Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters

Abstract

In this work, we present the results from direct numerical simulations of the fully turbulent channel flow of a polymer solution. Using constitutive equations derived from kinetic and network theories, in particular the FEN E-P and the Giesekus models, we predict drag reduction for a variety of rheological parameters, extending substantially previous calculations, [Sureshkumar et al., Phys. Fluids, 9 (1997) 743-755]. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial domain. The computations were carried out on a CRAY T3E-900 parallel supercomputer, under fully turbulent conditions. In this work, we demonstrate the existence of a critical range of the Weissenberg number, where the onset of drag reduction occurs, which is independent of the model and also remains the same as the chain extensibility is increased. By allowing for higher extensibility of the polymer chains, we also observed an almost triple in magnitude increase in drag reduction from previous and reported results. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consistent with available experimental results. In addition to decreased fluctuations in the streamwise vorticity and increased streak spacing, we have seen changes, such as the increase of the slope of the logarithmic layer asymptote for the mean velocity profile, which are consistent with high magnitude of drag reduction, as well as with the behaviour of more concentrated systems. This is more consistent with the use of the Giesekus model, which is well suited for concentrated systems, suggesting that there is potential with that model for capturing quite subtle changes in the structure of the turbulent flow field. Results for different contributions of molecular extensibility, L, and solvent viscosity ratio, β, indicate that for the FENE-P model the phenomena are determined almost exclusively by the extensional viscosity and Weissenberg number. However, results obtained with the Giesekus model, for the same extensional viscosity, demonstrate a further drag reducing effect which can be attributed to the non-zero second normal stress coefficient. All results point to a mechanism for drag reduction where a partial inhibition of eddies within the buffer layer by the macromolecules. The simulation results are consistent with the hypothesis that one of the prerequisites for the phenomenon of drag reduction is sufficiently enhanced extensional viscosity, corresponding to the level of intensity and duration of extensional rates typically encountered during the turbulent flow, as has been proposed by various investigators in the past.