Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T16:59:12.024Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady laminar boundary layer along the symmetry plane of an impulsively started prolate spheroid

Published online by Cambridge University Press:  21 April 2006

W. C. Xu  and
K. C. Wang
W. C. Xu
Affiliation:
Aerospace Engineering and Mechanics, San Diego State University, San Diego, CA 92182, USA
K. C. Wang
Affiliation:
Aerospace Engineering and Mechanics, San Diego State University, San Diego, CA 92182, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The symmetry-plane laminar boundary layer over an impulsively-started prolate spheroid of axes ratio 1/4 at various incidence is calculated in detail. Results agree with the steady solutions at large times. The most important one is concerned with the similarity between the distribution of the leeside skin friction at a fixed incidence, but varying in time, and that of the leeside skin friction for steady flows varying in incidence. The latter patterns led previously to the concept of an open and closed separation sequence for steady flows, likewise the newly found similarity suggests an unsteady open and closed sequence; i.e. at low incidence, separation starts around the rear stagnation point and gradually expands upstream in time, but it is always of the closed type. At moderate to high incidence, closed separation prevails at small times, open separation develops at large times, but separation may either remain open at moderate incidence or return to closed at high incidence as the steady-state condition is approached. The rate of approach toward the steady-state condition increases with incidence. For a less slender spheroid there is no open separation involved; unsteady separation lines are all of the closed type. For bodies other than spheroids, similar ideas may be applied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 413 - 435
Copyright
© 1988 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

Cebeci T., Khattab, A. K. & Stewartson K. 1980 On nose separation. J. Fluid Mech. 97, 435–454.Google Scholar
Cowley S. J. 1983 Computer extension and analytic continuation of Blasius' expansion for impulsive flow past a circular cylinder. J. Fluid Mech. 135, 389–405.Google Scholar
Krause E. 1969 Comment on solution of a three-dimensional boundary-layer flow with separation. AIAA J. 7, 575–576.Google Scholar
Moore, P. K. & Ostrach S. 1957 Displacement thickness of the unsteady boundary layer. J. Aero. Sci. 24, 77–78.Google Scholar
Raetz G. S. 1957 A method of calculating three-dimensional laminar boundary layers of steady compressible flows. Rep. No. NAI 58–73, Northrop Corporation, CA.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating laminar boundary layer. J. Comp. Phys. 38, 125–140.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1982 The genesis of separation. In Numerical and Physical Aspects of Aerodynamics Flows (ed. T. Cebeci), pp. 293–311. Springer.
Wang K. C. 1970 Three-dimensional boundary layer near the plane of symmetry of a spheroid at incidence. J. Fluid Mech. 43, 187–209.Google Scholar
Wang K. C. 1971 On the determination of the zones of influence and dependence for three-dimensional boundary layer equation. J. Fluid Mech. 48, 397–404.Google Scholar
Wang K. C. 1972 Separation pattern of boundary layer over an inclined body of revolution. AIAA J. 10, 1044–1050.Google Scholar
Wang K. C. 1974 Boundary layer over a blunt body at high incidence with an open-type of separation Proc. R. Soc. Lond. A 340, 33–55.Google Scholar
Wang K. C. 1975 Aspects of multi-time initial valued problem originating from boundary layer equations. Phys. Fluids 18, 951–955.Google Scholar
Wang K. C. 1979 Unsteady boundary layer separation. Martin Marietta Labs Rep. TR-79–16c.Google Scholar
Wang K. C. 1982 On the disputes of unsteady separation. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), pp. 279–291. Springer.
Wang, K. C. & Fan Z. G. 1982 Unsteady symmetry-plane boundary layer and 3-D unsteady separation. AF & EM TR-82–01, San Diego State University.Google Scholar
Xu, W. & Wang K. C. 1987 Unsteady laminar boundary layer along the symmetry-plane of an impulsively-started prolate spheroid. AE&EM TR-87–01, San Diego State University.Google Scholar
Zhang H. X. 1983 A general criterion for two-dimensional flow separation. Acta Mech. Sin. 6, 559–570.Google Scholar