# A Mathematical Model of Gas Suspension with Chemical Reactions in the Pair-Interaction Approximation

Yu.M. Kovalev, E.E. PigasovIn this paper we propose a mathematical model describing the transition of solid unitary fuel from combustion to explosion in a two-phase heterogeneous gas-solid environment. The model is invariant under the Galilean transformations. It turned out that the existing mathematical models of this phenomenon lack invariance under the Galilean transformations. We studied in detail the reasons making the conservation laws not invariant and eliminated them in the model we propose.Full text

- Keywords
- mathematical model; invariance; multi-component mixture; heterogeneous environments.
- References
- 1. Kovalev Yu.M., Cheremokhov A.Yu. [Weakening of Air Shock Waves System Lattices]. Problems of Atomic Science and Technology. Series: Mathematical Modelling of Physical Processes, 1997, vol. 3, pp. 39-43. (in Russian)

2. Kuropatenko V.F. New Models of Continuum Mechanics. Journal of Engineering Physics and Thermophysics, 2011, vol. 84, no. 1, pp. 77-99. DOI: 10.1007/s10891-011-0457-0

3. Grishin A.M., Kovalev Yu.М. [Experimental Study on the Impact of the Explosion of Condensed Explosives to the Front Crown Forest Fire]. Doklady Akademii Nauk, 1989, vol. 308, no. 5, pp. 1074-1078. (in Russian)

4. Grishin A.M., Kovalev Yu.M. Experimental and Theoretical Investigation of the Effect of an Explosion on the Front of Crown Forest Fires. Combustion, Explosion, and Shock Waves, 1989, vol. 25, no. 6, pp. 724-730. DOI: 10.1007/BF00758739

5. Kovalev Yu.M., Kuropatenko V.F. [Analysis of the Invariance of Some Mathematical Models of Multi-Media]. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 2012, no. 11 (270), pp. 4-7. (in Russian)

6. Kovalev Yu.M., Kuropatenko V.F. [Analysis of the Invariance under the Galilean Transformation of Some Mathematical Models of Multi-Media]. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming & Computer Software, 2012, no. 27 (286), pp. 69-73. (in Russian)

7. Vainshtein P.B., Nigmatulin R.I., Popov V.V., Rakhmatulin H.A. Nonstationary Problems of the Combustion of Aerosuspensions in Fuel that Contains the Oxidant. Fluid Dynamics, 1981, vol. 16, issue 1, pp. 14-19. DOI: 10.1007/BF01094807

8. Baer M., Nunziato J. F Two-Phase Mixture Theory for the Deflagration-to-Detonation Transition (DDT) in Reactive Granular Materials. Int. J. Multiphase Flow, 1986, vol. 12, pp. 861-889. DOI: 10.1016/0301-9322(86)90033-9

9. Kovalev Yu.M. [Analysis of Invariance under Galilean Transformations of Two-Phase Mathematical Models of Heterogeneous Enveronment]. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 2014, vol. 6, no. 1, pp. 30-35. (in Russian)

10. Kovalev Yu.M., Kovaleva E.A. Mathematical Analysis of Two-Phase Mixtures of Conservation. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming & Computer Software, 2014, vol. 7, no. 2, pp. 29-37. (in Russian)

11. Ivandeev A.I., Kutushev A.G., Nigmatulin R.I. [Gas Dynamics of Multiphase Media. Shock and Detonation Waves in Gas Suspensions]. Itogi nauki i tekhniki. Mekhanika zhidkosti i gaza [Results of Science and Technology. Series: Fluid Mechanics], 1981. vol. 16, pp. 209-287. (in Russian)

12. Nigmatulin R.I. Osnovi mehaniki geterogennih sred [Fundamentals of Mechanics of Heterogeneous Enveronment]. Moscow, 1978. 336 p.