An Analytical Solution of the Thick Axisymmetric Turbulent Boundary Layer on a Long Cylinder of Constant Radius.
IOWA INST OF HYDRAULIC RESEARCH IOWA CITY
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Two similarity laws for a thick, axisymmetric, turbulent boundary layer on a long circular cylinder have been established. The validity of the assumption of constant-stress moment in the law-of-the-wall region is analyzed under the assumption of similarity. A new logarithmic mixing length, which takes into consideration the effect of transverse curvature on turbulence, is proposed for the law-of-the-wall region. With this logarithmic mixing-length models, the mean-flow momentum equation yields a law-of-the-wall relation in terms of the exponential integral in the logarithmic portion of the inner layer. Comparisons with available data and other proposed relations reveal that this logarithmic law gives a definite improvement. Also a mathematical explanation is given as to why the cylinder data do not deviate appreciably from the classical two-dimensional law-of-the-wall, even though it is observed that the turbulent characteristics, such as the size of large eddies and the turbulent intensities are much smaller than for a flat plate.
- Fluid Mechanics