Skip to main content
Log in

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

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Ahuja S, Rowley CW (2010) Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators. J Fluid Mech 645:447–478

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

  • Dickinson MH, Lehmann FO, Sane SP (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284:1954–1960

    Article  Google Scholar 

  • 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

  • Engelbrecht AP (2007) Computational intelligence: an introduction. Wiley, Oxford

    Book  Google Scholar 

  • Fletcher CA (1984) Computational galerkin methods. Springer, Berlin

    Book  MATH  Google Scholar 

  • 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

  • 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

    Article  Google Scholar 

  • Gordon WJ, Thiel LC (1982) Transfinite mappings and their application to grid generation. Appl Math Comput 10:171–233

    MathSciNet  MATH  Google Scholar 

  • 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 44:945–972

    Article  MATH  Google Scholar 

  • Hassoun MH (1995) Fundamentals of artificial neural networks. MIT Press, Massachusetts

    MATH  Google Scholar 

  • Holmes P, Lumley JL, Berkooz G (1998) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • 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

  • Lehmann FO (2009) Wing–wake interaction reduces power consumption in insect tandem wings. Exp Fluids 46:765–775

    Article  Google Scholar 

  • Lehmann F-O (2012) Wake Structure and vortex development in flight of fruit flies using high-speed particle image velocimetry nature-inspired. Fluid Mech:65–79

  • 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

    Article  Google Scholar 

  • 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

  • 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

    Article  Google Scholar 

  • MacKay DJ (1992) A practical Bayesian framework for backpropagation networks. Neural Comput 4:448–472

    Article  Google Scholar 

  • 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 497:335–363

    Article  MathSciNet  MATH  Google Scholar 

  • 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 523:339–365

    Article  MathSciNet  MATH  Google Scholar 

  • Noack BR, Morzynski M, Tadmor G (2011) Reduced-order modelling for flow control. Springer, Wien

    Book  MATH  Google Scholar 

  • Ol MV, Bernal L, Kang CK, Shyy W (2009) Shallow and deep dynamic stall for flapping low Reynolds number airfoils. Exp Fluids 46:883–901

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Shyy W, Berg M, Ljungqvist D (1999) Flapping and flexible wings for biological and micro air vehicles. Prog Aerosp Sci 35:455–505

    Article  Google Scholar 

  • Shyy W et al (2008) Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications. Acta Mech Sin 24:351–373

    Article  MATH  Google Scholar 

  • 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 46:284–327

    Article  Google Scholar 

  • Shyy W, Aono H, Kang C-k, Liu H (2013) An introduction to flapping wing aerodynamics, vol 37. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Siegel S (2011) Feedback flow control in experiment and simulation using global neural network based models. Springer, Berlin

    Book  MATH  Google Scholar 

  • 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 610:1–42

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Sirovich L (1987) Turbulence and the dynamics of coherent structures. I—Coherent structures. II—Symmetries and transformations. III—Dynamics scaling Q Appl Math 45:561–571

    Article  MathSciNet  MATH  Google Scholar 

  • 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 109–124

  • 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

  • Tadmor G, Lehmann O, Noack BR, Morzyński M (2011) Galerkin models enhancements for flow control reduced-order modelling for flow control, pp 151–252

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Usherwood JR, Lehmann FO (2008) Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl. J R Soc Interface 5:1303–1307

    Article  Google Scholar 

  • Waibel A, Hanazawa T, Hinton G, Shikano K, Lang KJ (1989) Phoneme recognition using time-delay neural networks. IEEE Trans Acoust Speech Signal Process 37:328–339

    Article  Google Scholar 

  • Wakeling J, Ellington C (1997) Dragonfly flight. II. Velocities, accelerations and kinematics of flapping flight. J Exp Biol 200:557–582

    Google Scholar 

  • 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

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Victor Troshin.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 2701 KB)

Supplementary material 2 (MP4 2783 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Troshin, V., Seifert, A. Modeling of a pitching and plunging airfoil using experimental flow field and load measurements. Exp Fluids 59, 6 (2018). https://doi.org/10.1007/s00348-017-2462-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-017-2462-3

Navigation