Email this article Calculation of linear stability of fluid flow in a flat channel with walls wavy across the flow
- Authors: Trifonov Y.Y.1
-
Affiliations:
- zInstitute of Thermophysics named after. S.S. Kutateladze SB RAS
- Issue: No 5 (2023)
- Pages: 47-56
- Section: Articles
- URL: https://journals.rcsi.science/1024-7084/article/view/135091
- DOI: https://doi.org/10.31857/S102470842360015X
- EDN: https://elibrary.ru/GEZSYN
- ID: 135091
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Abstract
Using the full Navier-Stokes equations, the linear stability of a plane Poiseuille flow in a channel with a corrugated bottom wall is considered. The wall is corrugated across the flow, and the main flow has one velocity component. The perturbations of the velocity and pressure fields are three-dimensional with two wave numbers. The generalized eigenvalue problem is solved numerically. It is found that the critical Reynolds number, above which time-increasing disturbances appear, depends in a complex way on the dimensionless amplitude and the corrugation period. The magnitude of the ratio of the amplitude and the corrugation period divides the area of the dimensionless amplitude of the corrugation into two, where the dependences of the critical Reynolds number on the parameters of the corrugation are qualitatively different.
About the authors
Yu. Y. Trifonov
zInstitute of Thermophysics named after. S.S. Kutateladze SB RAS
Author for correspondence.
Email: trifonov@itp.nsc.ru
Novosibirsk, Russia
References
- Boiko A.V., Dovgal A.V., Grek G.R., Kozlov V.V. Physics of transitional shear flows. Berlin: Springer, 2011. 271 p.
- Goldstein D.B., Tuan T-C. Secondary flow induced by riblets // J. Fluid Mech. 1998. V. 363. P. 115–151.
- Sobey I.J. On flow through furrowed channels. Part I. Calculated flow patterns // J. Fluid Mech. 1980. V. 96. P. 1–26.
- Stepanoff K.D., Sobey I.J., Bellhouse B.J. On flow through furrowed channels. Part II. Observed flow patterns // J. Fluid Mech. 1980. V. 96. № 01. P. 27–32.
- Sparrow E.M., Hossfeld L.M. Effect of rounding of protruding edges on heat transfer and pressure drop in a duct // Int. J. Heat Mass Transfer. 1984. V. 27. P. 1715–1723.
- Beebe David J., Mensing Glennys A., Walker Glenn M. Physics and applications of microfluidics in biology // Annu. Rev. Biomed. Eng. 2002. V. 4. № 1. P. 261–286.
- Бойко А.В., Клюшнев H.В., Нечепуренко Ю.M. Устойчивость течения жидкости над оребренной поверхностью. М.: ИПМ им. М.В. Келдыша, 2016. 123 с.
- Григорьев О.А., Клюшнев H.В. Устойчивость течения Пуазейля в канале с гребенчатым оребрением // Журнал вычислительной математики и математической физики. 2018. Т. 58. № 4. С. 595–606.
- Kistle S.F., Schweizer P.M. Liquid Film Coating (Chapman and Hall, New York, 1997).
- Weinstein S.J., Ruschak K.J. Coating flows // Annu. Rev. Fluid Mech. 2004. V.36. P. 29–53.
- DeSantos J.M., Melli T.R., Scriven L.E. Mechanics of gas-liquid flow in packed-bed contactors // Annu. Rev. Fluid Mech. 1991. V. 23. P. 233–260.
- Trifonov Y.Y. Modeling of mixture separation in column with structured packing // Multiph. Sci. Technol. 2022. V. 34. № 1. P. 23–51.
- Kachanov Y.S. Physical mechanisms of laminar-boundary-layer transition // Annu. Rev. Fluid Mech. 1994. V. 26. P. 411–482.
- Nishimura T., Ohori Y., Kawamura Y. Flow characteristics in a channel with symmetric wavy wall for steady flow // J. Chem. Eng. Jpn. 1984. V. 17. № 5. P. 466–471.
- Nishimura T., Ohori Y., Kajimoto Y., Kawamura Y. Mass transfer characteristics in a channel with symmetric wavy wall for steady flow // J. Chem. Eng. Jpn. 1985. V. 18. № 6. P. 550–555.
- Nishimura T., Kajimoto and Kawamura Y. Mass transfer enhancement in channels with a wavy wall // J. Chem. Eng. Japan. 1986. V. 19. P. 142–144.
- Guzman A.M., Amon C.H. Transition to chaos in converging-diverging channel flows: Ruelle-Takens-Newhouse scenario // Phys. Fluids. 1994. V. 6. № 6. P. 1994–2002.
- Guzman A.M., Amon C.H. Dynamical flow characterization of transitional and chaotic regimes in converging- diverging channels // J. Fluid Mech. 1996. V. 321. P. 25–57.
- Amon C.H., Guzman A.M., Morel B. Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging diverging channel flows // Phys. Fluids. 1996. V. 8. № 5. P. 1192–1206.
- Szumbarski J. Instability of viscous incompressible flow in a channel with transversely corrugated walls // J. Theor. App. Mech-Pol. 2007. V.45. № 3. P. 659–683.
- Yadav Nikesh, Gepner S.W., Szumbarski J. Instability in a channel with grooves parallel to the flow // Phys. Fluids. 2017. V. 29. № 10. 084104.
- Cho K.J., Kim M.-U., Shin H.D. Linear stability of two-dimensional steady flow in wavy-walled channels // Fluid Dyn. Res. 1998. V. 23. № 6. P. 349–370.
- Cabal A., Szumbarski J., Floryan J.M. Stability of flow in a wavy channel // J. Fluid Mech. 2002. V. 457. P. 191–212.
- Floryan J.M., Floryan C. Traveling wave instability in a diverging converging channel // Fluid Dyn. Res. 2010. V. 42. № 2. 025509.
- Trifonov Y.Y. Stability of a film flowing down an inclined corrugated plate: The direct Navier-Stokes computations and Floquet theory // Phys. Fluids. 2014. V. 26. 114101.
- Schörner M., Reck D., Aksel N., Trifonov Y. Switching between different types of stability isles in films over topographies // Acta Mech. 2018. V. 229. P. 423–436.
- Mohammadi A., Moradi H.V., Floryan J.M. New instability mode in a grooved channel // J. Fluid Mech. 2015. V. 778. P. 691–720.
- Moradi H.V., Floryan J.M. Stability of flow in a channel with longitudinal grooves // J. Fluid Mech. 2014. V. 757. P. 613–648.
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