Specificities of Acoustic Streaming under Isothermal Boundary Conditions in Cavities of Different Diameters

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

Anna V. Pyatkova, Cand. Sci. (Phys.-Math.), Research Associate, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Research Associate, Institute of Mechanics and Engineering Kazan Scientific Center of the Russian Academy of Sciences; annyakovenko@yandex.ru

Abstract:

Acoustic streaming (or secondary streaming) is a time-average mass transfer, which has a vortex character, and arises in addition to the oscillatory motion in the acoustic field. Acoustic streaming is widely studied at present both theoretically and experimentally. It allows enhancing the heat transfer process and improving the operation of thermoacoustic refrigerators, acoustic resonators, or other devices, in which the connection of mechanical and thermal energy is realized. The boundary conditions on the cavity walls have a significant effect on the shape and direction of rotation of the acoustic streaming vortices. This manifests itself especially when the vibration frequency is distant from the resonant one. Flows under similar conditions are not sufficiently studied.

This study aims to obtain the acoustic streaming patterns when heat exchange is taken into account (under isothermal boundary conditions) when the vibration frequency is moving away from the resonant one for cavities of different diameters. The problem was solved numerically. An implicit numerical scheme was used to find a numerical solution. The equations were discretized using the control volume method. The program code was previously repeatedly tested, and a comparison with the approximate analytical solution was made.

In this work, the authors found that with a decrease in the vibration frequency at a fixed cavity diameter, the Schlichting streaming vortices decrease in size, move away from the ends of the cavity and are displaced to the center of the lateral surface, or disappear completely. It was also found that with a decrease in the cavity radius, the Rayleigh streaming vortices do not disappear, as was the case when the vibration frequency was close to the resonant one, but concentrated near the ends of the cavity.

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