Linear stability analysis of wind turbine wakes performed on wind tunnel measurements

Journal of Fluid Mechanics

Volumn 737, Issue , 2013, Pages 499-526

  Iungo, G V ^a   Viola, F ^a   Camarri, S ^b   Porte Agel F ^a   Gallaire, F ^a  

^a EPFL   (Switzerland)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

absolute convective instability; vortex instability; wakes jets

Indexed keywords

VORTEX FLOW; WAKES; WIND TUNNELS; WIND TURBINES;

ABSOLUTE/CONVECTIVE INSTABILITIES; HOT WIRE MEASUREMENTS; STREAMWISE DIRECTIONS; TEMPORAL AND SPATIAL; TRANSVERSAL OSCILLATIONS; VORTEX INSTABILITY; WAKES/JETS; WIND TUNNEL MEASUREMENTS;

LINEAR STABILITY ANALYSIS;

JET FLOW; STABILITY ANALYSIS; VORTEX; WAKE; WAVE VELOCITY; WIND TUNNEL; WIND TURBINE;

EID: 84901745947     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2013.569     Document Type: Article

References (50)

1. ALFREDSSON, P. H. & DAHLBERG, J. A. 1979 A preliminary wind tunnel study of windmill wake dispersion in various flow conditions. Technical Note AU-1499, Part 7, FFA, Stockholm, Sweden.
2. ANTKOWIAK, A. 2005 Short-term dynamics of an isolated vortex. PhD thesis, IMFT-Université Paul Sabatier.
3. BARKLEY, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 37 (5), 750-756.
4. BURTON, T., SHARPE, D., JENKINS, N. & BOSSANYI, N. 2001 Wind Energy Handbook. Wiley.
5. CAMARRI, S., FALLENIUS, B. E. G. & FRANSSON, J. H. M. 2013 Stability analysis of experimental flow fields behind a porous cylinder for the investigation of the large-scale wake vortices. J. Fluid Mech. 715, 499-536.
6. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 1993 Spectral Methods in Fluid Dynamics. Springer.
7. CHAMORRO, L. P. & PORTÉ-AGEL, F. 2009 A wind-tunnel investigation of wind-turbine wakes: boundary-layer turbulence effects. Boundary-Layer Meteorol. 132 (1), 129-149.
8. CHAMORRO, L. P. & PORTÉ-AGEL, F. 2010 Effects of thermal stability and incoming boundary-layer flow characteristics on wind-turbine wakes: a wind-tunnel study. Boundary-Layer Meteorol. 136 (3), 515-533.
9. CHOMAZ, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357-392.
10. COUAIRON, A. & CHOMAZ, J.-M. 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11 (12), 3688-3703.
11. FELLI, M., CAMUSSI, R. & DIFELICE, F. 2011 Mechanisms of evolution of the propeller wake in the transition and far fields. J. Fluid Mech. 682, 5-53.
12. GALLAIRE, F. & CHOMAZ, J. M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 222-224.
13. GASTER, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic instability. J. Fluid Mech. 14, 222-224.
14. GUPTA, B. P. & LOEWY, R. G. 1974 Theoretical analysis of the aerodynamic stability of multiple, interdigitated helical vortices. AIAA J. 12, 1381-1387.
15. HUERRE, P. 1998 Hydrodynamic Instabilities in Open Flows. Cambridge University Press.
16. IUNGO, G. V. & LOMBARDI, E. 2011 A procedure based on proper orthogonal decomposition for time-frequency analysis of time series. Exp. Fluids 51, 969-985.
17. IVANELL, S., MIKKELSEN, R., SØRENSEN, J. N. & HENNINGSON, D. 2010 Stability analysis of the tip vortices of a wind turbine. Wind Energy 13, 705-715.
18. IVANELL, S., SØRENSEN, J. N., MIKKELSEN, R. & HENNINGSON, D. 2009 Analysis of numerically generated wake structures. Wind Energy 12, 63-80.
19. JOUKOWSKI, N. E. 1912 Vortex theory of a rowing screw. Trudy Otdeleniya Fizicheskikh Nauk Obshchestva Lubitelei Estestvoznaniya 16 (1)in Russian.
20. JUNIPER, M. P., TAMMISOLA, O. & LUNDELL, F. 2011 The local and global stability of confined planar wakes at intermediate Reynolds number. J. Fluid Mech. 686, 218-238.
21. KERSWELL, R. R. & DAVEY, A. 1996 On the linear instability of elliptic pipe flow. J. Fluid Mech. 316, 307-324.
22. KLEIN, R., MAJDA, A. J. & DAMODARAN, K. 1995 Simplified equations for the interaction of nearly parallel vortex filaments. J. Fluid Mech. 288, 201-248.
