Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T21:22:14.180Z Has data issue: false hasContentIssue false
  • English
  • Français

Coherent structures in the turbulent channel flow of an elastoviscoplastic fluid

Published online by Cambridge University Press:  06 February 2020

S. Le Clainche Open the ORCID record for S. Le Clainche [Opens in a new window] ,
D. Izbassarov ,
M. Rosti Open the ORCID record for M. Rosti [Opens in a new window] ,
L. Brandt Open the ORCID record for L. Brandt [Opens in a new window]  and
O. Tammisola Open the ORCID record for O. Tammisola [Opens in a new window]
S. Le Clainche*
Affiliation:
School of Aerospace Engineering, Universidad Politécnica de Madrid, E-28040 Madrid, Spain
D. Izbassarov
Affiliation:
Linné Flow Centre and SeRC, KTH Mechanics, S-100 44 Stockholm, Sweden
M. Rosti
Affiliation:
Linné Flow Centre and SeRC, KTH Mechanics, S-100 44 Stockholm, Sweden
L. Brandt
Affiliation:
Linné Flow Centre and SeRC, KTH Mechanics, S-100 44 Stockholm, Sweden
O. Tammisola
Affiliation:
Linné Flow Centre and SeRC, KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this numerical and theoretical work, we study the turbulent channel flow of Newtonian and elastoviscoplastic fluids. The coherent structures in these flows are identified by means of higher order dynamic mode decomposition (HODMD), applied to a set of data non-equidistant in time, to reveal the role of the near-wall streaks and their breakdown, and the interplay between turbulent dynamics and non-Newtonian effects. HODMD identifies six different high-amplitude modes, which either describe the yielded flow or the yielded–unyielded flow interaction. The structure of the low- and high-frequency modes suggests that the interaction between high- and low-speed streamwise velocity structures is one of the mechanisms triggering the streak breakdown, dominant in Newtonian turbulence where we observe shorter near-wall streaks and a more chaotic dynamics. As the influence of elasticity and plasticity increases, the flow becomes more correlated in the streamwise direction, with long streaks disrupted for short times by localised perturbations, reflected in reduced drag. Finally, we present streamwise-periodic dynamic mode decomposition modes as a viable tool to describe the highly complex turbulent flows, and identify simple well-organised groups of travelling waves.

