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Article information
2019 , Volume 24, № 2, p.67-77
Kistovich A.V., Chaplina T.O., Stepanova E.V.
Spiral structure of the liquid particles trajectories near free surface of the vortex
The work is aimed to compare results of analytical and experimental modeling of vortex fluid flow. The compound flow of liquid (water) occurs in a vertical cylindrical container without upper endwall under the action of the disk rotating at the bottom endwall. The two main components of the emerging flow are the toroidal vortex and the vortex with vertical axis. The equations are written in the cylindrical coordinate system dictated by the geometry of the problem. On the basis of the existing analytical expression, which describes the free surface form of the compound vortex in the zero approximation, an approach is developed to describe the trajectories of individual “liquid particles”. The obtained result allows to explore the velocity field structure near the free surface. The obtained expressions indicate that the velocity field near free surface becomes more pronounced in the tangent direction. This result is confirmed in the experimental studies of the compound vortex flow. The analytical forms of liquid particle trajectories near and on the free surface of the compound vortex are obtained. The general particle movement is from the container sidewall along the free surface to its center and further down the spiral-helical line. The images of the visualized particles trajectories both on the free surface (logarithmic spiral) and in the liquid depth are obtained in experiments and testify in favor of the implemented approach to the construction of analytical solution of the liquid particle motion for the vortex flow of the mentioned type. The correspondence of the calculated free surface forms obtained with the help of analytical expressions and those observed in the experiments with different parameters of the vortex flow shows that the developed approach to the problem can be based on a simplified description.
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Keywords: compound vortex, waves, spiral structure, free surface, phase boundary
doi: 10.25743/ICT.2019.24.2.006
Author(s):
Kistovich Anatoliy Vasilievich
Dr. , Associate Professor
Position: Head of Laboratory
Office: All-Russia Scientific Research Institute of Physical-Technical and Radiotechnical Measurements
Address: 141570, Russia, Mendeleevo
E-mail: kavmendeleevo@mail.ru
SPIN-code: 5927-5562Chaplina Tatyana Olegovna
PhD.
Position: Senior Research Scientist
Office: Moscow State University
Address: 119991, Russia, Moscow
E-mail: tanya75.06@mail.ru
Stepanova Evgeniya Vyacheslavovna
PhD.
Position: Senior Research Scientist
Office: Ishlinsky Institute for Problems in Mechanics RAS
Address: 119526, Russia, Moscow
E-mail: step@ipmnet.ru
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Bibliography link:
Kistovich A.V., Chaplina T.O., Stepanova E.V. Spiral structure of the liquid particles trajectories near free surface of the vortex // Computational technologies. 2019. V. 24. № 2. P. 67-77
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