We present direct numerical simulation data for turbulent duct flow of a finite-extensibility non-linear elastic dumbbell model with the Peterlin approximation (FENE-P) fluid in the high drag reduction regime. While the secondary flow pattern is qualitatively similar to that in a Newtonian fluid, its magnitude is significantly reduced, resulting in a less uniformly distributed velocity profile and hence smaller gradients at the wall. The Reynolds stress tensor in the polymer-laden flow was found to be increasingly anisotropic with most of the turbulent kinetic energy retained in the streamwise component, . We introduce a novel approach for investigating polymer stretching using the anisotropy invariant map of the polymer stress tensor and observe the persistence of both uniaxial and biaxial extension. Analysis of the transport equation for the mean kinetic energy indicates that polymer stretching and relaxation is a highly dissipative process; hence, the introduction of an additional channel for dissipation in a flow is key to drag reduction.
References
1.
R.
Benzi
and E. S.
Ching
, “Polymers in fluid flows
,” Annu. Rev. Condens. Matter Phys.
9
, 163
–181
(2018
).2.
L.
Xi
, “Turbulent drag reduction by polymer additives: Fundamentals and recent advances
,” Phys. Fluids
31
, 121302
(2019
).3.
J. L.
Lumley
, “Drag reduction in turbulent flow by polymer additives
,” J. Polym. Sci.
7
, 263
–290
(1973
).4.
Y.
Dubief
, C. M.
White
, V. E.
Terrapon
, E. S.
Shaqfeh
, P.
Moin
, and S. K.
Lele
, “On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows
,” J. Fluid Mech.
514
, 271
–280
(2004
).5.
V.
Terrapon
, Y.
Dubief
, P.
Moin
, E. S.
Shaqfeh
, and S. K.
Lele
, “Simulated polymer stretch in a turbulent flow using brownian dynamics
,” J. Fluid Mech.
504
, 61
–71
(2004
).6.
P. S.
Virk
, “Drag reduction fundamentals
,” AIChE J.
21
, 625
–656
(1975
).7.
G. H.
Choueiri
, J. M.
Lopez
, and B.
Hof
, “Exceeding the asymptotic limit of polymer drag reduction
,” Phys. Rev. Lett.
120
, 124501
(2018
).8.
J. M.
Lopez
, G. H.
Choueiri
, and B.
Hof
, “Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit
,” J. Fluid Mech.
874
, 699
–719
(2019
).9.
M. D.
Warholic
, H.
Massah
, and T. J.
Hanratty
, “Influence of drag-reducing polymers on turbulence: Effects of Reynolds number, concentration and mixing
,” Exp. Fluids
27
, 461
–472
(1999
).10.
B. E.
Owolabi
, D. J.
Dennis
, and R. J.
Poole
, “Turbulent drag reduction by polymer additives in parallel-shear flows
,” J. Fluid Mech.
827
, R4
(2017
).11.
E. J.
Soares
, “Review of mechanical degradation and de-aggregation of drag reducing polymers in turbulent flows
,” J. Non-Newtonian Fluid Mech.
276
, 104225
(2020
).12.
R.
Bird
, P.
Dotson
, and N.
Johnson
, “Polymer solution rheology based on a finitely extensible bead-spring chain model
,” J. Non-Newtonian Fluid Mech.
7
, 213
–235
(1980
).13.
I.
Procaccia
, V. S.
L'vov
, and R.
Benzi
, “Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence
,” Rev. Mod. Phys.
80
, 225
(2008
).14.
L.
Zhu
, H.
Schrobsdorff
, T. M.
Schneider
, and L.
Xi
, “Distinct transition in flow statistics and vortex dynamics between low-and high-extent turbulent drag reduction in polymer fluids
,” J. Non-Newtonian Fluid Mech.
262
, 115
–130
(2018
).15.
L.
Warwaruk
and S.
Ghaemi
, “A direct comparison of turbulence in drag-reduced flows of polymers and surfactants
,” J. Fluid Mech.
917
, A7
(2021
).16.
L.
Zhu
and L.
Xi
et al., “Nonasymptotic elastoinertial turbulence for asymptotic drag reduction
,” Phys. Rev. Fluids
6
, 014601
(2021
).17.
G.
Sun
, D.
Wan
, and M.
Zhang
, “Nonlinear evolutions of streaky structures in viscoelastic pipe flows
,” J. Non-Newtonian Fluid Mech.
295
, 104622
(2021
).18.
H.
Teng
, N.
Liu
, X.
Lu
, and B.
Khomami
, “Turbulent drag reduction in plane Couette flow with polymer additives: A direct numerical simulation study
,” J. Fluid Mech.
846
, 482
(2018
).19.
A.
Shahmardi
, S.
Zade
, M. N.
Ardekani
, R. J.
Poole
, F.
Lundell
, M. E.
Rosti
, and L.
Brandt
, “Turbulent duct flow with polymers
,” J. Fluid Mech.
859
, 1057
–1083
(2019
).20.
M.
Uhlmann
, A.
Pinelli
, G.
Kawahara
, and A.
Sekimoto
, “Marginally turbulent flow in a square duct
,” J. Fluid Mech.
