Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T14:44:48.563Z Has data issue: false hasContentIssue false
  • English
  • Français

Impulsively started planar actuator surfaces in high-Reynolds-number steady flow

Published online by Cambridge University Press:  23 September 2013

P. B. Johnson ,
A. Wojcik ,
K. R. Drake  and
I. Eames
P. B. Johnson*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK School of Engineering, Nazarbayev University, 53 Kabanbay batyr, Astana, Kazakhstan
A. Wojcik
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
K. R. Drake
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
I. Eames
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
*
†Email address for correspondence: peter.johnson@ucl.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The characteristics of unbounded flow past an impulsively started planar energy extracting device, such as a wind or tidal turbine, are studied theoretically, numerically and experimentally. The initial thrust on an impulsively started device, which can be more than double the steady thrust, is an important consideration for design and safe operation. The energy sink is modelled here as an ‘actuator surface’ which imposes a uniform pressure discontinuity in the fluid proportional to the square of the fluid speed normal to the surface, the fluid density, and a dimensionless resistance coefficient. The flow past the actuator is studied theoretically for the case of weak resistance using an unsteady model which recovers steady linear momentum theory in the limit of long time. For the case of strong resistance the flow is studied numerically using the point vortex method. Experimental measurements of thrust on a mesh towed through static water are compared to the numerical results and show good agreement. The thrust on an impulsively started device is estimated, for a typical installation, to fall to within 10 % of the steady value within ∼1 min. The numerical model is also used to simulate the gradual startup of a device, yielding estimates of the time constant necessary in a control system in order to reduce peak thrusts in practice.

