Influence of swirl on the stability of a rod in annular leakage flow |
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| Affiliation: | 1. Department of Mechanical Systems Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa-shi, Yamagata 992-8510, Japan;2. Department of Mechanical Engineering, Osaka Sangyo University, 3-1-1 Nakagaito, Daito-shi, Osaka 574-8530, Japan;1. National University of Singapore, Department of Civil and Environmental Engineering, 1 Engineering Drive 2, Singapore 117576, Singapore;2. University of Messina, Department of Civil and Environmental Engineering, DICIEAMA, Villaggio S. Agata, 98166 Messina, Italy;1. Mechanical Engineering Department, National Institute of Technology Durgapur, Durgapur, India;2. Applied Mechanics Department, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India;3. Department of Mechanical and Industrial Engineering, Faculty of Applied Science and Engineering, University of Toronto, Toronto, Ontario, Canada;1. College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414006, China;2. College of Electronic Engineering, Guangxi Normal University, Guilin 541004, China |
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| Abstract: | The influence of swirl (flow rotation) on the stability of a rod in annular leakage flow is investigated. Under the assumption of laminar flow and plane vibrations (no whirling), it is shown that the swirl acts, in effect, as an elastic foundation with negative foundation stiffness, the magnitude being proportional to the mean circumferential flow rate squared. Consequently, swirl always lowers the critical axial flow speed in case of divergence instability of a rod of finite length. Numerical analysis is needed to predict the effect of swirl in case of flutter instability of a finite rod; this is not performed here. However, for the flutter-like instability of travelling waves in an infinite rod-channel system, it is shown analytically that swirl again always lowers the critical axial flow speed. Finally, it is found that by circumferential flow alone, the travelling waves are extinguished at a certain flow rate, followed by a divergence-like instability. |
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