JFM classification

Instability: Nonlinear instability Non-Newtonian Flows: Viscoelasticity Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A5
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Balmforth, I., Frigaard, I. A. & Ovarlez, G. 2014 Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu. Rev. Fluid Mech. 46, 121–146.CrossRefGoogle Scholar
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, 43–59.CrossRefGoogle Scholar
Biancofiore, L., Brandt, L. & Zaki, T. A. 2017 Streak instability in viscoelastic Couette flow. Phys. Rev. Fluids 2 (4), 043304.CrossRefGoogle Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 80–96.CrossRefGoogle Scholar
Brandt, L. & de Lange, H. C. 2008 Streak interactions and breakdown in boundary layer flows. Phys. Fluids 20, 024107.CrossRefGoogle Scholar
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.Google ScholarPubMed
Chen, K. K., Tu, J. H. & Rowley, C. W. 2012 Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses. J. Nonlinear Sci. 22, 887–915.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E. & Casciola, C. M. 2013 Paths of energy in turbulent channel flows. J. Fluid Mech. 715, 436–451.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E., Jimenez, J. & Casciola, C. M. 2016 Cascades and wall-normal fluxes in turbulent channel flows. J. Fluid Mech. 796, 417–436.CrossRefGoogle Scholar
Cossu, C., Brandt, L., Bagheri, S. & Henningson, D. 2011 Secondary threshold amplitudes for sinuous streak breakdown. Phys. Fluids 23, 074103.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Esmael, A., Nouar, C., Lefévre, A. & Kabouya, N. 2010 Transitional flow of a non-Newtonian fluid in a pipe: experimental evidence of weak turbulence induced by shear-thinning behavior. Phys. Fluids 22, 101701.CrossRefGoogle Scholar
Firouznia, M., Metzger, B., Ovarlez, G. & Hormozi, S. 2018 The interaction of two spherical particles in simple-shear flows of yield stress fluids. J. Non-Newtonian Fluid Mech. 255, 19–38.CrossRefGoogle Scholar
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), 5378–5401.CrossRefGoogle ScholarPubMed
Gómez, F., Clainche, S. L., Paredes, P., Hermanns, M. & Theofilis, V. 2012 Four decades of studying global linear instability. AIAA J. 50 (12), 2731–2743.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Holenberg, Y., Lavrenteva, O. M., Shavit, U. & Nir, A. 2012 Particle tracking velocimetry and particle image velocimetry study of the slow motion of rough and smooth solid spheres in a yield-stress fluid. Phys. Rev. E 86 (6), 066301.CrossRefGoogle Scholar
Höpffner, J., Brandt, L. & Henningson, D. S. 2005 Transient growth on boundary layer streaks. J. Fluid Mech. 537, 91–100.CrossRefGoogle Scholar
Hormozi, S. & Frigaard, I. A. 2012 Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow. J. Non-Newtonian Fluid Mech. 169, 61–73.CrossRefGoogle Scholar
Izbassarov, D., Rosti, M. E., Ardekani, M. N., Hormozi, M. S. S., Brandt, L. & Tammisola, O. 2018 Computational modeling of multiphase viscoelastic and elastoviscoplastic flows. Intl J. Numer. Meth. Fluids 88, 521–543.CrossRefGoogle Scholar
Jiménez, J. & Pineli, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Johansson, A. V. & Alfredsson, H. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579–599.CrossRefGoogle Scholar
Kawahara, G., Jiménez, J., Uhlmann, M. & Pinelli, A.1998 The instability of streaks in near-wall turbulence. CTR Annu. Res. Briefs 1998, pp. 115–170. Center for Turbulence Research.Google Scholar
Landahl, T. 1980 A note on an algebraic instability of inviscid parallel shear flow. J. Fluid Mech. 98, 243.CrossRefGoogle Scholar
Le Clainche, S., Lorente, L. & Vega, J. M. 2018a Wind predictions upstream wind turbines from a lidar database. Energies 11 (3), 543.CrossRefGoogle Scholar
Le Clainche, S., Moreno-Ramos, R., Taylor, P. & Vega, J. M. 2018b A new robust method to study flight flutter testing. J. Aircraft 56 (1), 336–343.CrossRefGoogle Scholar
Le Clainche, S., Pérez, J. M. & Vega, J. M. 2018c Spatio-temporal flow structures in the three-dimensional wake of a circular cylinder. Fluid Dyn. Res. 50 (5), 051406.CrossRefGoogle Scholar
Le Clainche, S., Sastre, F., Velazquez, A. & Vega, J. M. 2017a Higher order dynamic mode decomposition applied to study flow structures in noisy PIV experimental data. In Proceedings of 47th AIAA Fluid Dynamics Conference, 5–9 June, Denver, CO, USA; AIAA 2017-3304.Google Scholar
Le Clainche, S. & Vega, J. M. 2017a Higher order dynamic mode decomposition. SIAM J. Appl. Dyn. Sys. 16 (2), 882–925.CrossRefGoogle Scholar
Le Clainche, S. & Vega, J. M. 2017b Higher order dynamic mode decomposition to identify and extrapolate flow patterns. Phys. Fluids 29 (8), 084102.CrossRefGoogle Scholar
Le Clainche, S. & Vega, J. M. 2018 Spatio-temporal Koopman decomposition. J. Nonlinear Sci. 28 (3), 1–50.CrossRefGoogle Scholar
Le Clainche, S., Vega, J. M. & Soria, J. 2017b Higher order dynamic mode decomposition of noisy experimental data: the flow structure of a zero-net-mass-flux jet. Exp. Therm. Fluid Sci. 88, 336–353.CrossRefGoogle Scholar
Metivier, C., Nouar, C. & Brancher, J. P. 2005 Linear stability involving the Bingham model when the yield stress approaches zero. Phys. Fluids 17, 104106.CrossRefGoogle Scholar
Moffatt, H. K. 1967 The autonomous cycle of near wall turbulence. In Proceedings of the URSI-IUGG Colloquium on Atoms (ed. Yaglom, A. & Tatarsky, V. I.), pp. 139–154. Nauka.Google Scholar
Moyers-Gonzalez, M. A., Frigaard, I. A. & Nouar, C. 2004 Nonlinear stability of a visco-plastically lubricated viscous shear flow. J. Fluid Mech. 506, 117–146.CrossRefGoogle Scholar
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, 349–372.CrossRefGoogle Scholar
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, 127–149.CrossRefGoogle Scholar
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, 211–239.CrossRefGoogle 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.CrossRefGoogle Scholar
Peterlin, A. 1966 Hydrodynamics of macromolecules in a velocity field with longitudinal gradient. J. Polymer Sci. 4 (4), 287–291.CrossRefGoogle Scholar
Reddy, S. C., Schmid, P. J., Baggett, J. S. & Henningson, D. S. 1998 On the stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365, 269–303.CrossRefGoogle Scholar
Rosti, M. E., Izbassarov, D., Tammisola, O., Hormozi, S. & Brandt, L. 2018a Turbulent channel flow of an elastoviscoplastic fluid. J. Fluid Mech. 853, 488–514.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Saramito, P. 2007 A new constitutive equation for elastoviscoplastic fluid flows. J. Non-Newtonian Fluid Mech. 145 (1), 1–14.CrossRefGoogle Scholar
Schmid, P. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Schmid, P. J. 2011 Application of the dynamic mode decomposition to experimental data. Exp. Fluids 50 (4), 1123–1130.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. 2011 Stability and Transition in Shear Flows. Springer.Google Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Shahmardi, A., Zade, S., Ardekani, M. N., Poole, R. J., Lundell, F., Rosti, M. E. & Brandt, L. 2019 Turbulent duct flow with polymers. J. Fluid Mech. 859, 1057–1083.CrossRefGoogle Scholar
Tucker, L. R. 1966 Some mathematical notes on three-mode factor analysis. Psikometrica 31, 279–311.CrossRefGoogle ScholarPubMed
Virk, P. S. 1971 Drag reduction in rough pipes. J. Fluid Mech. 45 (2), 225–246.CrossRefGoogle Scholar
Waleffe, F. 1995 Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process. Stud. Appl. Maths 95, 319–343.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle 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.CrossRefGoogle Scholar
Zade, S., Shamu, T. J., Lundell, F. & Brandt, L.2019 Finite-size spherical particles in a square duct flow of an elastoviscoplastic fluid: an experimental study. arXiv:1905.07260.CrossRefGoogle Scholar
Zhang, M., Lashgari, I., Zaki, T. & Brandt, L. 2013 Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids. J. Fluid Mech. 737, 249–270.CrossRefGoogle Scholar