Direct and large eddy numerical simulations of turbulent viscoelastic drag reduction

Abstract

This work deals with direct numerical simulations (DNS) and temporal large eddy simulations (TLES) of turbulent drag reduction induced by injection of heavy-weight long-chain polymers in a Newtonian solvent. The phenomenon is modelled for the three-dimensional wall-bounded channel flow of a FENE-P dilute polymer solution. The DNS are undertaken with an optimized hybrid high-order finite difference spectral code running in parallel using domain decomposition (mpi) and threading (openmp) on each mpi process.The flows computed have friction Reynolds numbers ranging from Reτ = 180 to 590. Various Weissenberg numbers and polymer molecular lengths are considered to obtain percent drag reductions from 28 to 59%. Results of DNS show that viscoelastic drag reduction is characterized by a marked anisotropy of the Reynolds stress and extra-stress tensors, thus confirming the recent findings of Frohnapfel et al. (J. Fluid Mech. 577:457-466, 2007) who postulate that strong anisotropy is a common feature to all drag reduction situations. The large eddy simulations (TLES) are based upon temporal causal filters (Pruett et al. in Humphrey et al. (eds.) Proc. of the 4th International Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, 2005, vol. 2, pp. 705-710). A key point of the TLES model lies in subfilter modeling of the stretching terms and of the non-linear spring force in the conformation tensor equation, which proves necessary to obtain correct predictions for the percent drag reduction with respect to DNS.