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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Fazio, R. 1992. The Blasius problem formulated as a free boundary value problem. Acta Mechanica, Vol. 95, Issue. 1-4, p. 1.
    Duck, Peter W. 1991. The unsteady laminar boundary layer on an axisymmetric body subject to small-amplitude fluctuations in the free-stream velocity. Journal of Fluid Mechanics, Vol. 232, Issue. -1, p. 415.
    Duck, P. W. 1990. The response of a laminar boundary layer in supersonic flow to small-amplitude progressive waves. Journal of Fluid Mechanics, Vol. 219, Issue. -1, p. 423.
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A numerical method for treating time-periodic boundary layers

  • P. W. Duck (a1)
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.

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© 1989 Cambridge University Press
References
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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.
Brown, S. N. & Stewartson, K., 1973a On the propagation of disturbances in a laminar boundary layer I. Proc. Camb. Phil. Soc. 73, 493.
Brown, S. N. & Stewartson, K., 1973b On the propagation of disturbances in a laminar boundary layer II. Proc. Camb. Phil. Soc. 73, 503.
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.
Dennis, S. C. R.: 1972 The motion of a viscous fluid past an impulsively started semi-infinite plate. J. Inst. Maths Applies 10, 105.
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.
Duck, P. W.: 1981 Torsional oscillations of a finite disk. SIAM J. Appl. Maths 41, 247.
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.
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.
Hall, M. G.: 1969 The boundary layer on an impulsively started flat plate. Proc. R. Soc. Lond. A 320, 332.
Lam, S. H. & Rott, N., 1960 Theory of linearised time-dependent boundary layers. Cornell Univ. GSAE Rep. AF0512 TN-60–1100.
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.
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.
Moore, F. K.: 1951 Unsteady laminar boundary layer flow. NACA Tech. Note 2471.
Moore, F. K.: 1957 Aerodynamic effects of boundary-layer unsteadiness. Proc. 6th Anglo-Amer. Conf. R. Aero. Soc. Folkstone, p. 439.
Pedley, T. J.: 1972 Two-dimensional boundary layers in a free stream which oscillates without reversing. J. Fluid Mech. 55, 359.
Rosenhead, L. (ed.) 1963 Laminar Boundary Layers. Oxford University Press.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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