Numerical Simulation of Richtmyer-Meshkov Instability at Vapor-Liquid Interface Under Single and Double Bubbles’ Conditions
Authors: Chen Helin , Peng Cheng , Li Dong , Deng Jian 
Published: November 2024

Abstract
A large amount of paramount research on interface instability has been carried out in fluid mechanics field, particularly on Richtmyer-Meshkov instability (RM instability), which has strong background and research value in both academic and engineering applications. The scholarly community has given the issue of RM instability a great deal of attention ever since it was raised. In the event of a severe accident, the high-temperature molten fuel and coolant may come into contact leading to a potential steam explosion. Then, the high-temperature melt’s surface may be triggered, endangering the integrity of the reactor cavity outside the pressure vessel, as a result of the RM instability due to the interaction between the explosion shock wave and the vapor bubble/coolant interface initialized by the coolant’s evaporation. In this study, the RM instability of the vapor-liquid interface driven by hydrodynamic effect under single and double bubbles’ condition is numerically modeled in two-dimensional geometry. The vapor-liquid interface is tracked by using the coupled Volume of Fluid (VOF) and Level-Set methods. We utilize mesh adaptive techniques, refining the mesh appropriately based on changes in the gas-liquid interface during the calculation process. This enhances the resolution of the flow field adjacent to the vapor-liquid interface, facilitating a clearer observation of the occurrence of RM instability. Under varying shock wave strengths propagating in the same direction along the buoyancy force, the velocity field, pressure field, and vapor-liquid two-phase distribution in the calculation domain are obtained. The duration time for the bubble to departure from the spherical wall is discovered to have an inverse proportional relation with the triggering pressure, the larger the triggering pressure (0.5–2MPa), the shorter the bubble’s departure time from the spherical wall. The amplitude of the disturbance at the vapor-liquid interface starts to show at the same time that the trigger pressure increases to a threshold (1 MPa in this investigation). Entrainment of droplet in the bubble will happen as a result of RM’s instability, and the trigger pressure has a quadratic relationship with the entrained droplet’ quality. The entrainment of droplets may affect the surface heat transfer efficiency of high-temperature molten materials and worsen heat transfer. The bigger the entrainment mass of the droplet in the bubble, the earlier the interfacial disturbance emerges, and the more fully the interfacial perturbation develops with an increase in triggering pressure. Furthermore, in the double bubble condition, both two bubbles will still have RM instability and droplet entrainment, but the bubble shape at the end of the bubble detachment from the spherical wall will be quite different from that in the single bubble condition. This work can offer a phenomenological reference for the development of RM instability at the vapor-liquid interface, and provide technical assistance in clarifying the triggering stage of fuel-coolant interaction in severe accident.