Email this article 
MODELING OF ICE-WATER PHASE TRANSITION IN A PIPE WITH SMALL ICE BUILDUPS ON THE WALL
- Authors: Gaidukov R.K.1, Danilov V.G.1
-
Affiliations:
- National Research University—Higher School of Economics (HSE University)
- Issue: Vol 64, No 6 (2024)
- Pages: 1055-1063
- Section: Mathematical physics
- URL: https://journal-vniispk.ru/0044-4669/article/view/273770
- DOI: https://doi.org/10.31857/S0044466924060134
- EDN: https://elibrary.ru/XYDHYY
- ID: 273770
Cite item
Open Access
Access granted
Subscription Access
Abstract
The mathematical modeling of the ice-water phase transition during fluid flow inside a pipe with a small ice buildup on the wall at high Reynolds numbers is considered. As a mathematical model describing the dynamics of the phase transition, a double-deck boundary layer model and a phase field system are used. The results of numerical simulation are presented.
About the authors
R. K. Gaidukov
National Research University—Higher School of Economics (HSE University)
Email: roma1990@gmail.com
Moscow, 109028 Russia
V. G. Danilov
National Research University—Higher School of Economics (HSE University)Moscow, 109028 Russia
References
- Danilov V. G., Gaydukov R. K. Ice-water phase transition on a substrate // Rus. J. Math. Phys. 2023. V. 30. P. 165–175.
- Гайдуков Р. К., Данилов В. Г., Фонарева А. В. Моделирование таяния-намерзания льда в задаче обтекания жидкостью малой неровности // Изв. РАН. Механ. жидкости и газа, в печати, 2023.
- Aydın O., Avcı M. Viscous-dissipation effects on the heat transfer in a poiseuille flow, 2006.
- Danilov V. G., Gaydukov R. K. Double-deck structure of the boundary layer in the problem of flow in an axially symmetric pipe with small irregularities on the wall for large Reynolds numbers // Rus. J. Math. Phys. 2017. V. 24. P. 1–18.
- Meirmanov A. M. The Stefan Problem. De Gruyter, 1992.
- Caginalp G. An analysis of a phase field model of a free boundary // Arch. Ration. Mech. Anal. 1986. V. 92. P. 205–245.
- 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.
- Медведев Д. А., Ершов А. П. Моделирование намерзания льда на подводной трубе газопровода // Вестн. НГУ. Сер. матем., мех., информ. 2013. Т. 13. С. 96–101.
- Gaydukov R. K. Double-deck structure in the fluid flow problem over plate with small irregularities of timedependent shape // Europ. J. Mech. B/Fluid. 2021. V. 89. P. 401–410.
- Fonareva A. V., Gaydukov R. K. Nonstationary double-deck structure of boundary layers in compressible flow problem inside a channel with small irregularities on the walls // Rus. J. Math. Phys. 2021. V. 28. P. 224–243.
- Fernandez R., Barduhn A. J. The growth rate of ice crystals // Desalinat. 1967. V. 3. P. 330–342.
- 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. P. 395–404.
- Danilov V. G., Omel’yanov G. A., Radkevich E. V. Hugoniot-type conditions and weak solutions to the phasefield system // Europ. J. Appl. Math. 1999. V. 10. P. 55–77.
- Danilov V. G., Omel’yanov G. A., Shelkovich V. M. Weak asymptotics method and interaction of nonlinear waves, 2003.
- Roache P. J. Computational fluid dynamics. Hermosa Publ., Albuquerque, 1976.
- Yapalparvi R. Double-deck structure revisited // Europ. J. Mech. B/Fluid. 2012. V. 31. P. 53–70.
- Кикоин И. К. Таблицы физических величин. Справочник. М.: Атомиздат, 1976.
- Григорьев И. C., Мейлихов Е. З. Физические величины. Справочник. М.: Энергоатомиздат, 1991.
- Кузнецов В. В., Усть-Качкинцев В. Ф. Физическая и коллоидная химия: Уч. пособие. М.: Высш. школа, 1976.
Supplementary files
