Influence of a non-condensable gas on mixing of a melt with water in a stratified configuration

The influence of bubbles of hot non-condensable gas formed at the interface between the melt and water on the formation of a mixture of melt with water capable of producing steam explosions is considered. The dynamics of such a bubble in subcooled water is analyzed numerically in a one-dimensional spherically symmetric approximation. It is shown that with significant initial superheat of the bubble relative to the water, a rapid drop in pressure in the bubble occurs due to strong heat removal into the water. This leads to the collapse of the bubble and the appearance of an accompanying flow of water. The results obtained made it possible to approximately describe the stage of collapse of the bubble as the polytropic process and to determine its index. The axisymmetric problem of the impact of the water jet on the surface of a melt during collapse of a gas bubble near the interface between the melt and water is numerically investigated. In this case, the obtained polytropic process equation is used to determine the pressure in the bubble. It is found that the resulting impact on the melt is capable of knocking out melt droplets into the water to a height of several centimeters, which leads to the formation of a layer of water mixed with the melt droplets, which is capable of producing strong steam explosions.

One approach to the axisymmetric problem of impact of fine shells of the S.P. Timoshenko type on elastic half-space

Refined model of S.P. Timoshenko makes it possible to consider the shear and the inertia rotation of the transverse section of the shell. Disturbances spread in the shells of S.P. Timoshenko type with finite speed. Therefore, to study the dynamics of propagation of wave processes in the fine shells of S.P. Timoshenko type is an important aspect as well as it is important to investigate a wave processes of the impact, shock in elastic foundation in which a striker is penetrating. The method of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind and the convergence of this solution are well studied. Such approach has been successfully used for cases of the investigation of problems of the impact a hard bodies and an elastic fine shells of the Kirchhoff-Love type on elastic a half-space and a layer. In this paper an attempt is made to solve the axisymmetric problem of the impact of an elastic fine spheric shell of the S.P. Timoshenko type on an elastic half-space using the method of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind. It is shown that this approach is not acceptable for investigated in this paper axisymmetric problem. The discretization using the Gregory methods for numerical integration and Adams for solving the Cauchy problem of the reduced infinite system of Volterra equations of the second kind results in a poorly defined system of linear algebraic equations: as the size of reduction increases the determinant of such a system to aim at infinity. This technique does not allow to solve plane and axisymmetric problems of dynamics for fine shells of the S.P. Timoshenko type and elastic bodies. This shows the limitations of this approach and leads to the feasibility of developing other mathematical approaches and models. It should be noted that to calibrate the computational process in the elastoplastic formulation at the elastic stage, it is convenient and expedient to use the technique of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind.