Effect of curvature on dual solutions of flow through a curved circular tube |
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| Affiliation: | 1. Department of Engineering Sciences, Faculty of Engineering, Okayama University, Okayama 700, Japan;2. Department of Mechanical Engineering, Faculty of Engineering, Okayama University, Okayama700, Japan;1. Renewable Energy and Energy Efficiency Group, Department of Infrastructure Engineering, The University of Melbourne, Victoria 3010, Australia;2. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia;3. Center of Research Excellence in Renewable Energy (CoRE-RE), Research Institute, King Fahd University of Petroleum & Minerals (KFUPM), Dhahran 31261, Saudi Arabia;4. UM Power Energy Dedicated Advanced Centre (UMPEDAC), Level 4, Wisma R & D, University of Malaya, 59990 Kuala Lumpur, Malaysia;1. Department of Energy and Electrical Engineering, Korea Polytechnic University, Siheung, Republic of Korea;2. Energy Innovation Center, Central Research Institute of Electric Power Industry, Yokosuka, Japan;3. Department of Electrical, Electronics & Communication Engineering Edu., Chungnam National University, Daejeon, Republic of Korea;4. Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA;5. Department of Energy System Engineering, Chung-Ang University, Seoul, Republic of Korea;1. Department of Aeronautical & Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK;2. Jaguar Land Rover, Gaydon, CV35 0RR, UK;1. School of Mechanical and Aerospace Engineering, Seoul National University, Gwanak-gu, Seoul 151-744, Republic of Korea;2. Department of Mechanical Engineering, Kyung Hee University, Seochun 1, Yongin, Gyeonggi 446-701, Republic of Korea |
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| Abstract: | Dual solutions, i.e., two-vortex and four-vortex solutions, of the flow through a curved circular tube are numerically obtained by the spectral method for 0 ⩽ δ ⩽ 0.8 and 500 ⩽ Dn ⩽ 10000, where δ is the non-dimensional curvature of the tube and Dn the Dean number. It is found that the critical Dean number above which the four-vortex solution exists takes the lowest value 956 at δ = 0 and increases with δ. In terms of the Reynolds number of the flow, however, the critical Reynolds number decreases from infinity as δ increases from zero, takes the minimum value of about 250 at δ ≈ 0.52, and then increases again. |
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