Article 5120

Title of the article



Tukmakov Dmitriy Alekseevich, Candidate of physical and mathematical sciences, researcher, Federal Research Center “Kazan Scientific Center of the Russian Academy of Sciences” (2/31, Lobachevskogo street, Kazan, Russia), E-mail: 

Index UDK

57.043, 543; 51-7 




Background. The processes associated with the dynamics of multiphase media are found both in natural nature and in industrial technologies. The aim of this work is to study the influence of the dispersed component parameters on the reflection of a shock wave from a solid surface in a mono- and polydisperse dusty medium.
Materials and methods. To describe the dynamics of the carrier medium, a twodimensional system of Navier-Stokes equations is used, written with allowance for interphase force interaction and interphase heat transfer. To describe the dynamics of the dispersed phase, for each of its fractions, a system of equations is solved that includes the continuity equation for the “average density” of the fraction, the conservation equation for the spatial components of the momentum, and the conservation equation for the thermal energy of the gas suspension fraction.
Results. In this work, shock-wave processes in dusty media with a uniform composition of a dispersed phase and in dusty media with a dispersed phase are numerically modeled, the particles of which differed in the size and density of the material. The processes of motion and reflection of shock waves from a solid wall were studied depending on the parameters of the dispersed phase. The regularities of the effect of particle size on the intensity of the reflected shock wave in mono and polydisperse gas suspensions are determined.
Conclusions. The influence of the physical density of the dispersed phase and particle size on the characteristics of the shock wave reflected from the solid surface is revealed. The patterns revealed for a monodisperse gas suspension were generalized to the case of a dusty medium, the solid phase of which consists of several components with different physical properties of dispersed particles. 

Key words

multiphase media, mathematical modeling, multi-fraction mixture, inter-component interaction, shock waves, Navier-Stokes equation, explicit finitedifference scheme 

 Download PDF

1. Nigmatulin R. I. Dinamika mnogofaznykh sred [The dynamics of multiphase media]. Moscow: Nauka, 1987, part 1, 464 p. [In Russian]
2. Kutushev A. G. Matematicheskoe modelirovanie volnovykh protsessov v aerodispersnykh i poroshkoobraznykh sredakh [Mathematical modeling of wave processes in aero-dispersed and powdery media]. Saint-Petersburg: Nedra, 2003, 284 p. [In Russian]
3. Sternin L. E. Dvukhfaznye mono- i polidispersnye techeniya gaza s chastitsami [Twophase mono- and polydisperse gas flows with particles]. Moscow: Mashinostroenie, 1980, 176 p. [In Russian]
4. Fedorov A. V., Fomin V. M., Khmel' T. A. Volnovye protsessy v gazovzvesyakh chastits metallov [Wave processes in gas-suspended particles of metals]. Novosibirsk: Parallel', 2015, 301 p. [In Russian]
5. Verevkin A. A., Tsirkunov Y. M. Journal of Applied Mechanics and Technical Physics. 2008, vol. 49, no. 5, pp. 789–798.
6. Varaksin A. Y., Protasov M. V., Yatsenko V. P. High Temperature. 2013, vol. 51, no. 5, pp. 665–672.
7. Glazunov A. A., Dyachenko N. N., Dyachenko L. I. Thermophysics and Aeromechanics. 2013, vol. 20, no. 1, pp. 79–86.
8. Aref'ev K. Yu., Voronetskiy A. V., Suchkov S. A. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [University proceedings. Machine-building]. 2015, no. 10, pp. 17–30. [In Russian]
9. Hishida M., Fujiwara T., Wolanski P. Shock Waves. 2009, vol. 19, iss. 1, pp. 1–10.
10. Gubaidullin D. A., Tukmakov D. A. Mathematical Models and Computer Simulations. 2015, vol. 7, no. 3, pp. 246–253.
11. Nigmatulin R. I., Gubaidullin D. A., Tukmakov D. A. Doklady Physics. 2016, vol. 61, no. 2, pp. 70–73.
12. Tukmakov D. A. Lobachevskii Journal of Mathematics. 2019, vol. 40, no. 6, pp. 824–827.
13. Tukmakov D. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2019, no. 4 (52), pp. 121–131. [In Russian]
14. Fletcher C. A. Computation Techniques for Fluid Dynacmics. Berlin: Springer-Verlang, 1988, 502 p.
15. Kovenya V. M., Tarnavskiy G. A., Chernyy S. G. Primenenie metoda rasshchepleniya v zadachakh aerodinamiki [Application of the splitting method in aerodynamics issues]. Novosibirsk: Nauka. Sibir. otd., 1990, 247 p. [In Russian]
16. Tukmakov A. L. Acoustical Physics. 2009, vol. 55, no. 2, pp. 253–260.
17. Muzafarov I. F., Utyuzhnikov S. V. Matematicheskoe modelirovanie [Mathematical modeling]. 1993, vol. 5, no. 3, pp. 74–83. [In Russian]
18. Gel'fand B. E., Gubanov A. V., Medvedev S. P., Tsyganov S. A., Timofeev E. I. Doklady Akademii nauk SSSR [Reports of the USSR Academy of Sciences]. 1985, vol. 281, no. 5, pp. 1113–1116. [In Russian]
19. Ovsyannikov L. V. Lektsii po osnovam gazovoy dinamiki [Lectures on the basics of gas dynamics]. Moscow: Institut komp'yuternykh issledovaniy, 2003, 336 p. [In Russian]


Дата создания: 06.05.2020 16:20
Дата обновления: 06.05.2020 16:57