Numerical simulation of the freezing process of hydrogen isotopes in a spherical container

摘要

Numerical simulation results related to the process of spherically symmetric freezing microsphere filled with gaseous DT(or one of the hydrogen isotopes)are presented. The mathematical problem is the Stefan problem with tow phase transitions, and takes into account the motion of the gas under freezing. The proposed system of equations consists of the heat conduction equation for a multilayered medium and gasdynamics equation for a fuel inside the shell. To solve the problem on fast symmetric freezing of a gas-filled microsphere, a computational algorithm has been developed and realized in the form of a program, in which the method of splitting according to physical process is used and computational space is divided into segments, the number of which is varied during the computing process. the numerical solution is found by the iteration emthod. The computations allowed us to determine the characteristic times of cooling, condensation and solidification, and also the time during which the cryogenic layer is in the liquid state. We have determined computationally the temperature distribution inside the target, positions of the phase transition boundaries, sensitivity of the freezing kinetics to inaccuracy in determining the hydrogen isotopes properties and to the temperature dependence of these properties. The computations have revealed overcooling of gaseous fuel inside a microsphere, which occurs at certain pressures of the heat exchange gas during freezing. We have studied the degree of this overcooling versus the target parameters and its freezing conditions.