Semi-Empirical Model of Droplet Size Distribution From the Maximum Entropy Principle in Sodium Spray

Abstract

When a sodium leakage accident occurs in the sodium-cooled fast reactor, the leaked sodium reacts violently with the air in the form of droplets, resulting in the phenomenon of sodium spray fire. The droplet size distribution formed by liquid sodium injection is the key factor affecting the accident analysis of sodium spray fire. Based on the theory of the maximum entropy principle, a semi-empirical model of sodium spray droplet size distribution is constructed, which is constrained by the mass equation or the momentum equation with viscous resistance, respectively. Based on the existing liquid fuel droplet size distribution experiment results and the sodium spray fire experiment results, the semi-empirical model is verified, which shows that the prediction result with the semi-empirical model constrained by the momentum equation is in good agreement with the experimental result with the error of about 20%. Furthermore, the proposed sodium spray droplet model is compared with other models of the empirical model, the semi-empirical model, and the model based on the maximum entropy principle constrained by the simplified mass equation. The simulation result with the proposed model matches the experimental data better with minor error.