Abstract
A compilation of theoretical results from the literature on the finite flat-plate flow at zero incidence is presented. This includes the Blasius solution, the Triple Deck at the trailing edge, asymptotics in the wake, and properties near the edges of the plate. In addition, new formulas for skin friction at the plate and velocity overshoot at the boundary-layer edge are given. The relevance of the theoretical predictions is shown by a comparison with numerical results calculated with a compressible Navier-Stokes solver at low Mach number and Reynolds numbers between 103 and 105. This comparison gives clear evidence for the quantitative correctness of the significant upstream influence predicted by the trailing-edge Triple Deck theory.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Batchelor, G. K. (1970) An Introduction to Fluid Mechanics, Cambridge University Press, Cambridge.
Brandsma, F. J., Vogels, M. E. S., Van der Vooren, J., Dijkstra, D., and Kuerten, J. G. M. (1988) ‘Pre-design document of the ISNaS compressible flow simulator’, ISNaS 88.04.027.
Brandsma, F. J., and Kuerten, J. G. M. (1990) ‘The ISNaS compressible Navier-Stokes solver; First results for single airfoils’, in K. W. Morton (ed.), Twelfth International Conference on Numerical Methods in Fluid Dynamics, Springer-Verlag, Berlin, 152–156.
Dennis, S. C. R., and Dunwoody, J. (1966) ‘The steady flow of a viscous fluid past a flat plate’, J. Fluid Mech., 24, 577–595.
Dijkstra, D. (1974) ‘The solution of the Navier-Stokes equations near the trailing edge of a flat plate’, Thesis, University of Groningen.
Goldstein, S. (1930) ‘Concerning some solutions of the boundary-layer equations in hydrodynamics’, Proc. Cambr. Phil. Soc., 26, 1–30.
Jobe, C. E., and Burggraf, O. R. (1974) ‘The numerical solution of the asymptotic equations of trailing edge flow’, Proc. Roy. Soc., A340, 91–111.
Melnik, R. E., and Chow, R. (1975) ‘Asymptotic theory of two dimensional trailing edge flows’, Grumman Res. Dept. Report RE 510j.
Messiter, A. F. (1970) ‘Boundary layer flow near the trailing edge of a flat plate’, SIAM J. Appl. Math., 18, 241–257.
Stewartson, K. (1969) ‘On the flow near the trailing edge of a flat plate’, Mathematika, 16, 106–121.
Veldman, A. E. P. (1975) ‘A new calculation of the wake of a flat plate’, J. Engg. Math., 9, 65–70.
Veldman, A. E. P. (1976) ‘Boundary layer flow past, a finite flat plate’, Thesis, University of Groningen.
Van de Vooren, A. I., and Dijkstra, D. (1970) ‘The Navier-Stokes solution for laminar flow past a semi-infinite flat plate’, J. Engg. Math., 4, 9–27.
Yoshizawa, A. (1970) ‘Laminar viscous flow past a semi-infinite flat plate’, J. Phys. Soc. Japan, 28, 776–779.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Dijkstra, D., Kuerten, J.G.M. (1993). Asymptotics and Numerics for Laminar Flow Over a Finite Flat Plate. In: Kaper, H.G., Garbey, M., Pieper, G.W. (eds) Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. NATO ASI Series, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1810-1_1
Download citation
DOI: https://doi.org/10.1007/978-94-011-1810-1_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4798-2
Online ISBN: 978-94-011-1810-1
eBook Packages: Springer Book Archive