Instability model of water–steam–liquid metal three-phase jet flow during steam generator tube rupture accident in a fast reactor

The steam generator tube rupture (SGTR) accident in a lead-cooled fast reactor (LFR) results in an injection of high-pressure subcooled water from the secondary circuit into the high-temperature liquid lead-bismuth eutectic (LBE) pool in the primary loop. Rapid depressurization and phase-change heat transfer generate the steam between the water jet and liquid LBE. Based on jet instability theory, this study develops a temporal instability model focusing on the water–steam–liquid LBE three-phase flow in a cylindrical coordinate to investigate the breakup characteristics of water jet. By introducing velocity and pressure disturbances and adopting a linear assumption to the hydrodynamic governing equations, a dispersion equation is developed, and jet characteristic parameters are then defined. The effects of various operating parameters and key dimensionless numbers are further studied. By solving the dispersion equation, it is found that smaller steam film thickness and higher steam velocity enhance jet instability. Increasing jet velocity and reducing jet radius accelerate jet breakup and promote droplet refinement, while at higher jet velocities, the influence of jet radius diminishes. Additionally, the co-flow of LBE with the jet and the viscosity effect of LBE both stabilize the water jet. This model enables quantitative prediction of the breakup behavior of water jets in liquid LBE during the initial stage of SGTR accident, aiming to reveal the fundamental mechanisms of the physical process and provide theoretical guidance for safety analysis of LFR.