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A numerical method for integrating the unsteady boundary-layer equations when there are regions of backflow

Published online by Cambridge University Press:  29 March 2006

J. H. Phillips  and
R. C. Ackerberg
J. H. Phillips
Affiliation:
Polytechnic Institute of Brooklyn, Graduate Center, Farmingdale, New York 11735
R. C. Ackerberg
Affiliation:
Polytechnic Institute of Brooklyn, Graduate Center, Farmingdale, New York 11735
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Abstract

A numerical method for integrating the unsteady twodimensional boundarylayer equations using a second-order-accurate implicit method, which allows for arbitrary mesh spacing in the space and time variables, is developed. A unique feature of the method is the use of an asymptotic solution valid at the downstream end of the integration mesh which permits backflow to be taken into account. Newton's iterative technique is used to solve the nonlinear finite-difference equations a t each computation step, using a rapid algorithm for solving the resulting linearized equations. The method is applied to a flow which is periodic in time and contains regions of backflow. The numerical computations are compared with known numerical and asymptotic solutions and the agreement is excellent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 3 , 8 May 1973 , pp. 561 - 579
Copyright
© 1973 Cambridge University Press

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References

Ackerberg, R. C. 1965 The viscous incompressible flow inside a cone. J. Fluid Mech. 21, 47–81.Google Scholar
Ackerberg, R. C. & Phillips, J. H. 1972 The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity. J. Pluid Mech. 51, 137–167.CrossRefGoogle Scholar
Ackerberg, R. C. & Phillips, J. H. 1973 A numerical method for highly accelerated laminar boundary-layer flows. Siam J. on Numerical Anal. 10, 147–160.Google Scholar
Dennis, S. C. R. 1972 The motion of a viscous fluid past an impulsively started semi-infinite flat plate. J. Inst. Math. Applics. 10, 105–117.Google Scholar
Gibson, W. E. 1957 Ph.D. Thesis, Massachusetts Institute of Technology.
Hall, M. G. 1969a The boundary layer over a4 impulsively started flat plate. Proc. Roy. Soc. A 310, 410–414.Google Scholar
Hall, M. G. 1969b A numerical method for calculating unsteady two-dimensional laminar boundary layers. Ing. Arch. 38, 97–106.Google Scholar
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods. Wiley.
Keller, H. B. & Cebeci, T. 1971 Accurate numerical methods for boundary layer flows. Part 1. Two-dimensional laminar flows. Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dyn. pp. 92–100. Lecture Notes in Physics no. 8. Springer.
Lightkill, M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. Roy. Soc. A 224, 1–23.Google Scholar
Lin, C. C. 1967 Motion in the boundary layer with a rapidly oscillating external flow. Proc. 9th Ins. Gong. on Appl. Mech., Brussels, 4, 155–167.Google Scholar
Moore, F. K. 1951 Unsteady laminar boundary-layer flow. N.A.C.A. Tech. Note, no. 2471.
Pedley, T. J. 1972 Two-dimensional boundary layers in a free stream which oscillates without reversing. J. Fluid Mech. 55, 359–383.Google Scholar
Phillips, J. H. 1972 Ph.D. Thesis, Polytechnic Institute of Brooklyn.
Sears, W. R. & Telionis, D. P. 1971 Unsteady boundary-layer separation. Ptoc. Iutam Symp. on Umteady Boundary Layers, pp. 404–447. Lava1 University, Quebec, Canada.
Stewartson, K. 1951 On the impulsive motion of a flat plate in a viscous fluid. Quart. J. Mech. Appl. Math. 4, 182–198.Google Scholar
Stewartson, K. 1960 The theory of unst, eady laminar boundary layers. In Advances in Applied Mechanics, vol. 4, pp. 1–37. Academic.
Tikhonov, A. N. & Samarseii, A. A. 1963 Equations of Mathematical Physics. Pergamon.