Numerical Modeling of Wind Turbine Wakes
Tóm tắt
An aerodynamical model for studying three-dimensional flow fields about wind turbine rotors is presented. The developed algorithm combines a three-dimensional Navier-Stokes solver with a so-called actuator line technique in which the loading is distributed along lines representing the blade forces. The loading is determined iteratively using a blade-element approach and tabulated airfoil data. Computations are carried out for a 500 kW Nordtank wind turbine equipped with three LM19.1 blades. The computed power production is found to be in good agreement with measurements. The computations give detailed information about basic features of wind turbine wakes, including distributions of interference factors and vortex structures. The model serves in particular to analyze and verify the validity of the basic assumptions employed in the simple engineering models.
Từ khóa
Tài liệu tham khảo
Glauert, H., 1963, “Airplane Propellers,” Aerodynamic Theory, Durand, W. F., ed., Dover, New York.
Miller, R. H. , 1983, “The Aerodynamic and Dynamic Analysis of Horizontal Axis Wind Turbines,” J. Wind. Eng. Ind. Aerodyn., 15, pp. 329–340.
Simoes, F. J., and Graham, J. M. R., 1991, “Prediction of Loading on a Horizontal Axis Wind Turbine using a Free Vortex Wake Model,” Proc. 13th BWEA Wind Energy Conference, Quarton, D. C. and Fenton, V. C., eds., Mechanical Engineering Publications Limited, London, U.K., pp. 247–254.
Bareiss, R., and Wagner, S., 1993, “A Hybrid Wake Model for HAWT,” Proc. of the Sixth IEA Symposium on the Aerodynamics of Wind Turbines, McAnulty, K. F., ed., ETSU, Harwell, pp. 7.1–7.10.
Voutsinas, S. G., Beleiss, M. A., and Rados, K. G., 1995, “Investigation of the Yawed Operation of Wind Turbines by Means of a Vortex Particle Method,” AGARD Conf. Proc., 552, pp. 1–11.
van Holten, Th., 1975, “The Computation of Aerodynamic Loads on Helicopter Blades in Forward Flight using the Method of the Acceleration Potential,” Report VTH-189, Dept. of Aerospace Eng., Delft Univ. of Techn., The Netherlands.
van Bussel, G. J. W., 1995, “The Aerodynamics of Horizontal Axis Wind Turbine Rotors Explored with Asymptotic Expansion Methods,” Doctoral dissertation, Technische Universiteit Delft, The Netherlands.
Wu, T. Y. , 1962, “Flow Through a Heavily Loaded Actuator Disc,” Schiffstechnik, 9, pp. 134–138.
Greenberg, M. D. , 1972, “Nonlinear Actuator Disc Theory,” Z. Flugwiss., 20 (3), pp. 90–98.
Conway, J. , 1995, “Analytical Solutions for the Actuator Disk with Variable Radial Distribution of Load,” J. Fluid Mech., 297, pp. 327–355.
Conway, J. , 1998, “Exact Actuator Disk Solution for Non-uniform Heavy Loading and Slipstream Contraction,” J. Fluid Mech., 365, pp. 235–267.
Sørensen, J. N., and Myken, A., 1992, “Unsteady Actuator Disc Model for Horizontal Axis Wind Turbines,” J. Wind. Eng. Ind. Aerodyn., 39, pp. 139–149.
Sørensen, J. N., and Kock, C. W., 1995, “A model for Unsteady Rotor Aerodynamics,” J. Wind. Eng. Ind. Aerodyn., 58, pp. 259–275.
Madsen, H. Aa., 1996, “A CFD Analysis for the Actuator Disc Flow Compared with Momentum Theory Results,” Proc. of the 10th IEA Symposium on the Aerodynamics of Wind Turbines, Pedersen, B. M., ed., Department of Fluid Mechanics, Technical University of Denmark, pp. 109–124.
Fejtek, I., and Roberts, L., 1992, “Navier-Stokes Computation of Wing/rotor Interaction for a Tilt Rotor in Hover,” AIAA J., 30 (11), pp. 2595–2603.
Rajagopalan, R. G., and Mathur, S. R., 1993, “Three Dimensional Analysis of a Rotor in Forward Flight,” J. Am. Helicopter Soc., 38 (3).
Sørensen, J. N., Shen, W. Z., and Munduate, X., 1998, “Analysis of Wake States by a Full-field Actuator Disc Model,” Wind Energy, 1, pp. 73–88.
Sørensen, J. N., 1986, “Three-level, Viscous-inviscid Interaction Technique for the Prediction of Separated Flow Past Rotating Wings,” Ph.D. thesis, AFM Report 86-07, Department of Fluid Mechanics, The Technical University of Denmark.
Berkman, M. E., Sankar, L. N., Berezin, C. R., and Torok, M. S., 1997, “A Navier-Stokes/full potential/free wake Method for Rotor Flows,” AIAA Paper 97-0401.
Xu, G., and Sankar, L. N., 1999, “Computational Study of Horizontal Axis Wind Turbines,” AIAA Paper 99-0042.
Hansen, M. O. L., Sørensen, J. N., Michelsen, J. A., and Sørensen, N. N., 1997, “A Global Navier-Stokes Rotor Prediction Model,” AIAA Paper 97-0970.
Ekaterinaris, J. A., 1997, “Numerical Simulation of Incompressible Two-bladed Rotor Flow Field,” AIAA Paper 97-0398.
Duque, E. P. N., van Dam, C. P., and Hughes, S., 1999, “Navier-Stokes Simulations of the NREL Combined Experiment Phase II Rotor,” AIAA Paper 99-0037.
Sørensen, N. N., and Michelsen, J. A., 2000, “Aerodynamic Predictions for the Unsteady Aerodynamics Experiment Phase-II Rotor at the National Renewable Energy Laboratory,” AIAA Paper 2000–0037.
Huang, Y., and Ghia, U., 1992, “A Multigrid Method for Solution of Vorticity Velocity Form of 3-D Navier-Stokes Equations,” Commun. Appl. Numer. Methods, 8 (10), pp. 707–719.
Shen, W. Z., and Ta Phouc, L., 1997, “Numerical Method for Unsteady 3D Navier-Stokes Equations in Velocity-vorticity Form,” Comput. Fluids, 26, pp. 93–216.
Sørensen, J. N., Shen, W. Z., and Hansen, M. O. L., 2002, “A Vorticity-velocity Formulation of the 3D Navier-Stokes Equations in Cylindrical Coordinates,” Submitted.
Snel, H., Houwink, R., and Piers, W. J., 1993, “Sectional Prediction of 3D Effects for Separated Flow on Rotating Blades,” Proc. of the ECWEC ’93 Conference, pp. 395–399.
Chaviaropoulos, P. K., and Hansen, M. O. L., 2000, “Investigating Three-dimensional and Rotational Effects on Wind Turbine Blades by Means of a Quasi-3D Navier-Stokes Solver,” ASME J. Fluids Eng., 197, pp. 330–336.
Hoerner, S. F., 1965, Fluid-Dynamic Drag, published by the author.
Hansen, M. O. L., 1999, “Polar for NACA 63-415 Airfoil,” Report ET-AFM-9902, Department of Energy Engineering, Technical University of Denmark.
Abbott, I. H., and Doenhoff, A. E., 1959, Theory of Wing Sections, Dover Publications, New York.
Bjo¨rck, A., 1996, “A Guide to Data Files from Wind Tunnel Test of a FFA-W3-211 Airfoil at FFA,” Technical Report FFA P-V-019, FFA, Bromma, Sweden.
Riegels, F. W., 1961, Aerofoil Sections, Butterworths, London.