Numerical simulation of the clouds evolution in the ground explosion of the carrier-rocket
DOI:
https://doi.org/10.26577/jmmcs-2017-3-478Keywords:
explosion, proton-M, evolution, cloud, turbulenceAbstract
In this paper, the evolution of a cloud under the influence of the buoyancy force is considered, taking
into account turbulent mixing and adiabatic expansion. Numerical simulation is carried out on the
basis of the solution of the three-dimensional filtered non-stationary Navier-Stokes equation, the
continuity equation, the concentration equation, the enthalpy equation, and the equation of state
for compressible media. The modified solver is based on the OpenFOAM mathematical physics
library. To close the basic equations, a viscous model of turbulence is used. The dependence of the
height of the lifting of the fireball in the atmosphere on the thermodynamic parameters, during
the explosion of the Proton-M rocket carrier on July 2, 2013, was obtained.
References
[1] Tekhnicheskiye pravila vedeniya vzryvnykh rabot na dnevnoy poverkhnosti / pod red. F.A. Avdeyeva.- M: Nedra. 1972.
–P. 239.
[2] Ershin. Sh.A.. Sakipov. Z.B. Issledovaniye nachalnogo uchastka turbulentnoy strui szhimayemogo gaza // Zhurnal
tekhnicheskoy fiziki. – 1959. – Vol. 2.No.1. - P. 21-23.
[3] Ferziger and Peric, Computational Methods for Fluid Dynamics. - 3., rev. ed. – Berlin; Heidelberg; New York; Barcelona;
Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002. ISBN 3-540-42074-6,-P.251-253.
[4] Fizika vzryva / pod red. L.P. Orlenko. – M.: FIZMATLIT. 2002. - Izd. 3-e. pererabotannoye. - Vol. 1. -P. 832.
[5] Garnier, E., Adams, N., and Sagaut, P.: Large Eddy Simulation for Compressible Flows, doi:10.1007/978-90-481-2819-8,
Springer, the Netherlands,2009. -P.276.
[6] Gostintsev Yu.A.. Solodovnik A.F. Moshchnyy turbulentnyy termik v ustoychivo stratifitsirovannoy atmosfere. Chislennoye
modelirovaniye // PMTF. 1987. Vol.1. -P.47.
[7] Issa, R.I., Gosman, A.D., and Watkins, A.P. The Computation of Compressible and Incompressible Recirculating Flow
by a Non-Iterative Implicit Scheme, Journal of Computational Physics, 1986, -Vol.62. -P.66-82.
[8] Lapin, Yu.V.. Strelets, M.Kh. Vnutrenniye techeniya gazovykh smesey. – M.: Nauka. 1989, -P.368.
[9] Moin, P., Squires, K., Cabot, W., and Lee, S.: A dynamic subgrid scale model for compressible turbulence and scalar
transport, Phys. Fluids A-Fluid,1992. Vol.3, -P.2746, doi:10.1063/1.858164.
[10] Machta L. Eintrainment and the maximum height of an atomic cloud // Bull. Amer. Meteor. Soc. 1950. -Vol. 31. № 6. -P.
215–216.
[11] Nicoud, F. and Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow Turbul.
Combust.,1999. -Vol. 62. P. 183–200, doi:10.1023/A:1009995426001.
[12] Onufriyev, A.T. Teoriya dvizheniya vikhrevogo koltsa pod peystviyem sily tyazhesti. Podyem oblaka atomnogo vzryva //
PMTF. 1967. №2. -P.3-15.
[13] Piscaglia, F., Montorfano, A., and Onorati, A.: Towards the LES simulation of IC engines with parallel topologically
changing meshes, SAE Int. J. Engines, 6, 926–940, doi:10.4271/2013-01-1096, 2013.
[14] Deystviye yadernogo oruzhiya / pod red. E.M. Sominskogo. – M: Voyennoye izdatelstvo ministerstva oborony SSSR. 1965.
–P. 679.
[15] Sutton O.G. The Atom bomb as an experiment in convection // Weather. 1947. Vol.2. №4. -P. 20.
[16] Vulis. L.A. Terekhina. N.A. Rasprostraneniye turbulentnoy strui gaza v srede inoy plotnosti // Zhurnal tekhnicheskoy
fiziki. 1956. – Vol. 26. № 6. -P. 22-23.
[17] Veremey,N.E., Dovgalyuk, Yu.A., Stankova, E.N. Chislennoye modelirovaniye konvektivnykh oblakov. razvivayushchikhsya
v atmosfere pri chrezvychaynykh situatsiyakh//Izvestiya RAN. Fizika atmosfery i okeanov. 2007.- Vol.43. №6. -P. 792-806.
