Exact operator solutions of general three-dimensional boundary-layerflow equations

Abstract

The general compressible, turbulent, three-dimensional boundary-layer flow equations are solved exactly using an efficient semi-analytical iteration scheme which develops when the equations are cast into an integral type fixed point form. Transformation of the governing equations into similarity type coordinates yields distinct groups of terms involving only the derivatives normal to the surface as well as balancing groups of terms containing all the surface derivatives. An exponential integrating factor is employed in formal integrations which cast the equations into the form X=F(X), with X being the highest order derivatives (velocity and enthalpy gradients) and F, the integral relations which decay exponentially with approach to the freestream. The stability and versatility of the solution technique are illustrated in a straightforward, practical engineering calculation of flow on the full scale Whitcomb supercritical wing in transonic flight.