Dynamical modelling of the flow over a flapping wing using proper orthogonal decomposition and system identification techniques

References

• Azuma , A. , Masato , O. , Kunio , Y. and Mueller , T.J. 2001 . Aerodynamic characteristics of wings at low Reynolds numbers, fixed and flapping wings aerodynamics for micro air vehicle applications . AIAA Prog. Astronaut. Aeronaut. , 195 : 341 – 398 .
   Google Scholar
• Fearing , R.S. , Chiang , K.H. , Dickinson , M. , Pick , D. , Sitti , M. and Yan , J. Wing Transmission for a Micromechanical Flying Insect . Proceedings of the 2000 IEEE, International Conference on Robotics & Automation . San Francisco , CA . pp. 1509 – 1516 . New York : Institute of Electrical and Electronics Engineers (IEEE) .
   Google Scholar
• Ho , S. , Nassef , H. , Pornsinsirirak , N. , Tai , Y.C. and Ho , C.M. 2003 . Unsteady aerodynamics and flow control for flapping wing flyers . Prog. Aerosp. Sci. , : 635 – 681 .
   Web of Science ®Google Scholar
• Frauenfelder , M. 2006 . MAKE: Technology on Your Time , Vol. 8 , Sebastopol , CA : O'Reilly Media .
   Google Scholar
• Lentink , D. , Van Heijst , G.J. , Muijres , F.T. and Van Leeuwen , J.L. 2010 . Vortex interactions with flapping wings and fins can be unpredictable . R. Soc. Biol. Lett. , 6 : 394 – 397 .
   PubMed Web of Science ®Google Scholar
• Kurtulus , D.F. 2008 . Ability to forecast unsteady aerodynamic forces of flapping airfoils by artificial neural network . Neural Comput. Appl. , 18 ( 4 ) : 359 – 368 .
   Web of Science ®Google Scholar
• Kurtulus , D.F. , David , L. , Farcy , A. and Alemdaroglu , N. 2008 . Aerodynamic characteristics of flapping motion in hover . Exp. Fluids , 44 : 23 – 36 .
   Web of Science ®Google Scholar
• Deng , X. , Schenato , L. and Sastry , S.S. 14–19 September 2003 . Model identification and attitude control scheme for a micromechanical flying insect , 14–19 September , Taiwan : International Conference on Robotics and Automation .
   Google Scholar
• Zbikowski , R. 2002 . On aerodynamic modeling of an insect-like flapping wing in hover for micro air vehicle . Phil. Trans. R. Soc. Lond. A , : 273 – 290 .
   Google Scholar
• Rowley , C.W. , Colonius , T. and Murray , R.M. 2004 . Model reduction for compressible flows using POD and Galerkin projection . Phys. D , 189 : 115 – 129 .
   Web of Science ®Google Scholar
• Noack , B.R. , Afanasiev , K. , Morzynski , M. , Tadmor , G. and Thiele , F. 2003 . A hierarchy of low-dimensional models for the transient and post-transient cylinder wake . J. Fluid Mech. , 497 : 335 – 363 .
   Web of Science ®Google Scholar
• Erbil , T.N. and Kasnakoglu , C. 2009 . Feedback flow control employing local dynamical modeling with wavelets . Math. Comput. Model. Dyn. Syst. , 15 : 493 – 513 .
   Web of Science ®Google Scholar
• Wilcox , K. and Peraire , J. 2002 . Balanced model reduction via proper orthogonal decomposition method . AIAA J. , 40 ( 11 ) : 2323 – 2330 .
   Google Scholar
• Tran , H.T. and Ly , H.V. 2001 . Modeling and control of physical process using proper orthogonal decomposition . Math. Comput. Model. , 33 ( 1–3 ) : 223 – 236 .
   Web of Science ®Google Scholar
• Bourguet , R. , Braza , M. and Dervieux , A. 2007 . Reduced-order modeling for unsteady transonic flows around an airfoil . Phys. Fluids , 19 ( 11 ) : 1 – 4 .
   Google Scholar
• Noack , B.R. , Morzynski , M. and Tadmor , G. 2011 . Reduced-Order Modelling for Flow Control , New York : Springer . ISBN: 978–3709107577
   Google Scholar
• Prasad , A.K. , Hopkins , L.M. , Kellya , J.T. and Wexler , A.S. 2000 . Particle image velocimetry measurements in complex geometries . Exp. Fluids , 29 : 91 – 95 .
   Web of Science ®Google Scholar
• Raffel , M. , Willert , C. , Wereley , S. and Kompenhans , J. 1998 . Particle Image Velocimetry: A Practical Guide , New York : Springer .
   Google Scholar
• Scarano , F. and Riethmuller , M.L. 1999 . Iterative multigrid approach in PIV image processing with discrete window offset . Exp. Fluids , 26 : 513 – 523 .
   Web of Science ®Google Scholar
• Daichin , W. Kang and Zhao , L. 2007 . PIV measurements of the near wake flow of an airfoil above a free surface . Sci. Direct J. Hydrodyn. Ser. B , 19 ( 4 ) : 482 – 487 .
   Web of Science ®Google Scholar
• Druault , P. and Challiou , C. 2007 . Use of proper orthogonal decomposition for reconstructing the 3D in-cylinder mean-flow field from PIV data . C. R. Méc. , 335 ( 1 ) : 42 – 47 .
   Web of Science ®Google Scholar
• Druault , P. , Guibert , P. and Alizon , F. 2005 . Use of proper orthogonal decomposition for time interpolation from PIV data . Exp. Fluids , 39 ( 6 ) : 1009 – 1023 .
