The effect of the properties of a real gas on solution of riemann problem in detonating gas

DOI: 10.34759/trd-2022-123-10

Аuthors

Gidaspov V. Y.^*, Duong M. D.^**

*e-mail: gidaspov@mai.ru
**e-mail: dmd.lqd@gmail.com

Abstract

The article considers a self-similar Riemann problem on the border between multicomponent gases which properties are being described by a virial thermal equation of state with a single-fluid mixing model. A physical-and-mathematical model, computational algorithms and numerical simulation results are presented. The computational model is implemented for the three cases, namely, the first one is “frozen”, i.e. physico-chemical processes in gases do not originate, and the components concentrations do not change. The second one is “equilibrium”, which means that concentrations of chemical components satisfy the chemical equilibrium conditions. The third is a combined one, i.e. the of components concentrations to the left and right of the gap can be eother “frozen” or “equilibrium”. The solution of Riemann problem always includes a discontinuity separating the initial gas mixtures and, depending on the initial parameters, a fan of rarefaction waves or a shock wave propagating to the left and right of the discontinuity. In the case of an explosive mixture, a recompressed detonation wave or a Chapman-Jouget detonation wave with a fan of rarefaction waves docked to it can propagate through it, while it is assumed that the composition of the combustion products is equilibrium.

A computational algorithm has been developed for solving the corresponding system of differential-algebraic equations expressing the laws of conservation of mass, momentum and energy for the cases of continuous flows (fan of rarefaction waves) and discontinuous flows (shock and detonation waves), supplemented by thermal and caloric equations of state and, if necessary, thermodynamic equilibrium conditions.

Computational and theoretical studies of the decay of the gap at the boundary: argon – methane-air combustible mixture and helium – hydrogen-air combustible mixture have been performed. The initial data ranges at which the results of calculations using the thermal equation of state of real and perfect gases differ significantly are determined.

Keywords:

real gas, equilibrium adiabatic, detonation, thermodynamic modeling, decay of an arbitrary gap in an equilibrium-reacting and detonating gas

References

1. Jouget E. On the propogation of chemical reaction in gases, Journal of Inequalities in Pure and Applied Mathematics, 1905, Online ISSN: 1443-5756, no. 7, pp. 347-425.

2. Zel'dovich Ya.B. Teoriya goreniya i detonatsii gazov (Theory of combustion and detonation of gases), Moscow, Izd-vo AN SSSR, 1944, 71 p.

3. Bam-Zelikovich G.M. Teoreticheskaya gidromekhanika, 1949, no. 4, pp. 112-141.

4. Godunov S.K., Zabrodin A.V., Ivanov M.Ya., Kraiko A.N., Prokopov G.P. Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki (Numerical solution of multidimensional problems of gas dynamics), Moscow, Nauka, 1976, 400 p.

5. Chernyi G.G. Gazovaya dinamika (Gas dynamics), Moscow, Nauka, 1988, 424 p.

6. Gidaspov V.Yu. Matematicheskoe modelirovanie, 2006, vol. 18, no. 8, pp. 64-76.

7. Gidaspov V.Yu., Severina N.S. Nekotorye zadachi fizicheskoi gazovoi dinamiki (Some problems of physical gas dynamics), Moscow, Izd-vo MAI, 2016, 196 p.

8. Belov G.V. Termodinamicheskoe modelirovanie: metody, algoritmy, programmy (Thermodynamic modeling: methods, algorithms, programs), Moscow, Nauchnyi Mir, 2002, 184 p.

9. Orlenko L.P. Fizika vzryva (Explosion physics), Moscow, Fizmatlit, 2004, vol. 1, 832 p.

10. Gidaspov V.Yu. Trudy MAI, 2013, no. 66. URL: https://trudymai.ru/eng/published.php?ID=40233

11. Gidaspov V.Yu. Trudy MAI, 2011, no. 49. URL: https://trudymai.ru/eng/published.php?ID=28605&PAGEN_2=3

12. Gidaspov V.Yu. Vestnik Moskovskogo aviatsionnogo instituta, 2010, vol. 17, no. 6, pp. 72-79.

13. Pogosbekyan M.Yu., Sergievskaya A.L., Krupnov A.A. Trudy MAI, 2018, no. 102. URL: https://trudymai.ru/eng/published.php?ID=98822

14. Kuli-zade M.E., Reshetnikova O.F., Skorokhod E.P. Trudy MAI, 2018, no. 98. URL: https://trudymai.ru/eng/published.php?ID=90094

15. Nazyrova R.R. Trudy MAI, 2017, no. 92. URL: http://trudymai.ru/eng/published.php?ID=76946

16. Nazyrova R.R. Matematicheskoe modelirovanie, 2018, vol. 30, no. 1, pp. 76-90.

17. Duong Minh Dyk. Trudy MAI, 2021, no. 120. URL: URL: https://trudymai.ru/eng/published.php?ID=161415. DOI: 10.34759/trd-2021-120-03

18. Duong Minh Dyk., Gidaspov V.Yu. Trudy MAI, 2020, no. 112. URL: URL: https://trudymai.ru/eng/published.php?ID=116331. . DOI: 10.34759/trd-2020-112-4

19. Girshfel'der D., Kertiss Ch., Berd R. Molekulyarnaya teoriya gazov i zhidkosti (Molecular theory of gases and liquids), Moscow, Izd-vo Inostrannoi literatury, 1961, 929 p.

20. Gibbs Dzh. V. Termodinamika. Statisticheskaya mekhanika (Thermodynamics. Statistical mechanics), Moscow, Nauka, 1982, 584 p.

21. Vatolin N.A., Moiseev G.K., Trusov B.G. Termodinamicheskoe modelirovanie v vysokotemperaturnykh neorganicheskikh smesyakh (Thermodynamic modeling in high-temperature inorganic mixtures), Moscow, Metallurgiya, 1994, 352 p.

22. Nedostup V.I., Gal'kevich E.P., Kaminskii E.S. Termodinamicheskie svoistva gazov pri vysokikh temperaturakh i davleniyakh (Thermodynamic properties of gases at high temperatures and pressures), Kiev, Nauka dumka, 1990, 196 p.

23. Gurvich L.V., Veits I.V., Medvedev V.A. et al. Termodinamicheskie svoistva individual'nykh veshchestv (Thermodynamic properties of individual substances), Moscow, Nauka, 1978.

24. Rid R., Prausnits Dzh., Shervud T. Svoistva gazov i zhidkostei (Properties of gases and liquids), Leningrad, Khimiya, 1982, 592 p.

25. Ryabin V.A., Ostroumov M.A., Svit T.F. Termodinamicheskie svoistva veshchestv (Thermodynamic Properties of Substances), Leningrad, Khimiya, 1977, 392 p.

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