Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T18:08:15.329Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical investigation of the high-speed conical flow past a sharp fin

Published online by Cambridge University Press:  26 April 2006

Argyris G. Panaras
Argyris G. Panaras
Affiliation:
DLR, Bunsenstrasse 10, Göttingen, Germany Present address: Agias Elenis 63, Athens 15772, Greece.
Get access Rights & Permissions [Opens in a new window]

Abstract

The supersonic flow past a fin mounted on a flat plate is simulated numerically by solving the Reynolds averaged Navier—Stokes equations. The results agree well with the experimental data. Post-processing of the numerical solution provides the missing flow-field evidence for confirming the currently accepted flow model, whose conception was based mainly on surface data. It is found that the flow is dominated by a large vortical structure, which lies on the plate and whose core has a remarkably conical shape with flattened elliptical cross-section. Along the fin and close to the corner, a slowly growing smaller vortex develops. On top of the conical vortex and along it a λ-shock is formed. Quantitative data are presented, which show that the flow is not actually purely conical but a small deviation exists, especially at the part between the separation shock and the plate. This deviation is detected when the stream wise extent of the flow is more than 20–30 initial boundary-layer thicknesses. Owing to the rather quasi-conical nature of the flow, the various flow variables do not remain constant along rays that start at the origin of the conical flow field, but they vary slowly. Data are presented which support the view that this deviation from conical behaviour is mainly due to the effect of the smaller rate of development of the boundary later of the plate, compared to the conical vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 607 - 633
Copyright
© 1992 Cambridge University Press

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

Alvi, F. S. & Settles, G. S. 1990 Structure of swept shock wave/boundary-layer interactions using conical shadowgraphy. AIAA paper 90–1644.Google Scholar
Baldwin, B. S. & Lomax, H. 1978 Thin layer approximation and algebraic model for separated turbulent flows. AIAA paper 78–257.Google Scholar
Horstmann, C. C. & Hung, C. M. 1979 Computation of three-dimensional turbulent separated flows at supersonic speeds. AIAA paper 79–0002.Google Scholar
Hung, C. M. & MacCormack, R. W. 1977 Numerical solution of supersonic laminar flow over a three-dimensional compression corner. AIAA paper 77–694.Google Scholar
Hung, C. M. & MacCormack, R. W. 1978 Numerical solution of three-dimensional shock wave and turbulent boundary-layer interaction. AIAA J. 16, 1090–1096.Google Scholar
Knight, D. D., Horstman, C. C., Shapey, B. & Bogdonoff, S. 1987 Structure of supersonic turbulent flow past a sharp fin. AIAA J. 25, 1331–1337.Google Scholar
Kubota, H. & Stollery, J. L. 1982 An experimental study of the interaction between a glancing shock wave and a turbulent boundary layer. J. Fluid Mech. 116, 431–458.Google Scholar
Lighthill, M. J. 1963 Attachment and separation in three-dimensional flow. In Laminar Boundary Layers. Oxford University Press.
Lu, F. K. & Settles, G. S. 1989 Inception to a fully developed fin-generated shock-wave boundary-layer interaction. AIAA paper 89–1850.Google Scholar
Maskell, E. C. 1955 Flow separation in three dimensions. RAE Rep. Aero. 2565.Google Scholar
Müller, B. 1990 Development of an upwind relaxation method to solve the 3D Euler and Navier—Stokes equations for hypersonic flow. GAMM Wissenschaftliche Jahrestagung, Hannover, April 1990.
Roe, P. L. 1981 Approximate Riemann solvers, parameters vectors, and difference schemes. J. Comp. Phys. 43, 357–372.Google Scholar
Shapey, B. & Bogdonoff, S. M. 1987 Three-dimensional shock wave/turbulent boundary layer interaction for a 20° sharp fin at Mach 3. AIAA paper 87–0554.Google Scholar
Settles, G. S. & Dolling, D. S. 1986 Swept shock wave/boundary-layer interactions. In AIAA Progress in Aeronautics and Astronautics: Tactical Missile Aerodynamics (ed. M. Hemsch & J. Nielsen), vol. 104, pp. 297–379.
Settles, G. S. & Teng, H. Y. 1984 Cylindrical and conical flow regimes of three-dimensional shock/boundary-layer interactions. AIAA J. 22, 194–200.Google Scholar
Token, K. H. 1974 Heat transfer due to shock wave/turbulent boundary layer interactions on high speed weapon systems. AFFDL TR-74–77.Google Scholar
Vollmers, H. 1989 A concise introduction to Comadi. DLR IB 221–89 A 22.Google Scholar
Vollmers, H., Kreplin, H. P. & Meier, H. U. 1983 Aerodynamics of vortical type flows in three dimensions. AGARD Conf. Proc. 342, paper 14.Google Scholar
Yee, H. C. & Harten, A. 1987 Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates. AIAA J., 25, 266–274.Google Scholar