Bell–Plesset instability analysis for an inward centralized sloshing

Abstract Liquid sloshing is a typical phenomenon when liquid in a container has an unrestrained surface. In fast reactors under core disruptive accidents (CDAs) conditions specific sloshing motions could be encountered that can be described as a centralized sloshing. It is important to investigate the mitigating and augmenting factors for such centralized sloshing motions. Any retardation or instability effects that reduce the compaction speed and resulting reactivity ramp rate are of importance, requiring an understanding of the kinetic energy dissipation of an inward centralized slosh. In this paper, the Bell–Plesset (BP) instability has been studied theoretically and numerically based on a corresponding inward centralized sloshing experiment. The theoretical analysis is based on the classical perturbation theory and the simulation has been conducted by a fully mesh-free, Lagrangian particle numerical method. With our experimental data, the initial perturbation length 1.3 mm is approximated by the numerical calculation as supplement of the purely theoretical analysis. The outward and inward sloshing timings have been re-checked from the experiment that the inward velocity is reduced by around 20% compared to outward velocity. It experimentally confirms reasonably well the numerical result 17.5%. The experimental, numerical and theoretical analysis show that BP instability plays a certain role in azimuthal energy dissipation when the sloshing waves are moving inwards and converging in cylindrical geometry, for the experiment case the velocity reduction may be 17.5%.