Trajectories of prill motion at the outlet of a vibropriller rotating basket of mineral fertilizer melt [in Ukrainian]
Year: 2026
Type: article
Abstract: The subject of this study is the aerodynamics of prill motion in the working space of a prill tower equipped with a vibropriller, which is among the most efficient devices for producing monodisperse mineral fertilizer prills by breaking melt jets into droplets under forced vibration in accordance with the Rayleigh instability criterion. The relevance of the work is due to the fact that engineering calculations of tower height of a prill tower require reliable information about the trajectory of prill motion, since the length of this trajectory determines the residence time of a prill in contact with the cooling air and, consequently, the prill strength and quality of the final product. An unjustified increase of tower height, in turn, considerably raises construction costs. Basket rotation, which is used to distribute jets and droplets across the tower cross-section, imparts to the melt droplets, besides the radial and axial components, an additional circumferential component of the initial velocity, so that the trajectory takes the form of a spatial spiral rather than a plane parabola. This effect had not previously been quantified in engineering terms. The aim of the work is to develop a calculation method for the spatial trajectory of a prill formed at the outlet of a rotating vibropriller basket. The methodology is based on Newton's second law written in a cylindrical coordinate system (r, θ, z) with a quadratic aerodynamic drag force acting along each of the three axes. The obtained nonlinear second-order differential equations were reduced to a system of first-order equations with respect to the velocity projections, complemented by kinematic equations and by initial conditions in which the initial circumferential velocity is expressed through the basket angular velocity and the radius of the hole. The resulting system was solved numerically by the fourth-order Runge–Kutta method. As a computational model, the trajectory of a 2 mm carbamide (urea) prill was calculated for an industrial prill tower 82 m high and 26 m in diameter, with a vibropriller basket 0.5 m in diameter rotating at 180 rpm. The calculated length of the spiral trajectory equals 136.48 m, which is almost 1.5 times greater than the length of the parabolic trajectory obtained for the same tower when the basket does not rotate. The practical significance of the results lies in the possibility of a more accurate calculation of the required tower height, the residence time of prills in the cooling air flow and the prill cooling rate, which is particularly important for large-diameter towers, where higher basket rotation speeds are required to distribute prills over the entire cross-section and, consequently, the effect of the additional trajectory length is the most pronounced. It is concluded that engineering calculations of vibroprillers and prill towers must take into account the circumferential component of the initial droplet velocity caused by basket rotation, since neglecting it leads to a considerable underestimation of the real prill path length and residence time in the tower.
Authors: Vsevolod Sklabinskyi, Andrii Karutskyi
Institution: Sumy State University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
SDG: Zero hunger
Open Access status: diamond
OpenAlex ID: W7214947729