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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.

This paper considers numerical modeling of cloud formation under the action of buoyancy force, taking into account the turbulent mixing and the adiabatic expansion. Based on 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 numerical modeling of cloud formation is carried out. The modified solver is based on the library Open Foam of solution of mathematical physics problems. To close the basic equations the viscosity model of turbulence is used. Numerical modeling of the formation of clouds formed at ground explosion of the launch vehicle "Proton-M" 2nd July 2013, shows the dependence of the fireball height from the thermodynamic parameters in the atmosphere. Comparison of the cloud rise height as a function of the explosion power with the analytic formula of Satton confirmed the applicability of the mathematical model used to the cloud formation problem in a surface explosion of a launch vehicle. The explosion power is calculated from the funnel size.

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