{"title":"Nonlinear Resonant Gas Oscillations in Resonators with Variable Cross-section","authors":"D. A. Gubaidullin, B. A. Snigerev","doi":"10.1134/s1995080224602170","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602170","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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.
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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