Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T05:38:24.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Repicturing viscoelastic drag-reducing turbulence by introducing dynamics of elasto-inertial turbulence

Published online by Cambridge University Press:  11 April 2022

Wen-Hua Zhang ,
Hong-Na Zhang Open the ORCID record for Hong-Na Zhang [Opens in a new window] ,
Zi-Mu Wang ,
Yu-Ke Li Open the ORCID record for Yu-Ke Li [Opens in a new window] ,
Bo Yu Open the ORCID record for Bo Yu [Opens in a new window]  and
Feng-Chen Li
Wen-Hua Zhang
Affiliation:
Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, MOE, School of Mechanical Engineering, Tianjin University, Tianjin 300350, PR China
Hong-Na Zhang*
Affiliation:
Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, MOE, School of Mechanical Engineering, Tianjin University, Tianjin 300350, PR China
Zi-Mu Wang
Affiliation:
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, PR China
Yu-Ke Li
Affiliation:
Department of Physics of Complex System, Weizmann Institute of Science, Rehovot 7610001, Israel
Bo Yu
Affiliation:
School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, PR China
Feng-Chen Li*
Affiliation:
Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, MOE, School of Mechanical Engineering, Tianjin University, Tianjin 300350, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently, the nature of viscoelastic drag-reducing turbulence (DRT), especially the maximum drag reduction (MDR) state, has become a focus of controversy. It has long been regarded as polymer-modulated inertial turbulence (IT), but is challenged by the newly proposed concept of elasto-inertial turbulence (EIT). This study is to repicture DRT in parallel plane channels by introducing dynamics of EIT through statistical, structural and budget analysis for a series of flow regimes from the onset of drag reduction to EIT. Some underlying mechanistic links between DRT and EIT are revealed. Energy conversion between velocity fluctuations and polymers as well as pressure redistribution effects are of particular concern, based on which a new energy self-sustaining process (SSP) of DRT is repictured. The numerical results indicate that at low Reynolds number ($Re$), weak IT flow is replaced by a laminar regime before the barrier of EIT dynamics is established with the increase of elasticity, whereas, at moderate $Re$, EIT-related SSP can get involved and survive from being relaminarized. This further explains the reason why relaminarization phenomenon is observed for low $Re$ while the flow directly enters MDR and EIT at moderate $Re$. Moreover, with the proposed energy picture, the newly discovered phenomenon that streamwise velocity fluctuations lag behind those in the wall-normal direction can be well explained. The repictured SSP certainly justifies the conjecture that IT nature is gradually replaced by that of EIT in DRT with the increase of elasticity.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Polymers Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A31
Check for updates
Copyright
© The Author(s), 2022. 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

