Mathematical calculations for determining the hydrodynamic characteristics of granules movement in the workspace of the vortex granulator, which is the main ultimate process of chemical technology and forms properties of ordinary and porous ammonium nitrate and carbamide, are presented in this paper. Components of a granule velocity and the granulator design impact on them are analytically determined. Comparison of theoretical and experimental studies is performed.

Abstract. This paper presents the prospective line of studying such chemical process as granulation and the advantages of small universal vortex granulators usage in chemical processes, for example, for the production of nitrogen mineral fertilizers, complex mineral fertilizers and porous ammonium nitrate (PAN). The mathematical calculations for determining the hydrodynamic characteristics of gas flow movement, which ultimately affect the crystallization process in the workspace of the vortex granulator, are described. Components of a gas flow velocity and the granulator design impact on them are analytically determined. A comparison of theoretical and experimental studies is given.

This article deals with the development of the university activities model to ensure the quality of education and technology transfer (SDG 4) and to create a successful background in achieving SDG 7. We conduct an analysis of the literature on the achievement of SDGs through governmental instruments of influence, as well as the creation of effective university model ensuring the education quality and technology transfer. In addition, we demonstrate the role of the government in financing higher education in Ukraine. We also present the evaluation of the popularity of educational programs related to energy efficiency and a “clean” environment in Ukrainian universities after the adoption of the 2030 Agenda for Sustainable Development. The indicators of the use of various energy types by Ukraine are assessed, and a comparative analysis of these indicators with the data for EU-28 is performed. Based on the data presented, conclusions are drawn about the need to improve the quality of university training and to activate the university technology transfer. Successful practical approaches that can be of use for different higher education institutions are outlined. A combined model of quality assurance and technology transfer at the university is presented. An algorithm for testing the model and assessing the technological level of readiness for implementation is developed. The presented chain “combined model – model testing algorithm – determination of the technological level of readiness” is also assessed from the point of view of socio-economic impact on the main stakeholders. The use of the combined model lays background for the university’s own sustainable development as a tool for achieving SDGs.

The article presents a theoretical model by means of which processes of classifi cation and separation that occur in suspended-layer vortex granulators with variable-height cross-sectional area may be described. Dependences that enable us to establish the distribution law of the granules in the work space of a suspended-layer vortex granulator of given confi guration are obtained. The results of calculations are confi rmed by experimental investigations performed on a prototype of a suspended-layer vortex granulator. The optimum design of the work space of a suspended-layer vortex granulator as a function of the required fractional composition of the granulated product may be determined on the basis of results of theoretical and experimental investigations.Swirling of fl ows is one of the most effi cient methods of intensifying heat and mass exchange processes in chemical engineering [1][2][3].Through the use of vortex fl ows, it becomes possible to achieve stabilization of the hydrodynamic conditions in an apparatus and to equalize the temperature inside the apparatus.The introduction of suspended-layer vortex granulators into the technology employed in producing mineral fertilizers, granules with special properties, or multilayer granules has made it possible to raise the specifi c output of granulation plants and increase the degree of monodispersivity of the fi nished product, and to also realize production effi ciency [4].The creation of multifunctional apparatuses that can achieve several processes in a single work cycle (for example, granulation and cooling, granulation and drying, granulation and classifi cation) [5] represents a promising direction in the development of the technology of granulation.Granulators with constant cross-sectional area do not fully assure realization of processes of classifi cation and separation in view of the fact that in these types of apparatuses the ascending (fl ow) component of the total velocity of the gas fl ow is constant and equal to the working rate of suspension of particles of a given dimension (polydispersed system of narrow fractional composition). The value of the working rate of suspension for suspended-layer apparatuses is given bywhere v cr is the velocity of the gas corresponding to the start of the transition of the particles into the suspended state (fi rst critical velocity), m/sec.The process of classifi cation in such granulators (predominantly cylindrical granulators) in fact reduces to a division of a polydispersed system into two fractions, one of which is in the suspended state while the other is removed from the work space of the apparatus. In this case, it is not possible to use the fi ne fraction as internal refl ux. The process of classifi cation

