Theoretical and Computational Fluid Dynamics

, Volume 33, Issue 6, pp 561–576 | Cite as

Analytical and experimental study of the substance transport in the vortex flow

  • A. V. Kistovich
  • T. O. ChaplinaEmail author
  • E. V. Stepanova
Original Article


The characteristics of the vortex flow with a free surface formed in a vertical cylindrical container filled with water, where the source of motion is the disk at the bottom endwall, are studied experimentally and analytically. Different types of oils and petroleum are used in experiments as admixtures. The problem of an “oil body” form in a complex vortex flow is considered on the basis of the analysis of equations for the mechanics of immiscible liquids of different densities with physically based boundary conditions. The calculations of the free surface forms are carried out in cases of one- and two-component fluid. The relations obtained are in satisfactory agreement with the experimentally registered forms of the interfaces. The flow structure near a rotating disk is studied, the shapes of the trajectories of moving liquid particles in the water column near the disk are determined. The coincidence of the types of spiral movement of liquid particles on the surface and near the disk indicates that the characteristic features of the vortex flow are determined in the boundary layer on the rotating disk and then transferred to the entire spatial region occupied by the liquid. Experimental and theoretical study of the vortex flow showed that the trajectories of moving liquid particles near the water surface are spatial spirals along which these particles move from the periphery to the center. The expressions obtained for the form of trajectories of liquid particles accelerated by the rotating disk coincide with the type of registered tracers’ trajectories in the depth of liquid and on the free surface of the flow.


Vortex flow Free surface Cylindrical container Immiscible admixture Spiral structure 



This work is supported by the Russian Foundation for Basic Research (Project 18-01-00116).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • A. V. Kistovich
    • 1
  • T. O. Chaplina
    • 2
    • 3
    Email author
  • E. V. Stepanova
    • 3
  1. 1.All-Russian Scientific Research Institute of Physico-Technical and Radiotechnical MeasurementsMedeleevoRussia
  2. 2.Faculty of PhysicsM.V. Lomonosov Moscow State UniversityMoscowRussia
  3. 3.A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia

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