Momentum Thickness Measurements for Thick Axisymmetric Turbulent Boundary Layers

Abstract

Experimental measurements of the mean wall shear stress and boundary layer momentum thickness on long, thin cylindrical bodies are presented. To date, the spatial growth of the boundary layer and the related boundary layer parameters have not been measured for cases where δ/a (a=cylinder radius) is much greater than one. Moderate Reynolds numbers 104<Reθ<105 encountered in hydrodynamic applications are considered. Tow tests of cylinders with diameters of 0.61, 0.89, and 2.5 mm and lengths ranging from approximately 30 meters to 150 meters were performed. The total drag (axial force) was measured at tow speeds up to 17.4 m/sec. These data were used to determine the tangential drag coefficients on each test specimen, which were found to be two to three times greater than the values for the corresponding hypothetical flat-plate cases. Using the drag measurements, the turbulent boundary layer momentum thickness at the downstream end of the cylindrical bodies is determined, using a control volume analysis. The results show that for the smallest diameter cylinders, there is no indication of relaminarization, and a fully developed turbulent boundary layer exists. A scaling law for the momentum thickness versus length Reynolds number is determined from the data. The results indicate that the spatial growth of the boundary layers over the entire length is less than for a comparable flat-plate case.