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  • Letter
  • Open Access

Unified view of elastic and elasto-inertial turbulence in channel flows at low and moderate Reynolds numbers

Giulio Foggi Rota1, Christian Amor1, Soledad Le Clainche2, and Marco Edoardo Rosti1,*

  • *Contact author: marco.rosti@oist.jp
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Phys. Rev. Fluids 9, L122602 – Published 30 December, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.L122602

Abstract

The chaotic flow of elastic fluids at low Reynolds number (Re) is typically distinguished into elasto-inertial and elastic turbulence (EIT/ET). However, the clear separation among these two turbulent regimes in parallel flows with a gradual Re decrease remains elusive. Here, spanning Re over four orders of magnitude, we investigate the statistical and structural nature of the flows computed by fully resolved 3D numerical simulations, revealing that as inertia becomes subdominant all flows share similar dynamical properties. Supported by the results, we thus propose a unified view of fully developed ET and EIT in parallel flows.

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References (50)

  1. A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezić, H. A. Stone, and G. M. Whitesides, Chaotic mixer for microchannels, Science 295, 647 (2002).
  2. T. J. Ober, D. Foresti, and J. A. Lewis, Active mixing of complex fluids at the microscale, Proc. Natl. Acad. Sci. USA 112, 12293 (2015).
  3. J. Y. Han, J. N. La Fiandra, and D. L. DeVoe, Microfluidic vortex focusing for high throughput synthesis of size-tunable liposomes, Nat. Commun. 13, 6997 (2022).
  4. A. M. Vargason, A. C. Anselmo, and S. Mitragotri, The evolution of commercial drug delivery technologies, Nat. Biomed. Eng. 5, 951 (2021).
  5. P. Yager, T. Edwards, E. Fu, K. Helton, K. Nelson, M. R. Tam, and B. H. Weigl, Microfluidic diagnostic technologies for global public health, Nature (London) 442, 412 (2006).
  6. A. Groisman and V. Steinberg, Efficient mixing at low Reynolds numbers using polymer additives, Nature (London) 410, 905 (2001).
  7. F. Serafini, F. Battista, P. Gualtieri, and C. M. Casciola, Drag reduction in turbulent wall-bounded flows of realistic polymer solutions, Phys. Rev. Lett. 129, 104502 (2022).
  8. A. Groisman and V. Steinberg, Stretching of polymers in a random three-dimensional flow, Phys. Rev. Lett. 86, 934 (2001).
  9. Y. Dubief, V. E. Terrapon, and B. Hof, Elasto-inertial turbulence, Annu. Rev. Fluid Mech. 55, 675 (2023).
  10. D. Samanta, Y. Dubief, M. Holzner, C. Schäfer, A. N. Morozov, C. Wagner, and B. Hof, Elasto-inertial turbulence, Proc. Natl. Acad. Sci. USA 110, 10557 (2013).
  11. J. Page, Y. Dubief, and R. R. Kerswell, Exact traveling wave solutions in viscoelastic channel flow, Phys. Rev. Lett. 125, 154501 (2020).
  12. M. Khalid, V. Shankar, and G. Subramanian, Continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow, Phys. Rev. Lett. 127, 134502 (2021).
  13. P. Garg, I. Chaudhary, M. Khalid, V. Shankar, and G. Subramanian, Viscoelastic pipe flow is linearly unstable, Phys. Rev. Lett. 121, 024502 (2018).
  14. S. Berti and G. Boffetta, Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow, Phys. Rev. E 82, 036314 (2010).
  15. R. B. Bird, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics (Wiley, 1987).
  16. N. K. Jha and V. Steinberg, Elastically driven Kelvin–Helmholtz-like instability in straight channel flow, Proc. Natl. Acad. Sci. USA 118, e2105211118 (2021).
  17. Y. Li and V. Steinberg, Mechanism of vorticity amplification by elastic waves in a viscoelastic channel flow, Proc. Natl. Acad. Sci. USA 120, e2305595120 (2023).
  18. J. Song, N. Liu, X. Lu, and B. Khomami, Direct numerical simulation of elastic turbulence in the Taylor–Couette flow: Transition pathway and mechanistic insight, J. Fluid Mech. 949, A49 (2022).
  19. M. Lellep, M. Linkmann, and A. Morozov, Purely elastic turbulence in pressure-driven channel flows, Proc. Natl. Acad. Sci. USA 121, e2318851121 (2024).
  20. G. Boffetta, A. Celani, A. Mazzino, A. Puliafito, and M. Vergassola, The viscoelastic Kolmogorov flow: Eddy viscosity and linear stability, J. Fluid Mech. 523, 161 (2005).
  21. A. Bistagnino, G. Boffetta, A. Celani, A. Mazzino, A. Puliafito, and M. Vergassola, Nonlinear dynamics of the viscoelastic Kolmogorov flow, J. Fluid Mech. 590, 61 (2007).
