The features of supersonic steam-water jets formation under outflow through a thin nozzle from a high-pressure chamber are considered. The modes of emerging vibration processes are investigated, depending on variation of initial saturation states determined by pressure and temperature. The proposed system of model equations for steam-water mixture in three-dimensional formulation, in two-temperature, single-pressure, and single-velocity approximations, takes into account the interphase heat exchange, evaporation and condensation phenomena. The numerical implementation of this problem is carried out by the authors developed solver in the OpenFOAM package. The process of supersonic jet development with the formation of Mach disk is studied and the causes of acoustic pressure pulsations are investigated. The analysis of influence of initial saturation states of vapor-water fluid located in a high-pressure chamber on intensity and frequency of acoustic vibrations is given. To validate the numerical method using the OpenFOAM package, the obtained numerical solution is compared with an experimental picture of a supersonic nitrogen jet flowing through a cylindrical nozzle from a high-pressure reservoir.