Numerical simulation of the interactions of highly entangled polymers with coherent structure in a turbulent channel flow

Abstract

Abstract Direct numerical simulations have been conducted with many cluster models of beads and connecting springs in a turbulent channel flow in order to investigate how the low-speed streaks and the small-scale flow related to the streaks are affected by the cluster models. The cluster model represents highly entangled polymers observed in the quiescent and flowing aqueous solution. The cluster models were introduced in the buffer region to simulate the experiments of Tiederman et al. (Tiederman, W.G., Luchik, T.S., Bogard, D.G., 1985. Wall-layer structure and drag reduction. J. Fluid Mech. 156, 419–437) in which the polymer solution was injected from a slot in the channel wall. An experiment has been carried out for visual observation of highly entangled polymers in a turbulent channel flow of the same Reynolds number in order to determine a parameter of the cluster model. The computational results show that the minor streaks and the small-scale eruptive flows associated with the streamwise vortices are attenuated selectively by the cluster models. The length scale and time scale of these structures are comparable to those of the cluster model. On the other hand, the dynamics of large-scale streaks are found to be basically unchanged. These results are consistent with the measurement of a suppression of low threshold Reynolds-stress producing motion by Harder and Tiederman (Harder, K.J., Tiederman, W.G., 1991. Drag reduction and turbulent structure in two-dimensional channel flows. Philos. Trans. R. Soc. Lond. 336, 19–34).