Abstracts

NIS participants

The numerical three-dimensional model of the heavy gas dispersion in the atmospheric boundary later has been developed. The unfiltered system of heavy gas hydrodynamic equations was solved. The equations of the system are averaged by the Favre-Reynolds procedure. The turbulence processes are parameterized by the gradient relations, that keep the tenzor invariance for compressible flows. The turbulence closure was held by solving the equations of transport ofturbulence energy and dissipation rate. Unlike the known 3D models, in the presented model the heat exchange with Earth surface was parameterized by relations for mixed convection. For the non-isothermal releases the coupled problem of heat exchange of cold gas with the surface Earth layer was solved.

The statement of problem was used with the equation of the internal energy transport in the form of equation for pressure.(Kovenya, Yanenko,1984). It is modified for the case of turbulent flows. That allowed to separate the initial system of equations on two subsystems. The numerical solution of both subsystems is carried out with different time steps. A comparison with the traditional for the modeling of these processes problem statement with temperature (enthalpy)equation showed, that solving of both subsystems with different time steps increased the numerical efficiency of the method by the factor of almost two. The numerical solving of the model equations was held with the use of implicit finite-difference splitting schemes upon spatial directions and physical processes (Yanenko 1967, Marchuk 1988).

With the help of the developed model, the dynamics of heavy gas plume,appeared as the result of the instantaneous release in calm atmosphere and as result of continious release into the air flow upon the Earth, was investigated. In the case of instantaneous release the appearance of toroidal vortex on the initial stage of dispersion was shown. The gravitational waves appeared on the cloud top surface. The dependences of integral potential and kinetic average energies and turbulence kinetic energy upon time are presented. The rapid growth of turbulent energy on the initial stage of heavy gas dispersion was shown. The damping of turbulence energy is much more rapid then that of average kinetic and potential energies, due to dissipation and stable stratification in the cloud. The good agreement of model predictions with laboratory and field-test data was shown.

In the case of instantaneous releases the numerical analyses of the mistake in the continuity equation, due to Bussinesque or "full anelastic" (Chan) approximations was held. They are frequently used in the models of these processes. That mistake remains rather big (near 30%)on the initial stage of heavy gas dispersion. In the case of "full anelastic" approximation it leads to the loss of the mass of gas.

The investigation of interaction of heavy gas with the atmospheric boundary layer was held. The comparison with laboratory data (Arya, Zhu) is presented. As the result of damping of turbulence due to the stable stratification, the friction force is reduced on the top boundary of the heavy gas cloud. Hence, the velocity profile changes. The air becomes sliding on the heavy gas surface, that cover the rough Earth surface, and slope of velocity profile increases, because of reduced friction.

The influence of heat exchange on the dynamics of heavy gas cloud was investigated. It was shown, that nonadiabatic effects lead to the significant reduce of the cloud buoyancy, and, as result, to the reduction of gravitational flow velocity. At the same time, that process influences on the turbulence characteristics of the cloud. On the top surface of the cloud the turbulence energy remains damped, as in the case of adiabatic current, while inside the cloud it is generated by the unstable stratification. It was shown, that free convection is dominated, when the wind speeds are low and moderate. The forced convection is damped near the source because of the boundary layer displacement and reduction of the horizontal component of wind speed. The free convection dominates in the regions, where the difference of temperatures of gas and Earth is large. Near the source it is big and decreases with distance from it. As the result, the total heat exchange coefficient in the field experiment Burro and in the model predictions is weekly dependent upon the distance from the source.

The comparison of the solving of model problem of heat exchange of air (with constant temperature) with Earth surface layer with analytical solving is presented. Two cases of numerical solving are presented: of constant heat exchange coefficient and coefficient, defined by the relations for mixed convection. By solving that model problem it was shown, that taking into account the free convection essentially changes the cooling of Earth surface even for low nondimensional times. The numerical solving of unstationary problem of cold heavy gas dispersion above the Earth surface confirms that result.

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