Unified Direct-Inverse Procedure for Two-Dimensional Boundary Layers Using Spline/Finite Difference Discretization

摘要

A unified approach is presented for solving the two dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient, or displacement thickness distributions. Turbulent flow is treated using a two piece algebraic eddy viscosity model, with the modified Levy Lees transformation applied to capture the growth of laminar and turbulent layers. Fourth order spline discretization approximates normal derivatives with three and two point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton Raphson iteration together with partial pivoting. Numerical solutions are presented for several nonsimilar flows and compared with published results. (Theses)