Volume 7, no. 2Pages 29 - 37
A Mathematical Study of the Conservation Equation for Two-Phase MixturesYu.M. Kovalev, E.A. Kovaleva
We study the invariance under the Galilean transformations of the Baer - Nunziato equations for interpenetrating interacting flows which describe the transition from combustion to explosion in two-phase mixtures. We show that the original Baer - Nunziato model is invariant. In addition, we establish the invariance of the kinetic and total energy equations for the components and mixture. But the conservation equations for the total energy of the mixture in the Baer - Nunziato model and in the model of Nigmatulin's group have different behavior. Thus, additional study is required to choose the model describing more adequately the transition from combustion to explosion in two-phase mixtures. Full text
- mathematical model; invariance; multicomponent mixture.
- 1. Grishin А.М., Kovalev Yu.М. [Experimental Study on the Impact of the Explosion of Condensed Explosives on the Front Crown Forest Fire]. Doklady Akademii Nauk, 1989, vol. 308, no. 5, pp. 1074-1078. (in Russian)
2. Grishin А.М., Kovalev Yu.М. [Experimental and Theoretical Study of the Interaction of the Explosion on the Front Crown Forest Fire]. Combustion, Explosion, and Shock Waves, 1989, vol. 25, issue 6, pp. 724-730. DOI: 10.1007/BF00758739
3. Kovalev Yu.М., Cheremokhov A.Yu. [The Weakening of the System of Air Shock Wave Gratings]. Voprosy atomnoy nauki i tekhniki. Seriya: Matematicheskoe modelirovanie fizicheskikh protzessov [Problems of Atomic Science and Technology. Series: Mathematical Modelling of Physical Processes], 1997, no. 3, pp. 39-43. (in Russian)
4. Nigmatulin R.I. Osnovy mekhaniki geterogennykh sred [Fundamentals of Mechanics of Heterogeneous Media]. Moscow, Nauka, 1978. 336 p.
5. Kuropatenko V.F. [New Models of Continuum Mechanics]. [Novie modeli mechanici sploshnikhsred]. Journal Engineering Physics and Thermophysics , 2011, vol. 84, no. 1, pp. 74-92. (in Russian) DOI: 10.1007/s10891-011-0457-0
6. Rakhmatulin K.A. [Fundamentals of gas dynamics of interpenetrating motions of compressible media]. Prikladnaya matematika i mekhanika [Journal of Applied Mathematics and Mechanics], 1956, vol. 20, no. 27, pp. 184-195. (in Russian)
7. Kovalev Yu.М., 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)
8. Kovalev Yu.М., 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), issue 12, pp. 69-73. (in Russian)
9. Baer M.F, Nunziato J. 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
10. Vaynshteyn 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, no. 1, pp. 14-19. DOI: 10.1007/BF01094807