Calculation of stationary thermal detonation wave in the multiphase system “water drops, surrounded by steam films, in continuous molten lead”

A mathematical model of a thermal detonation wave in a multiphase system “water droplets in vapor shells located in a high-temperature heavy metal melt”, which can form after a rupture of the heat exchange tube of steam generator of a fast neutron reactor with a liquid lead or lead-bismuth coolant, is proposed. The model is based on the equations of the mechanics of multiphase systems. Interphase heat transfer and friction are described by well-known correlations validated on numerous experimental data. The key mechanism of thermal detonation wave propagation is the fragmentation of water droplets in the shock wave front. Fragmentation is carried out due to the difference in the velocities of drops and melt, which occurs on the shock wave due to the difference in their densities. The propagation velocity of a thermal detonation wave is determined by calculation of the Hugoniot adiabat. The parameters on the leading shock wave are calculated from relations expressing the laws of conservation of mass, momentum, and energy of a multiphase mixture. The calculated pressure distribution behind the shock wave has a maximum near the shock wave plane. The calculation results revealed that the thermal equilibrium of the phases is achieved much later than their velocity equilibrium.