{"title":"由圆柱体夹紧的倒旗的起始不稳定性","authors":"Haokui Jiang, Yujia Zhao, Shunxiang Cao","doi":"10.1016/j.jfluidstructs.2025.104373","DOIUrl":null,"url":null,"abstract":"<div><div>We numerically investigate the hydrodynamic characteristics and analyze the instability mechanism of a two-dimensional inverted flag clamped by a cylinder. There are two transition routes and a total of six kinds of solutions existing under this configuration for different diameters of cylinders. Specifically, for small cylinders, the undeformed equilibrium UE transitions to deformed-deflected stable SDS through a supercritical pitchfork bifurcation, which is judged by the weakly nonlinear analysis together with the global linear instability analysis. The instability mechanism is the lifting effect of the ‘symmetry-breaking’ mode SM working at the leading edge of the elastic flag. For large cylinders, another unstable ‘vortex-shedding’ mode VM (decoupled with structure mode) causes the disappearance of the UE and SDS solutions, replaced by a small amplitude flapping. The SM and the VM mainly contribute to the growth of perturbations in flag and downstream cylinder regions respectively, which can excite multi-mode oscillating transition analyzed by proper orthogonal decomposition. Moreover, we define two critical diameters <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>V</mi><mi>M</mi></mrow></msub></math></span> dividing the transition from UE to deformed-deflected stable or small amplitude flapping, and both <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>V</mi><mi>M</mi></mrow></msub></math></span> decreases with the increase of Reynolds number. Finally, we prove downstream vortex shedding can induce upward vortex-induced vibration of the flag and further improve the efficiency of energy transfer from the fluid to the structure during small-deflection flapping.</div></div>","PeriodicalId":54834,"journal":{"name":"Journal of Fluids and Structures","volume":"137 ","pages":"Article 104373"},"PeriodicalIF":3.5000,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Onset instability of inverted flags clamped by a cylinder\",\"authors\":\"Haokui Jiang, Yujia Zhao, Shunxiang Cao\",\"doi\":\"10.1016/j.jfluidstructs.2025.104373\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We numerically investigate the hydrodynamic characteristics and analyze the instability mechanism of a two-dimensional inverted flag clamped by a cylinder. There are two transition routes and a total of six kinds of solutions existing under this configuration for different diameters of cylinders. Specifically, for small cylinders, the undeformed equilibrium UE transitions to deformed-deflected stable SDS through a supercritical pitchfork bifurcation, which is judged by the weakly nonlinear analysis together with the global linear instability analysis. The instability mechanism is the lifting effect of the ‘symmetry-breaking’ mode SM working at the leading edge of the elastic flag. For large cylinders, another unstable ‘vortex-shedding’ mode VM (decoupled with structure mode) causes the disappearance of the UE and SDS solutions, replaced by a small amplitude flapping. The SM and the VM mainly contribute to the growth of perturbations in flag and downstream cylinder regions respectively, which can excite multi-mode oscillating transition analyzed by proper orthogonal decomposition. Moreover, we define two critical diameters <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>V</mi><mi>M</mi></mrow></msub></math></span> dividing the transition from UE to deformed-deflected stable or small amplitude flapping, and both <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>V</mi><mi>M</mi></mrow></msub></math></span> decreases with the increase of Reynolds number. Finally, we prove downstream vortex shedding can induce upward vortex-induced vibration of the flag and further improve the efficiency of energy transfer from the fluid to the structure during small-deflection flapping.</div></div>\",\"PeriodicalId\":54834,\"journal\":{\"name\":\"Journal of Fluids and Structures\",\"volume\":\"137 \",\"pages\":\"Article 104373\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2025-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fluids and Structures\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0889974625001082\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fluids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0889974625001082","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Onset instability of inverted flags clamped by a cylinder
We numerically investigate the hydrodynamic characteristics and analyze the instability mechanism of a two-dimensional inverted flag clamped by a cylinder. There are two transition routes and a total of six kinds of solutions existing under this configuration for different diameters of cylinders. Specifically, for small cylinders, the undeformed equilibrium UE transitions to deformed-deflected stable SDS through a supercritical pitchfork bifurcation, which is judged by the weakly nonlinear analysis together with the global linear instability analysis. The instability mechanism is the lifting effect of the ‘symmetry-breaking’ mode SM working at the leading edge of the elastic flag. For large cylinders, another unstable ‘vortex-shedding’ mode VM (decoupled with structure mode) causes the disappearance of the UE and SDS solutions, replaced by a small amplitude flapping. The SM and the VM mainly contribute to the growth of perturbations in flag and downstream cylinder regions respectively, which can excite multi-mode oscillating transition analyzed by proper orthogonal decomposition. Moreover, we define two critical diameters and dividing the transition from UE to deformed-deflected stable or small amplitude flapping, and both and decreases with the increase of Reynolds number. Finally, we prove downstream vortex shedding can induce upward vortex-induced vibration of the flag and further improve the efficiency of energy transfer from the fluid to the structure during small-deflection flapping.
期刊介绍:
The Journal of Fluids and Structures serves as a focal point and a forum for the exchange of ideas, for the many kinds of specialists and practitioners concerned with fluid–structure interactions and the dynamics of systems related thereto, in any field. One of its aims is to foster the cross–fertilization of ideas, methods and techniques in the various disciplines involved.
The journal publishes papers that present original and significant contributions on all aspects of the mechanical interactions between fluids and solids, regardless of scale.