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Turbulent duct flow with polymers

Published online by Cambridge University Press:  28 November 2018

Armin Shahmardi ,
Sagar Zade ,
Mehdi N. Ardekani Open the ORCID record for Mehdi N. Ardekani [Opens in a new window] ,
Rob J. Poole Open the ORCID record for Rob J. Poole [Opens in a new window] ,
Fredrik Lundell ,
Marco E. Rosti Open the ORCID record for Marco E. Rosti [Opens in a new window]  and
Luca Brandt Open the ORCID record for Luca Brandt [Opens in a new window]
Armin Shahmardi
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
Sagar Zade
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
Mehdi N. Ardekani
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
Rob J. Poole
Affiliation:
Department of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, UK
Fredrik Lundell
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
Marco E. Rosti*
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
Luca Brandt
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl’s secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Polymers Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 1057 - 1083
Copyright
© 2018 Cambridge University Press 

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References

Alves, M. A., Pinho, F. T. & Oliveira, P. J. 2000 Effect of a high-resolution differencing scheme on finite-volume predictions of viscoelastic flows. J. Non-Newtonian Fluid Mech. 93 (2), 287–314.Google Scholar
Biancofiore, L., Brandt, L. & Zaki, T. A. 2017 Streak instability in viscoelastic Couette flow. Phys. Rev. Fluids 2 (4), 043304.Google Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.Google Scholar
Brundrett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19 (3), 375–394.Google Scholar
Cho, Y. I. & Harnett, J. P. 1982 Non-Newtonian fluids in circular pipe flow. Adv. Heat Transfer 15, 59–141.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.Google Scholar
De Angelis, E., Casciola, C. M. & Piva, R. 2002 DNS of wall turbulence: dilute polymers and self-sustaining mechanisms. Comput. Fluids 31 (4), 495–507.Google Scholar
De Vita, F., Rosti, M. E., Izbassarov, D., Duffo, L., Tammisola, O., Hormozi, S. & Brandt, L. 2018 Elastoviscoplastic flow in porous media. J. Non-Newtonian Fluid Mech. 258, 10–21.Google Scholar
Dealy, J. M. 2010 Weissenberg and Deborah numbers – their definition and use. Rheol. Bull. 79 (2), 14–18.Google Scholar
Den Toonder, J. M. J., Hulsen, M. A., Kuiken, G. D. C. & Nieuwstadt, F. T. M. 1997 Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments. J. Fluid Mech. 337, 193–231.Google Scholar
Dimitropoulos, C. D., Sureshkumar, R., Beris, A. N. & Handler, R. A. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13 (4), 1016–1027.Google Scholar
Dubief, Y., Terrapon, V. E., White, C. M., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 New answers on the interaction between polymers and vortices in turbulent flows. Flow Turbul. Combust. 74 (4), 311–329.Google Scholar
Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271–280.Google Scholar
Dupret, F. & Marchal, J. M. 1986 Loss of evolution in the flow of viscoelastic fluids. J. Non-Newtonian Fluid Mech. 20, 143–171.Google Scholar
Escudier, M. P., Nickson, A. K. & Poole, R. J. 2009 Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: quantification of turbulence anisotropy. J. Non-Newtonian Fluid Mech. 160 (1), 2–10.Google Scholar
Escudier, M. P., Presti, F. & Smith, S. 1999 Drag reduction in the turbulent pipe flow of polymers. J. Non-Newtonian Fluid Mech. 81 (3), 197–213.Google Scholar
Escudier, P. & Smith, S. 2001 Fully developed turbulent flow of non-Newtonian liquids through a square duct. Proc. R. Soc. Lond. A 457, 911–936.Google Scholar
