Nonlinear Resonant Gas Oscillations in Resonators with Variable Cross-section

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI:10.1134/s1995080224602170
D. A. Gubaidullin, B. A. Snigerev
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Abstract

In a number of studies, it has been shown that the geometry of an acoustic resonator strongly affects its resonant frequencies, as well as the nonlinear shape of the standing pressure waves generated inside the cavity. In this paper, we consider three resonators with different wall shapes (cone, exponential and bulb-shaped resonators) in which gas vibrations are formed due to an external periodic force. The acoustic field in the resonators is generated by the vibration of the left wall of the enclosure. The oscillation frequency of this wall is chosen so that the lowest acoustic mode can propagate along the resonator. The fully compressible form of the Navier–Stokes equations is used, and the explicit time-stepping algorithm is employed for modeling the motion of acoustic waves. The structure of acoustic flows of the second order, resulting from the interaction between the wave field and viscous effects on the walls, leads to the formation of flow patterns. These patterns can be revealed by averaging solutions over a specific period of time. To evaluate the performance of resonators, the pressure amplitude gain factor is used. This is defined as the ratio of pressure amplitude at the small end of the resonator to the pressure amplitude at its large end. It has been found that the best performance is observed in a flask-shaped resonator.

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可变截面谐振器中的非线性共振气体振荡
摘要 大量研究表明,声共振器的几何形状对其谐振频率以及腔内产生的驻留压力波的非线性形状有很大影响。在本文中,我们考虑了三个具有不同壁形(锥形、指数形和球形谐振器)的谐振器,在这些谐振器中,气体振动是由外部周期性力引起的。谐振器中的声场由外壳左壁的振动产生。选择这面墙的振动频率是为了让最低的声学模式能够沿着谐振器传播。采用纳维-斯托克斯方程的完全可压缩形式,并使用显式时间步进算法来模拟声波的运动。二阶声波流的结构是由波场和壁面上的粘性效应相互作用产生的,从而形成了流动模式。通过对特定时间段内的解求取平均值,可以揭示这些模式。为了评估谐振器的性能,使用了压力振幅增益因子。其定义为谐振器小端压力振幅与大端压力振幅之比。研究发现,瓶形谐振器的性能最佳。
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来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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