Modeling of melting-freezing of ice in problem of fluid flow along a small irregularity

Cover Page

Cite item

Full Text

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

Abstract

In this paper, we study the phase transition in a fluid flow along an ice surface with a small localized irregularity for large Reynolds numbers. In the framework of the double-deck structure of the boundary layer, a mathematical modelbased on the phase field system is constructed that describes the dynamics of the phase transition, and the results of numerical simulation are presented.

About the authors

P. K. Gaidukov

National Research University Higher School of Economics

Email: roma1990@gmail.com
Moscow, Russia

V. G. Danilov

National Research University Higher School of Economics

Email: vgdanilov@mail.ru
Moscow, Russia

A. V. Fonareva

National Research University Higher School of Economics

Author for correspondence.
Email: afonareva@hse.ru
Moscow, Russia

References

  1. Danilov V.G., Makarova M.V. Asymptotic and numerical analysis of the flow around a plate with small periodic irregularities // Russ. J. Math. Phys. 1994. V. 2. P. 49–56.
  2. Danilov V.G., Gaydukov R.K. Double-deck structure of the boundary layer in problems of flow around localized perturbations on a plate // Math. Notes. 2015. V. 98. № 4. P. 561–571.
  3. Gaydukov R.K. Double-deck structure in the problem of a compressible flow along a plate with small localized irregularities on the surface // Eur. J. Mech. B/Fluids. 2018. V. 71. P. 59–65.
  4. Gaydukov R.K. Double-deck structure in the fluid flow problem over plate with small irregularities of time-dependent shape // Eur. J. Mech. B/Fluids. 2021. V. 89. P. 401–410.
  5. Neiland V.Ya. Theory of laminar boundary layer separation in supersonic flow // Fluid Dyn. 1969. V. 4. № 4. P. 33–35.
  6. Stewartson K., Williams P.G. Self-induced separation // Proc. Royal Soc. A. 1969. V. 312. P. 181–206.
  7. Smith F.T. Laminar flow over a small hump on a flat plate // J. Fluid Mech. 1973. V. 57. P. 803–824.
  8. Lipatov I.I. Disturbed Boundary Layer Flow with Local Time-Dependent Surface Heating // Fluid Dyn. 2006. V. 41. № 5. P. 725–735.
  9. Lipatov I.I., Koroteev M.V. Local temperature perturbations of the boundary layer in the regime of free viscous-inviscid interaction // J. Fluid Mech. 2012. V. 707. P. 595–605.
  10. Lipatov I.I., Koroteev M.V. Supersonic Boundary Layer in Regions with Small Temperature Perturbations on the Wall // SIAM J. Appl. Math. 2009. V. 70. № 4. P. 1139–1156.
  11. Aljohani A.F., Gajjar J.S.B. Subsonic flow past localised heating elements in boundary layers // J. Fluid Mech. 2017. V. 821. P. R2.
  12. Aljohani A.F., Gajjar J.S.B. Transonic flow over localised heating elements in boundary layers // J. Fluid Mech. 2018. V. 844. P. 746–765.
  13. Вишик М.И., Люстерник Л.А. Регулярное вырождение и пограничный слой для линейных дифференциальных уравнений с малым параметром // УМН. 1957. Т. 12. №. 5. С. 3–122.
  14. Danilov V.G., Gaydukov R.K. Vortices in the Prandtl boundary layer induced by irregularities on a plate // Russ. J. Math. Phys. 2015. V. 22. № 2. P. 161–173.
  15. Danilov V.G., Gaydukov R.K. Equations for velocity oscillations in problems of a fluid flow along a plate with small periodic irregularities on the surface for large Reynolds numbers // Proc. Int.Conf. DAYS on DIFFRACTION 2018. IEEE, 2018. P. 118–123.
  16. Danilov V.G., Gaydukov R.K. Multideck structures of boundary layers in compressible flows // Proc. Int.Conf. DAYS on DIFFRACTION 2019. IEEE, 2019. P. 51–56.
