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Turbulent channel flow of an elastoviscoplastic fluid

  • Marco E. Rosti (a1), Daulet Izbassarov (a1), Outi Tammisola (a1), Sarah Hormozi (a2) and Luca Brandt (a1)...

Abstract

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier–Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.

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Corresponding author

Email address for correspondence: merosti@mech.kth.se

References

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Balmforth, N. J., Frigaard, I. A. & Ovarlez, G. 2014 Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu. Rev. Fluid Mech. 46, 121146.
Bentrad, H., Esmael, A., Nouar, C., Lefevre, A. & Ait-Messaoudene, N. 2017 Energy growth in Hagen–Poiseuille flow of Herschel–Bulkley fluid. J. Non-Newtonian Fluid Mech. 241, 4359.
Beris, A. N. & Dimitropoulos, C. D. 1999 Pseudospectral simulation of turbulent viscoelastic channel flow. Comput. Meth. Appl. Mech. Engng 180 (3–4), 365392.
Berman, N. S. 1978 Drag reduction by polymers. Annu. Rev. Fluid Mech. 10 (1), 4764.
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 3572.
Cheddadi, I., Saramito, P., Dollet, B., Raufaste, C. & Graner, F. 2011 Understanding and predicting viscous, elastic, plastic flows. Eur. Phys. J. E 34 (1), 1.
Crochet, M. J. & Walters, K. 1983 Numerical methods in non-Newtonian fluid mechanics. Annu. Rev. Fluid Mech. 15 (1), 241260.
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, 1021.
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, 193231.
Dollet, B. & Graner, F. 2007 Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow. J. Fluid Mech. 585, 181211.
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), 311329.
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, 271280.
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), 210.
Escudier, M. P., Poole, R. J., Presti, F., Dales, C., Nouar, C., Desaubry, C., Graham, L. & Pullum, L. 2005 Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids. J. Non-Newtonian Fluid Mech. 127 (2–3), 143155.
Escudier, M. P. & Presti, F. 1996 Pipe flow of a thixotropic liquid. J. Non-Newtonian Fluid Mech. 62 (2–3), 291306.
Escudier, M. P., Presti, F. & Smith, S. 1999 Drag reduction in the turbulent pipe flow of polymers. J. Non-Newtonian Fluid Mech. 81 (3), 197213.
Escudier, P. & Smith, S. 2001 Fully developed turbulent flow of non-Newtonian liquids through a square duct. Proc. R. Soc. Lond. A 457, 911936.
Founargiotakis, K., Kelessidis, V. C. & Maglione, R. 2008 Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus. Can. J. Chem. Engng 86 (4), 676683.
Fraggedakis, D., Dimakopoulos, Y. & Tsamopoulos, J. 2016 Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids. Soft Matt. 12 (24), 53785401.
Frigaard, I. A., Howison, S. D. & Sobey, I. J. 1994 On the stability of Poiseuille flow of a Bingham fluid. J. Fluid Mech. 263, 133150.
García-Mayoral, R. & Jiménez, J. 2011 Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317347.
Gordon, R. J. & Schowalter, W. R. 1972 Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions. Trans. Soc. Rheol. 16 (1), 7997.
Guang, R., Rudman, M., Chryss, A., Slatter, P. & Bhattacharya, S. 2011 A DNS investigation of the effect of yield stress for turbulent non-Newtonian suspension flow in open channels. Particul. Sci. Technol. 29 (3), 209228.
Guzel, B., Frigaard, I. & Martinez, D. M. 2009 Predicting laminar–turbulent transition in Poiseuille pipe flow for non-Newtonian fluids. Chem. Engng Sci. 64 (2), 254264.
Hanks, R. W. 1963 The laminar-turbulent transition for flow in pipes, concentric annuli, and parallel plates. AIChE J. 9 (1), 4548.
Hanks, R. W. 1967 On the flow of Bingham plastic slurries in pipes and between parallel plates. Soc. Petrol. Engng J. 7 (04), 342346.
Hanks, R. W. & Dadia, B. H. 1971 Theoretical analysis of the turbulent flow of non-Newtonian slurries in pipes. AIChE J. 17 (3), 554557.
Hormozi, S. & Frigaard, I. A. 2012 Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow. J. Non-Newtonian Fluid Mech. 169, 6173.
Izbassarov, D., Rosti, M. E., Niazi, A. M., Sarabian, M., Hormozi, S., Brandt, L. & Tammisola, O. 2018 Computational modeling of multiphase viscoelastic and elastoviscoplastic flows. Intl J. Numer. Meth. Fluids (accepted, https://doi.org/10.1002/fld.4678).
Kanaris, N., Kassinos, S. C. & Alexandrou, A. N. 2015 On the transition to turbulence of a viscoplastic fluid past a confined cylinder: a numerical study. Intl J. Heat Fluid Flow 55, 6575.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308323.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Logan, S. E. 1972 Laser velocimeter measurement of Reynolds stress and turbulence in dilute polymer solutions. AIAA J. 10 (7), 962964.
