Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2013)

Investigation of bubble cluster dynamics

About the authors:

Amir A. Gubaidullin, Dr. Sci. (Phys.-Math.), Professor, Сhief Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; eLibrary AuthorID, ORCID, Web of Science ResearcherID, Scopus AuthorID, a.a.gubaidullin@yandex.ru

Aleksey S. Gubkin, Junior Researcher, Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the RAS; Senior Lecturer, Department of Mechanics of Multiphase Systems, Tyumen State University; alexshtil@gmail.com


The behavior of a single bubble in the compression waves in the group of bubbles may differ from the behavior of a single bubble in the infinite liquid due to the collective hydrodynamic interaction. The mathematical model describing the dynamics of the system of changing radii bubbles in the infinite fluid with its compressibility and viscosity, as well as taking into account the hydrodynamic interaction between bubbles is given. Heat exchange of gas bubbles with liquid is considered within a twotemperature scheme. The expression for the heat flux per unit surface of the bubble which allows to describe a heat exchange of the gas bubbles with liquid in a wide range of pressures and temperatures of the liquid is presented. A numeric simulation of the nonlinear dynamics of various configurations of bubble clusters when subjected to pressure waves is done. The behavior of the single bubble into the group of bubbles under effect of compression waves is studied. It is shown that under certain conditions some bubbles need significant degree of compression, as a consequence, there are high pressures and temperatures. The example of clusters with three nested dodecahedrons of linear cluster shows that the cluster configuration can have a strong influence on its dynamics.


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