an:05787227
Zbl 1195.76034
Li, C. F.; Gupta, V. K.; Sureshkumar, R.; Khomami, B.
Turbulent channel flow of dilute polymeric solutions: drag reduction scaling and an eddy viscosity model
EN
J. Non-Newton. Fluid Mech. 139, No. 3, 177-189 (2006).
00188790
2006
j
76A05 76M22
turbulent drag reduction; slope increment; Reynolds stress; viscoelastic; FENE-P; direct numerical simulation (DNS); eddy viscosity model
Summary: Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, \(Re_{\tau}\), and Weissenberg number, \(We_{\tau}\) and percent drag reduction (\%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; \(0 \leq \%DR \leq 20\)), high drag reduction (HDR; \(20 \leq \%DR \leq 52\)) and MDR (\(52 \leq \%DR \leq 74\)) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.