Background The article is devoted to the development of new utilization methods of exhaust gases by cleaning them from fine particles, dust and harmful gas components. The basic design solutions, which allow to increase the degree of exhaust gases cleaning, were presented. The effectiveness of design solutions was supported by the results of experimental studies. Analysis of the research results allowed developing of new designs of equipment for dehydration in fluidized bed. The article also presents the calculation algorithm of eco-friendly dryers with fluidized bed. Methods Physical modeling was based on methods of similarity theory. In studies in dryers experimental models the installation scale was changed (compared with industrial conditions). Geometric similarity was maintained by equity of constants and invariants of geometric similarity. Always similarity of respective particles movement and their trajectories in industrial design and in experimental models was also maintained. The creation of graphical dependences was carried out by differential methods of mathematical analysis and integral calculus. The reliability of obtained experiment results was caused by the application of time-tested in practice methods. Results and discussion Control of product fractional composition allowed to make a selection of required fractions (including the fine granules) in a certain place of device. This allowed to increase the degree of purification of exhaust gas even before it output from the dryer working space. The process of separating the granules into fractions and the selection of fine fraction can be performed due to structural changes in dryer units and selection of optimal hydrodynamic conditions of fluidizing agent motion. Installation of special units in the dryers allowed to extract other contaminants from the exhaust gases. Conclusions Proposed constructive solutions for fluidized bed dryers allowed to:-provided of granules classification to the desired number of fractions with a simultaneous release and discharged of fine fraction from the working volume of dryer without the exhaust gases; -increased the degree of monodispersity of commodity granules on 25-35%; -reduced the amount of dust in the exhaust gases on 35-65%; -reduced the ammonia content in the exhaust gas on 90-95%.

Purpose. To identify the current level and trends of convergence to justify the directions of adjustment of approaches to the management of the national economy. Methodology. The methodological basis of the study is economic and mathematical modelling using Barro-regression and variational analysis. Integral indicators for the characteristics of the components of the studied chain are defined as the arithmetic mean of partial indicators of economic development (24 indicators), educational development (28 indicators), digitalization (12indicators) and national security (53 indicators), normalized by the method of natural normalization. To assess the pairwise, triple and complex convergent relationships in the studied chain, a multiplicative convolution of the corresponding integral indicators characterizing a pair, triple or four of the studied concepts, was performed. The sample consisted of 11 countries from Central and Eastern Europe (Croatia, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, Slovenia, Ukraine). The research period includes 19992020. Findings. The existence of dynamic convergent links in the national security digitalization, education national security digitalization chains is confirmed, which indicates the need for further interstate integration of regulatory practices in the field of digitalization impact on the national security (including digital education effects). The links in the economy education, economy national security, education national security, economy education national security chains have a fairly high static level of convergence, which indicates the need to level the differences in national practices of regulation of these directions. At the same time, current trends in the digitalization of education and the digitalization of the economy remain quite diversified, which determines the need to apply specific national government practices in this area. Originality. Methodological principles of integrated assessment of convergent relationships in the economy education national security digitalization chain differ from the existing ones by using integrated indicators of characteristics of single, pair, triple and complex relationships within the studied chain to determine the levels of their - and -convergence. This allowed identifying the presence of the achieved level of convergence and dynamic convergent trends that arise in the process of economic and educational transformations in the context of overcoming security challenges in the national economy in the context of digitalization. Practical value. The achieved significant level of convergence of the economy, education and digitalization of the studied countries has been revealed, as well as stable convergent links of integrated development of their economy, education and national security have been formed. The results obtained can be used as a scientific substantiation of adjustment of directions of state regulation of economy and education in the conditions of digitalization and in the context of overcoming security challenges.

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Thermophysical model of liquid-steam stream compressor, results of analysis of experimental researches of boiling up streams of liquid in the broadening ducting and running part of liquid-steam stream compressor, description of forming of three critical modes of flow and structural inversion of stream are presented in this article. The mathematical model of working process which allows to determine parameters and characteristics of liquid-steam stream compressor is presented.