Comparison of Acoustic Streaming In Rectangular and Cylindrical Cavities

About the authors:

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

Anna S. Semenova, Master Student, Department of Mathematical Modeling, University of Tyumen; Vik040767@yandex.ru

Abstract:

In an acoustic field, in addition to periodic motion of the medium, a directed time average mass flow can appear, representing steady vortices. Appearance of the vortices leads to the formation of an acoustic streaming. Features of acoustic processes must be taken into account when developing various devices related to vibration, acoustic resonators, thermoacoustic refrigerators. Acoustic streaming is widely studied both experimentally and theoretically. The modern methods of numerical modeling opened new opportunities for calculation of the non-linear modes of streaming. Most often researches are conducted for cylindrical cavities (tubes) or in rectangular two-dimensional cavities.

However, there is no description of the same effect in rectangular and cylindrical cavity. This article defines the influence of the cavity geometry on features of acoustic streaming is defined and compares acoustic streaming in rectangular and cylindrical cavities. The authors study the case of small vibration amplitude at different vibration frequencies, as well as the case of a fixed vibration frequency with increasing vibration amplitude, which leads to an increase in the nonlinearity of the process. The walls of the cavities are maintained at constant temperature (isothermal boundary conditions). The problem is solved numerically with the use of the finite volume method and the implicit scheme. As a test, comparison of wave motion of the gas with the available analytical solution by other authors is executed. For rectangular and cylindrical cavities, a difference in amplitudes of free oscillations at the initial stage of the process, as well as in the damping rates of free oscillations, is revealed. The distortion of acoustic streaming vortices and formation of new vortices with increasing of nonlinearity of the process are illustrated. The streaming structure essentially depends on the cavity geometry.

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