Evaluation of melt-water premixture formation due to Rayleigh-Taylor instabilities

Abstract

Abstract A linear analysis of the stability of the three-layer stratified hydrodynamic system “water (top) – steam – melt (bottom)” has been performed. Kinematic and dynamic conditions on the “water – steam” and “steam – melt” interfaces are formulated, and on their basis a dispersion equation is obtained that relates the circular frequency of perturbations to the wavenumber. Analysis of this equation made it possible to determine the region of instability of this system and to find the wavenumber of the most fastly growing harmonics. The results obtained were used to estimate the size of bubbles formed at the interface between steam and water due to the development of the Rayleigh-Taylor instability. The obtained theoretical results are consistent with experimental observations in such systems. The heights of the melt splashes into water due to the collapse of the formed steam bubble were estimated. The obtained estimations demonstrate possibilities of the formation of melt-water mixture region during the spreading of the melt under a water layer, in which a strong steam explosion can occur.