REFERENCES

Chaudhary, I., Garg, P., Shankar, V. & Subramanian, G. 2019 Elasto-inertial wall mode instabilities in viscoelastic plane Poiseuille flow. J. Fluid Mech. 881, 119–163.CrossRefGoogle Scholar
Chaudhary, I., Garg, P., Subramanian, G. & Shankar, V. 2021 Linear instability of viscoelastic pipe flow. J. Fluid Mech. 908, A11.CrossRefGoogle Scholar
Choueiri, G.H., Lopez, J.M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501.CrossRefGoogle ScholarPubMed
Choueiri, G.H., Lopez, J.M., Varshney, A., Sankar, S. & Hof, B. 2021 Experimental observation of the origin and structure of elasto-inertial turbulence. Proc. Natl Acad. Sci. 118 (45), e2102350118.CrossRefGoogle Scholar
Dubief, Y., Terrapon, V.E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25 (11), 110817.CrossRefGoogle ScholarPubMed
Garg, P., Chaudhary, I., Khalid, M., Shankar, V. & Subramanian, G. 2018 Viscoelastic pipe flow is linearly unstable. Phys. Rev. Lett. 121, 024502.CrossRefGoogle ScholarPubMed
de Gennes, P.G. 1990 Introduction to Polymer Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Gillissen, J.J.J. 2019 Two-dimensional decaying elasto-inertial turbulence. Phys. Rev. Lett. 123, 144502.CrossRefGoogle Scholar
Graham, M.D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26 (10), 101301.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 53–55.CrossRefGoogle Scholar
Jha, N.K. & Steinberg, V. 2021 Elastically driven Kelvin-Helmholtz-like instability in straight channel flow. Proc. Natl Acad. Sci. 118 (34), e2105211118.CrossRefGoogle ScholarPubMed
Khalid, M., Chaudhary, I., Garg, P., Shankar, V. & Subramanian, G. 2021 The centre-mode instability of viscoelastic plane Poiseuille flow. J. Fluid Mech. 915, A43.CrossRefGoogle Scholar
Leighton, R., Walker, D.T., Stephens, T. & Garwood, G. 2003 Reynolds stress modeling for drag reducing viscoelastic flows. In Paper Presented at the ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference.CrossRefGoogle Scholar
Li, W. & Graham, M. 2007 Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow. Phys. Fluids 19, 083101.CrossRefGoogle Scholar
Li, W., Xi, L. & Graham, M. 2006 Nonlinear travelling waves as a framework for understanding turbulent drag reduction. J. Fluid Mech. 565, 353–362.CrossRefGoogle Scholar
Lumeley, J.L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367–384.CrossRefGoogle Scholar
Masoudian, M., Kim, K., Pinho, F. & Sureshkumar, R. 2013 A viscoelastic $k-\varepsilon -\overline {v^2}-f$ turbulent flow model valid up to the maximum drag reduction limit. J. Non-Newtonian Fluid Mech. 202, 99–111.CrossRefGoogle Scholar
Masoudian, M., Kim, K., Pinho, F.T. & Sureshkumar, R. 2015 A Reynolds stress model for turbulent flow of homogeneous polymer solutions. Intl J. Heat Fluid Flow 54 (August), 220–235.CrossRefGoogle Scholar
Min, T., Choi, H. & Yoo, J.Y. 2003 Maximum drag reduction in a turbulent channel flow by polymer additives. J. Fluid Mech. 492, 91–100.CrossRefGoogle Scholar
Page, J., Dubief, Y. & Kerswell, R.R. 2020 Exact travelling wave solutions in viscoelastic channel flow. Phys. Rev. Lett. 125, 154501.CrossRefGoogle Scholar
Pinho, F. 2003 A GNF framework for turbulent flow models of drag reducing fluids and proposal for a $k-\varepsilon$ type closure. J. Non-Newtonian Fluid Mech. 114 (2-3), 149–184.CrossRefGoogle Scholar
Pinho, F.T., Li, C.F., Younis, B.A. & Sureshkumar, R. 2008 A low Reynolds number turbulence closure for viscoelastic fluids. J. Non-Newtonian Fluid Mech. 154 (2), 89–108.CrossRefGoogle Scholar
Ptasinski, P.K., Boersma, B.J., Nieuwstadt, F.T.M., Hulsen, M.A.B., Van Den Brule, 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.CrossRefGoogle Scholar
Resende, P., Kim, K., Younis, B., Sureshkumar, R. & Pinho, F. 2011 A FENE-P $k-\varepsilon$ turbulence model for low and intermediate regimes of polymerInduced drag reduction. J. Non-Newtonian Fluid Mech. 166, 639–660.CrossRefGoogle Scholar
Resende, P.R., Pinho, F.T. & Cruz, D.O. 2013 A Reynolds stress model for turbulent flows of viscoelastic fluids. J. Turbul. 14 (12), 1–36.CrossRefGoogle Scholar
Samanta, D., Dubief, Y., Holzner, M., Schafer, C., Morozov, A.N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110, 10557–10562.CrossRefGoogle ScholarPubMed
Shekar, A., Mcmullen, R., Mckeon, B. & Graham, M. 2020 Self-sustained elastoinertial Tollmien–Schlichting waves. J. Fluid Mech. 897, A3.CrossRefGoogle Scholar
Shekar, A., Mcmullen, R.M., Mckeon, B.J. & Graham, M.D. 2021 Tollmien–Schlichting route to elastoinertial turbulence in channel flow. Phys. Rev. Fluids 6 (9), 093301.CrossRefGoogle Scholar
Shekar, A., Mcmullen, R.M., Wang, S.N., Mckeon, B.J. & Graham, M.D. 2019 Critical-layer structures and mechanisms in elastoinertial turbulence. Phys. Rev. Lett. 122, 124503.CrossRefGoogle ScholarPubMed
Sid, S., Terrapon, V.E. & Dubief, Y. 2018 Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction. Phys. Rev. Fluids 3, 011301(R).CrossRefGoogle Scholar
Terrapon, V.E., Dubief, Y. & Soria, J. 2015 On the role of pressure in elasto-inertial turbulence. J. Turbul. 16 (1), 26–43.CrossRefGoogle Scholar
Toms, B.A. 1949 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. 1st International Congress on Rheology 2, 135–141.Google Scholar
Virk, P.S. 1971 An elastic sublayer model for drag reduction by dilute solutions of linear macromolecules. J. Fluid Mech. 45, 417–440.CrossRefGoogle Scholar
Virk, P.S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.CrossRefGoogle Scholar
Virk, P.S., Merril, 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, 305–328.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2010 Coil-stretch transition in ensemble of polymers in isotropic turbulence. Phys. Rev. E 81, 066301.Google ScholarPubMed
Watanabe, T. & Gotoh, T. 2014 Power-law spectra formed by stretching polymers in decaying isotropic turbulence. Phys. Fluids 26, 035110.CrossRefGoogle Scholar
White, C.M. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.CrossRefGoogle Scholar
Xi, L. 2019 Turbulent drag reduction by polymer additives: fundamentals and recent advances. Phys. Fluids 31 (12), 121302.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, 218301.CrossRefGoogle ScholarPubMed
Xi, L. & Graham, M.D. 2012 Dynamics on the laminar-turbulent boundary and the origin of the maximum drag reduction asymptote. Phys. Rev. Lett. 108, 028301.CrossRefGoogle ScholarPubMed
Xiong, X., Zhang, Y. & Rahman, M.A. 2020 Reynolds-averaged simulation of the fully developed turbulent drag reduction flow in concentric annuli. J. Fluids Engng 142 (10), 101209.CrossRefGoogle Scholar
Zhang, W.H., et al. 2021 Comparative study on numerical performances of log-conformation representation and standard conformation representation in the simulation of viscoelastic fluid turbulent drag-reducing channel flow. Phys. Fluids 33 (2), 023101.CrossRefGoogle Scholar
Zhang, W.H., Shao, Q.Q., Li, Y.K., Ma, Y., Zhang, H.N. & Li, F.C. 2021 a On the mechanisms of sheet-like extension structures formation and self-sustaining process in elasto-inertial turbulence. Phys. Fluids 33 (8), 085107.CrossRefGoogle Scholar
Zhang, W.H., Zhang, H.N., Li, Y.K., Yu, B. & Li, F.C. 2021 b Role of elasto-inertial turbulence in viscoelastic drag-reducing turbulence. Phys. Fluids 33 (8), 081706.CrossRefGoogle Scholar
Zhu, L. & Xi, L. 2021 Nonasymptotic elastoinertial turbulence for asymptotic drag reduction. Phys. Rev. Fluids 6, 014601.CrossRefGoogle Scholar