The Mathematical Model for the Secondary Breakup of Dropping Liquid

Ivan Pavlenko, 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
Additional contact information
Ivan Pavlenko: Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 40007 Sumy, Ukraine
Vsevolod Sklabinskyi: Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 40007 Sumy, Ukraine
Michał Doligalski: Faculty of Computer, Electrical and Control Engineering, University of Zielona Góra, 65-516 Zielona Góra, Poland
Marek Ochowiak: Department of Chemical Engineering and Equipment, Poznan University of Technology, 60-965 Poznan, Poland
Marcin Mrugalski: Faculty of Computer, Electrical and Control Engineering, University of Zielona Góra, 65-516 Zielona Góra, Poland
Oleksandr Liaposhchenko: Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 40007 Sumy, Ukraine
Maksym Skydanenko: Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 40007 Sumy, Ukraine
Vitalii Ivanov: Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 40007 Sumy, Ukraine
Sylwia Włodarczak: Department of Chemical Engineering and Equipment, Poznan University of Technology, 60-965 Poznan, Poland
Szymon Woziwodzki: Department of Chemical Engineering and Equipment, Poznan University of Technology, 60-965 Poznan, Poland
Izabela Kruszelnicka: Department of Chemical Engineering and Equipment, Poznan University of Technology, 60-965 Poznan, Poland
Dobrochna Ginter-Kramarczyk: Department of Chemical Engineering and Equipment, Poznan University of Technology, 60-965 Poznan, Poland
Radosław Olszewski: Faculty of Chemistry, Adam Mickiewicz University, 61-614 Poznan, Poland
Bernard Michałek: Faculty of Chemistry, Adam Mickiewicz University, 61-614 Poznan, Poland

Energies, 2020, vol. 13, issue 22, 1-17

Abstract: 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.

Keywords: oscillatory wall; vibrational impact; Weber number; critical value; nonstable droplet (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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