Geodesic
Numerical simulation of a jet impact on a wall
Matematičeskoe modelirovanie, Tome 29 (2017) no. 3, pp. 123-138.

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

A technique of computing high-speed liquid jet impact on a wetted wall has been realized. During such impact shock waves arise in the jet, in the liquid layer on the wall and in the gas surrounding the liquid, the interphase boundary strongly deforms. The technique is based on the CIP-CUP method along with the dynamically adaptive soroban-grids. The gas dynamics equations describing the liquid and gas flow are integrated without explicit separation of the liquidgas boundary. Such an approach is shown to be efficient for the problems considered. It allows one to obtain the solution without oscillations in the vicinity of the contact boundaries, including their interaction with the shock waves. For the purposes of illustration, results of computing a number of one- and two-dimensional problems with the features characteristic of the high-speed liquid jet impact on a wall as well as their comparison with the known analytic and numerical solutions are presented and also some results of computation of the problem of the high-speed liquid jet impact on a wall covered by a thin liquid layer are given.
Keywords: shock waves, contact boundary, CIP-CUP method, adaptive soroban-grids. 
@article{MM_2017_29_3_a9,
     author = {A. A. Aganin and T. S. Guseva},
     title = {Numerical simulation of a jet impact on a wall},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {123--138},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_3_a9/}
}
TY  - JOUR
AU  - A. A. Aganin
AU  - T. S. Guseva
TI  - Numerical simulation of a jet impact on a wall
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 123
EP  - 138
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_3_a9/
LA  - ru
ID  - MM_2017_29_3_a9
ER  - 
%0 Journal Article
%A A. A. Aganin
%A T. S. Guseva
%T Numerical simulation of a jet impact on a wall
%J Matematičeskoe modelirovanie
%D 2017
%P 123-138
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_3_a9/
%G ru
%F MM_2017_29_3_a9
A. A. Aganin; T. S. Guseva. Numerical simulation of a jet impact on a wall. Matematičeskoe modelirovanie, Tome 29 (2017) no. 3, pp. 123-138. http://geodesic.mathdoc.fr/item/MM_2017_29_3_a9/

[1] F. P. Bowden, J. H. Brunton, “The deformation of solids by liquid impact at supersonic speeds”, Proc. R. Soc. Lond. A, 263 (1961), 433–450 | DOI

[2] N. K. Bourne, “On impacting liquid jets and drops onto polymethylmethacrylate targets”, Proc. R. Soc. A, 461 (2005), 1129–1145 | DOI

[3] M. Kornfeld, L. Suvorov, “On the destructive action of cavitation”, J. Appl. Phys., 15 (1944), 495–506 | DOI

[4] N. A. Hawker, Y. Ventikos, “Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study”, J. Fluid Mech., 701 (2012), 59–97 | DOI | Zbl

[5] Yu. P. Golovachev, E. A. Notkina, A. V. Chizhov, A. A. Schmidt, “Simulation of free-surface flows involving shock waves”, Comput. Math. Math. Phys., 41:1 (2001), 151–162 | MR | Zbl

[6] A. A. Aganin, T. F. Khalitova, N. A. Khismatullina, “Metod chislennogo resheniya zadach silnogo szhatiya nesfericheskogo kavitatsionnogo puzyrka”, Vychislitelnye tekhnologii, 15:1 (2010), 14–32

[7] R. Abgrall, S. Karni, “Computations of compressible multifluids”, J. Comp. Phys., 169 (2001), 594–623 | DOI | MR | Zbl

[8] T. Yabe, P. Y. Wang, “Unified numerical procedure for compressible and incompressible fluid”, J. Phys. Soc. Japan, 60:7 (1991), 2105–2108 | DOI | MR

[9] A. A. Aganin, T. S. Guseva, “Chislennoe modelirovanie kontaktnogo vzaimodeistviia szhimaemykh sred na eilerovykh setkakh”, Uchenye Zapiski Kazanskogo Universiteta. Seriia Fiziko-Matematicheskie Nauki, 154, no. 4 (2012), 74–99

[10] A. A. Aganin, T. S. Guseva, “Raschet kontaktnogo vzaimodeistviia szhimaemykh sred bez iavnogo vydeleniia mezhfaznykh granits”, Vestn. Bashkir. Univ., 18:3 (2013), 646–661

[11] K. Takizawa, T. Yabe, Y. Tsugawa, T. E. Tezduyar, H. Mizoe, “Computation of free-surface flows and fluid-object interactions with the CIP method based on adaptive meshless Soroban grids”, Comput. Mech., 40 (2007), 167–183 | DOI | MR | Zbl

[12] A. Staniforth, J. Cote, “Semi-Lagrangian integration schemes for atmospheric models — A review”, Mon. Weather Rev., 119 (1991), 2206–2223 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[13] T. Yabe, F. Xiao, T. Utsumi, “The constrained interpolation profile method for multiphase analysis”, J. Comput. Phys., 169:2 (2001), 556–593 | DOI | MR | Zbl

[14] Y. Ogata, T. Yabe, “Shock capturing with improved numerical viscosity in primitive Euler representation”, Comput. Phys. Commun., 119:2–3 (1999), 179–193 | DOI | Zbl

[15] M. B. Lesser, “Analytic solutions of liquid-drop impact problems”, Proc. R. Soc. Lond. A, 377 (1981), 289–308 | DOI | MR

[16] J. E. Field, M. B. Lesser, J. P. Dear, “Studies of Two-Dimensional Liquid-Wedge Impact and Their Relevance to Liquid-Drop Impact Problems”, Proc. R. Soc. Lond. A, 401 (1985), 225–249 | DOI

[17] F. J. Heymann, “High-speed impact between a liquid drop and a solid surface”, J. Appl. Phys., 40:13 (1969), 5113–5122 | DOI

[18] S. L. Sun, G. X. Wu, “Oblique impact of a water cone on a solid wall”, European Journal of Mechanics B/Fluids, 43 (2014), 120–130 | DOI | MR | Zbl

[19] V. V. Podlubnyi, A. S. Fonarev, “Reflection of a spherical blast wave from a planar surface”, Fluid Dynamics, 9:6 (1974), 921–926 | DOI