Numerical simulation of polymer solution flow for Kolmogorov flow

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A numerical method approximating the equations of the dynamics of the polymer solution flow is proposed. The developed methodology is based on a hybrid approach. The hydrodynamic component of the flow is described by a system of Navier–Stokes equations and is numerically approximated by the linearized Godunov method. The polymer component of the flow is described by a system of equations for the polymer stretching vector R and is numerically approximated by the Kurganov–Tadmor method. Using the constructed scheme, the problem of the stability of the polymer solution flow at low Reynolds numbers Re ∼ 10 in a square periodic cell under the action of an external periodic force is investigated. The instability of this type of flow, characterized by a violation of its laminarity, has been studied by numerical experiment. Spectral characteristics of the polymer solution at low Reynolds numbers are constructed.

作者简介

V. Denisenko

Institute of Design Automation of the Russian Academy of Sciences

Email: ned13@rambler.ru
Moscow, Russia

S. Fortova

Institute of Design Automation of the Russian Academy of Sciences

Moscow, Russia

V. Lebedev

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences

Chernogolovka, Russia

V. Kolokolov

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences

Chernogolovka, Russia

参考

  1. Victor Steinberg. Elastic Turbulence: An Experimental View on Inertialess Random // Flow. Annu. Rev. Fluid Mech. 2021. V. 53. P. 27-58.
  2. Armin Shahmardi, Sagar Zade, Mehdi N. Ardekani, Rob J. Poole, Fredrik Lundell, Marco E. Rosti, and Luca Brandt. Turbulent duct flow with polymers // J. Fluid Mech. 2019. V. 859. P. 1057-1083.
  3. Belan S., Chernykh A. , Lebedev V. Boundary layer of elastic turbulence // J. Fluid Mech. 2018. V. 855. P. 910-921.
  4. Zhang Hong-Na, Li Feng-Chen, Cao Yang, Kunugi Tomoaki, Yu Bo. Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow // Chin. Phys. B 2013. V. 22. No 2. 024703.
  5. Larson R.G, Shaqfeh E.S.G., Muller S.J. A purely elastic instability in Taylor-Couette flow //J. Fluid Mech. 1990. V 218. P 573-600.
  6. Groisman A., Steinberg V. Elastic versus inertial instability in a polymer solution flow // 1998a. Europhys. Lett. 43:165-70.
  7. Groisman A., Steinberg V. Mechanism of elastic instability in Couette flow of polymer solutions: experiment // 1998b. Phys. Fluids 10:2451-63.
  8. Steinberg V, Groisman A. Elastic versus inertial instability in Couette-Taylor flow of a polymer solution: review // Philos. Mag. B 1998. V. 78. P. 253-63.
  9. McKinley G.H, Byars J.A, Brown R.A, Armstrong R.C. Observations on the elastic instability in cone-and-plate and parallel-plate flows ofa polyisobutylene Boger fluid// J. Non-Newton. Fluid Mech. 1991. V. 40:201-29.
  10. Oeztekin A., Brown R.A. Instability of a viscoelastic fluid between rotating parallel disks: analysis for the Oldroyd-B fluid // J. Fluid Mech. 1993. 255:473-502.
  11. Byars J.A, Oeztekin A., Brown R.A., McKinley G.H. Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks // 1994. J. Fluid. Mech. 271:173-218.
  12. Oeztekin A., Brown R.A., McKinley G.H. Quantitative prediction of the viscoelastic instability in coneand plate flow of a Boger fluid using a multi-mode Giesekus model // J. Non-Newton. Fluid Mech. 1994. 54:351-77.
  13. Joo Y.L, Shaqfeh E.S.G. A purely elastic instability in Dean and Taylor-Dean flow // 1992. Phys. Fluids. A. 1992. V. 4:524-42.
  14. Burghelea T., Segre E., Bar-Joseph I., Groisman A., Steinberg V. Chaotic flow and efficient mixing in a microchannel with a polymer solution // Phys. Rev. 2004.E 69:066305.
