By applying a boundary condition for vorticity [1] in addition to that for velocity, a velocity distribution on a flat plate set in a parallel homogeneous flow has been numerically obtained through a one-way calculation from surface to infinity, without the “matching” procedure between an analysis from surface to infinity and that from infinity to surface. The numerical results obtained were in excellent agreement with those by Howarth [2]. The usage of the boundary condition for vorticity has raised the accuracy of velocity distribution near a plate’s surface and made it possible to realize the one-way calculation from surface to infinity.
References
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Ueyama, K. (2020) An Invitation to a World of Full-Fledged Fluid Dynamics. Lap Lambert Academic Publishing, Chisinau, 10-19.
[2]
Howarth, L. (1938) On the Solution of the Laminar Boundary Layer Equations. Proceedings of the Royal Society of London, A164, 547-579. https://doi.org/10.1098/rspa.1938.0037
[3]
Brøns, M., Thompson, M.C., Leweke, T. and Hourigan, K. (2014) Vorticity Generation and Conservation for Two-Dimensional Interfaces and Boundaries. Journal of Fluid Mechanics, 758, 63-93. https://doi.org/10.1017/jfm.2014.520
[4]
Blasius, H. (1908) Grenzschiten in Fluessigkeiten mit Kleiner Reibung. Zeitschrift für angewandte Mathematik und Physik, 56, 1-37.
[5]
Toepfer, C. (1912) Bemerkungen zu dem Aufsatz von H. Blasius, Grenzschichten in Fluessigkeiten mit kleiner Reibung. Zeitschrift für angewandte Mathematik und Physik, 60, 397-398.
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Bairstow, L. (1925) Skin Friction. The Journal of the Royal Aeronautical Society, 29, 3-23. https://doi.org/10.1017/S0368393100139380
[7]
Goldstein, S. (1930) Concerning Some Solutions of the Boundary Layer Equations in Hydrodynamics. Mathematical Proceedings of the Cambridge Philosophical Society, 26, 1-30. https://doi.org/10.1017/S0305004100014997
[8]
Schlichting, H. (1979) Boundary Layer Theory. 6th Edition, McGraw-Hill Book Company, New York, 135-139.
[9]
Saffman, P. (1965) The Lift on a Small Sphere in a Slow Shear Flow. Journal of Fluid Mechanics, 22, 385-400. https://doi.org/10.1017/S0022112065000824
