Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-12T05:10:42.317Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral/hp element technology for global flow instability and control

Published online by Cambridge University Press:  04 July 2016

V. Theofilis,
D. Barkley and
S. Sherwin
V. Theofilis
Affiliation:
DLR, Institute of Fluid Mechanics, Göttingen, Germany
D. Barkley
Affiliation:
Mathematics Institute, University of Warwick, UK
S. Sherwin
Affiliation:
Dept of Aeronautics, Imperial College, UK
Get accessRights & Permissions [Opens in a new window]

Abstract

The objective of our paper is to demonstrate the use of spectral/hp element technology in unravelling global flow instability mechanisms. Understanding these mechanisms is central to devising flow control approaches based on theoretically-founded physical principles. Global instability theory is concerned with prediction and control of linear and nonlinear disturbances developing in flows that are inhomogeneous in more than one spatial direction. As such, this theory encompasses the classic analysis of Tollmien which is valid for simple geometries of academic interest (e.g. a flat-plate) and therefore broadens the scope of this well-established but simplified methodology to include realistic problems encountered in aeronautical engineering. Compared with a direct numerical simulation approach, global instability theory can be used to explore efficiently far wider parameters ranges and deliver physical information to be used as handle for effective flow control.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 106 , Issue 1065 , November 2002, pp. 619 - 625
Copyright
Copyright © Royal Aeronautical Society 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Karniadakis, G. and Sherwin, S.J. Spectral/hp Element Methods for CFD. Oxford University Press, 1999 Google Scholar
2. Drazin, P.G. and Reid, W.H. Hydrodynamic Stability. Cambridge University Press, 1981.Google Scholar
3. Barkley, D. and Henderson, R.D. Three-dimensional Floquet stability analysis of the wake of a circular cylinder, J Fluid Mech., 322: 215–241, 1996 Google Scholar
4. Theofilis, V. Linear instability in two spatial dimensions. In Papailiou, K.D. (Ed), Fourth European Computational Fluid Dynamics Conference ECCOMAS 98, pp 547–552, Chichester, N.York, 1998, J. Wiley and Sons.Google Scholar
5. Theofilis, V. Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog Aero Sciences, 2002. to appear.Google Scholar
6. Hall, P., Malik, M.R. and Poll, D.I.A. On the stability of an infinite swept attachment-line boundary layer. Proc Roy Soc Lond A, 395: 229–245, 1984.Google Scholar
7. Theofilis, V. Spatial stability of incompressible attachment line flow. Theor Comput Fluid Dyn, 7: 159–171, 1995.Google Scholar
8. Schubauer, G.B. and Skramstad, H.K. Laminar boundary layer oscillations and stability of laminar flow. J Aero Sci, 14: 69–78, 1947.Google Scholar
9. Mack, L.M. Boundary layer linear stability theory, In AGARD Report No.709, Special course on stability and transition of laminar flow, pp 3–1–3–81, 1984.Google Scholar
10. Herbert, . Parabolized stability equations. Ann Rev Mech, 29: 245–283, 1997.Google Scholar
11. Theofilis, V. Hein, S and Dallman, U.Ch.. On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil Trans Roy Soc London (A), 358, 2000. to appear.Google Scholar
12. Theofilis, V. Global linear instability in laminar separated boundary layer flow. In Saric, W. and Fasel, H. (Eds), Proc. of the IUTAM Laminar-Turbulent Symposium V, Sedona, AZ, USA, 1999.Google Scholar
13. Theofilis, V. Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog Aero Sci, to appear, 2002.Google Scholar
14. Barkley, D. and Henderson, R.D. Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J Fluid Mech, 322: 215–241, September 1996.Google Scholar
15. Arnoldi, W.E. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quart Appl Math, 9: 17–29, 1951.Google Scholar
16. Theofilis, V. Linear instability in two spatial dimensions. In Papailiou, K. et al, (Ed), Proc. of the European Computational Fluid Dynamics Conference ECCOMAS 98, pp 547–552, Athens, Greece, 1998.Google Scholar
17. Howard, R.J.A. and Sandham, N.D. Simulation and modelling of a skewed turbulent channfle flow. Flow Tubul Combust, 65: 83–109, 2000.Google Scholar
18. Sherwin, S.J. and Karniadakis, G.E. A triangular spectral element method; applications to the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 123: 189, 1995.Google Scholar
19. Sherwin, S.J. and Karniadakis, G.E. A new triangular and tetrahedral basis for high-order finite element methods. Int J Numerical Methods in Engineering, 38, 1995.Google Scholar
20. Poll, D.I.A. Transition in the infinite swept attachment line boundary layer. Aeronaut Q, 30: 607–629, 1979.Google Scholar
21. Theofilis, V. On linear and nonlinear instability of the incompressible swept attachment-line boundary layer. J Fluid Mech, 355: 193–227, 1998.Google Scholar
22. Lin, R.S. and Malik, M.R. On the stability of attachment-line boundary layers. Part 1. the incompressible swept Hiemenz flow. J Fluid Mech, 311: 239–255, 1996.Google Scholar
23. Theofilis, V. Fedorov, A. Obrist, D. and Dallmann, U. An extended Gortler-Hammerlin model for linear and nonlinear instability in the three-dimensional incompressible swept attachment line boundary layer. J Fluid Mech, (in review), 2002.Google Scholar
24. Ding, Y. and Kawahara, M. Linear stability of incompressible flow using a mixed finite element method. J Comput Phys, 139: 243–273, 1998.Google Scholar
25. Aidun, C.K. Triantafillopoulos, N.G. and Benson, J.D. Global stability of a lid-driven cavity with throughflow: Flow visualisation studies. Phys Fluids A, 3: 2081, 1991.Google Scholar
26. Benson, J.D. and Aidun, C.K. Transition to unsteady nonperiodic states in a throughflow lid-driven cavity. Phys Fluids A, 4: 2316, 1992.Google Scholar
27. Theofilis, V. and Sherwin, S.J., Global instabilities in trailing-edge laminar separated flow on a NACA 0012 aerofoil. In Proceeding. ISABE, 2001. Bangalore, India.Google Scholar
28. Tollmien, W. Uber die Entstehung der Turbulenz Nach Ges Wiss Gottingen.pp 21–44, 1929.Google Scholar