Mean field representation of the natural and actuated cylinder wake

Physics of Fluids

Volumn 22, Issue 3, 2010, Pages 2-22

  Tadmor, Gilead ^a   Lehmann, Oliver ^b   Noack, Bernd R ^c   Morzyński, Marek ^d  

^a Northeastern University   (United States)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c UNIVERSITÉ DE POITIERS   (France)

^d POZNAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDERS (SHAPES); GALERKIN METHODS; WAKES;

BILATERAL COUPLINGS; DYNAMIC PROPERTY; ENERGY FLOW ANALYSIS; EXPLICIT FORMULATION; GALERKIN MODEL; GEOMETRIC APPROACHES; MEAN FIELD VARIATION; TRANSIENT DYNAMICS;

NAVIER STOKES EQUATIONS;

EID: 77953468682     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3298960     Document Type: Article

References (88)

1. Karhunen K. Über lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci.Fenn.Ser. A1: Math.-Phys. 194637:1. 0031-8914
2. Loève M.M. Probability Theory 1955(Van NostrandPrinceton)
3. Lorenz E.N. Empirical orthogonal functions and statistical weather prediction. 1956Scientific Report No. 1Statistical Forecasting ProjectDepartment of MeteorologyMassachusetts Institute of TechnologyBoston.
4. Algazi V.R. Sakrison D.J. On the optimality of the Karhunen-Loève expansion. IEEE Trans. Inf. Theory 196915:319. IETTAW0018-944810.1109/TIT.1969.1054286and
5. Sirovich L. Turbulence and the dynamics of coherent structuresPart I: Coherent structures; Part II: Symmetries and transformations; Part III: Dynamics and scaling. Q. Appl. Math. 198745:561. QAMAAY0033-569X
6. Holmes P. Lumley J.L. Berkooz G. TurbulenceCoherent StructuresDynamical Systems and Symmetry 1998and(Cambridge UniversityCambridge).
7. Smith T.R. Moehlis J. Holmes P. Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial. Nonlinear Dyn. 200541:275. NODYES0924-090X10.1007/s11071-005-2823-yand
8. Jackson C.P. A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 1987182:23. JFLSA70022-112010.1017/S0022112087002234
9. Zebib A. Stability of viscous flow past a circular cylinder. J. Eng. Math. 198721:155. JLEMAU0022-083310.1007/BF00127673
10. Åkervik E. Hœpffner J. Ehrenstein U. Henningson D.S. Optimal growthmodel reduction and control in a separated boundary-layer flow using global eigenmodes. J. Fluid Mech. 2007579:305. JFLSA70022-112010.1017/S0022112007005496and
11. Chevalier M. Hœpffner J. Åkervik E. Henningson D.S. Linear feedback control and estimation applied to instabilities in spatially developing boundary layers. J. Fluid Mech. 2007588:163. JFLSA70022-112010.1017/S0022112007007392and
12. Lall S. Marsden J.E. Glavaski S. A subspace approach to balanced truncation for model reduction of nonlinear control systems. Int. J. Robust Nonlinear Control 200212:519. IJRCEA1049-892310.1002/rnc.657and
13. Willcox K. Peraire J. Balanced model reduction via the proper orthogonal decomposition. AIAA J. 200240:2323. AIAJAH0001-145210.2514/2.1570and
14. Rowley C.W. Model reduction for fluidsusing balanced proper orthogonal decomposition. Int. J. Bifurcation Chaos 200515:997. 10.1142/S02181274050124290218-1274
15. Ma Z. Rowley C.W. Tadmor G. Snapshot-based balanced truncation for linear time-periodic systems. IEEE Trans. Autom. Control 201055:469. IETAA90018-928610.1109/TAC.2009.2036335and