  17. Гайдуков Р.К., Данилов В.Г. Многопалубные структуры в задачах обтекания поверхностей с малыми периодическими возмущениями // XII Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики: сборник трудов в 4 томах. Т. 2: Механика жидкости и газа. Уфа: РИЦ БашГУ, 2019. С. 92–94.
  18. Mauss J. Asymptotic Modelling for separating boundary layers // Asymptotic Modelling in Fluid Mechanics. Lecture Notes in Physics, vol 442. Springer, 1995. P. 239–254.
  19. Ландау Л.Д., Лифшиц Е.М. Теоретическая физика. Том 6. Гидродинамика. М.:Физматлит, 2006. 736 с.
  20. Meirmanov A.M. The Stefan Problem. De Gruyter, 1992. 255 p.
  21. Caginalp G. An analysis of a phase field model of a free boundary // Arch. Ration. Mech. Anal. 1986. V. 92. № 3. P. 205–245.
  22. Caginalp G. Stefan and Hele-shaw type models as asymptotic limits of the phase field equations // Phys. Rev. A. 1989. V. 39. P. 5887–5896.
  23. Медведев Д.А., Ершов А.П. Моделирование намерзания льда на подводной трубе газопровода // Вестн. НГУ. Сер. матем., мех., информ. 2013. Т. 13. № 4. С. 96–101.
  24. Makkonen L. On the Methods To Determine Surface Energies // Langmuir. 2000. V. 16. № 20. P. 7669–7672.
  25. Ward C.A., Neumann A.W. On the surface thermodynamics of a two-component liquid-vapor-ideal solid system // J. Colloid and Interface Sci. 1974. V. 49. № 2. P. 286–290.
  26. Spelt J.K., Absolom D.R., Neumann A.W. Solid surface tension: The interpretation of contact angles by the equation of state approach and the theory of surface tension components // Langmuir. 1986. V. 2. № 5. P. 620–625.
  27. Della Volpe C., Siboni S., Morra M. Comments on Some Recent Papers on Interfacial Tension and Contact Angles // Langmuir. 2002. V. 18. № 4. P. 1441–1444.
  28. Mazhukin V.I. Kinetics and Dynamics of Phase Transformations in Metals Under Action of Ultra-Short High-Power Laser Pulses // Laser Pulses: Theory, Technology, and Applications. IntechOpen, 2012. P. 219–276.
  29. Rodway G.H., Hunt J.D. Thermoelectric investigation of solidification of lead I. Pure lead // J. Crystal Growth. 1991. V. 112. № 2–3. P. 554–562.
  30. Plotnikov P.I., Starovoitov V.N. The Stefan problem with surface tension as a limit of the phase field model // Differ. Equat. 1993. V. 29. № 3. P. 395–404.
  31. Danilov V.G., Omel’yanov G.A., Radkevich E.V. Hugoniot-type conditions and weak solutions to the phase-field system // Eur. J. Appl. Math. 1999. V. 10. P. 55–77.
  32. Danilov V.G., Omel’yanov G.A., Shelkovich V.M. Weak asymptotics method and interaction of nonlinear waves // Asymptotic Methods of Wave and Quantum Problems. AMS Transl. Ser. 2, Vol. 208. AMS, 2003. P. 33–165.
  33. Кикоин И.К. Таблицы физических величин. Справочник. М.: Атомиздат, 1976. 1008 с.
  34. Григорьев И.C., Мейлихов Е.З. Физические величины. Справочник. М.: Энергоатомиздат, 1991. 1232 с.
  35. Кузнецов В.В., Усть-Качкинцев В.Ф. Физическая и коллоидная химия: Учебное пособие. М.:Высшая школа, 1976. 390 с.
  36. Fernandez R., Barduhn A.J. The growth rate of ice crystals // Desalination. 1967. V. 3. № 3. P. 330–342.
  37. Roache P.J. Fundamentals of Computational Fluid Dynamics. Hermosa Publishers, 1976. 648 p.
  38. Yapalparvi R. Double-deck structure revisited // Eur. J. Mech. B/Fluids. 2012. V. 31. P. 53–70.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2.

Download (30KB)
Indexing metadata
3.

Download (163KB)
Indexing metadata
4.

Download (61KB)
Indexing metadata
5.

Download (53KB)
Indexing metadata
6.

Download (98KB)
Indexing metadata
7.

Download (90KB)
Indexing metadata
8.

Download (179KB)
Indexing metadata

Copyright (c) 2023 Russian Academy of Sciences

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies