By G. E. A. Meier (auth.), G. E. A. Meier, K. R. Sreenivasan, H.-J. Heinemann (eds.)
Prandtl’s well-known lecture with the name “Über Flüssigkeitsbewegung bei sehr kleiner Reibung” was once offered on August 12, 1904 on the 3rd Internationalen Mathematischen Kongress in Heidelberg, Germany. This lecture invented the word “Boundary Layer” (Grenzschicht). The paper was once written in the course of Prandtl’s first educational place on the collage of Hanover. The reception of the tutorial global to this striking paper was once at the beginning lukewarm. yet Felix Klein, the well-known mathematician in Göttingen, instantly discovered the significance of Prandtl’s notion and provided him an instructional place in Göttingen. There Prandtl turned the founding father of smooth aerodynamics. He used to be a professor of utilized mechanics on the Göttingen collage from 1904 till his loss of life on August 15, 1953. In 1925 he turned Director of the Kaiser Wilhelm Institute for Fluid Mechanics. He constructed many additional rules in aerodynamics, similar to move separation, base drag and airfoil concept, specially the legislation of the wall for turbulent boundary layers and the instability of boundary layers en path to turbulence. in the course of the fifty years that Prandtl was once within the Göttingen examine middle, he made very important contributions to fuel dynamics, particularly supersonic circulation thought. All experimental recommendations and dimension thoughts of fluid mechanics attracted his robust curiosity. Very early he contributed a lot to the improvement of wind tunnels and different aerodynamic amenities. He invented the soap-film analogy for the torsion of noncircular fabric sections; even within the fields of meteorology, aeroelasticity, tribology and plasticity his simple principles are nonetheless in use.
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Extra resources for IUTAM Symposium on One Hundred Years of Boundary Layer Research: Proceedings of the IUTAM Symposium held at DLR-Göttingen, Germany, August 12-14, 2004
Example text
All grid generators are attuned to wall units and to the grid-stretching ratios acceptable in the logarithmic layer. These accuracy requirements derive from the physics of the wall layer and are easy to implement before any solution is obtained, the friction velocity needed to express wall units being fairly predictable. The true difficulty is to predict the boundary-layer thickness, in order to switch from a “viscous grid” inside the boundary-layer to an “Euler grid” outside it with both good accuracy and economy.
The concept itself is not under attack here. Similarly, challenges to the log law itself and proposals to replace it with a power law are, in the author’s opinion, without merit [5, 6]. They are incompatible with the Galilean invariance that is implied in much of the thinking in turbulence, and is built into all transport-equation turbulence models. Mixing-length theory and log law are equivalent only when the turbulent shear stress is independent of the position. Experiments and simulations suggest that when it is not the case, because of a pressure gradient, the log law is closer to being preserved.
The logarithmic scaling obtained by Oberlack (2001) using first principles by employing Lie group methods only once again confirmed the validity of the law though in slightly extended form u ¯+ 1 = 1 ln(x2 + + A+ ) + C + . κ (2) This scaling law was nicely confirmed by Lindgren et al. (2004) using the experimental data of the KTH data-base for turbulent boundary layers for a wide range of Reynolds numbers. They found that with the extra constant A+ , numerically fixed to A+ ≈ 5, the modified law describes the experimental data + down to x+ 2 ≈ 100 instead of x2 ≈ 200 for the classical logarithmic law.