Approximate solution of second-order boundary- layer equations.

Abstract

The Dorodnitzyn method of approximate solution using integral equations is applied to Crocco forms (in which the first-order velocity ratio u replaces the normal distance as an independent variable) of the first- and second-order incompressible, two-dimensional boundarylayer equations. Polynomials in u are used to approximate the first-order shear stress divided by a proper function of u; the function of u insures the convergence of certain first- and second-order integrals. Second-order velocity ratios are also approximated by polynomials in u. The number of strips in the Dorodnitzyn method is equal to the number of undetermined coefficients. However, the number of strips for first- and second-order problems need not be the same. The resultant coupled differential equations are solved by an implicit numerical scheme. Application is made to the analysis of the second-order incompressible boundary-layer development on a two-dimensional Rankine half-body. Vorticity, curvature, and displacement effects are considered. The approximate numerical results compare favorably with those of more accurate numerical computations.