Abstract
Due to the anomalous behaviour of the Joukowsky rotor, this model is analysed in details for small tip speed ratios. The analysis is carried analytically and by comparison to additional CFD computations and some recent experiments. It is found that the model only attains a well-defined optimum for tip speed ratios larger than 0.93, but that other inherent features of the equations by themselves will limit the power performance at smaller tip speed ratios.
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References
Delery, J.M.: Aspects of vortex breakdown. Prog. Aerospace Sci. 30, 1–59 (1994)
De Vries, O.: Fluid dynamic aspects of wind energy conversion. AGARDograph No. 243. AGARD (1979). ISBN: 92-835-1326-6
Glauert, H.: Airplane Propellers. In: Durand, W.F. (ed.) Division L in Aerodynamic Theory, vol. IV, pp. 169–360. Springer: Berlin (1935)
Joukowsky, N.E.: Vortex theory of a rowing screw. Trudy Otdeleniya Fizicheskikh Nauk Obshchestva Lubitelei Estestvoznaniya 16, 1 (1912). (in Russian)
Lam, G.C.K.: Wind energy conversion efficiency limit. Wind Eng. 30(5), 431 (2006)
Leweke, T., Quaranta, H.U., Mikkelsen, R.F., Sørensen, J.N.: Vortex breakdown and wake characteristics of a Joukowsky rotor at small tip speed ratios. In: Submitted to the Wake Conference, Visby, Sweden (2015)
Madsen, H.A., Mikkelsen, R., Øye, S., Bak, B., Johansen, J.: A detailed investigation of the blade element momentum (BEM) model based on analytical and numerical results and proposal for modifications of the BEM model. Making torque from wind. J. Phys. Conf. Ser. 75, 012016 (2007). doi:10.1088/1742-6596/75/1/012016
Mikkelsen, R.F.: Actuator disc methods applied to wind turbines. Ph.D. Dissertation, Technical University of Denmark, MEK-FM-PHD 2003-02 (2003)
Mikkelsen, R.F., Øye, S., Sørensen, J.N., Madsen, H.Aa., Shen, W.Z.: Analysis of wake expansion and induction near tip. In: Proceedings of EWEC 2009, European Wind Energy Association (EWEA), Brussels (2009)
Sharpe, D.J.: A general momentum theory applied to an energy-extracting actuator disc. Wind Energy 7, 177–188 (2004)
Sørensen, J.N., Kock, C.W.: A model for unsteady rotor aerodynamics. J. Wind Eng. Ind. Aerodyn. 58, 259–275 (1995)
Sørensen, J.N., Mikkelsen, R.: An upper limit of the power performance of wind turbines operating at low tip speed ratios (2015). (To be submitted)
Sørensen, J.N., Myken, A.: Unsteady actuator disc model for horizontal axis wind turbines. J. Wind Eng. Ind. Aerodyn. 139, 139–149 (1992)
Sørensen, J.N., Shen, W.Z., Munduate, X.: Analysis of wake-states by a full-field actuator disc model. Wind Energy 1, 73–88 (1998)
Sørensen, J.N., van Kuik, G.A.M.: General momentum theory for wind turbines at low tip speed ratios. Wind Energy 14, 821–839 (2011)
Squire, H.B.: Analysis of the vortex breakdown phenomenon, Part I. Imperial College of Science and Technology, Report no. 102 (1960)
Wilson, R.E., Lissaman, P.B.S.: Applied aerodynamics of wind power machines. Oregon State University, Corvallis (1974)
Wood, D.H.: Including swirl in the actuator disc analysis of wind turbines. Wind Eng. 31(5), 317–323 (2007)
Xiros, M.I., Xiros, N.I.: Remarks on wind turbine power absorption increase by including the axial force due to the radial pressure gradient in the general momentum theory. Wind Energy 10, 99–102 (2007)
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Sørensen, J.N. (2016). Detailed Analysis of the Joukowsky Model. In: General Momentum Theory for Horizontal Axis Wind Turbines. Research Topics in Wind Energy, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-22114-4_6
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DOI: https://doi.org/10.1007/978-3-319-22114-4_6
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