ON A FINITE-DIFFERENCE SOLUTION FOR CONSTANT-PPRPERTY TURBULENT BOUNDARY LAYER

A finite-difference method has been developed for the solutions to the governing partial differential equations for the constant-property turbulent boundary layer. Prandtlμs mixinglength concept was used to express the apparent turbulent shearing stress according to a hypothesized mixing-length distribution through the boundary layer. The model for the mixing-length distribution is in general agreement with experimental data for a variety of flow conditions. The method, an always stable explicit finite-difference formulation that requires no iterative procedures, is numerically more direct than other methods recently proposed and is unique in its evaluation of the apparent shearing stress by using an assumed mixing-length distribution as the only empirical input. The predicted skin-friction coefficients and velocity profiles agree well with experimental data for the several comparisons made, which included flows in both favorable and adverse pressure gradients as well as flat plate cases with and without blowing. The numerical method presented is not restricted to use with the particular mixing-length model tentatively proposed in this work, but can be used to compare various models and help establish their properties and range of applicability, thereby serving to further understanding of the most fundamental aspects of turbulent flow. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.