Two-Phase Stefan Problem for the Modeling of Urea Prilling Tower

Abstract

In the manufacturing of granular urea and ammonium nitrate, the technique of prilling is utilized rather frequently. The liquid droplets that are produced fall along the tower to the ground and become solid due to the removal of heat by the cooling air, which flows in the opposite direction of the stream. Generally, three sequential thermal intervals for the solidification of urea droplets are considered: the cooling of liquid drops, solidification at the freezing temperature of the liquid phase, and cooling of complete solid particles. In this study, the solidification of the urea droplets was considered as a two-phase Stefan problem with a convective flux boundary condition rather than dividing the whole process into three sequential steps. The heat transfer problem was solved numerically using the enthalpy method. The particles were assumed to attain the terminal velocity immediately. The convective heat transfer was determined from the terminal velocity. The temperature distribution of the droplets and the minimum height for complete solidification at different particle diameters were investigated.

Keywords

• prilling
• urea
• spray crystallizaúon
• mathematical modeling
• simulation
• Stefan problem