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Experiments in Fluids

, 59:6 | Cite as

Modeling of a pitching and plunging airfoil using experimental flow field and load measurements

  • Victor TroshinEmail author
  • Avraham Seifert
Research Article

Abstract

The main goal of the current paper is to outline a low-order modeling procedure of a heaving airfoil in a still fluid using experimental measurements. Due to its relative simplicity, the proposed procedure is applicable for the analysis of flow fields within complex and unsteady geometries and it is suitable for analyzing the data obtained by experimentation. Currently, this procedure is used to model and predict the flow field evolution using a small number of low profile load sensors and flow field measurements. A time delay neural network is used to estimate the flow field. The neural network estimates the amplitudes of the most energetic modes using four sensory inputs. The modes are calculated using proper orthogonal decomposition of the flow field data obtained experimentally by time-resolved, phase-locked particle imaging velocimetry. To permit the use of proper orthogonal decomposition, the measured flow field is mapped onto a stationary domain using volume preserving transformation. The analysis performed by the model showed good estimation quality within the parameter range used in the training procedure. However, the performance deteriorates for cases out of this range. This situation indicates that, to improve the robustness of the model, both the decomposition and the training data sets must be diverse in terms of input parameter space. In addition, the results suggest that the property of volume preservation of the mapping does not affect the model quality as long as the model is not based on the Galerkin approximation. Thus, it may be relaxed for cases with more complex geometry and kinematics.

Notes

Acknowledgements

The authors would like to thank the Tel-Aviv University Renewable Energy Center for financial support of this project.

Supplementary material

Supplementary material 1 (MP4 2701 KB)

Supplementary material 2 (MP4 2783 KB)

