Studies of Von Karman's Similarity Theory and Its Extension to Compressible Flows. Investigation of Turbulent Boundary Layer Over a Flat Plate in Compressible Flow by the Similarity Theory.

摘要

Investigation of the turbulent-boundary-layer flow over a flat plate in compressible flow is carried out on the basis of the scheme established in NACA TN 2542. By averaging the Navier-Stokes equations, differential equations for the mean flow are obtained. A temperature-velocity relation follows without a specified form of the length scale. To derive the velocity distribution in the boundary layer, a choice of the length scale has to be made. The temperature- velocity relation reduces to Reynolds' analogy and the velocity distribution goes back to Von Karman's logarithmic law for the special case of incompressible flow. There are essentially three universal constants, arising out of the correlations in the energy equation, to be determined by comparing with suitable experiments of the temperature-velocity relation at any known Mach number and heat transfer at wall. The behavior at other Mach numbers and heat-transfer conditions may then be readily predicted. Because of the lack of accurate experimental data, attempts to carry out such determinations are not included in the present report.