A Three-Dimensional Integral Method for Calculating Incompressible Turbulent Skin Friction

A new integral method is proposed for the analysis of three-dimensional incompressible turbulent boundary layers. The method utilizes velocity profile expressions in wall-law form to derive two coupled partial differential equations for the two components of surface skin friction. No shape factors or empirical shear stress correlations are needed in the method. The only requirements are a knowledge of the external velocity and streamline distribution and initial values of skin friction along a starting crossflow line of the flow. The method is insensitive to sidewall conditions and may be continued downstream until the complete three-dimensional separation line of the flow has been computed. Two comparisons with experiment are shown: a curved-duct unseparated flow and a T-shaped-box separated flow. The calculations are very straightforward and agree reasonably well with the data for friction, crossflow angle, and separation line.