JFM classification

Wakes/Jets: Shear layers Vortex Flows: Vortex dynamics Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 302 - 324
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Betz, A. 1920 Das Maximum der theoretisch moglichen Ausnutzung des Windes durch Windmotoren. Z. Gesamte Turbinenwesen 26, 307–309.Google Scholar
Burton, T., Sharpe, D., Jenkins, N. & Bossanyi, E. 2001 Wind Energy Handbook. John Wiley & Sons.Google Scholar
Castro, I. P. 1971 Wake characteristics of two-dimensional perforated plates normal to an air-stream. J. Fluid Mech. 46 (3), 599–609.CrossRefGoogle Scholar
Cottet, G.-H. & Koumoutsakos, P. D. 2000 Vortex Methods; Theory and Practice. Cambridge University Press.Google Scholar
Eames, I., Johnson, P. B., Roig, V. & Risso, F. 2011a Effect of turbulence on the downstream velocity deficit of a rigid sphere. Phys. Fluids 23 (9), 095103.Google Scholar
Eames, I., Jonsson, C. & Johnson, P. B. 2011b The growth of a cylinder wake in turbulent flow. J. Turbul. 12, N39.Google Scholar
Fraenkel, P. 2010 Development and testing of marine current turbine’s SeaGen 1.2 MW tidal stream turbine. In Proceedings of the 3rd International Conference on Ocean Energy (ICOE).Google Scholar
Fraenkel, P. L. 2013 Articulated false seabed. Patent EP1704324.Google Scholar
Froude, R. E. 1889 On the part played in propulsion by differences of fluid pressure. Trans. (R.) Inst. Naval Archit. 30, 390–405.Google Scholar
Johnson, P. B. 2012 Hydrodynamics of tidal stream energy extractors with two rows of blades. PhD thesis, University College London.Google Scholar
Johnson, P. B., Jonsson, C., Achilleos, S. & Eames, I. 2012 On the effect of ambient turbulence on wake decay. In Proceedings of The Science of Making Torque From Wind 2012.Google Scholar
Jonsson, C., Johnson, P. B. & Eames, I. 2011 Energy extractors in turbulent flow: wake decay and implications for farm layout. In Proceedings of the 9th European Wave and Tidal Energy Conference (EWTEC).Google Scholar
Joukowsky, N. 1920 Windmill of the NEJ type. Transactions of the Central Institute for Aero-Hydrodynamics of Moscow. Also published in Joukowsky NE. Collected Papers Vol VI. The Joukowsky Institute for AeroHydrodynamics, Moscow: vol VI, 405–409, 1937 (in Russian).Google Scholar
Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123–155.Google Scholar
Krasny, R. 1991 Vortex Sheet Computations: Roll-up, Wakes, Separation, Lectures in Applied Mathematics: Vortex Dynamics and Vortex Methods (ed. Anderson, C. R. & Greengard, C.), vol. 28.Google Scholar
Kuchemann, D. & Weber, J. 1953 Aerodynamics of Propulsion/Dietrich Kuchemann, Johanna Weber. McGraw-Hill.Google Scholar
van Kuik, G. A. M. 1991 On the limitations of Froude’s actuator disc concept. PhD thesis, Technische Universiteit Eindhoven.Google Scholar
van Kuik, G. A. M. 2003 The edge singularity of an actuator disc with a constant normal load. In 22nd AIAA/ASMA Wind Energy Symposium.Google Scholar
van Kuik, G. A. M. 2004a The flow induced by Prandtlś self-similar vortex sheet spirals at infinite distance from the spiral kernel. Eur. J. Mech. (B/Fluids) 23, 607–616.Google Scholar
van Kuik, G. A. M. 2004b The generation of vorticity by actuator disc force fields, with an exact solution of Wu’s equation. In Special Topic Conference ‘The Science of Making Torque from Wind’.Google Scholar
van Kuik, G. A. M. 2007 The Lanchester–Betz–Joukowsky limit. Wind Energy 10 (3), 289–291.CrossRefGoogle Scholar
Lanchester, F. W. 1915 A contribution to the theory of propulsion and the screw propeller. Trans. (R.) Inst. Naval Archit. 57, 98–116.Google Scholar
Lee, J. H. W. & Greenberg, M. 1984 Line momentum source in shallow inviscid fluid. J. Fluid Mech. 145, 287–304.Google Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comput. Phys. 37 (3), 289–335.CrossRefGoogle Scholar
Lovalenti, P. M. & Brady, J. F. 1993 The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561–605.Google Scholar
McAdam, R., Houlsby, G., Oldfield, M. & McCulloch, M. 2010 Experimental testing of the transverse horizontal axis water turbine. IET Renewable Power Generation 4, 510–519.Google Scholar
Moore, D. 1974 Numerical study of roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225–235.Google Scholar
Moore, D. W. 1981 On the point vortex method. SIAM J. Sci. Stat. Comput. 2 (1), 65–84.Google Scholar
Nicolle, A. & Eames, I. 2011 Numerical study of flow through and around a circular array of cylinders. J. Fluid Mech. 679, 1–31.CrossRefGoogle Scholar
Okulov, V. & van Kuik, G. 2012 The Betz–Joukowsky limit: on the contribution to rotor aerodynamics by the British, German and Russian scientific schools. Wind Energy 15 (2), 335–344.CrossRefGoogle Scholar
O’Neill, F. 2006 Source models of flow through and around screens and gauzes. Ocean Engng 33 (14–15), 1884–1895.Google Scholar
Peters, D. A. 2003 Review of dynamic wake models for application to dynamics and stability of rotorcraft. In Proceedings of the 4th Australian Pacific Vertiflite Conference On Helicopter Technology.Google Scholar
Pitt, D. M. & Peters, D. A. 1981 Theoretical prediction of dynamic-inflow derivatives. Vertica 5 (1), 21–34.Google Scholar
Ponta, F., Seminara, J. & Otero, A. 2007 On the aerodynamics of variable-geometry oval-trajectory Darrieus wind turbines. Renewable Energy 32 (1), 35–56.Google Scholar
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex sheets. J. Fluid Mech. 88 (3), 401–430.Google Scholar
Pullin, D. I. & Perry, A. E. 1980 Some flow visualization experiments on the starting vortex. J. Fluid Mech. 97 (2), 239–255.Google Scholar
Rankine, W. J. M. 1865 On the mechanical principles of the action of propellers. Trans. (R.) Inst. Naval Archit. 6, 13–30.Google Scholar
Snel, H., Schepers, J. & Nederland, S. E. C. 1995 Joint Investigation of Dynamic Inflow Effects and Implementation of an Engineering Method. Netherlands Energy Research Foundation ECN.Google Scholar
Takami, H. 1964 A numerical experiment with discrete vortex approximation with reference to the rolling up of a vortex sheet. Tech. Rep. SUDAER 202. Dept. of Aeron. & Astron., Stanford University.Google Scholar
Taylor, G. I. 1944 Air resistance of a flat plate of very porous material. Aero. Res. Counc. R. and M. 2236.Google Scholar
Taylor, G. I. & Davies, R. M. 1944 The aerodynamics of porous sheets. Aero. Res. Counc. R. and M. 2237.Google Scholar
Whelan, J. I., Graham, J. M. R. & Peir, J. 2009 A free-surface and blockage correction for tidal turbines. J. Fluid Mech. 624, 281–291.Google Scholar