INSTABILITY OF THE FLOW IN A PLANE CHANNEL WITH COMPLIANT WALLS OF FINITE THICKNESS

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The model of the stability of viscous incompressible flow in a channel with thick compliant walls is developed and studied under the assumption of the disturbance smallness. The eigenvalue problem thus obtained is solved numerically using the collocation method. The calculations are carried out for several viscoelastic materials. Some new results concerning the effect of the wall thickness and the characteristic flow velocity on the flow stability are obtained. The effect of viscoelastic properties of the channel wall material on the suppression of the Tollmien–Schlichting instability is estimated.

About the authors

A. V Boiko

Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences

Novosibirsk, Russia

E. S Golub

Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Email: e.golub@g.nsu.ru
Novosibirsk, Russia; Novosibirsk, Russia

A. P Chupakhin

Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Novosibirsk, Russia

References

  1. Kramer M.O. Boundary layer stabilization by distributed damping // JAS. 1957. V. 24. P. 459–460.
  2. Xia Q.J., Huang W.X., Xu C.X. Direct numerical simulation of a turbulent boundary layer over an anisotropic compliant wall // Acta. Mech. Sin. 2019. V. 35. P. 384–400. https://doi.org/10.1007/s10409-018-0820-x
  3. Musleh A.A., Frendi A. On the effects of a flexible structure on boundary layer stability and transition // J. Fluids Eng. 2011. V. 133. No. 7. https://doi.org/10.1115/1.4004490
  4. Avila M., Barkley D., Hof B. Transition to turbulence in pipe flow // Annu. Rev. Fluid Mech. 2023. V. 55. No. 1. P. 575–602. https://doi.org/10.1146/annurev-fluid-120720-025957
  5. Веденеев В.В. Одномодовый флаттер пластины с учетом пограничного слоя // Изв. РАН. МЖГ. 2012. № 3. С. 147–160.
  6. Kumaran V. Stability and the transition to turbulence in the flow through conduits with compliant walls // J. Fluid Mech. 2021. V. 924. P1. https://doi.org/10.1017/jfm.2021.602
  7. Carpenter P.W., Gajjar J.S.B. A general theory for two-and three-dimensional wall-mode instabilities in boundary layers over isotropic and anisotropic compliant walls // Theoret. Comput. Fluid Dyn. 1990. V. 1. No. 6. P. 349–378. https://doi.org/10.1007/bf00271796
  8. Gad-el-Hak M. Compliant coatings: a decade of progress // Appl. Mech. Rev. 1996. V. 49. No. 10S. https://doi.org/10.1115/1.3101966
  9. Squires T.M., Quake S.R. Microfluidics: Fluid physics at the nanoliter scale // Rev. Mod. Phys. 2005. V. 77. No. 3. P. 977–1026. https://doi.org/10.1103/RevModPhys.77.977
  10. Eggert M.D., Kumar S. Observations of instability, hysteresis, and oscillation in low-Reynolds-number flow past polymer gels // J. Colloid Interface Sci. 2004. V. 278. No. 1. P. 234–242. https://doi.org/10.1016/j.jcis.2004.05.043
  11. Mehdari A., Agouzoul M. and Hasnaoui M. Analytical Modeling For Newtonian Fluid Flow through an Elastic Tube // JMEA. 2018. V. 8. No. 1. P. 25–29. https://doi.org/10.29354/diag/81237.
  12. Benjamin T.B. The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows // J. Fluid Mech. 1963. V. 16. No. 3. P. 436–450. https://doi.org/10.1017/S0022112063000884
  13. Landahl M.T. On the stability of a laminar incompressible boundary layer over a flexible surface // J. Fluid Mech. 1962. V. 13. No. 4. P. 609–632.
  14. Patne R., Shankar V. Stability of flow through deformable channels and tubes: implications of consistent formulation // J. Fluid Mech. 2019. V. 860. P. 837–885. https://doi.org/10.1017/jfm.2018.908
  15. Heil M., Hazel A.L. Fluid-structure interaction in internal physiological flows // Annu. Rev. Fluid Mech. 2011. V. 43. No. 1. P. 141–162. https://doi.org/10.1146/annurev-fluid-122109-160703
  16. Pedley T.J., Pihler-Puzovic D. Flow and oscillations in collapsible tubes: Physiological applications and lowdimensional models // Sadhana. 2015. V. 40. № 3. P. 891–909. https://doi.org/10.1007/s12046-015-0363-9.
  17. Grotberg J.B., Jensen O.E. Biofluid mechanics in flexible tubes // Annu. Rev. Fluid Mech. 2004. V. 36. No. 1. P. 121–147. https://doi.org/10.1146/annurev.fluid.36.050802.121918
  18. Бойко А.В. О моделировании устойчивости течений жидкости в податливых трубах применительно к задачам гемодинамики // Вестн. Новосиб. гос. ун-та. Сер. Физика. 2015. Т. 10. № 4. С. 29–42.
  19. Ганиев Р.Ф., Украинский Л.Е., Устенко И.Г. О стабилизации малых возмущений течения Пуазейля в канале с упругими стенками // Изв. АН СССР. МЖГ. 1988. № 3. С. 67–72.
  20. Бойко А.В., Кулик В.М. Устойчивость пограничного слоя плоской пластины над монолитными вязкоупругими покрытиями // Докл. РАН. 2012. Т. 445. № 3. С. 283–285.
  21. Даржаин А.Э., Бойко А.В., Кулик В.М., Чупахин А.П. Анализ устойчивости пограничного слоя плоской пластины над двухслойным податливым покрытием конечной толщины // ПМТФ. 2019. Т. 60, № 4. С. 35–46.
  22. Stewart P.S., Waters S.L., Jensen O.E. Local and global instabilities of flow in a flexible-walled channel // Eur. J. Mech. B-Fluids. 2009. V. 28. № 4. P. 541–557. https://doi.org/10.1016/j.euromechflu.2009.03.002
  23. Stewart P.S., Waters S.L., Jensen O.E. Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer // Phys. Fluids. 2010. V. 22. № 3. https://doi.org/10.1063/1.3337824
  24. Boiko A.V., Demyanko K.V. On numerical stability analysis of fluid flows in compliant pipes of elliptic cross-section // J. Fluids. Struct. 2022. V. 108. P. 103414. https://doi.org/10.1016/j.jfluidstructs.2021.103414
  25. Lebbal S., Alizard F., Pier B. Revisiting the linear instabilities of plane channel flow between compliant walls // Phys. Rev. Fluids. 2022. V. 7. No. 2. P. 023903. https://doi.org/10.1103/PhysRevFluids.7.023903
  26. Бойко А.В., Грек Г.Р., Довгаль А.В., Козлов В.В. Физические механизмы перехода к турбулентности в открытых течениях. М.: Ижевск: НИЦ “Регулярная и хаотическая динамика”, Институт компьютерных исследований, 2006. 304с.
  27. Weideman J.A.C., Reddy S.C. A MATLAB Differentiation Matrix Suite // ACM Trans. Math. Softw. 2000. V. 26. No. 4. P. 465–519. https://doi.org/10.1145/365723.365727
  28. Yeo K.S. The stability of boundary-layer flow over single- and multi-layer viscoelastic walls // J. Fluid Mech. 1988. V. 196. P. 359–408. https://doi.org/10.1017/S0022112088002745

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2025 Russian Academy of Sciences