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Item Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process(MDPI, 2020) Павленко, Іван Володимирович; Павленко, Иван Владимирович; Pavlenko, Ivan Volodymyrovych; Склабінський, Всеволод Іванович; Склабинский, Всеволод Иванович; Sklabinskyi, Vsevolod Ivanovych; Piteľ, J.; Kuric, I.; Іванов, Віталій Олександрович; Иванов, Виталий Александрович; Ivanov, Vitalii Oleksandrovych; Скиданенко, Максим Сергійович; Скиданенко, Максим Сергеевич; Skydanenko, Maksym Serhiiovych; Ляпощенко, Олександр Олександрович; Ляпощенко, Александр Александрович; Liaposhchenko, Oleksandr OleksandrovychThis article was aimed to solve an urgent problem of ensuring quality for prilling processes in vibrational prilling equipment. During the research, the need for the application of vibrational prilling to create a controlled impact on the process of jet decay on droplets with the proper characteristics was substantiated. Based on the experimental and theoretical studies of the process of decay of a liquid jet into drops, axisymmetric droplet oscillation modes for the different frequencies were observed. Frequency ranges of transition between modes of decay of a jet into drops were obtained. As a result, the mathematical model of the droplet deformation was refined. The experimental research data substantiated this model, and its implementation allowed determining the analytical dependencies for the components of the droplet deformation velocity. The proposed model explains the existence of different droplet oscillation modes depending on the frequency characteristics of the superimposed vibrational impact. Based on an analytical study of the droplet deformation velocity components, the limit values of the characteristics defining the transition between the different droplet oscillation modes were discovered. Analytical dependencies were also obtained to determine the diameter of the satellites and their total number.Item Identification of the Interfacial Surface in Separation of Two-Phase Multicomponent Systems(MDPI, 2020) Павленко, Іван Володимирович; Павленко, Иван Владимирович; Pavlenko, Ivan Volodymyrovych; Ляпощенко, Олександр Олександрович; Ляпощенко, Александр Александрович; Liaposhchenko, Oleksandr Oleksandrovych; Склабінський, Всеволод Іванович; Склабинский, Всеволод Иванович; Sklabinskyi, Vsevolod Ivanovych; Стороженко, Віталій Якович; Стороженко, Виталий Яковлевич; Storozhenko, Vitalii Yakovych; Михайловський, Яків Емануілович; Михайловский, Яков Эммануилович; Mykhailovskyi, Yakiv Emanuilovych; Ochowiak, M.; Іванов, Віталій Олександрович; Иванов, Виталий Александрович; Ivanov, Vitalii Oleksandrovych; Pitel, J.; Старинський, Олександр Євгенович; Старинский, Александр Евгеньевич; Starynskyi, Oleksandr Yevhenovych; Włodarczak, S.; Krupińska, A.; Markowska, M.The area of the contact surface of phases is one of the main hydrodynamic indicators determining the separation and heat and mass transfer equipment calculations. Methods of evaluating this indicator in the separation of multicomponent two-phase systems were considered. It was established that the existing methods for determining the interfacial surface are empirical ones, therefore limited in their applications. Consequently, the use of the corresponding approaches is appropriate for certain technological equipment only. Due to the abovementioned reasons, the universal analytical formula for determining the interfacial surface was developed. The approach is based on both the deterministic and probabilistic mathematical models. The methodology was approved on the example of separation of two-phase systems considering the different fractional distribution of dispersed particles. It was proved that the area of the contact surface with an accuracy to a dimensionless ratio depends on the volume concentration of the dispersed phase and the volume of flow. The separate cases of evaluating the contact area ratio were considered for different laws of the fractional distribution of dispersed particles. As a result, the dependence on the identification of the abovementioned dimensionless ratio was proposed, as well as its limiting values were determined. Finally, a need for the introduction of the correction factor was substantiated and practically proved on the example of mass-transfer equipment.Item The Mathematical Model for the Secondary Breakup of Dropping Liquid(MDPI, 2020) Павленко, Іван Володимирович; Павленко, Иван Владимирович; Pavlenko, Ivan Volodymyrovych; Склабінський, Всеволод Іванович; Склабинский, Всеволод Иванович; Sklabinskyi, Vsevolod Ivanovych; Doligalski, M.; Ochowiak, M.; Mrugalski, M.; Ляпощенко, Олександр Олександрович; Ляпощенко, Александр Александрович; Liaposhchenko, Oleksandr Oleksandrovych; Скиданенко, Максим Сергійович; Скиданенко, Максим Сергеевич; Skydanenko, Maksym Serhiiovych; Іванов, Віталій Олександрович; Иванов, Виталий Александрович; Ivanov, Vitalii Oleksandrovych; Włodarczak, S.; Woziwodzki, S.; Kruszelnicka, I.; Ginter-Kramarczyk, D.; Olszewski, R.; Michałek, B.Investigating characteristics for the secondary breakup of dropping liquid is a fundamental scientific and practical problem in multiphase flow. For its solving, it is necessary to consider the features of both the main hydrodynamic and secondary processes during spray granulation and vibration separation of heterogeneous systems. A significant difficulty in modeling the secondary breakup process is that in most technological processes, the breakup of droplets and bubbles occurs through the simultaneous action of several dispersion mechanisms. In this case, the existing mathematical models based on criterion equations do not allow establishing the change over time of the process’s main characteristics. Therefore, the present article aims to solve an urgent scientific and practical problem of studying the nonstationary process of the secondary breakup of liquid droplets under the condition of the vibrational impact of oscillatory elements. Methods of mathematical modeling were used to achieve this goal. This modeling allows obtaining analytical expressions to describe the breakup characteristics. As a result of modeling, the droplet size’s critical value was evaluated depending on the oscillation frequency. Additionally, the analytical expression for the critical frequency was obtained. The proposed methodology was derived for a range of droplet diameters of 1.6–2.6 mm. The critical value of the diameter for unstable droplets was also determined, and the dependence for breakup time was established. Notably, for the critical diameter in a range of 1.90–2.05 mm, the breakup time was about 0.017 s. The reliability of the proposed methodology was confirmed experimentally by the dependencies between the Ohnesorge and Reynolds numbers for different prilling process modes.