Liquid entrainment by an expanding core disruptive accident bubble—a Kelvin/Helmholtz phenomenon

The final stage of a postulated energetic core disruptive accident (CDA) in a liquid metal fast breeder reactor is believed to involve the expansion of a high-pressure core-material bubble against the overlying pool of sodium. Some of the sodium will be entrained by the CDA bubble which may influence the mechanical energy available for damage to the reactor vessel. The following considerations of liquid surface instability indicate that the Kelvin–Helmholtz (K–H) mechanism is primarily responsible for liquid entrainment by the expanding CDA bubble. First, an instability analysis is presented which shows that the K–H mechanism is faster than the Taylor acceleration mechanism of entrainment at the high fluid velocities expected within the interior of the expanding CDA bubble. Secondly, a new model of liquid entrainment by the CDA bubble is introduced which is based on spherical-core-vortex motion and entrainment via the K–H instability along the bubble surface. The model is in agreement with new experimental results presented here on the reduction of nitrogen-gas-simulant CDA bubble work potential. Finally, a one-dimensional air-over-water parallel flow experiment was undertaken which demonstrates that the K–H instability results in sufficiently rapid and fine liquid atomization to account for observed CDA gas-bubble work reductions. An important byproduct of the theoretical and experimental work is that the liquid entrainment rate is well described by the Ricou–Spalding entrainment law.