Theoretical Analysis of Molten Jet Breakup in a Rotating Granulation System Under Unforced Conditions

This paper presents a theoretical framework for predicting molten jet breakup at the outlet of a rotating granulation system operating without forced excitation. The study focuses on the critical regime in which mechanical excitation is absent, and jet disintegration is governed solely by intrinsic hydrodynamic instabilities. The analysis is based on the linear stability theory of viscous liquid jets, employing the Rayleigh–Plateau and Tomotika approaches adapted to melt conditions typical of industrial granulation processes. The Navier–Stokes equations are formulated in a cylindrical coordinate system for an axisymmetric, incompressible viscous jet with appropriate kinematic and dynamic boundary conditions at the free surface. The breakup mechanism is characterized using key dimensionless parameters, including the Ohnesorge, Weber, Reynolds, and Capillary numbers, enabling identification of the dominant instability regime. Analytical expressions are derived for the most unstable wavelength, perturbation growth rate, breakup time, and characteristic droplet diameter. These relationships are evaluated for representative thermophysical properties of molten urea. Theoretical predictions obtained from classical Rayleigh theory, viscosity-corrected models, and modern empirical correlations show strong agreement, with deviations not exceeding 7%. Sensitivity analysis indicates limited dependence of the predicted droplet diameter on moderate variations in viscosity, surface tension, and jet velocity. The proposed model provides a physically grounded basis for predicting and controlling granule size distribution in rotating granulation systems operating without external mechanical excitation.