16. Deane A.E. Kevrekidis I.G. Karniadakis G.E. Orszag S.A. Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders. Phys. Fluids A 19913:2337. PFADEB0899-821310.1063/1.857881
17. Noack B.R. Afanasiev K. Morzyński M. Tadmor G. Thiele F. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 2003497:335. JFLSA70022-112010.1017/S0022112003006694and
18. Rempfer D. Empirische Eigenfunktionen und Galerkin-Projektionen zur Beschreibung des laminar-turbulenten Grenzschichtumschlags (transl.: Empirical eigenfunctions and Galerkin projection for the description of the laminar-turbulent boundary-layer transition). 1995Habilitation thesisFakultät für Luft- und RaumfahrttechnikUniversität Stuttgart.
19. Rempfer D. On low-dimensional Galerkin models for fluid flow. Theor. Comput. Fluid Dyn. 200014:75. TCFDEP0935-496410.1007/s001620050131
20. Foias C. Sell G.R. Temam R. Inertial manifolds for nonlinear evolutionary equations. J. Differ. Equations 198873:309. JDEQAK0022-039610.1016/0022-0396(88)90110-6and
21. Ahuja S. Rowley C.W. Kevrekidis I.G. Wei M. Colonius T. Tadmor G. Low-dimensional models for control of leading-edge vortices: Equilibria and linearized models. 2007andProceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit,AIAA Paper 2007-0709.
22. Aubry N. Holmes P. Lumley J.L. Stone E. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 1988192:115. JFLSA70022-112010.1017/S0022112088001818and
23. Stuart J.T. On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 19584:1. JFLSA70022-112010.1017/S0022112058000276
24. Stuart J.T. Nonlinear stability theory. Annu. Rev. Fluid Mech. 19713:347. ARVFA30066-418910.1146/annurev.fl.03.010171.002023
25. Dušek J. Le Gal P. Fraunie P. A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 1994264:59. JFLSA70022-112010.1017/S0022112094000583and
26. Zielinska B.J. A. Wesfreid J.E. On the spatial structure of global modes in the wake flow. Phys. Fluids 19957:1418. PHFLE61070-663110.1063/1.868529
27. Wesfreid J.E. Goujon-Durand S. Zielinska B.J. A. Global mode behavior of the streamwise velocity in wakes. J. Phys. II 19966:1343. JPAHER1155-431210.1051/jp2:1996135and
28. Zielinska B.J. A. Goujon-Durand S. Dušek J. Wesfreid J.E. Strongly nonlinear effect in unstable wakes. Phys. Rev. Lett. 199779:3893. PRLTAO0031-900710.1103/PhysRevLett.79.3893and
29. Gerhard J. Pastoor M. King R. Noack B.R. Dillmann A. Morzyński M. Tadmor G. Model-based control of vortex shedding using low-dimensional Galerkin models. 2003Proceedings of the 33rd AIAA Fluids Conference and Exhibit,AIAA Paper 2003-4262.
30. Siegel S. Cohen K. McLaughlin T. Feedback control of a circular cylinder wake in experiment and simulation. 2003andProceedings of the 33rd AIAA Fluids Conference and Exhibit,AIAA Paper 2003-3571.
31. Siegel S. Cohen K. McLaughlin T. Experimental variable gain feedback control of a circular cylinder wake. 2004andProceedings of the 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference,AIAA Paper 2004-2611.
32. Tadmor G. Noack B.R. Morzyński M. Siegel S. Low-dimensional models for feedback flow control. Part II: Controller design and dynamic estimation. 2004andProceedings of the 2nd AIAA Flow Control Conference,AIAA Paper 2004-2409.
33. Noack B.R. Tadmor G. Morzyński M. Low-dimensional models for feedback flow control. Part I: Empirical Galerkin models. 2004Proceedings of the 2nd AIAA Flow Control Conference,AIAA Paper 2004-2408.
