Analytical prediction of the incompressible turbulent boundary layer with arbitrary pressure distribution (Incompressible two dimensional turbulent boundary layer equations with arbitrary pressure distribution solved by weighted residual method)

Abstract

The boundary-layer equations for incompressible two-dimensional turbulent flows with arbitrary pressure distributions are solved by the method of weighted residuals. The method is capable of predicting skin friction, boundary-layer integral parameters, and velocity profiles. The analytical technique contains a theoretical convergence criterion and enables computations to be made to any desired accuracy subject to the accuracy of the selected turbulence model. To obtain solutions a mixing length model for the turbulent shear description is used in conjunction with initial profile data modified by orthogonal functions. Analytical results are compared with three experimental cases: the Schubauer and Klebanoff flow over an airfoil-like body which includes favorable and adverse pressure gradients and leads to separation, the equilibrium flow with an adverse pressure gradient of Bradshaw, and the favorable pressure gradient equilibrium flow of Herring and Norbury. In all three cases agreement is satisfactory. The method is sufficiently rapid to permit its use as a subprogram in analyses of broader extent.