{"title":"平均流管道中热声不稳定性的格林函数辅助方法","authors":"","doi":"10.1016/j.jsv.2024.118673","DOIUrl":null,"url":null,"abstract":"<div><p>Thermoacoustic instabilities arise from the feedback between an acoustic field and the unsteady heat released in a burner, yielding self-sustained oscillations. A fundamental framework for modelling thermoacoustic instabilities in systems where a mean flow is present is introduced, based on the definition of the adjoint Green’s function which permits to convert the acoustic analogy equation into an integral equation. The adjoint Green’s problem produces sensitivity functions which quantify the response of the system to initial, boundary or other forcing terms. A simple one-dimensional system is examined; it includes a steady uniform mean flow and a nonlinear heat source with an amplitude-dependent time-delay heat release model. The versatility of the approach is demonstrated by applying it to two resonators characterized by different acoustic boundary conditions: a Rijke tube and a quarter-wave resonator. The control parameters are: heat source position, heater power and tube length. The results reveal that the proposed analytical framework successfully captures the limit cycles, triggering phenomena, hystereses, and Hopf bifurcations observed in experiments. We show that the mean flow velocity cannot be discarded in the study of such systems; by increasing it, a stabilization generally ensues, with a modification of the bistability characteristics of the system.</p></div>","PeriodicalId":17233,"journal":{"name":"Journal of Sound and Vibration","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022460X24004358/pdfft?md5=c7d011c009672a04a523b9ad6e2e67db&pid=1-s2.0-S0022460X24004358-main.pdf","citationCount":"0","resultStr":"{\"title\":\"An adjoint Green’s function approach for thermoacoustic instabilities in a duct with mean flow\",\"authors\":\"\",\"doi\":\"10.1016/j.jsv.2024.118673\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Thermoacoustic instabilities arise from the feedback between an acoustic field and the unsteady heat released in a burner, yielding self-sustained oscillations. A fundamental framework for modelling thermoacoustic instabilities in systems where a mean flow is present is introduced, based on the definition of the adjoint Green’s function which permits to convert the acoustic analogy equation into an integral equation. The adjoint Green’s problem produces sensitivity functions which quantify the response of the system to initial, boundary or other forcing terms. A simple one-dimensional system is examined; it includes a steady uniform mean flow and a nonlinear heat source with an amplitude-dependent time-delay heat release model. The versatility of the approach is demonstrated by applying it to two resonators characterized by different acoustic boundary conditions: a Rijke tube and a quarter-wave resonator. The control parameters are: heat source position, heater power and tube length. The results reveal that the proposed analytical framework successfully captures the limit cycles, triggering phenomena, hystereses, and Hopf bifurcations observed in experiments. We show that the mean flow velocity cannot be discarded in the study of such systems; by increasing it, a stabilization generally ensues, with a modification of the bistability characteristics of the system.</p></div>\",\"PeriodicalId\":17233,\"journal\":{\"name\":\"Journal of Sound and Vibration\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022460X24004358/pdfft?md5=c7d011c009672a04a523b9ad6e2e67db&pid=1-s2.0-S0022460X24004358-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Sound and Vibration\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022460X24004358\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Sound and Vibration","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022460X24004358","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ACOUSTICS","Score":null,"Total":0}
An adjoint Green’s function approach for thermoacoustic instabilities in a duct with mean flow
Thermoacoustic instabilities arise from the feedback between an acoustic field and the unsteady heat released in a burner, yielding self-sustained oscillations. A fundamental framework for modelling thermoacoustic instabilities in systems where a mean flow is present is introduced, based on the definition of the adjoint Green’s function which permits to convert the acoustic analogy equation into an integral equation. The adjoint Green’s problem produces sensitivity functions which quantify the response of the system to initial, boundary or other forcing terms. A simple one-dimensional system is examined; it includes a steady uniform mean flow and a nonlinear heat source with an amplitude-dependent time-delay heat release model. The versatility of the approach is demonstrated by applying it to two resonators characterized by different acoustic boundary conditions: a Rijke tube and a quarter-wave resonator. The control parameters are: heat source position, heater power and tube length. The results reveal that the proposed analytical framework successfully captures the limit cycles, triggering phenomena, hystereses, and Hopf bifurcations observed in experiments. We show that the mean flow velocity cannot be discarded in the study of such systems; by increasing it, a stabilization generally ensues, with a modification of the bistability characteristics of the system.
期刊介绍:
The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application.
JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.