References

  1. Ahuja S, Rowley CW (2010) Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators. J Fluid Mech 645:447–478MathSciNetCrossRefzbMATHGoogle Scholar
  2. Anttonen JSR, King PI, Beran PS (2003) POD-based reduced-order models with deforming grids. Math Comput Model 38:41–62.  https://doi.org/10.1016/S0895-7177(03)90005-7 MathSciNetCrossRefzbMATHGoogle Scholar
  3. Anttonen JSR, King PI, Beran PS (2005) Applications of multi-POD to a pitching and plunging airfoil. Math Comput Model 42:245–259.  https://doi.org/10.1016/j.mcm.2005.06.003 MathSciNetCrossRefzbMATHGoogle Scholar
  4. Brunton SL, Rowley CW, Williams DR (2013) Reduced-order unsteady aerodynamic models at low Reynolds numbers. J Fluid Mech 724:203–233.  https://doi.org/10.1017/jfm.2013.163 CrossRefzbMATHGoogle Scholar
  5. Dawson ST, Schiavone NK, Rowley CW, Williams DR (2015) A data-driven modeling framework for predicting forces and pressures on a rapidly pitching airfoil. In: 45th AIAA fluid dynamics conference. AIAA AVIATION Forum. American Institute of Aeronautics Astronautics.  https://doi.org/10.2514/6.2015-2767
  6. Dickinson MH, Lehmann FO, Sane SP (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284:1954–1960CrossRefGoogle Scholar
  7. Donea J, Huerta A, Ponthot JP, Rodríguez-Ferran A (2004) Arbitrary Lagrangian–Eulerian methods. In: Encyclopedia of computational mechanics. Wiley, Oxford.  https://doi.org/10.1002/0470091355.ecm009
  8. Engelbrecht AP (2007) Computational intelligence: an introduction. Wiley, OxfordCrossRefGoogle Scholar
  9. Fletcher CA (1984) Computational galerkin methods. Springer, BerlinCrossRefzbMATHGoogle Scholar
  10. Fumitaka I, San-Mou J, Kelly C (2010) Proper orthogonal decomposition and Fourier analysis on the energy release rate dynamics. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Aerospace Sciences Meetings. American Institute of Aeronautics and Astronautics.  https://doi.org/10.2514/6.2010-22
  11. Glaz B, Friedmann PP, Liu L, Cajigas JG, Bain J, Sankar LN (2013) Reduced-order dynamic stall modeling with swept flow effects using a surrogate-based recurrence framework. AIAA J 51:910–921.  https://doi.org/10.2514/1.j051817 CrossRefGoogle Scholar
  12. Gordon WJ, Thiel LC (1982) Transfinite mappings and their application to grid generation. Appl Math Comput 10:171–233MathSciNetzbMATHGoogle Scholar
  13. Graham W, Peraire J, Tang K (1999) Optimal control of vortex shedding using low-order models. Part I—open-loop model development. Int J Numer Methods Eng 44:945–972CrossRefzbMATHGoogle Scholar
  14. Hassoun MH (1995) Fundamentals of artificial neural networks. MIT Press, MassachusettszbMATHGoogle Scholar
  15. Holmes P, Lumley JL, Berkooz G (1998) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, CambridgezbMATHGoogle Scholar
  16. Kotecki K, Hausa H, Nowak M, Stankiewicz W, Roszak R, Morzyński M (2015) Deformation of curvilinear meshes for aeroelastic analysis. In: Kroll N, Hirsch C, Bassi F, Johnston C, Hillewaert K (eds) IDIHOM: industrialization of high-order methods—a top-down approach: results of a collaborative research Project Funded by the European Union, 2010–2014. Springer, Cham, pp 125–131.  https://doi.org/10.1007/978-3-319-12886-3_7
  17. Lehmann FO (2009) Wing–wake interaction reduces power consumption in insect tandem wings. Exp Fluids 46:765–775CrossRefGoogle Scholar
  18. Lehmann F-O (2012) Wake Structure and vortex development in flight of fruit flies using high-speed particle image velocimetry nature-inspired. Fluid Mech:65–79Google Scholar
  19. Lewin GC, Haj-Hariri H (2005) Reduced-order modeling of a heaving airfoil. AIAA J 43:270–283.  https://doi.org/10.2514/1.8210 CrossRefGoogle Scholar
  20. Liberge E, Hamdouni A (2010) Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder. J Fluids Struct 26:292–311.  https://doi.org/10.1016/j.jfluidstructs.2009.10.006
  21. Lucia DJ, Beran PS, Silva WA (2004) Reduced-order modeling: new approaches for computational physics. Progress Aerosp Sci 40:51–117  https://doi.org/10.1016/j.paerosci.2003.12.001 CrossRefGoogle Scholar
  22. MacKay DJ (1992) A practical Bayesian framework for backpropagation networks. Neural Comput 4:448–472CrossRefGoogle Scholar
  23. Noack BR, Afanasiev K, Morzynski M, Tadmor G, Thiele F (2003) A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J Fluid Mech 497:335–363MathSciNetCrossRefzbMATHGoogle Scholar
  24. Noack BR, Papas P, Monkewitz PA (2005) The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J Fluid Mech 523:339–365MathSciNetCrossRefzbMATHGoogle Scholar
  25. Noack BR, Morzynski M, Tadmor G (2011) Reduced-order modelling for flow control. Springer, WienCrossRefzbMATHGoogle Scholar
  26. Ol MV, Bernal L, Kang CK, Shyy W (2009) Shallow and deep dynamic stall for flapping low Reynolds number airfoils. Exp Fluids 46:883–901CrossRefGoogle Scholar
  27. Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Kevin Tucker P (2005) Surrogate-based analysis and optimization. Progress Aerosp Sci 41:1–28.  https://doi.org/10.1016/j.paerosci.2005.02.001 CrossRefzbMATHGoogle Scholar
  28. Shyy W, Berg M, Ljungqvist D (1999) Flapping and flexible wings for biological and micro air vehicles. Prog Aerosp Sci 35:455–505CrossRefGoogle Scholar
  29. Shyy W et al (2008) Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications. Acta Mech Sin 24:351–373CrossRefzbMATHGoogle Scholar
  30. Shyy W, Aono H, Chimakurthi S, Trizila P, Kang CK, Cesnik C, Liu H (2010) Recent progress in flapping wing aerodynamics and aeroelasticity. Progress Aerosp Sci 46:284–327CrossRefGoogle Scholar
  31. Shyy W, Aono H, Kang C-k, Liu H (2013) An introduction to flapping wing aerodynamics, vol 37. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  32. Siegel S (2011) Feedback flow control in experiment and simulation using global neural network based models. Springer, BerlinCrossRefzbMATHGoogle Scholar
  33. Siegel SG, SEIDEL J, Fagley C, Luchtenburg D, Cohen K, Mclaughlin T (2008) Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition. J Fluid Mech 610:1–42MathSciNetCrossRefzbMATHGoogle Scholar
  34. Silva W (2005) Identification of nonlinear aeroelastic systems based on the Volterra theory. Progress Oppor Nonlinear Dyn 39:25–62.  https://doi.org/10.1007/s11071-005-1907-z MathSciNetCrossRefzbMATHGoogle Scholar
  35. Sirovich L (1987) Turbulence and the dynamics of coherent structures. I—Coherent structures. II—Symmetries and transformations. III—Dynamics scaling Q Appl Math 45:561–571MathSciNetCrossRefzbMATHGoogle Scholar
  36. Stankiewicz W, Roszak R, Morzyński M (2013) Arbitrary Lagrangian–Eulerian approach in reduced order modeling of a flow with a moving boundary. In: Progress in flight physics. EDP Sciences, Les Ulis, pp 109–124Google Scholar
  37. Tadmor G, Noack BR, Morzynski M (2006) Control oriented models and feedback design in fluid flow systems: a review. In: 2006 14th Mediterranean Conference on Control and Automation, 28–30 June 2006, pp 1–12.  https://doi.org/10.1109/med.2006.328757
  38. Tadmor G, Lehmann O, Noack BR, Morzyński M (2011) Galerkin models enhancements for flow control reduced-order modelling for flow control, pp 151–252Google Scholar
  39. Trizila P, Kang C-K, Aono H, Shyy W, Visbal M (2011) Low-Reynolds-number aerodynamics of a flapping rigid flat plate. AIAA J 49:806–823.  https://doi.org/10.2514/1.j050827 CrossRefGoogle Scholar
  40. Troshin V, Seifert A, Sidilkover D, Tadmor G (2016) Proper orthogonal decomposition of flow-field in non-stationary geometry. J Comput Phys 311:329–337.  https://doi.org/10.1016/j.jcp.2016.02.006 MathSciNetCrossRefzbMATHGoogle Scholar
  41. Usherwood JR, Lehmann FO (2008) Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl. J R Soc Interface 5:1303–1307CrossRefGoogle Scholar
  42. Waibel A, Hanazawa T, Hinton G, Shikano K, Lang KJ (1989) Phoneme recognition using time-delay neural networks. IEEE Trans Acoust Speech Signal Process 37:328–339CrossRefGoogle Scholar
  43. Wakeling J, Ellington C (1997) Dragonfly flight. II. Velocities, accelerations and kinematics of flapping flight. J Exp Biol 200:557–582Google Scholar
  44. Willcox K, Megretski A (2003) Fourier series for accurate, stable, reduced-order models for linear CFD applications. In: 16th AIAA Computational Fluid Dynamics Conference. Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics Astronautics.  https://doi.org/10.2514/6.2003-4235

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mechanical Engineering, Faculty of EngineeringTel-Aviv UniversityTel-AvivIsrael

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