Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-09T19:28:03.068Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical method for treating time-periodic boundary layers

Published online by Cambridge University Press:  26 April 2006

P. W. Duck
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The development of an incompressible, laminar, pulsatile boundary layer over a semi-infinite flat plate is studied. Although the undisturbed free stream flow is taken to be non-reversing (following previous studies), sufficiently far downstream, the flow in part of the boundary layer must ultimately reverse direction during part of the cycle.

A novel numerical (finite-difference) scheme is described, which builds in the time periodicity of the flow, and also takes into account the direction of the flow in deciding the form of the differencing in the streamwise direction. The effect of variations in numerical grid is investigated, and comparison is made with asymptotic formulae applicable close to and far from the leading edge of the plate, together with linearized (small oscillation) results obtained using the analysis of Ackerberg & Phillips (1972), which is shown to yield remarkably accurate results when compared with the solution for the full problem, even for quite large oscillation amplitudes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 549 - 561
Copyright
© 1989 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

Ackerberg, R. L. & Phillips, J. H., 1972 The unsteady boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity. J. Fluid Mech. 51, 137.Google Scholar
Brown, S. N. & Stewartson, K., 1973a On the propagation of disturbances in a laminar boundary layer I. Proc. Camb. Phil. Soc. 73, 493.Google Scholar
Brown, S. N. & Stewartson, K., 1973b On the propagation of disturbances in a laminar boundary layer II. Proc. Camb. Phil. Soc. 73, 503.Google Scholar
Cowley, S. J., Hocking, L. M. & Tutty, O. R., 1985 On the stability of solutions of the classical unsteady boundary-layer equations. Phys. Fluids 20, 441.Google Scholar
Dennis, S. C. R.: 1972 The motion of a viscous fluid past an impulsively started semi-infinite plate. J. Inst. Maths Applies 10, 105.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. 30, 125.Google Scholar
Duck, P. W.: 1981 Torsional oscillations of a finite disk. SIAM J. Appl. Maths 41, 247.Google Scholar
Duck, P. W.: 1984 The interaction between a steady laminar boundary layer and an oscillatory flap the condensed problem. In Numerical and Physical Aspects of Aerodynamic Flows II (ed. T. Cebeci). Springer.
Gibson, W. E.: 1957 Unsteady boundary layers. Ph.D. dissertation, MIT.
Goldstein, M. E.: 1983 The evolution of Tollmein-Schlichting waves near a leading edge. J. Fluid Mech. 127, 59.Google Scholar
Goldstein, M. E., Pockol, P. M. & Sanz, J., 1983 The evolution of Tollmien-Schlichting waves near a leading-edge. Part 2. Numerical determinaton of amplitudes. J. Fluid Mech. 129, 443.Google Scholar
Hall, M. G.: 1969 The boundary layer on an impulsively started flat plate. Proc. R. Soc. Lond. A 320, 332.Google Scholar
Lam, S. H. & Rott, N., 1960 Theory of linearised time-dependent boundary layers. Cornell Univ. GSAE Rep. AF0512 TN-60–1100.Google Scholar
Lighthill, M. J.: 1954 The response laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. R. Soc. Lond. A 224, 1.Google Scholar
Lin, C. C.: 1956 Motion in the boundary layer with a rapidly oscillatory external flow. Proc. IX Intl Appl. Mech. Brussels, vol. 4, p. 155.Google Scholar
Moore, F. K.: 1951 Unsteady laminar boundary layer flow. NACA Tech. Note 2471.Google Scholar
Moore, F. K.: 1957 Aerodynamic effects of boundary-layer unsteadiness. Proc. 6th Anglo-Amer. Conf. R. Aero. Soc. Folkstone, p. 439.Google Scholar
Pedley, T. J.: 1972 Two-dimensional boundary layers in a free stream which oscillates without reversing. J. Fluid Mech. 55, 359.Google Scholar
Rosenhead, L. (ed.) 1963 Laminar Boundary Layers. Oxford University Press.