588
, 153
–162
(2007
).21.
A.
Pinelli
, M.
Uhlmann
, A.
Sekimoto
, and G.
Kawahara
, “Reynolds number dependence of mean flow structure in square duct turbulence
,” J. Fluid Mech.
644
, 107
–122
(2010
).22.
P. A.
Stone
, F.
Waleffe
, and M. D.
Graham
, “Toward a structural understanding of turbulent drag reduction: Nonlinear coherent states in viscoelastic shear flows
,” Phys. Rev. Lett.
89
, 208301
(2002
).23.
R.
Sureshkumar
, A. N.
Beris
, and R. A.
Handler
, “Direct numerical simulation of the turbulent channel flow of a polymer solution
,” Phys. Fluids
9
, 743
–755
(1997
).24.
C. M.
White
and M. G.
Mungal
, “Mechanics and prediction of turbulent drag reduction with polymer additives
,” Annu. Rev. Fluid Mech.
40
, 235
–256
(2008
).25.
C.-Y.
Lin
and C.-A.
Lin
, “Direct numerical simulations of turbulent channel flow with polymer additives
,” J. Mech.
36
, 691
–698
(2020
).26.
W.
Lo
and C.-A.
Lin
, “Mean and turbulence structures of Couette-Poiseuille flows at different mean shear rates in a square duct
,” Phys. Fluids
18
, 068103
(2006
).27.
H.-W.
Hsu
, J.-B.
Hsu
, W.
Lo
, and C.-A.
Lin
, “Large eddy simulations of turbulent Couette–Poiseuille and Couette flows inside a square duct
,” J. Fluid Mech.
702
, 89
–101
(2012
).28.
C.-C.
Liao
and C.-A.
Lin
, “Influence of prandtl number on the instability of natural convection flows within a square enclosure containing an embedded heated cylinder at moderate Rayleigh number
,” Phys. Fluids
27
, 013603
(2015
).29.
B. E.
Owolabi
and C.-A.
Lin
, “Marginally turbulent Couette flow in a spanwise confined passage of square cross section
,” Phys. Fluids
30
, 075102
(2018
).30.
C.-C.
Liao
, W.-W.
Hsiao
, T.-Y.
Lin
, and C.-A.
Lin
, “Simulations of two sedimenting-interacting spheres with different sizes and initial configurations using immersed boundary method
,” Comput. Mech.
55
, 1191
–1200
(2015
).31.
P. L.
Roe
, “Characteristic-based schemes for the Euler equations
,” Annu. Rev. Fluid Mech.
18
, 337
–365
(1986
).32.
B.
Yu
and Y.
Kawaguchi
, “Direct numerical simulation of viscoelastic drag-reducing flow: A faithful finite difference method
,” J. Non-Newtonian Fluid Mech.
116
, 431
–466
(2004
).33.
A. S.
Pereira
, G.
Mompean
, L.
Thais
, and E. J.
Soares
, “Transient aspects of drag reducing plane Couette flows
,” J. Non-Newtonian Fluid Mech.
241
, 60
–69
(2017
).34.
H.
Abe
, H.
Kawamura
, and Y.
Matsuo
, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence
,” J. Fluids Eng.
123
, 382
–393
(2001
).35.
J.
Jiménez
and P.
Moin
, “The minimal flow unit in near-wall turbulence
,” J. Fluid Mech.
225
, 213
–240
(1991
).36.
B. E.
Owolabi
, R. J.
Poole
, and D. J.
Dennis
, “Experiments on low-Reynolds-number turbulent flow through a square duct
,” J. Fluid Mech.
798
, 398
–410
(2016
).37.
D.
Samanta
, Y.
Dubief
, M.
Holzner
, C.
Schäfer
, A. N.
Morozov
, C.
Wagner
, and B.
Hof
, “Elasto-inertial turbulence
,” Proc. Natl. Acad. Sci. U. S. A.
110
, 10557
–10562
(2013
).38.
V.
Steinberg
, “Elastic turbulence: An experimental view on inertialess random flow
,” Annu. Rev. Fluid Mech.
53
, 27
–58
(2021
).39.
40.
S.
Pirozzoli
, M.
Bernardini
, and P.
Orlandi
, “Turbulence statistics in Couette flow at high Reynolds number
,” J. Fluid Mech.
758
, 327
–343
(2014
).41.
C.
White
, Y.
Dubief
, and J.
Klewicki
, “Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow
,” Phys. Fluids
24
, 021701
(2012
).42.
P.
Escudier
and S.
Smith
, “Fully developed turbulent flow of non–Newtonian liquids through a square duct
,” Proc. R. Soc. London, Ser. A
457
, 911
–936
(2001
).43.
44.
P.
Ptasinski
, B.
Boersma
, F.
Nieuwstadt
, M.
Hulsen
, B.
Van den Brule
, and J.
Hunt
, “Turbulent channel flow near maximum drag reduction: Simulations, experiments and mechanisms
,” J. Fluid Mech.
490
, 251
–291
(2003
).45.
J. L.
Lumley
, “Computational modeling of turbulent flows
,” in Advances in Applied Mechanics
(Elsevier
, 1979
), Vol. 18
, pp. 123
–176
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