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The Mathematical Model for the Secondary Breakup of Dropping Liquid

Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 40007 Sumy, Ukraine
Faculty of Computer, Electrical and Control Engineering, University of Zielona Góra, 65-516 Zielona Góra, Poland
Department of Chemical Engineering and Equipment, Poznan University of Technology, 60-965 Poznan, Poland
Faculty of Chemistry, Adam Mickiewicz University, 61-614 Poznan, Poland
Author to whom correspondence should be addressed.
Energies 2020, 13(22), 6078;
Received: 16 October 2020 / Revised: 15 November 2020 / Accepted: 19 November 2020 / Published: 20 November 2020
(This article belongs to the Special Issue Multiphase Flows)
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. View Full-Text
Keywords: oscillatory wall; vibrational impact; Weber number; critical value; nonstable droplet oscillatory wall; vibrational impact; Weber number; critical value; nonstable droplet
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MDPI and ACS Style

Pavlenko, I.; Sklabinskyi, V.; Doligalski, M.; Ochowiak, M.; Mrugalski, M.; Liaposhchenko, O.; Skydanenko, M.; Ivanov, V.; Włodarczak, S.; Woziwodzki, S.; Kruszelnicka, I.; Ginter-Kramarczyk, D.; Olszewski, R.; Michałek, B. The Mathematical Model for the Secondary Breakup of Dropping Liquid. Energies 2020, 13, 6078.

AMA Style

Pavlenko I, Sklabinskyi V, Doligalski M, Ochowiak M, Mrugalski M, Liaposhchenko O, Skydanenko M, Ivanov V, Włodarczak S, Woziwodzki S, Kruszelnicka I, Ginter-Kramarczyk D, Olszewski R, Michałek B. The Mathematical Model for the Secondary Breakup of Dropping Liquid. Energies. 2020; 13(22):6078.

Chicago/Turabian Style

Pavlenko, Ivan, Vsevolod Sklabinskyi, Michał Doligalski, Marek Ochowiak, Marcin Mrugalski, Oleksandr Liaposhchenko, Maksym Skydanenko, Vitalii Ivanov, Sylwia Włodarczak, Szymon Woziwodzki, Izabela Kruszelnicka, Dobrochna Ginter-Kramarczyk, Radosław Olszewski, and Bernard Michałek. 2020. "The Mathematical Model for the Secondary Breakup of Dropping Liquid" Energies 13, no. 22: 6078.

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