Numerical analysis for sodium leakage and combustion using particle method. Final report

Leakage and combustion behavior of liquid sodium can be analyzed by considering combustion of sodium droplets and pools, spreading on the floor and accumulation of combustion products, and jet breakup. Japan Nuclear Cycle Development Institute (JNC) has been developing a code using a particle method to analyze complicated behavior of sodium leakage and combustion. The particle method for thermal-hydraulic analysis was developed by the authors. Compared with the conventional finite difference method, the particle method is useful for solidification and accumulation as well as fluid separation and merging. In this study, development of particle models for solid motion and solidification for the purpose of sodium solidification and accumulation of the combustion products. A new particle interaction model of elastic materials is developed. The elastic properties are described by Young's modulus and Poisson's ratio. In this model, elements, which the finite element method is based on, are not necessary, so that fracture as well as large deformation of elastic materials is easily analyzed. Particles have a degree of freedom concerning rotation, which leads to conservation of the angular momentum. In a test problem of assuming a sine distribution of displacement, the present model provides correct distributions of stress and pressure with those of analytical solutions. Next, a particle interaction model for analyzing solidification by combining the usual MPS method for thermal-hydraulics and the new model of elastic material for the solid are developed. We apply the present methods to the analysis of spreading of liquid sodium, which is initially located as a two-dimensional column of 10 cm wide and 20 cm high on a stainless steel floor of 1 cm thick and 1 m long. When the viscosity and the heat conductivity are artificially enhanced, the spreading is suppressed by viscosity and solidification at the front. This model is also available for accumulation of the combustion products. A particle model of surface tension is developed to incorporate its effect. Quantities of differential geometry, such as curvature, are evaluated from the particle number density without the shape of interfaces, so that this algorithm can be applied to fluid separation and coalescence. Vibration of an ethanol droplet is calculated and the result agrees with that of VOF method. This shows that the developed model is proper. Liquid spreading is analyzed when the surface tension is strong. The result shows that the spreading liquid is divided to droplets by surface tension. Jet breakup behavior is analyzed by the MPS method. A continuous jet is dispersed to droplets after traveling a certain length depending on the calculation conditions. The jet breakup length is longer when Weber number is larger, which qualitatively agrees with the existing correlations. (author)