   Web of Science ®Google Scholar
• Ford , M.D. , Nikolov , H.N. , Milner , J.S. , Lownie , S.P. , DeMont , E.M. , Kalata , W. , Loth , F. , Holdsworth , D.W. and Steinman , D.A. 2008 . PIV-measured versus CFD-predicted flow dynamics in anatomically realistic cerebral aneurysm models . J. Biomech. Eng. , 130 : 021015
   Web of Science ®Google Scholar
• Ranade , V.V. , Perrard , M. , Le Sauze , N. , Xuereb , C. and Bertrand , J. 2001 . Trailing vortices of rushton turbine: PIV measurements and CFD simulations with snapshot approach . Chem. Eng. Res. Des. , 79 ( 1 ) : 3 – 12 .
   Google Scholar
• Ravindran , S.S. 2000 . Reduced-order adaptive controllers for fluid flows using POD . J. Sci. Comput. , 15 ( 4 ) : 457 – 478 .
   Google Scholar
• Bleris , L.G. and Kothare , M.V. 2005 . Reduced order distributed boundary control of thermal transients in microsystems . IEEE Trans. Control Syst. Technol. , 13 ( 6 ) : 853 – 867 .
   Web of Science ®Google Scholar
• Kowalski , M.E. and Jin , J.M. 2003 . Model-order reduction of nonlinear models of electromagnetic phased-array hyperthermia . IEEE Trans. Biomed. Eng. , 50 ( 11 ) : 1243 – 1254 .
   PubMed Web of Science ®Google Scholar
• Gerhard , J. , Pastoor , M. , King , R. , Noack , B.R. , Dillmann , A. , Morzynski , M. and Tadmor , G. 2003 . Model-based control of vortex shedding using low-dimensional Galerkin models . AIAA Pap. 2003–4262, 33rd AIAA Fluid Dynamics Conference and Exhibit . June 23–26 2003 , Orlando , FL . Reston , VA : The American Institute of Aeronautics and Astronautics (AIAA) .
   Google Scholar
• Couplet , M. , Basdevant , C. and Sagaut , P. 2005 . Calibrated reduced-order POD-Galerkin system for fluid flow modelling . J. Comput. Phys. , 207 ( 1 ) : 192 – 220 .
   Web of Science ®Google Scholar
• Rapun , M.L. and Vega , J.M. 2010 . Reduced order models based on local POD plus Galerkin projection . J. Comput. Phys. , 229 ( 18 ) : 3046 – 3063 .
   Google Scholar
• Dantec Dynamics, Particle Image Velocimetry Measurement Principles, 2010. http://www.dantecdynamics.com/Default.aspx?ID=1049 (http://www.dantecdynamics.com/Default.aspx?ID=1049) (Accessed: 18 June 2012 ).
   Google Scholar
• Galletti , B. , Bottaro , A. , Bruneau , C.H. and Iollo , A. 2007 . Accurate model reduction of transient and forced wakes . Eur. J. Mech. B/Fluids , 26 : 354 – 366 .
   Web of Science ®Google Scholar
• Luchtenburg , D.M. , Noack , B.R. and Schlegel , M. 2009 . An introduction to the POD and Galerkin method for fluid flows with analytical examples and MATLAB source codes , Berlin : Tech. Rep. 01/2009, Berlin Institute of Technology .
   Google Scholar
• Kostas , J. , Soria , J. and Chong , M. 2002 . Particle image velocimetry measurements of a backward-facing step flow . Exp. Fluids , 33 : 838 – 853 .
   Web of Science ®Google Scholar
• Uzol , O. and Katz , J. 2007 . Flow measurement techniques in turbomachinery . Springer Handb. Exp. Fluid Mech. , 14 : 919 – 958 .
   Google Scholar
• Bergmann , M. , Cordier , L. and Brancher , J.P. 2005 . Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model . Phys. Fluids , 17 ( 9 ) : 097101
   Google Scholar
• Holmes , P. , Lumley , J.L. , Berkooz , G. and Rowley , C.W. 2012 . Turbulence, Coherent Structures, Dynamical System, and Symmetry , 2nd , Cambridge : Cambridge University Press . ISBN: 978-1-107-00825-0
   Google Scholar
• Sirovich , L. 1987 . Turbulence and the dynamics of coherent structures . Q. Appl. Math. , 45 : 561 – 50 .
   Web of Science ®Google Scholar
• Ljung , L. 1999 . System Identification: Theory for the User , Upper Saddle River , NJ : PTR Prentice Hall .
   Google Scholar
• Van Overschee , P. and De Moor , B. 1996 . Subspace Identification for Linear Systems: Theory-Implementation-Applications , Dordrecht : Kluwer Academic .
   Google Scholar
• Larimore , W.E. 1996 . Statistical optimality and canonical variate analysis system identification . Signal Process. , 52 : 131 – 144 .
   Web of Science ®Google Scholar
• Noack , B.R. , Schlegel , M. , Morzynski , M. and Tadmor , G. 2010 . System reduction strategy for Galerkin models of fluid flows . Int. J. Numer. Method Fluids , 63 ( 2 ) : 231 – 248 .
   Web of Science ®Google Scholar
• Siauw , W.L. , Bonnet , J.-P. , Tensi , J. , Cordier , L. , Noack , B.R. and Cattafesta III , L. 2010 . Transient dynamics of the flow around a NACA0015 airfoil using fluidic vortex generators . Int. J. Heat Fluid Flow , 31 : 450 – 459 .
   Web of Science ®Google Scholar
• Tadmor , G. , Lehmann , O. , Noack , B.R. and Morzynski , M. 2010 . Mean field representation of the natural and actuated cylinder wake flow . Phys. Fluids , 22 : 1 – 22 . 034102
   Google Scholar
• Shyy , W. 2008 . Aerodynamics of Low Reynolds Number Flyers , Cambridge : Cambridge University Press .
   Google Scholar