Maleki, A. & Hormozi, S. 2018 Submerged jet shearing of visco-plastic sludge. J. Non-Newtonian Fluid Mech. 252, 1927
Martinie, L., Buggisch, H. & Willenbacher, N. 2013 Apparent elongational yield stress of soft matter. J. Rheol. 57 (2), 627646.
Metivier, C., Nouar, C. & Brancher, J. P. 2005 Linear stability involving the Bingham model when the yield stress approaches zero. Phys. Fluids 17 (10), 104106.
Metivier, C., Nouar, C. & Brancher, J. P. 2010 Weakly nonlinear dynamics of thermoconvective instability involving viscoplastic fluids. J. Fluid Mech. 660, 316353.
Metzner, A. B. & Reed, J. C. 1955 Flow of non-Newtonian fluids – correlation of the laminar, transition, and turbulent-flow regions. AIChE J. 1 (4), 434440.
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), 2747.
Moyers-Gonzalez, M. A., Frigaard, I. A. & Nouar, C. 2004 Nonlinear stability of a visco-plastically lubricated viscous shear flow. J. Fluid Mech. 506, 117146.
Nouar, C. & Bottaro, A. 2010 Stability of the flow of a Bingham fluid in a channel: eigenvalue sensitivity, minimal defects and scaling laws of transition. J. Fluid Mech. 642, 349372.
Nouar, C. & Frigaard, I. A. 2001 Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria. J. Non-Newtonian Fluid Mech. 100 (1–3), 127149.
Nouar, C., Kabouya, N., Dusek, J. & Mamou, M. 2007 Modal and non-modal linear stability of the plane Bingham–Poiseuille flow. J. Fluid Mech. 577, 211239.
Orlandi, P. & Leonardi, S. 2008 Direct numerical simulation of three-dimensional turbulent rough channels: parameterization and flow physics. J. Fluid Mech. 606, 399415.
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.
Picano, F., Breugem, W. P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463487.
Pinho, F. T. & Whitelaw, J. H. 1990 Flow of non-Newtonian fluids in a pipe. J. Non-Newtonian Fluid Mech. 34 (2), 129144.
Poole, R. J. 2012 The Deborah and Weissenberg numbers. Rheol. Bull. 53, 3239.
Pope, S. B. 2001 Turbulent Flows. Cambridge University Press.
Putz, A. M. V., Burghelea, T. I., Frigaard, I. A. & Martinez, D. M. 2008 Settling of an isolated spherical particle in a yield stress shear thinning fluid. Phys. Fluids 20 (3), 033102.
Rosti, M. E. & Brandt, L. 2017 Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall. J. Fluid Mech. 830, 708735.
Rosti, M. E. & Brandt, L. 2018 Suspensions of deformable particles in a Couette flow. J. Non-Newtonian Fluid Mech. (accepted, https://doi.org/10.1016/j.jnnfm.2018.01.008).
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).
Rosti, M. E., Brandt, L. & Pinelli, A. 2018b Turbulent channel flow over an anisotropic porous wall – drag increase and reduction. J. Fluid Mech. 842, 381394.
Rosti, M. E., Cortelezzi, L. & Quadrio, M. 2015 Direct numerical simulation of turbulent channel flow over porous walls. J. Fluid Mech. 784, 396442.
Rudman, M. & Blackburn, H. M. 2006 Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method. Appl. Math. Model. 30 (11), 12291248.
Rudman, M., Blackburn, H. M., Graham, L. J. W. & Pullum, L. 2004 Turbulent pipe flow of shear-thinning fluids. J. Non-Newtonian Fluid Mech. 118 (1), 3348.
Ryan, N. W. & Johnson, M. M. 1959 Transistion from laminar to turbulent flow in pipes. AIChE J. 5 (4), 433435.
Saramito, P. 2007 A new constitutive equation for elastoviscoplastic fluid flows. J. Non-Newtonian Fluid Mech. 145 (1), 114.
Saramito, P. 2009 A new elastoviscoplastic model based on the Herschel–Bulkley viscoplastic model. J. Non-Newtonian Fluid Mech. 158 (1), 154161.
Saramito, P. 2016 Complex Fluids. Springer.
Saramito, P. & Wachs, A. 2016 Progress in numerical simulation of yield stress fluid flows. Rheol. Acta 79, 120.
Shahmardi, A., Zade, S., Ardekani, M. N., Poole, R. J., Lundell, F., Rosti, M. E. & Brandt, L. 2018 Turbulent duct flow with polymers. J. Fluid Mech. (under review).
Shaukat, A., Kaushal, M., Sharma, A. & Joshi, Y. M. 2012 Shear mediated elongational flow and yielding in soft glassy materials. Soft Matt. 8 (39), 1010710114.
Shu, C. W. 2009 High order weighted essentially nonoscillatory schemes for convection dominated problems. SIAM Rev. 51 (1), 82126.
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), 596627.
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), 461472.
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235256.
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.
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