Polymer chain dynamics in Newtonian and viscoelastic turbulent channel flows

Abstract

Polymer chain dynamics in Newtonian and viscoelastic turbulent channel flows are examined by Brownian dynamics simulations utilizing FENE and FENE–P [finitely extensible nonlinear elastic(–Peterlin)] dumbbell models. The chain extension is predicted by using an algorithm that combines the two-step semi-implicit predictor–corrector scheme for the evaluation of dumbbell trajectories with the direct numerical simulation of turbulent flow field. The influence of maximum extensibility of the polymer chain, b, the friction Reynolds number, Reτ, and friction Weissenberg number, Weτ, on the chain dynamics in the viscous sublayer, buffer layer, and turbulent core is examined. For a given value of b, the average chain extension, 〈|Q|〉, approaches an asymptotic value with increasing Weτ. For given values of Weτ and the friction Reynolds number, Reτ, 〈|Q|〉/b decreases although 〈|Q|〉 itself increases with increasing b. Significant qualitative and quantitative differences exist between the predictions obtained using the FENE and FENE–P models. Specifically, 〈|Q|〉 values predicted by the FENE–P model are greater than those predicted by the FENE model for given Weτ and b. The normalized probability distribution function (pdf) for 〈|Q|〉 predicted by the two models also shows differences. Violated states, i.e., configurations with |Q|>b, are seen for the FENE–P model while such states are not seen for the case of FENE model. Despite these differences, the quantitative differences between the predictions of the two models for 〈QQ〉 in the viscous sublayer and the buffer layer can be practically eliminated by suitable renormalization of the maximum extensibility parameter. This renormalization also reduces the disparity between the FENE and FENE–P model predictions for the shear stress and transient extensional viscosity. Since mean chain extension and transient extensional behavior play a significant role in drag reduction (DR) such renormalization procedures could be used to improve the accuracy of continuum-level model predictions of DR. Comparison of simulation results obtained for Reτ=125 and 180 shows that the dependence of pdf for 〈|Q|〉 on Weτ and the renormalization proposed are not strongly influenced by Reτ. However, the fraction of highly extended states is larger for Reτ=180 while the states with low to moderate extension are smaller. Consequently 〈QQ〉 increases only marginally with increasing Reτ.