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Numerical modeling of the relaxation of a body behind the transmitted shock wave
 
PIIS023408790001930-7-1
Publication type Article
Status Published
Authors
D. Sidorenko 
Affiliation: Institute for Computer Aided Design of Russian Academy of Sciences
Address: Russian Federation
P. Utkin
Affiliation: Moscow Institute of Physics and Technology
Address: Russian Federation
Journal nameMatematicheskoe modelirovanie
EditionVolume 30 Number 11
Pages91-104
Abstract

The problem of a planar shock wave – cylinder with different mass interaction is considered. The cylinder can move translationally under the action of the pressure force. The statement qualitatively corresponds to the problem of a particle relaxation behind the transmitted shock wave. Mathematical model is based on two-dimensional Euler equations. Numerical algorithm is based on the Cartesian grid method for the simulations of flows in the areas with varying geometry. The algorithm and its program realization are tested on the problem about the lifting of the cylinder behind the transmitted shock wave. The curves of the cylinder speed variation in time are plotted. The explanations about the qualitative view of the curves for the different cylinders masses are given. For one mass the analysis of the dynamics of the relaxation process is carried out from the point of view of the non-stationary shock waves patterns that are realized as a result of shock wave – cylinder interaction.

Keywordsshock wave, moving cylinder, numerical modeling, Cartesian grid method, Euler equations
Received09.11.2018
Publication date21.11.2018
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1. V.M. Boiko, V.P. Kiselev, S.P. Kiselev, A.N. Papyrin, S.V. Poplavsky, V.M. Fomin. Shock wave interaction with a cloud of particles // Shock Waves, 1997, v.7, p.275-285.
2. J.D. Regele, J. Rabinovitch, T. Colonius, G. Blanquart. Unsteady effects in dense, high speed, particle laden flows // Int. J. Multiphase Flow, 2014, v.61, p.1-13.
3. D.A. Sidorenko, P.S. Utkin. Kompleksnyj podkhod k probleme chislennogo issledovaniya vzaimodejstviya udarnoj volny s plotnym oblakom chastits // Gorenie i vzryv, 2017, t.10, №2, s.47-51;
4. P.S. Utkin. Matematicheskoe modelirovanie vzaimodejstviya udarnoj volny s plotnoj zasypkoj chastits v ramkakh dvukhzhidkostnogo podkhoda // Khim. fizika, 2017, t.36, №11, s.61-71;
5. I.A. Bedarev, A.V. Fedorov. Pryamoe modelirovanie relaksatsii neskol'kikh chastits za prokhodyaschimi udarnymi volnami // Inzh.-fiz. zhurnal, 2017, t.90, №2, s.450-457
6. D. Drikakis, D. Ofengeim, E. Timofeev, P. Voionovich. Computation of non-stationary shock wave/cylinder interaction using adaptive-grid methods // J. Fluids and Structures, 1997, v.11, №6, p.665-692.
7. K. Luo, Y. Luo, T. Jin, J. Fan. Studies on shock interactions with moving cylinders using immersed boundary method // Phys. Rev. Fluids, 2017, v.2, paper 064302.
8. Y. Sakamura, M. Oshima, K. Nakayama, K. Motoyama. Shock-induced motion of a spherical particle floating in air // Proc. 31st Int. Symp. on Shock Waves, Nagoya, Japan, 9–14 July 2017, p. 249.
9. I.S. Men'shov, M.A. Kornev. Metod svobodnoj granitsy dlya chislennogo resheniya uravnenij gazovoj dinamiki v oblastyakh s izmenyayuschejsya geometriej // Mat. mod., 2014, t.26, №5, s.99-112;
10. V.P. Kolgan. Primenenie printsipa minimal'nykh znachenij proizvodnoj k postroeniyu konechnoraznostnykh skhem dlya rascheta razryvnykh reshenij gazovoj dinamiki // Uchenye zapiski TsAGI, 1972, t.3, №6, s.68-77;
11. A. Chertock, A. Kurganov. A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries // Comm. Math. Sci., 2008, v.6, №3, p.531-556.
12. S.K. Sambasivan, H.S. Udaykumar. Ghost fluid method for strong shock interactions. Part 2: Immersed solid boundaries // AIAA J., 2009, v.47, №12, p.2923-2937.
13. M. Arienti, P. Hung, E. Morano, J.E. Shepherd. A level set approach to Eulerian – Lagrangian coupling // J. Comp. Phys., 2003, v.185, №1, p.213-251.
14. S. Tan, C.-W. Shu. A high order moving boundary treatment for compressible inviscid flows // J. Comp. Phys., 2011, v.230, №15, p.6023-6036.
15. H. Forrer, M. Berger. Flow simulations on Cartesian grids involving complex moving geometries // Proc. 7th Int. Conf. Hyper. Probl.: Theory, Numerics, Appl., 1999, Zurich, v.1, p.315-324.
16. K.M. Shyue. A moving-boundary tracking algorithm for inviscid compressible flow // Proc. 11th Int. Conf. Hyper. Probl.: Theory, Numerics, Appl., 2008, Lyon, July 17–21, 2006, p.989-996.
17. W.D. Henshaw, D.W. Schwendeman. Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow // J. Comp. Phys., 2006, v.216, №2, p.744-779.
18. B. Muralidharan, S. Menon. Simulations of unsteady shocks and detonation interactions with structures // Proc. 49th AIAA/ASME/SAE/ASEE Joint Prop. Conf. 2013, San Jose, CA, USA, July 14–17, 2013, AIAA p.2013-3655
19. V. Gol'dsmit. Udar. Teoriya i fizicheskie svojstva soudaryaemykh tel. – M.: Izd-vo liter. po stroitel'stvu, 1965, 448 s.
20. R.R. Nourgaliev, T.N. Dinh, T.G. Theofanous, J.M. Koning, R.M. Greenman, G.T. Nakafuji. Direct numerical simulation of disperse multiphase high-speed flows // Proc. 42nd AIAA Aerospace Sci. Meet.&Exhibit, Reno, Nevada, USA, January 5–8, 2004, AIAA p.2004-1284.
21. I.V. Abalakin, N.S. Zhdanova, T.K. Kozubskaya. Realizatsiya metoda pogruzhennykh granits dlya modelirovaniya zadach vneshnego obtekaniya na nestrukturirovannykh setkakh // Mat. mod., 2015, t.27, №10, s.5-20;

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