  22. S. Berti, A. Bistagnino, G. Boffetta, A. Celani, and S. Musacchio, Two-dimensional elastic turbulence, Phys. Rev. E 77, 055306(R) (2008).
  23. S. Sid, V. E. Terrapon, and Y. Dubief, Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction, Phys. Rev. Fluids 3, 011301(R) (2018).
  24. Y. Dubief, J. Page, R. R. Kerswell, V. E. Terrapon, and V. Steinberg, First coherent structure in elasto-inertial turbulence, Phys. Rev. Fluids 7, 073301 (2022).
  25. G. Buza, M. Beneitez, J. Page, and R. R. Kerswell, Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number, J. Fluid Mech. 951, A3 (2022).
  26. A. Morozov, Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia, Phys. Rev. Lett. 129, 017801 (2022).
  27. M. Beneitez, J. Page, and R. R. Kerswell, Polymer diffusive instability leading to elastic turbulence in plane Couette flow, Phys. Rev. Fluids 8, L101901 (2023).
  28. A. Peterlin, Hydrodynamics of macromolecules in a velocity field with longitudinal gradient, J. Polym. Sci., Part B: Polym. Lett. 4, 287 (1966).
  29. D. Vincenzi, S. Jin, E. Bodenschatz, and L. R. Collins, Stretching of polymers in isotropic turbulence: A statistical closure, Phys. Rev. Lett. 98, 024503 (2007).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevFluids.9.L122602 for technical details on the numerical methods. There, we also provide further insight on the flow statistics, elucidate the calibration of the modal decomposition algorithm, and investigate the dependence of the results from the polymer concentration, which includes Refs. [7, 9, 19, 24, 25, 27, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42].
  31. M. S. Abdelgawad, I. Cannon, and M. E. Rosti, Scaling and intermittency in turbulent flows of elastoviscoplastic fluids, Nat. Phys. 19, 1059 (2023).
  32. J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys. 59, 308 (1985).
  33. R. Fattal and R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newtonian Fluid Mech. 126, 23 (2005).
  34. F. De Vita, M. E. Rosti, D. Izbassarov, L. Duffo, O. Tammisola, S. Hormozi, and L. Brandt, Elastoviscoplastic flows in porous media, J. Non-Newtonian Fluid Mech. 258, 10 (2018).
  35. K. Sugiyama, S. Ii, S. Takeuchi, S. Takagi, and Y. Matsumoto, A full Eulerian finite difference approach for solving fluid–structure coupling problems, J. Comput. Phys. 230, 596 (2011).
  36. M. Beneitez, J. Page, Y. Dubief, and R. R. Kerswell, Multistability of elasto-inertial two-dimensional channel flow, J. Fluid Mech. 981, A30 (2024).
  37. E. De Angelis, C. M. Casciola, and R. Piva, DNS of wall turbulence: Dilute polymers and self-sustaining mechanisms, Comput. Fluids 31, 495 (2002).
  38. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2000).
  39. J. M. Vega and S. Le Clainche, Higher Order Dynamic Mode Decomposition and Its Applications (Elsevier Science, Cambridge, MA, 2020).
  40. P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5 (2010).
  41. M. M. P. Couchman, M. Beneitez, J. Page, and R. R. Kerswell, Inertial enhancement of the polymer diffusive instability, J. Fluid Mech. 981, A2 (2024).
  42. G. Buza, J. Page, and R. R. Kerswell, Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers, J. Fluid Mech. 940, A11 (2022).
  43. S. Tardu, Transport and Coherent Structures in Wall Turbulence (John Wiley & Sons, Hoboken, NJ, London, UK, 2014).
  44. R. K. Singh, P. Perlekar, D. Mitra, and M. E. Rosti, Intermittency in the not-so-smooth elastic turbulence, Nat. Commun. 15, 4070 (2024).
  45. M. Khalid, I. Chaudhary, P. Garg, V. Shankar, and G. Subramanian, The centre-mode instability of viscoelastic plane Poiseuille flow, J. Fluid Mech. 915, A43 (2021).
  46. G. H. Choueiri, J. M. Lopez, A. Varshney, S. Sankar, and B. Hof, Experimental observation of the origin and structure of elastoinertial turbulence, Proc. Natl. Acad. Sci. USA 118, e2102350118 (2021).
  47. A. N. Kolmogorov, The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR 30, 301 (1941).
  48. J. L. Lumley, Drag reduction by additives, Annu. Rev. Fluid Mech. 1, 367 (1969).
  49. V. Steinberg, Elastic turbulence: An experimental view on inertialess random flow, Annu. Rev. Fluid Mech. 53, 27 (2021).
  50. https://www.oist.jp/research/research-units/cffu/publications/publication-data.

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Phys. Rev. Fluids 9, L122602– Published 30 December, 2024
  • Received 25 March 2024
  • Accepted 6 December 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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