TY - JOUR
T1 - Turbulent channel flow of dilute polymeric solutions
T2 - Drag reduction scaling and an eddy viscosity model
AU - Li, C. F.
AU - Gupta, V. K.
AU - Sureshkumar, R.
AU - Khomami, B.
N1 - Funding Information:
The authors would like to acknowledge the financial support provided by DARPA, Grants MDA972-01-1-007 and 29773A. We also would like to thank Prof. Fernando Pinho for helpful suggestions and comments.
PY - 2006/12/15
Y1 - 2006/12/15
N2 - 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, Reτ, and Weissenberg number, Weτ 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 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 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.
AB - 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, Reτ, and Weissenberg number, Weτ 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 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 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.
KW - Direct numerical simulation (DNS)
KW - Eddy viscosity model
KW - FENE-P
KW - Reynolds stress
KW - Slope increment
KW - Turbulent drag reduction
KW - Viscoelastic
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U2 - 10.1016/j.jnnfm.2006.04.012
DO - 10.1016/j.jnnfm.2006.04.012
M3 - Article
AN - SCOPUS:33751171762
SN - 0377-0257
VL - 139
SP - 177
EP - 189
JO - Journal of Non-Newtonian Fluid Mechanics
JF - Journal of Non-Newtonian Fluid Mechanics
IS - 3
ER -