Gampert, B., Braemer, T., Eich, T. & Dietmann, T. 2005 Rheo-optical investigations and near-wall turbulence structure of polymer solutions in turbulent channel flow. J. Non-Newtonian Fluid Mech. 126 (2), 115–121.Google Scholar
Gampert, B. & Rensch, A. 1996 Polymer concentration and near wall turbulence structure of channel flow of polymer solutions. In Proceedings of ASME Fluids Engineering Division Summer Meeting, vol. 237, pp. 129–136. ASME.Google Scholar
Gampert, B. & Yong, C. K. 1990 The influence of polymer additives on the coherent structure of turbulent channel flow. In Structure of Turbulence and Drag Reduction, pp. 223–232. Springer.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011 Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317–347.Google Scholar
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101–129.Google Scholar
Gessner, F. B. 1973 The origin of secondary flow in turbulent flow along a corner. J. Fluid Mech. 58 (1), 1–25.Google Scholar
Izbassarov, D., Rosti, M. E., Niazi Ardekani, M., Sarabian, M., Hormozi, S., Brandt, L. & Tammisola, O. 2018 Computational modeling of multiphase viscoelastic and elastoviscoplastic flows. Intl J. Numer. Meth. Fluids; (in press, https://doi.org/10.1002/fld.4678).Google Scholar
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202–228.Google Scholar
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308–323.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Li, C. F., Sureshkumar, R. & Khomami, B. 2006 Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech. 140 (1), 23–40.Google Scholar
Logan, S. E. 1972 Laser velocimeter measurement of Reynolds stress and turbulence in dilute polymer solutions. AIAA J. 10 (7), 962–964.Google Scholar
Lvov, V. S., Pomyalov, A., Procaccia, I. & Tiberkevich, V. 2004 Drag reduction by polymers in wall bounded turbulence. Phys. Rev. Lett. 92 (24), 244503.Google Scholar
Madabhushi, R. K. & Vanka, S. P. 1991 Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A 3 (11), 2734–2745.Google Scholar
Melling, A. & Whitelaw, J. H. 1976 Turbulent flow in a rectangular duct. J. Fluid Mech. 78 (2), 289–315.Google Scholar
Min, T., Choi, H. & Yoo, J. Y. 2003a Maximum drag reduction in a turbulent channel flow by polymer additives. J. Fluid Mech. 492, 91–100.Google Scholar
Min, T., Yoo, J. Y. & Choi, H. 2001 Effect of spatial discretization schemes on numerical solutions of viscoelastic fluid flows. J. Non-Newtonian Fluid Mech. 100 (1), 27–47.Google Scholar
Min, T., Yoo, J. Y., Choi, H. & Joseph, D. D. 2003b Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213–238.Google Scholar
Mompean, G. & Deville, M. 1997 Unsteady finite volume simulation of Oldroyd-B fluid through a three-dimensional planar contraction. J. Non-Newtonian Fluid Mech. 72 (2–3), 253–279.Google Scholar
Nikuradse, J.1926 Untersuchung über die geschwindigkeitsverteilung in turbulenten strömungen. PhD thesis, Gottingen.Google Scholar
Orlandi, P. & Leonardi, S. 2008 Direct numerical simulation of three-dimensional turbulent rough channels: parameterization and flow physics. J. Fluid Mech. 606, 399–415.Google Scholar
Owolabi, B. E., Dennis, D. J. C. & Poole, R. J. 2017 Turbulent drag reduction by polymer additives in parallel-shear flows. J. Fluid Mech. 827, R4.Google Scholar
Owolabi, B. E., Poole, R. J. & Dennis, D. J. C. 2016 Experiments on low-Reynolds-number turbulent flow through a square duct. J. Fluid Mech. 798, 398–410.Google Scholar
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107–122.Google Scholar
Poole, R. J. 2012 The Deborah and Weissenberg numbers. Rheol. Bull. 53, 32–39.Google Scholar
Prandtl, L.1926 Uber die ausgebildete turbulenz. Verh. 2nd Intl Kong. für Tech. Mech., Zurich. English translation: NACA Tech. Memo 62, p. 435.Google Scholar
