Skip to main content
Skip to article control options
No AccessRegular Articles

Coherent Structure Interaction During Unsteady Separation

Published Online:https://doi.org/10.2514/1.J058059

Unsteady flow separation in rotationally augmented flow fields plays a significant role in the aerodynamic performance of industrial rotors, including wind turbines. Current computational models underestimate the aerodynamic loads due to the inaccurate prediction of the emergence and severity of unsteady flow separation, especially in response to a sudden change in the effective angle of attack. Through the use of time-resolved particle image velocimetry (PIV), coherent structure formation during the unsteady separation over an experimental wind turbine blade is examined. Time-dependent empirical mode decomposition results during a dynamic pitching cycle give insight into the spatio-temporal scales that influence the transition from attached to separated flow. Empirical mode decomposition (EMD) modes are represented as two-dimensional fields and are analyzed together with Lagrangian coherent structures, the spatial distribution of vortices, the location of the separation point, and velocity contours focusing on the role of vortex shedding and shear-layer perturbation in unsteady flow separation, stall, and reattachment. The combination of these analytical techniques provides experimental evidence that the location of the separation point and the stability of the shear layer are directly influenced by the presence of vortices. Within this paper, each of the scales represented by the EMD are directly connected to the size of the vortices present, from the smallest representing a vortex radius to the largest reaching to two full vortex diameters. The velocity scales and spatial scales provided by the EMD modes are also found to supply valuable inputs into the identification of Lagrangian coherent structures within each of the PIV snapshots. This indicates that the scales captured by the EMD can be used to extract important turbulent scales present at the point of flow separation where the vortices are created, providing relenvant insight into the separation dynamics of the airfoil.

References

  • [1] Leishman J. G. and Beddoes T. S., “A Semi-Empirical Model for Dynamic Stall,” Journal of the American Helicopter Society, Vol. 34, No. 3, 1989, pp. 3–17. doi:https://doi.org/10.4050/JAHS.34.3 CrossrefGoogle Scholar

  • [2] Huyer S. A., Simms D. and Robinson M. C., “Unsteady Aerodynamics Associated with a Horizontal-Axis Wind Turbine,” AIAA Journal, Vol. 34, No. 7, July 1996, pp. 1410–1419. doi:https://doi.org/10.2514/3.13247 LinkGoogle Scholar

  • [3] Reynolds W. C. and Carr L. W., “Review of Unsteady, Driven, Separated Flows,” Shear Flow Control Conference, 1985 doi:https://doi.org/10.2514/6.1985-527 LinkGoogle Scholar

  • [4] Himmelskamp H., Profile Investigations on a Rotating Airscrew, Vol. 832, Reports and Translations, MAP Völenrode, 1947. Google Scholar

  • [5] Hansen A. C. and Butterfield C. P., “Aerodynamics of Horizontal-Axis Wind Turbines,” Annual Review of Fluid Mechanics, Vol. 25, No. 1, 1993, pp. 115–149. doi:https://doi.org/10.1146/annurev.fl.25.010193.000555 CrossrefGoogle Scholar

  • [6] Sørensen J. N., Larsen P. S., Pedersen B. M. and Jensen J. T., “Three-Level, Viscous-Inviscid Interaction Technique for the Prediction of Separated Flow Past Rotating Wing,” Technical Univ. of Denmark (DTU), AFM, No.  86-03, Kongens Lyngby, Denmark, 1986. Google Scholar

  • [7] Xu B. F., Yuan Y. and Wang T. G., “Development and Application of a Dynamic Stall Model for Rotating Wind Turbine Blades,” Journal of Physics: Conference Series, Vol. 524, No. 1, 2014, Paper 012133. Google Scholar

  • [8] Du Z. and Selig M., “The Effect of Rotation on the Boundary Layer of a Wind Turbine Blade,” Renewable Energy, Vol. 20, No. 2, 2000, pp. 167–181. doi:https://doi.org/10.1016/S0960-1481(99)00109-3 CrossrefGoogle Scholar

