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Further Development of a Boundary Layer Profile for a given Pressure Distribution*

Published online by Cambridge University Press:  28 July 2016

H. Görtler
H. Görtler*
Affiliation:
Air Ministry Translation No. 1051.†
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Extract

The following paper forms a continuation of a recent work by Prandtl (I) “On the Calculation of Boundary Layers.” It deals with the problem of developing in detail the method, proposed in that paper, for continuing a given velocity profile in a laminar boundary layer when the pressure distribution is given; the method is tried out in practice by numerical evaluation of an example.

Type
Research Article
Information
The Aeronautical Journal , Volume 45 , Issue 362 , February 1941 , pp. 35 - 50
Copyright
Copyright © Royal Aeronautical Society 1954

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Footnotes

*

Z.A.M.M., Vol. 19, No. 3, June, 1939, pp. 129-140.

References

1. Z.A.M.M., Vol. 18, 1938, pp. 77–82.Google Scholar
2. Prandtl, L.. “ On Fluid Motion with very Small Friction ” : Proceedings of the 3rd International Mathematical Congress, Leipzig, 1905. Reprinted in Prandtl-Betz ” Four Publications on Hydrodynamics and Aerodynamics,” Göttingen, 1927.Google Scholar
3. Blasius, H.. “ Boundary Layers in Fluids with Small Friction.” Thesis, Göttingen, 1907. Published in Zeit. für Math. u. Physik, 1908, Vol. 56, pp. 1–37. T.2944.Google Scholar
4. Hiemenz, K.. “ The Boundary Layer on a Straight Circular Cyclinder immersed in a Uniform Fluid Flow.” Thesis, Göttingen, 1911. Published in Dingler's Polytechn. J., Vol. 326, 1911, pp. 321-42. 3023—F.M.32.Google Scholar
5. Howarth, L.. “ Steady Flow in the Boundary Layer near the Surface of a Cylinder in a Stream.” A.R.C.R. and M. 1632, 1933.Google Scholar
6. Prandtl, L.. See reference 1, p. 78, equation (4).Google Scholar
7. Prandtl, L.. See reference 1, p. 78.Google Scholar
8. Prandtl, L.. See reference 1, p. 78, and in particular p. 82.Google Scholar
9. Prandtl, L.. See reference 1, pp. 80–81.Google Scholar
10. It can easily be confirmed that the calculated expressions are valid over a region extending farther inside the boundary layer than is the case for (2.5). From the point of view of accuracy of the approximation obtained (2.5) is equivalent to a three-fold differentiation with respect to y, on the basis of the “ Bindungen.”Google Scholar
11. Hiemenz, K.. See reference 4.Google Scholar
12. Given by Hiemenz (see reference 4) with a pressure error.Google Scholar
13. As first generally recognised by Howarth. See reference 5, p. 7 onwards.Google Scholar
14. Howarth, L.. Loc. cit., pp. 51–52.Google Scholar
15. According to C. Runge (Graphical Methods, Leipzig and Berlin 1915, p. 112) graphical differentiation by repeatedly halving the chord will give more reliable results after a certain amount of practice than is generally assumed. Moreover this method has already been given by Lambert, see “ Applications of Mathematics II, ” Berlin 1770.Google Scholar
16. As in all methods of step-by-step procedure the errors made at each step can naturally add up.Google Scholar