[18] Yakush, S.E. Gidrodinamika i goreniye gazovykh i dvukhfaznykh vybrosov v otkrytoy atmosfere: Dis. . . . dok. fiz.-mat.
nauk / Institut problem mekhaniki RAN. - Moskva. 2000. – 336 s.
[19] Zatevakhin, M.A. Turbulent Thermal in a Humid Atmosphere// High Temperature. 2001. V. 39. N 4. P. 532–539.
–P. 239.
[2] Ershin. Sh.A.. Sakipov. Z.B. Issledovaniye nachalnogo uchastka turbulentnoy strui szhimayemogo gaza // Zhurnal
tekhnicheskoy fiziki. – 1959. – Vol. 2.No.1. - P. 21-23.
[3] Ferziger and Peric, Computational Methods for Fluid Dynamics. - 3., rev. ed. – Berlin; Heidelberg; New York; Barcelona;
Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002. ISBN 3-540-42074-6,-P.251-253.
[4] Fizika vzryva / pod red. L.P. Orlenko. – M.: FIZMATLIT. 2002. - Izd. 3-e. pererabotannoye. - Vol. 1. -P. 832.
[5] Garnier, E., Adams, N., and Sagaut, P.: Large Eddy Simulation for Compressible Flows, doi:10.1007/978-90-481-2819-8,
Springer, the Netherlands,2009. -P.276.
[6] Gostintsev Yu.A.. Solodovnik A.F. Moshchnyy turbulentnyy termik v ustoychivo stratifitsirovannoy atmosfere. Chislennoye
modelirovaniye // PMTF. 1987. Vol.1. -P.47.
[7] Issa, R.I., Gosman, A.D., and Watkins, A.P. The Computation of Compressible and Incompressible Recirculating Flow
by a Non-Iterative Implicit Scheme, Journal of Computational Physics, 1986, -Vol.62. -P.66-82.
[8] Lapin, Yu.V.. Strelets, M.Kh. Vnutrenniye techeniya gazovykh smesey. – M.: Nauka. 1989, -P.368.
[9] Moin, P., Squires, K., Cabot, W., and Lee, S.: A dynamic subgrid scale model for compressible turbulence and scalar
transport, Phys. Fluids A-Fluid,1992. Vol.3, -P.2746, doi:10.1063/1.858164.
[10] Machta L. Eintrainment and the maximum height of an atomic cloud // Bull. Amer. Meteor. Soc. 1950. -Vol. 31. № 6. -P.
215–216.
[11] Nicoud, F. and Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow Turbul.
Combust.,1999. -Vol. 62. P. 183–200, doi:10.1023/A:1009995426001.
[12] Onufriyev, A.T. Teoriya dvizheniya vikhrevogo koltsa pod peystviyem sily tyazhesti. Podyem oblaka atomnogo vzryva //
PMTF. 1967. №2. -P.3-15.
[13] Piscaglia, F., Montorfano, A., and Onorati, A.: Towards the LES simulation of IC engines with parallel topologically
changing meshes, SAE Int. J. Engines, 6, 926–940, doi:10.4271/2013-01-1096, 2013.
[14] Deystviye yadernogo oruzhiya / pod red. E.M. Sominskogo. – M: Voyennoye izdatelstvo ministerstva oborony SSSR. 1965.
–P. 679.
[15] Sutton O.G. The Atom bomb as an experiment in convection // Weather. 1947. Vol.2. №4. -P. 20.
[16] Vulis. L.A. Terekhina. N.A. Rasprostraneniye turbulentnoy strui gaza v srede inoy plotnosti // Zhurnal tekhnicheskoy
fiziki. 1956. – Vol. 26. № 6. -P. 22-23.
[17] Veremey,N.E., Dovgalyuk, Yu.A., Stankova, E.N. Chislennoye modelirovaniye konvektivnykh oblakov. razvivayushchikhsya
v atmosfere pri chrezvychaynykh situatsiyakh//Izvestiya RAN. Fizika atmosfery i okeanov. 2007.- Vol.43. №6. -P. 792-806.
[18] Yakush, S.E. Gidrodinamika i goreniye gazovykh i dvukhfaznykh vybrosov v otkrytoy atmosfere: Dis. . . . dok. fiz.-mat.
nauk / Institut problem mekhaniki RAN. - Moskva. 2000. – 336 s.
[19] Zatevakhin, M.A. Turbulent Thermal in a Humid Atmosphere// High Temperature. 2001. V. 39. N 4. P. 532–539.
Downloads
How to Cite
Zhakebayev, D. B., Karzhaubayev, K. K., Zhubat, K. Z., & Abdibekova, A. U. (2018). Numerical simulation of the clouds evolution in the ground explosion of the carrier-rocket. Journal of Mathematics, Mechanics and Computer Science, 95(3), 90–104. https://doi.org/10.26577/jmmcs-2017-3-478
Issue
Section
Applied Mathematics
