A criterion for detection of the onset of Dean instability in Newtonian fluids |
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| Affiliation: | 1. State Key Laboratory of Fluid Power and Mechatronic System, Department of Mechanics, Zhejiang University, Hangzhou 310027, China;2. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, China;1. CEFT, Departamento de Engenharia Química, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal;2. School of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH United Kingdom;3. CEFT, Departamento de Engenharia Mecânica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal;4. Departamento de Engenharia Electromecânica, C-MAST, Universidade da Beira Interior, 6201-001 Covilhã, Portugal;1. School of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, UK;2. Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan |
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| Abstract: | Dean instability for Newtonian fluids in laminar secondary flow in 180° curved channels was studied experimentally and numerically. The numerical study used Fluent CFD code to solve the Navier–Stokes equations, focusing on flow development conditions and the parameters influencing Dean instability. An accurate criterion based on the radial gradient of the axial velocity was defined that allows detection of the instability threshold, and this criterion is used to optimize the grid geometry. The effects on Dean instability of the curvature ratio (from 5.5 to 20) and aspect ratio (from 0.5 to 12) are studied. In particular, we show that the critical value of the Dean number decreases with the increasing duct curvature ratio. The variation of the critical Dean number with duct aspect ratio is less regular.In the experimental study, flows were visualized in several tangential positions of a 180° curved channel with aspect ratio 8 and curvature ratio 10. The flow is hydrodynamically developed at the entrance to the curved channel. The critical Dean number is detected and the development of secondary flow vortices by additional counter-rotating vortex pairs is observed. A diagram of different critical Dean numbers is established. |
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