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Numerical analysis of flow-induced rotation of an S-shaped rotor

Published online by Cambridge University Press:  21 March 2019

Y. Ueda Open the ORCID record for Y. Ueda [Opens in a new window]
Y. Ueda*
Affiliation:
Department of Mechanical Engineering, Faculty of Science and Engineering, Setsunan University, 17-8 Ikeda-Nakamachi, Neyagawa, Osaka 572-8508, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Flow-induced rotation of an S-shaped rotor is investigated using an adaptive numerical scheme based on a vortex particle method. The boundary integral equation with respect to Bernoulli’s function is solved using a panel method for obtaining the pressure distribution on the rotor surface which applies the torque to the rotor. The present work first addresses the validation of the scheme against the previous studies of a rotating circular cylinder. Then, we compute the automatic rotation start of an S-shaped rotor from a quiescent state for various values of the moment of inertia. The computed flow patterns where the rotor supplies (or is supplied with) the torque to (or from) the fluid are shown during one cycle of rotation. The vortex shedding from the tip of the advancing bucket is found to play a key role in generating positive torque on the rotor. A remarkable finding is the fact that, after the rotor reaches a stable rotation, the trajectory of the limit cycle in the present autonomous system accounts for the stable rotating movement of the rotor. Furthermore, the hydrodynamic scenario of the rotor automatically starting up from a quiescent state and entering the limit cycle is elucidated for various values of the moment of inertia and the initial angle of the rotor.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 77 - 113
Copyright
© 2019 Cambridge University Press 

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References

Afungchui, D., Kamoun, B. & Helali, A. 2014 Vortical structures in the wake of the Savonius wind turbine by the discrete vortex method. Renew. Energy 69, 174–179.Google Scholar
Badr, H. M. & Dennis, S. C. R. 1985 Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder. J. Fluid Mech. 158, 447–488.Google Scholar
Bar-Lev, M. & Yang, H. T. 1975 Initial flow field over an impulsively started circular cylinder. J. Fluid Mech. 72, 625–647.Google Scholar
Beale, J. T. & Majda, A. 1985 High order accurate vortex methods with explicit velocity kernels. J. Comput. Phys. 58, 188–208.Google Scholar
Cottet, G.-H. & Koumoutsakos, P. D. 2000 Vortex Methods: Theory and Practice. Cambridge University Press.Google Scholar
Cottet, G.-H. & Poncet, P. 2003 Advances in direct numerical simulations of 3D wall-bounded flows by vortex-in-cell methods. J. Comput. Phys. 193, 136–158.Google Scholar
Degond, P. & Mas-Gallic, S. 1989 The weighted particle method for convection-diffusion equations, Part 1: the case of an isotropic viscosity, Part 2: the anisotropic case. Math. Comput. 53, 485–525.Google Scholar
Fujisawa, N. 1992 On the torque mechanism of Savonius rotors. J. Wind Engng Ind. Aerodyn. 40, 277–292.Google Scholar
Fujisawa, N. 1996 Velocity measurements and numerical calculations on flow fields in and around Savonius rotors. J. Wind Engng Ind. Aerodyn. 59, 39–50.Google Scholar
Greengard, L. & Rokhlin, V. 1987 A fast algorithm for particle simulations. J. Comput. Phys. 73, 325–350.Google Scholar
Jaohindy, P., Ennamiri, H., Garde, F. & Bastide, A. 2014 Numerical investigation of airflow through a Savonius rotor. Wind Energy 17, 853–868.Google Scholar
Jaohindy, P., McTavish, S., Garde, F. & Bastide, A. 2013 An analysis of the transient forces acting on Savonius rotors with different aspect ratios. Renew. Energy 55, 286–295.Google Scholar
Kida, T., Sakate, H. & Nakajima, T. 1997 Pressure distribution obtained using two-dimensional vortex method. Trans. Japan Soc. Mech. Engrs B 63 (606), 378–386.Google Scholar
Koumoutsakos, P. 2005 Multiscale flow simulations using particles. Annu. Rev. Fluid Mech. 37, 457–487.Google Scholar
Koumoutsakos, P. & Leonard, A. 1995 High-resolution simulations of the flow around an impulsively started circular cylinder using vortex methods. J. Fluid Mech. 296, 1–38.Google Scholar
Koumoutsakos, P., Leonard, A. & Pépin, F. 1994 Boundary conditions for viscous vortex methods. J. Comput. Phys. 113, 52–61.Google Scholar
Lugt, H. J. 1983 Autorotation. Annu. Rev. Fluid Mech. 15, 123–147.Google Scholar
Nakajima, M., Iio, S. & Ikeda, T. 2008 Performance of double-step Savonius rotor for environmentally friendly hydraulic turbine. J. Fluid Sci. Technol. 3, 410–419.Google Scholar
Nasef, M. H., El-Askary, W. A., AbdEL-hamid, A. A. & Gad, H. E. 2013 Evaluation of Savonius rotor performance: static and dynamic studies. J. Wind Engng Ind. Aerodyn. 123, 1–11.Google Scholar
Noca, F., Shiels, D. & Jeon, D. 1997 Measuring instantaneous fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct. 11, 345–350.Google Scholar
Noca, F., Shiels, D. & Jeon, D. 1999 A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct. 13, 551–578.Google Scholar
Nozu, T. & Tamura, T. 1997 Application of computational fluid technique with high accuracy and conservation property to the wind resistant problems of buildings and structures. Part 1. Estimations of numerical errors of the interpolation method and its accuracy for the prediction of flows around a rectangular cylinder at low Reynolds numbers. J. Struct. Constr. Engng AIJ 494, 43–49.Google Scholar
Ploumhans, P. & Winckelmans, G. S. 2000 Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry. J. Comput. Phys. 165, 354–406.Google Scholar
Roy, S. & Saha, U. K. 2013 Review on the numerical investigations into the design and development of Savonius wind rotors. Renew. Sustainable Energy Rev. 24, 73–83.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Shaheen, M., El-Sayed, M. & Abdallah, S. 2015 Numerical study of two-bucket Savonius wind turbine cluster. J. Wind Engng Ind. Aerodyn. 137, 78–89.Google Scholar
Takahashi, Y. 1996 Introduction to Modern Mathematics, vol. 5, pp. 115–120. Iwanami (in Japanese).Google Scholar
Tian, W., Song, B., VanZwieten, J. H. & Pyakurel, P. 2015 Computational fluid dynamics prediction of a modified Savonius wind turbine with novel blade shapes. Energies 8, 7915–7929.Google Scholar
Ueda, Y., Kida, T. & Iguchi, M. 2013 Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders. J. Fluid Mech. 736, 414–443.Google Scholar
Uhlman, J. S.1992 An integral equation formulation of the equation of motion of an incompressible fluid. Tech. Rep. 10086. Naval Undersea Warfare Center.Google Scholar
Ushiyama, I., Nagai, H. & Shinoda, J. 1986 Experimentally determining the optimum design configuration for Savonius rotors. Trans. Japan Soc. Mech. Engrs B 52 (480), 2973–2982.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.Google Scholar
Zhou, T. & Rempfer, D. 2013 Numerical study of detailed flow field and performance of Savonius wind turbines. Renew. Energy 51, 373–381.Google Scholar