23. LEIBOVICH, S. & STEWARTSON, K. 1983 A sufficient condition for the instability of columnar vortices. J. Fluid Mech. 126, 335-356.
24. LEONTINI, J. S., THOMPSON, M. C. & HOURIGAN, K. 2010 A numerical study of global frequency selection in the time-mean wake of a circular cylinder. J. Fluid Mech. 645, 435-446.
25. LEVY, H. & FORSDYKE, A. G. 1928 The steady motion and stability of a helical vortex. Proc. R. Soc. Lond. A 120, 670-690.
26. LIGHTHILL, J. 1978 Waves in Fluids. Cambridge University Press.
27. LU, H. & PORTÉ-AGEL, F. 2011 Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer. Phys. Fluids 23 (6), 065101.
28. MASSOUH, F. & DOBREV, I. 2007 Exploration of the vortex wake behind of wind turbine rotor. J. Phys.: Conf. Ser. 75 012036.
29. MEDICI, D. & ALFREDSSON, P. H. 2006 Mesurements on a wind turbine wake: 3D effects and bluff body vortex shedding. Wind Energy 9 (3), 219-236.
30. MEDICI, D. & ALFREDSSON, P. H. 2008 Measurements behind model wind turbines: further evidence of wake meandering. Wind Energy 11, 211-217.
31. MELIGA, P., SIPP, D. & CHOMAZ, J.-M. 2009 Elephant modes and low frequency unsteadiness in a high Reynolds number, transonic afterbody wake. Phys. Fluids 21 (5), 054105.
32. MONKEWITZ, P. A. 1988 A note on vortex shedding from axisymmetric bluff bodies. J. Fluid Mech. 192, 561-575.
33. OBERLEITHNER, K., SIEBER, M., NAYERI, C. N., PASCHEREIT, C. O., PETZ, C., HEGE, H.-C., NOACK, B. R. & WYGNANSKI, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383-414.
34. OKULOV, V. L. 2004 On the stability of multiple helical vortices. J. Fluid Mech. 521, 319-342.
35. OKULOV, V. L. & SØRENSEN, J. N. 2007 Stability of helical tip vortices in a rotor far wake. J. Fluid Mech. 576, 1-25.
36. OLENDRARU, C. & SELLIER, A. 2002 Viscous effects in the absolute/convective instability of the Batchelor vortex. J. Fluid Mech. 459, 371-396.
37. OLENDRARU, C., SELLIER, A., ROSSI, M. & HUERRE, P. 1999 Inviscid instability of the Batchelor vortex: absolute-convective transition and spatial branches. Phys. Fluids 11, 1805-1820.
38. ORTEGA, J. M., BRISTOL, R. L. & SAVAS, Ö. 2003 Experimental study of the instability of unequal-strength counter-rotating vortex pairs. J. Fluid Mech. 474, 35-84.
39. PIER, B. & HUERRE, P. 2001 Nonlinear synchronization in open flows. J. Fluids Struct. 15, 471-480.
40. PORTÉ-AGEL, F., WU, Y-T., LU, H. & CONZEMIUS, R. J. 2011 Large-eddy simulation of atmospheric boundary layer flow through wind turbines and wind farms. J. Wind Engng Ind. Aerodyn. 99 (4), 154-168.
41. SARPKAYA, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545-559.
42. SCHITO, P. 2012 Large eddy simulations of wind turbines: interaction with turbulent flow. PhD thesis, Department of Mechanical Engineering, Politecnico di Milano.
43. SCHMID, P. J. & HENNINGSON, D. S. 2001 Stability and Transition in Shear Flows. Springer.
44. SHERRY, M., SHERIDAN, J. & LOJACONO, D. 2010 Horizontal axis wind turbine tip and root vortex measurements. In 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics.
45. SIPP, D. & LEBEDEV, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333-358.
46. SØRENSEN, J. N. 2011 Instability of helical tip vortices in rotor wakes. J. Fluid Mech. 682, 1-4.
47. VERMEER, L. J., SØRENSEN, J. N. & CRESPO, A. 2003 Wind turbine wake aerodynamics. Prog. Aerosp. Sci. 39 (6/7), 467-510.
48. WHALE, J., PAPADOPOULOS, K. H., ANDERSON, C. G., HELMIS, C. G. & SKYNER, D. J. 1996 A study of the near wake structure of a wind turbine comparing measurements from laboratory and full-scale experiments. Solar Energy 56 (6), 621-633.
49. WIDNALL, S. E. 1972 The stability of a helical vortex filament. J. Fluid Mech. 54 (4), 641-663.
50. ZHANG, W., MARKFORT, C. D. & PORTÉ-AGEL, F. 2012 Near-wake flow structure downwind of a wind turbine in a turbulent boundary layer. Exp. Fluids 52 (5), 1219-1235.