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Unsteady boundary layers with an intelligent numerical scheme

Published online by Cambridge University Press:  21 April 2006

Tuncer Cebeci
Tuncer Cebeci
Affiliation:
Douglas Aircraft Company, Long Beach, CA
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Abstract

A numerical method has been developed to represent unsteady boundary layers with large flow reversal. It makes use of the characteristic box scheme which examines the finite-difference grid in relation to the magnitude and direction of local velocity and reaches and implements a decision to ensure that the Courant, Friedricks & Lewey stability criterion is not violated. The method has been applied to the problem of an impulsively started circular cylinder and the results, though generally consistent with those of van Dommelen & Shen obtained with a Lagrangian method, show some differences. The time step is identified as very important and, with the present intelligent numerical scheme, the results were readily extended to times far beyond those previously achieved with Eulerian methods. Extrapolation of the results suggests that the much-discussed singularity for this unsteady flow is the same as that of the corresponding steady flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 129 - 140
Copyright
© 1986 Cambridge University Press

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References

Belcher, R. J., Burggraf, O. R., Cooke, J. C., Robins, A. J. & Stewartson, K. 1971 Limitless boundary layers. In Recent Research on Unsteady Boundary Layers. In Proc. Intl Union Theoret. Appl. Mech. (ed. E. A. Eichelbrenner), pp. 1444–1466.
Bradshaw, P., Cebeci, T. & Whitelaw, J. H. 1981 Engineering Calculation Methods for Turbulent Flows. Academic.
Cebeci, T. 1979 The laminar boundary layer on a circular cylinder started impulsively from rest. J. Comp. Phys. 31, 153–172.Google Scholar
Cebeci, T. 1982 Unsteady separation. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), pp. 265–277. Springer.
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.
Crank, J. & Nicolson, P. 1947 A practical method for numerical evaluation of solutions of partial-differential equations of the heat-conduction type. Proc. Camb. Phil. Soc. 43, 50–67.Google Scholar
Ingham, D. B. 1984 Unsteady separation. J. Comp. Phys. 53, 90–99.Google Scholar
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods. Wiley.
Keller, H. B. 1974 Accurate difference methods for two-point boundary-value problems. SIAM J. Numer. Anal. 11, 305–320.Google Scholar
Keller, H. B. 1978 Numerical methods in boundary-layer theory. Ann Rev. Fluid Mech. 10, 417–433.Google Scholar
Krause, E., Hirschel, E. H. & Bothmann, TH. 1968 Die numerische Integration der Bewegungsgleichungen dreidimensionaler laminarer kompressibler Grenzschichten, Bd 3, Fachtagung Aerodynamik, Berlin; D-LR-Fachlichreihe, 1–49.
Riley, N. 1975 Unsteady laminar boundary layers. SIAM Rev. 17, 274–297.Google Scholar
Sears, W. R. & Telionis, D. P. 1975 Boundary – layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215–235.Google Scholar
Shen, S. F. 1978 Unsteady separation according to the boundary-layer equations. Adv. Appl. Mech. 18, 177–200.Google Scholar
Telionis, D. P. 1979 Review — Unsteady boundary layers, separated and attached. Trans. ASME I: J. Fluids Engng 101, 29–43.Google Scholar
Telionis, D. P. & Tsahalis, D. T. 1974 Unsteady laminar separation over impulsively moved cylinders. Acta Astron. 1, 1487–1505.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1981 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 Aerodynamic Flows (ed. T. Cebeci), pp. 293–311. Springer.
Williams, J. C. 1977 Incompressible boundary-layer separation. Ann. Rev. Fluid Mech. 9, 113–144.Google Scholar