Ptasinski, P. K., Boersma, B. J., Nieuwstadt, F. T. M., Hulsen, M. A., Van den Brule, B. H. A. A. & Hunt, J. C. R. 2003 Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms. J. Fluid Mech. 490, 251–291.Google Scholar
Resende, P. R., Escudier, M. P., Presti, F., Pinho, F. T. & Cruz, D. O. A. 2006 Numerical predictions and measurements of Reynolds normal stresses in turbulent pipe flow of polymers. Intl J. Heat Fluid Flow 27 (2), 204–219.Google Scholar
Rosti, M. E. & Brandt, L. 2017 Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall. J. Fluid Mech. 830, 708–735.Google Scholar
Rosti, M. E. & Brandt, L. 2018 Suspensions of deformable particles in a Couette flow. J. Non-Newtonian Fluid Mech. 262 (C), 3–11.Google Scholar
Rosti, M. E., Brandt, L. & Mitra, D. 2018a Rheology of suspensions of viscoelastic spheres: deformability as an effective volume fraction. Phys. Rev. Fluids 3 (1), 012301(R).Google Scholar
Rosti, M. E., Brandt, L. & Pinelli, A. 2018b Turbulent channel flow over an anisotropic porous wall – drag increase and reduction. J. Fluid Mech. 842, 381–394.Google Scholar
Rosti, M. E., Cortelezzi, L. & Quadrio, M. 2015 Direct numerical simulation of turbulent channel flow over porous walls. J. Fluid Mech. 784, 396–442.Google Scholar
Rosti, M. E., Izbassarov, D., Tammisola, O., Hormozi, S. & Brandt, L. 2018c Turbulent channel flow of an elastoviscoplastic fluid. J. Fluid Mech. 853, 488–514.Google Scholar
Rudd, M. J. 1972 Velocity measurements made with a laser dopplermeter on the turbulent pipe flow of a dilute polymer solution. J. Fluid Mech. 51 (4), 673–685.Google Scholar
Samanta, A., Vinuesa, R., Lashgari, I., Schlatter, P. & Brandt, L. 2015 Enhanced secondary motion of the turbulent flow through a porous square duct. J. Fluid Mech. 784, 681–693.Google Scholar
Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S. & Matsumoto, Y. 2011 A full Eulerian finite difference approach for solving fluid–structure coupling problems. J. Comput. Phys. 230 (3), 596–627.Google Scholar
Sureshkumar, R. & Beris, A. N. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60 (1), 53–80.Google Scholar
Uhlmann, M., Pinelli, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153–162.Google Scholar
Vinuesa, R., Schlatter, P. & Nagib, H. M. 2015 On minimum aspect ratio for duct flow facilities and the role of side walls in generating secondary flows. J. Turbul. 16 (6), 588–606.Google Scholar
Virk, P. S. 1971 Drag reduction in rough pipes. J. Fluid Mech. 45 (2), 225–246.Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21 (4), 625–656.Google Scholar
Virk, P. S., Merrill, E. W., Mickley, H. S., Smith, K. A. & Mollo-Christensen, E. L. 1967 The Toms phenomenon: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 30 (2), 305–328.Google Scholar
Virk, P. S., Mickley, H. S. & Smith, K. A. 1970 The ultimate asymptote and mean flow structure in Toms’ phenomenon. Trans. ASME J. Appl. Mech. 37 (2), 488–493.Google Scholar
Warholic, M. D., Massah, H. & Hanratty, T. J. 1999 Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing. Exp. Fluids 27 (5), 461–472.Google Scholar
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag-reduced boundary layer flow. Exp. Fluids 36 (1), 62–69.Google Scholar
Xi, L. & Graham, M. D. 2010 Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids. Phys. Rev. Lett. 104 (21), 218301.Google Scholar
Xi, L. & Graham, M. D. 2012a Dynamics on the laminar–turbulent boundary and the origin of the maximum drag reduction asymptote. Phys. Rev. Lett. 108 (2), 028301.Google Scholar
Xi, L. & Graham, M. D. 2012b Intermittent dynamics of turbulence hibernation in Newtonian and viscoelastic minimal channel flows. J. Fluid Mech. 693, 433–472.Google Scholar