Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-20T16:19:04.017Z Has data issue: false hasContentIssue false
  • English
  • Français

Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes

Published online by Cambridge University Press:  25 September 2008

CHRISTOPH J. MACK ,
PETER J. SCHMID  and
JÖRN L. SESTERHENN
CHRISTOPH J. MACK
Affiliation:
Department of Numerical Mathematics, Universität der Bundeswehr (UniBw), D-85577 Munich, Germany
PETER J. SCHMID
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
JÖRN L. SESTERHENN
Affiliation:
Department of Numerical Mathematics, Universität der Bundeswehr (UniBw), D-85577 Munich, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The global linear stability of a three-dimensional compressible flow around a yawed parabolic body of infinite span is investigated using an iterative eigenvalue method in conjunction with direct numerical simulations. The computed global spectrum shows an unstable branch consisting of three-dimensional boundary layer modes whose amplitude distributions exhibit typical characteristics of both attachment-line and crossflow modes. In particular, global eigenfunctions with smaller phase velocities display a more pronounced structure near the stagnation line, reminiscent of attachment-line modes while still featuring strong crossflow vortices further downstream. This analysis establishes a link between the two prevailing instability mechanisms on a swept parabolic body which, so far, have only been studied separately and locally. A parameter study shows maximum modal growth for a spanwise wavenumber of β = 0.213, suggesting a preferred disturbance length scale in the sweep direction.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 611 , 25 September 2008 , pp. 205 - 214
Copyright
Copyright © Cambridge University Press 2008

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.)

References

REFERENCES

Bertolotti, F. P. 1999 On the connection between cross-flow vortices and attachment-line instabilities. In IUTAM Symp. on Laminar-Turbulent Transition, pp. 625–630. Sedona, USA.CrossRefGoogle Scholar
Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aero. Sci. 35, 363–412.CrossRefGoogle Scholar
Edwards, W. S., Tuckerman, L. S., Friesner, R. A. & Sorensen, D. C. 1994 Krylov methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 110, 82–102.CrossRefGoogle Scholar
Fabre, D., Jacquin, L. & Sesterhenn, J. 2001 Linear interaction of a cylindrical entropy spot with a shock. Phys. Fluids 13 (8), 2403–2422.CrossRefGoogle Scholar
Gray, W. E. 1952 The effect of wing sweep on laminar flow. Tech. Rep. RAE TM Aero 255. British Royal Aircraft Establishment.Google Scholar
Guégan, A., Schmid, P. J. & Huerre, P. 2006 Optimal energy growth and optimal control in swept Hiemenz flow. J. Fluid Mech. 566, 11–45.CrossRefGoogle Scholar
Hall, P., Malik, M. & Poll, D. I. A. 1984 On the stability of an infinite swept attachment-line boundary layer. Proc. R. Soc. Lond. A 395, 229–245.Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.CrossRefGoogle Scholar
Joslin, R. D. 1995 Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers. J. Fluid Mech. 291, 369–392.CrossRefGoogle Scholar
Le Duc, A., Sesterhenn, J. & Friedrich, R. 2006 Instabilities in compressible attachment-line boundary layers. Phys. Fluids 18, 044102.CrossRefGoogle Scholar
Lin, R. S. & Malik, M. R. 1995 Stability and transition in compressible attachment-line boundary-layer flow. Tech. Rep. 952041. SAE.CrossRefGoogle Scholar
Lin, R. S. & Malik, M. R. 1996 On the stability of attachment-line boundary layers. Part 1. The incompressible swept Hiemenz flow. J. Fluid Mech. 311, 239–255.CrossRefGoogle Scholar
Lin, R. S. & Malik, M. R. 1997 On the stability of attachment-line boundary layers. Part 2. The effect of leading edge curvature. J. Fluid Mech. 333, 125–137.CrossRefGoogle Scholar
Oswatitsch, K. 1956 Gas Dynamics. Academic.Google Scholar
Poll, D. I. A. 1979 Transition in the infinite swept attachment-line boundary layer. Aero. Q. 30, 607–628.CrossRefGoogle Scholar
Reed, H. L. & Saric, W. S. 1989 Stability of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 21, 235–284.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.CrossRefGoogle Scholar
Sesterhenn, J. 2001 A characteristic-type formulation of the Navier–Stokes equations for high-order upwind schemes. Comput. Fluids 30, 37–67.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct numerical study of leading-edge contamination. In AGARD-CP-438, pp. 5/1–5/13.Google Scholar