  • [9] Gersten K. and Schlichting H., Boundary-Layer Theory, Springer, Berlin, 2009. Google Scholar

  • [10] Gehlert P. and Babinsky H., “Linking the Unsteady Force Generation to Vorticity for a Translating and Rotating Cylinder,” AIAA Scitech 2019 Forum, AIAA Paper 2019-0347, 2019. LinkGoogle Scholar

  • [11] Roberts S. K. and Yaras M. I., “Large-Eddy Simulation of Transition in a Separation Bubble,” Journal of Fluids Engineering, Vol. 128, No. 2, 2006, pp. 232–238. doi:https://doi.org/10.1115/1.2170123 CrossrefGoogle Scholar

  • [12] Surana A., Jacobs G. B., Grunberg O. and Haller G., “An Exact Theory of Three-Dimensional Fixed Separation in Unsteady Flows,” Physics of Fluids, Vol. 20, No. 10, 2008, Paper 107101. doi:https://doi.org/10.1063/1.2988321 CrossrefGoogle Scholar

  • [13] Shen S.-F., “Unsteady Separation According to the Boundary-Layer Equation,” Advances in Applied Mechanics, Vol. 18, 1979, pp. 177–220. doi:https://doi.org/10.1016/S0065-2156(08)70267-9 CrossrefGoogle Scholar

  • [14] Van Dommelen L. and Shen S., “The Genesis of Separation,” Numerical and Physical Aspects of Aerodynamic Flows, Springer, New York, 1982, pp. 293–311. CrossrefGoogle Scholar

  • [15] Van Dommelen L. and Cowley S., “On the Lagrangian Description of Unsteady Boundary-Layer Separation. Part 1. General Theory,” Journal of Fluid Mechanics, Vol. 210, No. 1, 1990, pp. 593–626. doi:https://doi.org/10.1017/S0022112090001410 CrossrefGoogle Scholar

  • [16] Farazmand M. and Haller G., “Computing Lagrangian Coherent Structures from Their Variational Theory,” Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 1, 2012, Paper 013128. doi:https://doi.org/10.1063/1.3690153 CrossrefGoogle Scholar

  • [17] Shadden S. C., Lekien F. and Marsden J. E., “Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows,” Physica D: Nonlinear Phenomena, Vol. 212, Nos. 3–4, 2005, pp. 271–304. doi:https://doi.org/10.1016/j.physd.2005.10.007 CrossrefGoogle Scholar

  • [18] Melius M. S., Mulleners K. and Cal R. B., “The Role of Surface Vorticity During Unsteady Separation,” Physics of Fluids, Vol. 30, No. 4, 2018, Paper 045108. doi:https://doi.org/10.1063/1.5006527 CrossrefGoogle Scholar

  • [19] Mulleners K. and Raffel M., “Dynamic Stall Development,” Experiments in Fluids, Vol. 54, No. 2, 2013, pp. 1–9. doi:https://doi.org/10.1007/s00348-013-1469-7 CrossrefGoogle Scholar

  • [20] Jeong J. and Hussain F., “On the Identification of a Vortex,” Journal of Fluid Mechanics, Vol. 285, Feb. 1995, pp. 69–94. doi:https://doi.org/10.1017/S0022112095000462 CrossrefGoogle Scholar

  • [21] Graftieaux L., Michard M. and Grosjean N., “Combining PIV, POD and Vortex Identification Algorithms for the Study of Unsteady Turbulent Swirling Flows,” Measurement Science and Technology, Vol. 12, No. 9, 2001, pp. 1422–1429. doi:https://doi.org/10.1088/0957-0233/12/9/307 CrossrefGoogle Scholar

