Geodesic
Three-dimensional simulation of a tank filling with a viscous fluid using the VOF method
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 670-677.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper presents the results of 3D modeling of a Newtonian fluid flow with a free surface. The PLIC-VOF algorithm, which is developed to solve the problems of two-dimensional fluid flows with a free surface, is generalized to the case of three-dimensional flows. Efficiency of the developed algorithm and reliability of the obtained results are justified by comparing with available data in literature and by testing approximation convergence. Parametric calculations of a rectangular channel filling show that the free surface assumes a steady convex shape over time and then moves along the channel at a constant velocity. As a result of parametric studies, the dependences of geometric characteristics of the free surface shape on problem parameters have been plotted.
Keywords: Newtonian fluid flow, filling of a rectangular channel, free surface, 3D modeling, numerical simulation, VOF method, flow structure. 
@article{JSFU_2020_13_6_a1,
     author = {Evgeny I. Borzenko and Efim I. Hegaj},
     title = {Three-dimensional simulation of a tank filling with a viscous fluid using the {VOF} method},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {670--677},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a1/}
}
TY  - JOUR
AU  - Evgeny I. Borzenko
AU  - Efim I. Hegaj
TI  - Three-dimensional simulation of a tank filling with a viscous fluid using the VOF method
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 670
EP  - 677
VL  - 13
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a1/
LA  - en
ID  - JSFU_2020_13_6_a1
ER  - 
%0 Journal Article
%A Evgeny I. Borzenko
%A Efim I. Hegaj
%T Three-dimensional simulation of a tank filling with a viscous fluid using the VOF method
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 670-677
%V 13
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a1/
%G en
%F JSFU_2020_13_6_a1
Evgeny I. Borzenko; Efim I. Hegaj. Three-dimensional simulation of a tank filling with a viscous fluid using the VOF method. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 670-677. http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a1/

[1] I.A. Glushkov et al., Simulation of the molding of articles from free-molding compositions, Arkhitektura-S, M., 2007 (in Russian)

[2] N.D. Katopodes, Free-Surface Flow: Computational Methods, Butterworth-Heinemann, 2019

[3] B.D. Nichols, C.W. Hirt, R.S. Hotchkiss, SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries, Los Alamos Scientific Laboratory Report, LA-8355, 1980

[4] W. Jang, J. Jilesen, F.S. Lien, N. Ji, “A study on the extension of a VOF/PLIC based method to a curvilinear co-ordinate system”, International Journal of Computational Fluid Dynamics, 22:4 (2008), 241–257 | DOI | MR | Zbl

[5] A. Issakhov, Y. Zhandaulet, A. Nogaeva, “Numerical simulation of dam break flow for various forms of the obstacle by VOF method”, International Journal of Multiphase Flow, 109 (2018), 191–206 | DOI | MR

[6] D.M. Hargreaves, H.P. Morvan, N.G. Wright, “Validation of the Volume of Fluid Method for Free Surface Calculation: The Broad-Crested Weir”, Engineering Applications of Computational Fluid Mechanics, 1:2 (2007), 136–146 | DOI

[7] S. Hansch, D. Lucas, T. Hohne, E. Krepper, Gu. Montoya, “Comparative Simulations of Free Surface Flows Using VOF-Methods and a New Approach for Multi-Scale Interfacial Structures”, Proceedings of the ASME Fluids Engineering Summer Meeting, 2013, FEDSM2013-16104 | DOI

[8] S. Saincher, J. Banerjee, “A Redistribution-Based Volume Preserving PLIC-VOF Technique”, Numerical Heat Transfer, 67 (2015), 338–362 | DOI

[9] X. Yin, I. Zaricos, N.K. Karadimitriou, A. Raoof, S.M. Hassanizadeh, “Direct simulations of two-phase flow experiments of different geometry complexities using Volume-of-Fluid (VOF) method”, Chemical Engineering Science, 195 (2018), 820–827 | DOI

[10] M. Karimi, H. Droghetti, D.L. Marchisio, “Multiscale Modeling of Expanding Polyurethane Foams via Computational Fluid Dynamics and Population Balance Equation”, Macromol. Symp., 360 (2016), 108–122 | DOI

[11] L.G. Loytsyansky, Fluid and Gas Mechanics, Gostekhizdat, M.–L., 1950

[12] S. Patankar, Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, 1980 | Zbl

[13] G.R. Shrager, A.N. Kozlobrodov, V.A. Yakutenok, Modeling of hydrodynamic processes in polymer processing technology, TGU Publ., Tomsk, 1999