34. Lehmann O. Luchtenburg M. Noack B.R. King R. Morzynski M. Tadmor G. Wake stabilization using POD Galerkin models with interpolated modes. 2005500. Proceedings of 44th IEEE Conference on Decision Control European Control Conference ECCSevilleSpain
35. Siegel S. Seidel J. Fagley C. Luchtenburg M. Cohen K. McLaughlin T. Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition. J. Fluid Mech. 2008610:1. JFLSA70022-112010.1017/S0022112008002115
36. Luchtenburg M. Noack B.R. Günther B. King R. Tadmor G. A generalised mean-field model of the natural high-frequency actuated flow around a high-lift configuration. J. Fluid Mech. 2009623:283. JFLSA70022-112010.1017/S0022112008004965
37. Marquet O. Sipp D. Jacquin L. Sensitivity analysis passive control of cylinder flow. J. Fluid Mech. 2008615:221. JFLSA70022-112010.1017/S0022112008003662
38. Thiria B. Wesfreid J.E. Stability properties of forced wakes. J. Fluid Mech. 2007579:137. JFLSA70022-112010.1017/S0022112007004818
39. Protas B. Styczek A. Optimal rotary control of the cylinder wake in the laminar regime. Phys. Fluids 200214:2073. PHFLE61070-663110.1063/1.1476671
40. Protas B. Wesfreid J.E. Drag force in the open-loop control of the cylinder wake in the laminar regime. Phys. Fluids 200214:810. PHFLE61070-663110.1063/1.1432695
41. Lau L.D. Lifshitz E.M. Fluid Mechanics (Course of Theoretical Physics) 19876. (PergamonOxford)Vol.
42. Sreenivasan K.R. Strykowski P.J. Olinger D.J. Hopf bifurcationLau equation vortex shedding behind circular cylinders. Forum on Unsteady Flow Separation 198752:1-13. K. N. Ghiaedited by (American Society for Mechanical EngineersFluids Engineering DivisionNew York)pp.
43. Thompson M.C. Le Gal P. The Stuart-Lau model applied to wake transition revisited. Eur. J. Mech. B/Fluids 200423:219. EJBFEV0997-754610.1016/j.euromechflu.2003.09.012
44. Morzyński M. Afanasiev K. Thiele F. Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis. Comput. Methods Appl. Mech. Eng. 1999169:161. CMMECC0045-782510.1016/S0045-7825(98)00183-2
45. Karniadakis G.E. Triantafyllou G.S. Three-dimensional dynamics transition to turbulence in the wake of bluff bodies. J. Fluid Mech. 1992238:1. JFLSA70022-112010.1017/S0022112092001617
46. Noack B.R. Eckelmann H. A global stability analysis of the steady periodic cylinder wake. J. Fluid Mech. 1994270:297. JFLSA70022-112010.1017/S0022112094004283
47. Zhang H.-Q. Fey U. Noack B.R. König M. Eckelmann H. On the transition of the cylinder wake. Phys. Fluids 19957:779. PHFLE61070-663110.1063/1.868601
48. Barkley D. Henderson R.D. Three-dimensional floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 1996322:215. JFLSA70022-112010.1017/S0022112096002777
49. Morzyński M. Noack B.R. Tadmor G. Global flow stability analysis reduced order modeling for bluff-body flow control. Theor Appl. Mech. 200745:621.0285-6042
50. Unal M.F. Rockwell D. On the vortex formation from a cylinder; Part 2. Control by a splitter-plate interference. J. Fluid Mech. 1988190:513. JFLSA70022-112010.1017/S0022112088001430
51. Strykowski P.J. Sreenivasan K.R. On the formation suppression of vortex shedding at low Reynolds numbers. J. Fluid Mech. 1990218:71. JFLSA70022-112010.1017/S0022112090000933
52. Detemple-Laake E. Eckelmann H. Phenomenology of Kármán vortex streets in oscillatory flow. Exp. Fluids 19897:217. EXFLDU0723-486410.1007/BF00198001
53. Roussopoulos K. Feedback control of vortex shedding at low Reynolds numbers. J. Fluid Mech. 1993248:267. JFLSA70022-112010.1017/S0022112093000771
54. Roussopoulos K. Monkewitz P.A. Nonlinear modelling of vortex shedding control in cylinder wakes. Physica D 199697:264. PDNPDT0167-278910.1016/0167-2789(96)00151-0
55. Bergmann M. Cordier L. Brancher J.-P. Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced order model. Phys. Fluids 200517:097101. PHFLE61070-663110.1063/1.2033624
56. Kim B.H. Williams D.R. Nonlinear coupling of fluctuating drag lift on cylinders undergoing forced oscillations. J. Fluid Mech. 2006559:335. JFLSA70022-112010.1017/S0022112006000358
57. Protas B. Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys. Fluids 200416:4473. PHFLE61070-663110.1063/1.1808773
58. Noack B.R. Tadmor G. Morzyński M. Actuation models dissipative control in empirical Galerkin models of fluid flows. 20046:5722. Proceedings of the 2004 American Control Conference,p.
59. Lewin G.C. Haj-Hariri H. Reduced-order modeling of a heaving airfoil. AIAA J. 200543:270. AIAJAH0001-145210.2514/1.8210
60. Djouadi S.M. Camphouse R.C. Myatt J.H. Reduced order models for boundary feedback flow control. 20084005. Proceedings of the 2008 American Control Conference
61. Wallace R.D. ino M.Y. Glauser M.N. Camphouse R.C. Schmit R.F. Myatt J.H. Flow aero-optics around a turret Part 2: Surface pressure based proportional closed loop flow control. 2008Proceedings of the 39th AIAA Plasmadynamics Lasers Conference,AIAA Paper 2008-4217.
62. Ahuja S. Rowley C.W. Low-dimensional models for feedback stabilization of unstable steady states. 2008Proceedings of the 46th AIAA Aerospace Sciences Meeting Exhibit,AIAA Paper 2008-553.
63. Batchelor G.K. An Introduction to Fluid Dynamics 2000Mathematical Library Series (Cambridge University PressCambridge).
64. Stankiewicz W. Morzyński M. Noack B.R. Tadmor G. Reduced order Galerkin model of flow around a NACA-0012 airfoil. Math. Modell. Anal. 200813:113. 10.3846/1392-6292.2008.13.113-122
65. Tadmor G. Centuori M.D. Noack B.R. Luchtenburg M. Lehmann O. Morzyński M. Low order Galerkin models for the actuated flow around 2-D airfoils. 2007Proceedings of the 45th AIAA Aerospace Sciences Meeting Exhibit,AIAA Paper 2007-1313.
66. Raghu S. Monkewitz P.A. The bifurcation of a hot round jet to limit-cycle oscillations. Phys. Fluids A 19913:501. PFADEB0899-821310.1063/1.858109
67. Li F. Tadmor G. Banaszuk A. Noack B.R. Mehta P.G. A reduced order Galerkin model for the reacting flameholder. 2006Proceedings of the 3rd AIAA Flow Control Conference,AIAA Paper 2006-3487.
68. Farhood M. Beck C.L. Dullerud G.E. Model reduction of periodic systems: A lifting approach. Automatica 200541:1085. ATCAA90005-109810.1016/j.automatica.2005.01.008
69. Kolmanovskii V.B. Stability Periodic Solutions of Controlled Systems with Delay 1981(NaukaMoscow).
70. Bamieh B. Pearson J.B. Francis B.A. Tannenbaum A. A lifting technique for linear systems with applications to sampled-data control. Syst. Control Lett. 199117:79. SCLEDC0167-691110.1016/0167-6911(91)90033-B
71. Tadmor G. H∞ optimal sampled data control in continuous time systems. Int. J. Control 199256:99. IJCOAZ0020-717910.1080/00207179208934306
72. Noack B.R. Papas P. Monkewitz P.A. Low-dimensional Galerkin model of a laminar shear-layer. 2002Technical Report No. 2002-01Laboratoire de Mécanique des FluidesDépartement de Genie MécaniqueEcole Polytechnique Fédérale de LausanneSwitzerl.
73. Noack B.R. Papas P. Monkewitz P.A. The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J. Fluid Mech. 2005523:339. JFLSA70022-112010.1017/S0022112004002149
74. Ma X. Karniadakis G.E. A low-dimensional model for simulating three-dimensional cylinder flow. J. Fluid Mech. 2002458:181. JFLSA70022-112010.1017/S0022112002007991
75. Morzyński M. Stankiewicz W. Noack B.R. King R. Thiele F. Tadmor G. Continuous mode interpolation for control-oriented models of fluid flow. Active Flow Control 200795:260-278. R. King10.1007/978-3-540-71439-2_16inNotes on Numerical Fluid Mechanics Multidisciplinary Design edited by (Springer-VerlagBerlin)
76. IJzerman W.L. Signal representation modeling of spatial structures in fluids. 2000Ph.D. thesisUniversiteit Twente.
77. Borggaard J. Hay A. Pelletier D. Interval-based reduced order models for unsteady fluid flow. IJNAM 20074:353. 1705-5105
78. Hay A. Borggaard J. Pelletier D. Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition. J. Fluid Mech. 2009629:41. JFLSA70022-112010.1017/S0022112009006363
79. Barkley D. Linear analysis of the cylinder wake mean flow. Europhys. Lett. 200675:750. EULEEJ0295-507510.1209/epl/i2006-10168-7
80. Noack B.R. Schlegel M. Ahlborn B. Mutschke G. Morzyński M. Comte P. Tadmor G. A finite-time thermodynamics of unsteady flows. J. Non-Equilib. Thermodyn. 200833:103. JNETDY0340-020410.1515/JNETDY.2008.006
81. Noack B.R. Schlegel M. Morzyński M. Tadmor G. System reduction strategy for Galerkin models of fluid flows. Int. J. Numer. Methods Fluids IJNFDW0271-209110.1002/fld2049(in press).
82. Rempfer D. Rempfer D. Fasel H.F. Rempfer D. Fasel H.F. Dynamics of three-dimensional coherent structures in a flat-plate boundary layer. J. Fluid Mech. 1994275:257. JFLSA70022-112010.1017/S0022112094003551JFLSA70022-112010.1017/S00221120 94002351Ph.D. thesisFakultät Verfahrenstechnik der Universität Stuttgart. [Part of this work has been published in the following papers:].
83. Ukeiley L. Cordier L. Manceau R. Delville J. Glauser M. Bonnet J.P. Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model. J. Fluid Mech. 2001441:67. JFLSA70022-112010.1017/S0022112001004803
84. Couplet M. Sagaut P. Basdevant C. Intermodal energy transfers in a proper orthogonal decomposition-Galerkin representation of a turbulent separated flow. J. Fluid Mech. 2003491:275. JFLSA70022-112010.1017/S0022112003005615
85. Glezer A. Kadioglu Z. Pearlstein A.J. Development of an extended proper orthogonal decomposition its application to a time periodically forced plane mixing layer. Phys. Fluids A 19891:1363. PFADEB0899-821310.1063/1.857312
86. Galletti G. Bruneau C.H. Zannetti L. Iollo A. Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 2004503:161. JFLSA70022-112010.1017/S0022112004007906
87. Bergmann M. Bruneau C.-.H. Iollo A. Enablers for robust POD models. J. Comput. Phys. 2009228:516. JCTPAH0021-999110.1016/j.jcp.2008.09.024
88. Pastoor M. Henning L. Noack B.R. King R. Tadmor G. Feedback shear layer control for bluff body drag reduction. J. Fluid Mech. 2008608:161. JFLSA70022-112010.1017/S0022112008002073