  • [22] Mulleners K. and Raffel M., “The Onset of Dynamic Stall Revisited,” Experiments in Fluids, Vol. 52, No. 3, 2012, pp. 779–793. doi:https://doi.org/10.1007/s00348-011-1118-y CrossrefGoogle Scholar

  • [23] Haller G., “Exact Theory of Unsteady Separation for Two-Dimensional Flows,” Journal of Fluid Mechanics, Vol. 512, July 2004, pp. 257–311. doi:https://doi.org/10.1017/S0022112004009929 CrossrefGoogle Scholar

  • [24] Melius M. S., Cal R. B. and Mulleners K., “Dynamic Stall of an Experimental Wind Turbine Blade,” Physics of Fluids, Vol. 28, No. 3, 2016, Paper 034103. doi:https://doi.org/10.1063/1.4942001 CrossrefGoogle Scholar

  • [25] Huang N. E., Shen Z., Long S. R., Wu M. C., Shih H. H., Zheng Q., Yen N. C., Tung C. C. and Liu H. H., “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis,” Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, No. 1971, March 1998, pp. 903–995. Google Scholar

  • [26] Ansell P. J. and Balajewicz M. J., “Separation of Unsteady Scales in a Mixing Layer Using Empirical Mode Decomposition,” AIAA Journal, Vol. 55, No. 2, Feb. 2017, pp. 419–434. LinkGoogle Scholar

  • [27] Huang N. E., Wu M. L. C., Long S. R., Shen S. S., Qu W., Gloersen P. and Fan K. L., “A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis,” Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 459, No. 2037, 2003, pp. 2317–2345. Google Scholar

  • [28] Wu Z. and Huang N. E., “Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method,” Advances in Adaptive Data Analysis, Vol. 1, No. 1, 2009, pp. 1–41. doi:https://doi.org/10.1142/S1793536909000047 CrossrefGoogle Scholar

  • [29] Torres M. E., Colominas M. A., Schlotthauer G. and Flandrin P., “A Complete Ensemble Empirical Mode Decomposition with Adaptive Noise,” 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE Publ., Piscataway, NJ, 2011, pp. 4144–4147. Google Scholar

  • [30] Wu Z., Huang N. E. and Chen X., “The Multi-Dimensional Ensemble Empirical Mode Decomposition Method,” Advances in Adaptive Data Analysis, Vol. 1, No. 3, 2009, pp. 339–372. doi:https://doi.org/10.1142/S1793536909000187 CrossrefGoogle Scholar

  • [31] Nunes J. C., Bouaoune Y., Delechelle E., Niang O. and Bunel P., “Image Analysis by Bidimensional Empirical Mode Decomposition,” Image and Vision Computing, Vol. 21, No. 12, 2003, pp. 1019–1026. doi:https://doi.org/10.1016/S0262-8856(03)00094-5 CrossrefGoogle Scholar

  • [32] Nunes J. C., Guyot S. and Deléchelle E., “Texture Analysis Based on Local Analysis of the Bidimensional Empirical Mode Decomposition,” Machine Vision and Applications, Vol. 16, No. 3, 2005, pp. 177–188. doi:https://doi.org/10.1007/s00138-004-0170-5 CrossrefGoogle Scholar

  • [33] Arnold V., Vogtmann K. and Weinstein A., Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, Springer, New York, 2013. Google Scholar

  • [34] Tsai H.-C. and Colonius T., “Coriolis Effect on Dynamic Stall in a Vertical Axis Wind Turbine,” AIAA Journal, Vol. 54, No. 1, 2015, pp. 216–226. doi:https://doi.org/10.2514/1.J054199 LinkGoogle Scholar

  • [35] Wilson Z., Tutkun M. and Cal R., “Identification of Lagrangian Coherent Structures in a Turbulent Boundary Layer,” Journal of Fluid Mechanics, Vol. 728, Aug. 2013, pp. 396–416. doi:https://doi.org/10.1017/jfm.2013.214 CrossrefGoogle Scholar