  15. Burghelea T., Segre E., Steinberg V. Mixing by polymers: experimental test of decay regime of mixing // 2004b. Phys. Rev. Lett. 2004. V. 92:164501.
  16. Groisman A., Steinberg V. Elastic turbulence in curvilinear flows of polymer solutions // New J. Phys. 2004. V. 6:29-48.
  17. Jun Y., Steinberg V. Elastic turbulence in a curvilinear channel flow // Phys. Rev. E 2011. V. 84:056325.
  18. Soulies A., Aubril J., Castelain C., Burghelea T. Characterization of elastic turbulence in a serpentine micro-channel // Phys. Fluids. 2017. V. 29:083102.
  19. Arratia P.E., Thomas C.C., Diorio J., Gollub J.P. Elastic instabilities of polymer solutions in cross-channel flow // Phys. Rev. Lett. 2006. V. 96:144502.
  20. Poole R.J., Alves M.A., Oliveira P.J. Purely elastic flow asymmetries // Phys. Rev. Lett. 2007. V. 99:164503.
  21. Haward S.J., McKinley G.H. Instabilities in stagnation point flows of polymer solutions. // Phys. Fluids. 2013. V. 25:083104.
  22. Varshney A., Afik E., Kaplan Y., Steinberg V. Oscillatory elastic instabilities in an extensional viscoelastic flow // Soft Matter. 2016. 12:2186-91.
  23. McKinley G.H., Armstrong R.C., Brown R.A. The wake instability in viscoelastic flow past confined circular cylinders // Philos. Trans. R. Soc. A. 1993. 344:265-304.
  24. Vazquez-Quesada A., Ellero M. SPH simulations of a viscoelastic flow around a periodic array of cylinders confined in a channel // J. Non-Newton. Fluid Mech. 2012.167-68:1-8.
  25. Grilli M., Vazquez-Quesada A., Ellero M. Transition to turbulence and mixing in a viscoelastic fluid flowing inside a channel with a periodic array of cylindrical obstacles. // Phys. Rev. Lett. 2013. V. 110:174501.
  26. Varshney A., Steinberg V. Elastic wake instabilities ina creeping flow between two obstacles // Phys. Rev. Fluids. 2017. 2:051301(R).
  27. Larson R.G. Instabilities in viscoelastic flows // Rheol. Acta. 1992. 31:213—63.
  28. Shaqfeh E.S.G. Purely elastic instabilities in viscometric flows // Annu. Rev. Fluid Mech. 1996. V 28:129—85.
  29. Berti S., Bistagnino A., Boffetta G., Celani A., and Musacchio S. Two-dimensional elastic turbulence // Physical Review. E2008. 77, 055306 R.
  30. Anupam Gupta, Dario Vincenzi. Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence // 7 Mar 2019. arXiv:1809.09648v2 [physics.flu-dyn].
  31. Berti S., Boffetta G. Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow // Physical Review.2010 E 82, 036314.
  32. Dzanic V., From C.S., and Saurt E. Conserving elastic turbulence numerically using artificial diffusivity // 20 Jun 2022. arXiv: 2203.12962v2 [physics.flu-dyn].
  33. Денисенко В.В., Фортова С.В. Численное моделирование эластической турбулентности в ограниченной двумерной ячейке // Сиб.журнал индустриальной матем. 2023. Т. 26. № 1. С. 55—64.
  34. Zhang H. N., Li F. C., Cao Y., Yang J. C., Li X. B., Cai W. H. Proceedings of the 6th International Conference on Fluid Mechanics, 2011, June 30—July 3, Guangzhou, China, p. 107.
  35. Годунов С.К., Денисенко В.В., Ключинский Д.В., Фортова С.В., Шепелев В.В. Исследование энтропийных свойств линеаризованной редакции метода Годунова // Ж. вычисл. матем. и матем. физ. 2020. Т. 60. № 4. С. 639-651.
  36. Alexander Kurganov, Eitan Tadmor. New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations // J. of Comput.l Phys. 2000. V. 160. P. 241-282.
  37. Groisman A., Steinberg V. Nature. 2000. 405, 53.
  38. Burghelea T., Segre E., Steinberg V. Elastic turbulence in von Karman swirling flow between two disks // Phys. Fluids. 2007. 19, 053104.

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