(129j) On the Skin Friction Coefficient In Viscoelastic Turbulent Wall Bounded Flows

Despite the fact that significant progress has been made on the understanding of polymer-induced drag reduction during the last decades, there are still many unresolved issues. Direct numerical simulations of dilute and semi dilute polymer solutions in channels had a great contribution towards this goal. They have been proved very useful because they provide significant information regarding the detailed structure of high Reynolds wall turbulent flows modified by the presence of macromolecules which show viscoelastic behavior.  Given the large number of case studies for which simulation results are available, we present here an effort to find correlations among the model parameters and key results from the simulations, of importance to experiments, such as the skin friction coefficient. As a first effort, a preliminary analysis of the dependence of the skin friction coefficient on viscous, Reynolds and viscoelastic stress contributions is conducted, in parallel of the work of Fukagata et al. (1) for Newtonian wall bounded flows and the work of Yu and Kawaguchi (2).

In particular, the total skin friction coefficient is analyzed in viscous, viscoelastic and Reynolds stress contributions as these arise from a suitable momentum balance. More specifically, by averaging available DNS results for viscoelastic turbulent channel flow these three contributions are evaluated and presented as functions of the flow and rheological parameters. Three different viscoelastic constitutive equations are used; the Oldroyd-B, the FENE-P and the Giesekus models. In addition, for the FENE-P model we develop closed-form power law relationships that describe quantitatively the dependence of the viscoelastic contribution on the flow and material parameters of the problem. Comparison of the total skin friction coefficient with experimental data also shows good agreement, indicating the consistency of the numerical simulations.

References

[1]. K. Fukagata, K. Iwamoto & N. Kasagi, 2002, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids, 14(11) L73-L76.

[2]. B. Yu and Y. Kawaguchi, 2006, “Parametric study of surfactant-induced drag-reduction by DNS,” International Journal of Heat and Fluid Flow, 27 887–894.