Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-25T04:53:24.726Z Has data issue: false hasContentIssue false
  • English
  • Français

The flow at a rear stagnation point is eventually determined by exponentially small values of the velocity

Published online by Cambridge University Press:  20 April 2006

Leon L. van Dommelen  and
Shan Fu Shen
Leon L. van Dommelen
Affiliation:
FAMU/FSU College of Engineering, Tallahassee, FL, USA
Shan Fu Shen
Affiliation:
Cornell University, Ithaca, NY, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

It is suggested that current conceptions about unsteady rear-stagnation-point flow do not fully describe the physics, since they show discrepancies from recent numerical results. The previously neglected exponentially small rotational perturbation velocity above the boundary-layer proves to have a dominating influence on the final boundary-layer development. An asymptotic analysis reveals possible difficulties for common computational schemes for viscous flows. Failure of the usual asymptotic matching rule in the analysis is in accordance with Fraenkel's warning on logarithmic expansions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 157 , August 1985 , pp. 1 - 16
Copyright
© 1985 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

Blasius H.1908 Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. fur Math. Phys. 56, 1.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.Google Scholar
Fraenkel L. E.1969 On the method of matched asymptotic expansions. Proc. Camb. Phil. Soc. 65, 209.Google Scholar
Goldstein, S. & Rosenhead L.1936 Boundary layer growth. Proc. Camb. Phil. Soc. 32, 392.Google Scholar
Hommel M. J.1983 The laminar unsteady flow of a viscous fluid away from a plane stagnation point. J. Fluid Mech. 132, 407.Google Scholar
Kaplun S.1967 Fluid Mechanics and Singular Perturbations (ed. P. A. Lagerstrom, L. N. Howard & C. S. Liu), pp. 70–72, 97–100. Academic.
Lange C. G.1983 On spurious solutions of singular perturbation problems. Stud. Appl. Math. 68, 227.Google Scholar
Lo L. L.1983 The meniscus on a needle — a lesson in matching. J. Fluid Mech. 132, 65.Google Scholar
Moore D. W.1958 Some laminar viscous flows. Ph.D. thesis, University of Cambridge.
Moore, F. K. & Ostrach S.1957 Displacement thickness of the unsteady boundary layer. J. Aero. Sci. 24, 77.Google Scholar
Proudman, I. & Johnson K.1962 Boundary-layer growth near a rear stagnation point. J. Fluid Mech. 12, 161.Google Scholar
Robins, A. J. & Howarth J. A.1972 Boundary-layer development at a two-dimensional rear stagnation point. J. Fluid Mech. 56, 161.Google Scholar
Schlichting H.1979 Boundary Layer Theory. McGraw-Hill.
Van Dommelen L. L.1985 Lagrangian numerical and analytical description of unsteady boundary layer separation. Part 1. J. Fluid Mech. to be submitted.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.Google Scholar
Williams P. G.1982 Large-time boundary layer computations at a rear stagnation point using the asymptotic structure. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), p. 325. Springer-Verlag.
Wundt H.1955 Wachstum der laminaren Grenzschicht an schräg angeströmten Zylindern bei Anfahrt aus der Ruhe. Ingenieur-Archiv 23, 212.Google Scholar