Asymptotic study of flows induced by oscillations of cylindrical bodies

Cover Page

Cite item

Full Text

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

Abstract

Hydrodynamic flows induced by translational oscillations of cylindrical bodies of various cross-sectional shapes are studied. The motion of fluid around oscillating bodies is described using the system of Navier–Stokes equations written in a generalized curvilinear coordinate system. Transition to a given body shape is implemented using a conformal mapping. The problem is solved using the method of successive asymptotic expansions under the assumption that the oscillation amplitudes are small. In each asymptotic approximation, the subproblems are solved numerically using the finite-difference method. Based on the results of the work, estimates of the hydrodynamic effect are obtained, the applicability of the high-frequency asymptotic approximation is estimated, and secondary stationary flows near cylinders are studied, in particular, the occurrence of directed stationary flows near an oscillating asymmetric body is considered with reference to the Joukowski airfoil.

Full Text

Restricted Access

About the authors

A. N. Nuriev

Kazan Federal University

Author for correspondence.
Email: Artem.Nuriev@kpfu.ru
Russian Federation, Kazan

O. N. Zaitseva

Kazan Federal University

Email: olga_fdpi@mail.ru
Russian Federation, Kazan

A. M. Kamalutdinov

Kazan Federal University

Email: amkamalutdinov@kpfu.ru
Russian Federation, Kazan

E. E. Bogdanovich

Kazan Federal University

Email: helenbogdanovich03@gmail.com
Russian Federation, Kazan

A. R. Baimuratova

Kazan Federal University

Email: angelina.baimuratova@yandex.ru
Russian Federation, Kazan

References

  1. Tang G., Cheng L., Lu L., Teng Y., Zhao M., An H. Effect of oscillatory boundary layer on hydrodynamic forces on pipelines // Coast. Eng. 2018. V. 140. P. 114–123.
  2. Cheng L., An H., Draper S., White D. Effect of wave boundary layer on hydrodynamic forces on small diameter pipelines // Ocean Eng. 2016. V. 125. P. 26–30.
  3. Бужинский В.А., Петряхин Д.А., Соломонов Е.В. Колебания в жидкости пластин с ребрами жесткости // Изв. РАН. МЖГ. 2022. № 1. С. 39–46.
  4. Бужинский В.А. Колебания жидкости в цилиндрических баках с продольными демпфирующими перегородками // Изв. РАН. МЖГ. 2020. № 1. С. 9–21.
  5. Sader J.E. Frequency response of cantilever beams immersed in vis-cous fluids with applications to the atomic force microscope // J. Appl. Phys. 1998. V. 84. № 1. P. 64–76.
  6. Scherer M.P., Frank G., Gummer A.W. Experimental determina-tion of the mechanical impedance of atomic force microscopy cantilevers in fluids up to 70 kHz // J. Appl. Phys. 2000. V. 88. № 5. P. 2912–2920.
  7. Erturk A., Inman D. Piezoelectric energy harvesting. N.Y.: John Wiley & Sons, 2011. P. 416.
  8. Zhu H., Zhang P., Zhong Z., Xia J., Rich J., Mai J., Su X., Tian Z., Bachman H., Rufo J., Gu Y., Kang P., Chakrabarty K., Witelski T.P., Huang T.J. Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices // Science Advances. 2021. V. 7. № 2. P. eabc7885.
  9. Semati A., Amani E., Saffaraval F., Saffar-Avval M. Numerical simulation of oscillating plates at the visco-inertial regime for bio-inspired pumping and mix-ing applications // Phys. Fluids. 2020. V. 32. № 10. P. 101906.
  10. Yeh P.D., Demirer E., Alexeev A. Turning strategies for plunging elastic plate propulsor // Phys. Rev. Fluids. 2019. V. 4. № 064101.
  11. Гувернюк С.В., Дынников Я.А., Дынникова Г.Я., Малахова Т.В. Гидродинамические механизмы влияния упругой связи на пропульсивную силу крылового профиля при полудетерминированных колебаниях в потоке вязкой жидкости // Изв. РАН. МЖГ. 2022. № 5. С. 3–12.
  12. Nuriev A.N., Egorov A.G. Asymptotic theory of a flapping wing of a circular cross-section // J. Fluid Mech. 2022. V. 941. № A23.
  13. Нуриев А.Н., Камалутдинов А.М. Идентификация характеристик силового аэродинамического воздействия на колеблющиеся консольно-закрепленные балки // Изв. РАН. МЖГ. 2022. № 5. С. 62–79.
  14. Бужинский В.А. Вихревое сопротивление пластинки при колебаниях в маловязкой жидкости // ПММ.1990. Т. 54. Вып. 2. С. 233–238.
  15. Graham J.M.R. The forces on sharp-edged cylinders in oscillatory flow at low Keulegan-Carpenter numbers // J. Fluid Mech. 1980. V. 97. № 2. P. 331–346.
  16. Stokes G.G. On the effect of the internal friction of fluids on the motion of pendulums // Trans. Camb. Phil. Soc. 1851. V. 9. P. 8–106.
  17. Wang C.-Y. On high-frequency oscillatory viscous flows // J. Fluid Mech. 1968. V. 32. № 1. P. 55–68.
  18. Riley N. The steady streaming induced by a vibrating cylinder // J. Fluid Mech. 1975. V. 68. № 4. P. 801–812.
  19. Holtsmark J., Johnsen I., Sikkeland T., Skavlem S. Boundary layer flow near a cylindrical obstacle in an oscillating, incom-pressible fluid // J. Acoust. Soc. Am. 1954. V. 26. № 1. P. 26–39.
  20. Tuck E.O. Calculation of unsteady flows due to small motions of cylinders in a viscous fluid // J. Engng Maths 1969. V. 3. № 1. P. 29–44.
  21. Brumley D.R., Willcox M., Sader J.E. Oscillation of cylinders of rectangular cross section immersed in fluid // Phys. Fluids. 2010. V. 22. № 5. P. 052001.
  22. Ahsan S.N., Aureli M. Finite amplitude oscillations of flanged laminas in viscous flows: vortex-structure interactions for hydrodynamic damping control // J. Fluids Struct. 2015. V. 59. P. 297–315.
  23. Davidson B.J., Riley N. Jets induced by oscillatory motion // J. Fluid Mech. 1972. V. 53, № 2. P. 287–303.
  24. Nuriev A.N., Egorov A.G., Kamalutdinov A.M. Hydrodynamic forces acting on the elliptic cylinder performing high-frequency low-amplitude multi-harmonic oscillations in a viscous fluid // J. Fluid Mech. 2021. V. 913. P. A40.
  25. Weinan E., Liu J.G. Vorticity boundary conditions and related is-sues for finite difference schemes // J. Comput. Phys. 1996. V. 124. P. 368–382.
  26. Nuriev A.N., Egorov A.G., Zaitseva O.N. Bifurcation analysis of steady-state flows in the lid-driven cavity // Fluid Dyn. Res. 2016. V. 48. № 6. P. 061405.
  27. Morison J.R., Johnson J.W., Schaaf S.A. The force exerted by surface waves on piles //J. Pet. Technol 1950. V. 2. № 1. P. 149–154.
  28. Egorov A.G., Nuriev A.N. Steady streaming generated by low-amplitude oscillations of a cylinder // Lobachevskii J. Math. 2021. V. 42, № 9. P. 2102–2108.
  29. Schlichting H. Berechnung ebener periodischer grenzschichtstrоmungen // Phys. Zeit. 1932. V. 33. P. 327–335.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences