Capturing transition features around a wing by reduced-order modeling based on compressible Navier-Stokes equations

Physics of Fluids

Volumn 21, Issue 9, 2009, Pages

  Bourguet, Rémi ^a,b   Braza, Marianna ^a   Sévrain, Alain ^a   Bouhadji, Abdellatif ^a,c  

^a IMFT   (France)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c BALLARD POWER SYSTEMS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

PRINCIPAL COMPONENT ANALYSIS; REYNOLDS NUMBER; VISCOUS FLOW;

COMPRESSIBLE NAVIER-STOKES EQUATIONS; FLOW TRANSITIONS; GALERKIN PROJECTIONS; PROPER ORTHOGONAL DECOMPOSITIONS; REDUCED ORDER MODELS; SECONDARY INSTABILITY; THREE-DIMENSIONAL TRANSITION; TRANSITION FEATURES;

NAVIER STOKES EQUATIONS;

EID: 70449579092     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3234398     Document Type: Conference Paper

References (33)

1. D. Arnal, "Boundary-layer transition: Prediction, application to drag reduction," in Special Course on Skin Friction Drag Reduction, AGARD Technical Report No. 786, Loughton, Essex, 1992.
2. T. H. Pulliam and J. A. Vastano, "Transition to chaos in an open unforced 2D flow," J. Comput. Phys. JCTPAH0021-9991 105, 133 (1993). 10.1006/jcph.1993.1059
3. Y. Hoarau, M. Braza, Y. Ventikos, D. Faghani, and G. Tzabiras, "Organized modes and the three-dimensional transition to turbulence in the incompressible flow around a NACA0012 wing," J. Fluid Mech.JFLSA70022-1120 496, 63 (2003). 10.1017/S0022112003006530
4. A. Bouhadji and M. Braza, "Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil. Part I," Comput. Fluids CPFLBI0045-7930 32, 1233 (2003). 10.1016/ S0045-7930(02)00100-7
5. S. Bourdet, A. Bouhadji, M. Braza, and F. Thiele, "Direct numerical simulation of the three-dimensional transition to turbulence in the transonic flow around a wing," Flow, Turbul Combust. 71, 203 (2003). 10.1023/B:APPL.0000014932.28421.9e
6. A. Deane, I. Kevrekidis, G. E. Karniadakis, and S. Orszag, "Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders," Phys. Fluids A PFADEB0899-8213 3, 2337 (1991). 10.1063/1.857881
7. B. R. Noack, K. Afanasiev, M. Morzynski, G. Tadmor, and F. Thiele, "A hierarchy of low-dimensional models for the transient and post-transient cylinder wake," J. Fluid Mech. JFLSA70022-1120 497, 335 (2003). 10.1017/S0022112003006694
8. X. Ma and G. E. Karniadakis, "A low-dimensional model for simulating three-dimensional cylinder flow," J. Fluid Mech. JFLSA70022-1120 458, 181 (2002). 10.1017/S0022112002007991
9. M. Couplet, C. Basdevant, and P. Sagaut, "Calibrated reduced-order POD-Galerkin system for fluid flow modelling," J. Comput. Phys. JCTPAH0021-9991 207, 192 (2005). 10.1016/j.jcp.2005.01.008
10. B. R. Noack, M. Schlegel, B. Ahlborn, G. Mutschke, M. Morzyński, P. Comte, and G. Tadmor, "A finite-time thermodynamics of unsteady fluid flows," J. Non-Equilib. Thermodyn. JNETDY0340-0204 33, 103 (2008). 10.1515/JNETDY.2008.006
11. D. M. Luchtenburg, B. Günter, B. R. Noack, R. King, and G. Tadmor, "A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration," J. Fluid Mech. JFLSA70022-1120 623, 283 (2009). 10.1017/S0022112008004965
12. C. W. Rowley, T. Colonius, and R. M. Murray, "Model reduction for compressible flows using POD and Galerkin projection," Physica D PDNPDT0167-2789 189, 115 (2004). 10.1016/j.physd.2003.03.001
13. G. Vigo, A. Dervieux, M. Mallet, M. Ravachol, and B. Stoufflet, "Extension of methods based on the proper orthogonal decomposition to the simulation of unsteady compressible Navier-Stokes flows," CFD'98, Proceedings of the Fourth ECCOMAS Conference (Wiley, New York, 1998), pp. 648-653.
14. R. Bourguet, M. Braza, and A. Dervieux, "Reduced-order modeling for unsteady transonic flows around an airfoil," Phys. Fluids PHFLE61070-6631 19, 111704 (2007). 10.1063/1.2800042
15. P. L. Roe, "Approximate Riemann solvers, parameter vectors, and difference schemes," J. Comput. Phys. JCTPAH0021-9991 43, 357 (1981). 10.1016/0021-9991(81)90128-5
16. B. van Leer, "Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method," J. Comput. Phys. JCTPAH0021-9991 32, 101 (1979). 10.1016/0021-9991(79)90145-1
17. A. Bouhadji, "Analyse physique par simulation numérique de phénomènes de transition bi-et tridimensionnels dans l'écoulement compressible, visqueux autour d'une aile d'avion," Ph.D. thesis, Institut National Polytechnique de Toulouse, 1998.
18. M. Braza, D. Faghani, and H. Persillon, "Successive stages and the role of natural vortex dislocations in three-dimensional wake transition," J. Fluid Mech. JFLSA70022-1120 439, 1 (2001). 10.1017/ S002211200100458X
19. J. C. R. Hunt, A. Wray, and P. Moin, "Eddies, stream, and convergence zones in turbulent flows," Center for Turbulence Research Report No. S88, 1988.
20. C. H. K. Williamson, "The existence of two stages in the transition to three-dimensionality of a cylinder wake," Phys. Fluids PHFLE61070-6631 31, 3165 (1988). 10.1063/1.866925
21. C. H. K. Williamson, "The natural and forced formation of spot-like vortex dislocations in the transition of a wake," J. Fluid Mech. JFLSA70022-1120 243, 393 (1992). 10.1017/S0022112092002763
22. H.-Q. Zhang, U. Fey, B. R. Noack, M. König, and H. Eckelmann, "On the transition of the cylinder wake," Phys. Fluids PHFLE61070-6631 7, 779 (1995). 10.1063/1.868601
23. G. E. Karniadakis and G. S. Triantafyllou, "Three-dimensional dynamics and transition to turbulence in the wake of bluff objects," J. Fluid Mech. JFLSA70022-1120 238, 1 (1992). 10.1017/ S0022112092001617
24. G. J. Sheard, M. C. Thompson, and K. Hourigan, "From spheres to circular cylinders: The stability and flow structures of bluff ring wakes," J. Fluid Mech. JFLSA70022-1120 492, 147 (2003). 10.1017/ S0022112003005512
25. G. J. Sheard, M. C. Thompson, and K. Hourigan, "Subharmonic mechanism of the mode C instability," Phys. FluidsPHFLE61070-6631 111702, 1 (2005).
26. S. L. Marple, Digital Spectral Analysis (Prentice-Hall, Englewood Cliffs, 1987).
27. F. Scarano, C. Poelma, and J. Westerweel, Proceedings of the Seventh International Symposium on PIV, Rome, Italy, 2007, pp. 1-14.
28. F. Waleffe, "On the three-dimensional instability of strained vortices," Phys. Fluids A PFADEB0899-8213 2, 76 (1990). 10.1063/ 1.857682
29. G. Berkooz, P. Holmes, and J. L. Lumley, "The proper orthogonal decomposition in the analysis of turbulent flows," Annu. Rev. Fluid Mech. ARVFA30066-4189 25, 539 (1993). 10.1146/annurev.fl.25.010193.002543
30. J. L. Lumley and A. Poje, "Low-dimensional models for flows with density fluctuations," Phys. Fluids PHFLE61070-6631 9, 2023 (1997). 10.1063/1.869321
31. L. Sirovich, "Turbulence and the dynamics of coherent structures. Part I-III," Q. Appl. Math. QAMAAY0033-569X 45, 561 (1987).
32. L. Cordier, B. Abou El Majd, and J. Favier, "Calibration of POD reduced-order models by Tikhonov regularization," Int. J. Numer. Methods Fluids IJNFDW0271-2091 (in press).
33. A. N. Tikhonov and V. A. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, 1977).