Discussion: “Laminar and Turbulent Incompressible Boundary Layers on Slender Bodies of Revolution in Axial Flow” (Cebeci, T., 1970, ASME J. Basic Eng., 92, pp. 545–550)
The boundary-layer equations for both laminar and turbulent incompressible flows over slender bodies of revolution in axial flow are solved by an implicit finite-difference method. The Reynolds shear-stress term is eliminated by means of an eddy-viscosity concept. Velocity profiles and values of local skin-friction coefficient are obtained for various slender circular cylinders in both laminar and turbulent flows. The deviation of the cylinder skin friction from that of a flat plate is studied. The calculated velocity profiles for turbulent flow are compared with those of both Richmond’s and Yasuhara’s experimental data and with Rao’s proposed formulation of the law of the wall in thick, axisymmetric turbulent boundary layers. In both cases excellent agreement is obtained.
Velocity distributions in incompressible boundary layers on the various rotating bodies in axial flow were investigated experimentally. The rotating bodies consisted of a cylinder with nose section of three forms. Tests were run with two Reynolds numbers and the ratio of peripheral velocity of the body to main-stream velocity was in the range 0–4. The centrifugal force of the rotation considerably affected the meridian velocity profiles. Momentum thicknesses calculated from a theory with assumption of the quasi-two-dimensional velocity profile agreed well with the experiments except in the case of high rotating speed. The local shearing stress in the rotating direction is discussed.
Blades of axial flow compressors are often roughened by corrosion or erosion. There is only scant information about the influence of this roughening on the boundary layers of the blades and thereby on the compressor efficiency. To obtain detailed information for calculating the efficiency drop due to the roughness, experimental investigations with an enlarged cascade have been executed. The results enabled to develop new formulas for a modified friction coefficient in the laminar region and for the laminar-turbulent transition and the separation points of the boundary layer. Thus, together with the Truckenbrodt theory, it was possible, to get a good reproduction of the experimental results.
A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.
Closure to “Discussions of ‘Laminar and Turbulent Incompressible Boundary Layers on Slender Bodies of Revolution in Axial Flow’” (1970, ASME J. Basic Eng., 92, pp. 550–552)