an asymptotic behavior toward the transitional Reynolds number. The underlying mechanism of the DR onset is examined using both elastic and viscous theories—the elastic energy and the ratio of the maximum to the bulk-averaged polymer stretching, respectively. The elastic energy remains nearly constant before the onset, after which it increases rapidly and then approaches an asymptotic plateau. Interestingly, the stretching ratio exhibits a non-monotonic behavior, where it increases and reaches its peak at the onset, followed by a rapid decrease, and then saturates toward an asymptotic plateau. In addition, the maximum stretching ratio at the DR onset decreases rapidly with increasing elasticity, approaching an asymptotic plateau. These mechanistic findings should motivate the development of a unified model of the underlying onset mechanisms as well as post-onset DR mechanisms in viscoelastic turbulent flows.