The Effect of Nonlinearity on Acoustic Streaming in Cylindrical Cavities of Different Diameters
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The Effect of Nonlinearity on Acoustic Streaming in Cylindrical Cavities of Different Diameters A. A. Gubaidullin1, 2* and A. V. Pyatkova1** (Submitted by A. M. Elizarov) 1
Khristianovich Institute of Theoretical and Applied Mechanics, Tyumen Branch, Siberian Branch, Russian Academy of Sciences, Tyumen, 625026 Russia 2
University of Tyumen, Tyumen, 625003 Russia
Received March 10, 2020; revised March 19, 2020; accepted March 22, 2020
Abstract—Acoustic streaming in vibrating cylindrical cavities of different diameters under isothermal boundary conditions is numerically investigated. Two vibration frequencies are considered at various vibration amplitudes. The influence of increasing nonlinearity of the process on the structure of acoustic streaming is determined. The dynamics of an increase in the acoustic streaming velocity with an increase in the vibration amplitude is shown. The vibration amplitudes at which shock waves are formed in the regime of steady-state oscillations are revealed. DOI: 10.1134/S1995080220070185 Keywords and phrases: acoustic streaming, Rayleigh streaming, Schlichting streaming, isothermal boundary conditions, vibration frequency, vibration amplitude, shock wave.
1. INTRODUCTION The oscillatory motion of the gas filling the vibrating cavity leads to the appearance of acoustic streaming, which is a time-average mass flow that has a stable vortex structure. There are the Schlichting streaming vortices and the Rayleigh streaming vortices, which have a certain direction of rotation. Schlichting streaming is a series of vortices in the boundary layer, in which the medium is transported near the cavity wall from vibrational velocity nodes to antinodes. The Rayleigh streaming vortices are in free stream, the direction of their rotation is opposite to the direction of rotation of the Schlichting streaming vortices [1]. An increase in the vibrational effect on the cavity can lead to distortion of the acoustic streaming vortices, as well as affect the period average temperature, pressure, and density [2–9]. The thermal boundary conditions [6, 10–13] and the ratio of the cavity radius to the thickness of the acoustic boundary layer [14] have a significant effect on the acoustic streaming structure. In [15–17], the acoustic streaming structure in cavities of different diameters at small vibration amplitude was revealed. In the present paper, acoustic streaming in cylindrical cavities at isothermal boundary conditions is studied in the case of increasing nonlinearity of the process, which occurs due to an increase in the amplitude of cavity vibration. Vibration frequency and cavity radius vary. * **
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THE EFFECT OF NONLINEARITY ON ACOUSTIC STREAMING
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Acos(Zt) r
T0
T0
T0 2R0
x
L Fig. 1. Problem statement.
2. PROBLEM FORMULATION Let us consider a cylindrical cavity (Fig. 1) of length L and radius R0 with impermeable walls. The cavity is filled with air. The cavity is subjected to vibration effect with frequency ω and amplitude A. The
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