Cross-stream pressure gradients can be important in the trailing edge region of an airfoil. This thesis presents the development of two interactive airfoil calculation procedures, applicable to fully-attached incompressible flow, which include cross-stream pressure gradients and other higher-order terms in both the turbulent viscous equations and the viscid-inviscid matching conditions. The first procedure utilizes the second-order boundary layer equations and a second-order approximation to the displacement effect matching condition. The second procedure employs a partially-parabolized form of the Navier-Stokes equations together with an exact matching condition. The viscous equations are solved with an implicit finite-difference procedure along with an algebraic turbulence model. Solution of the Navier-Stokes equations is accomplished using an iterative marching technique which accounts for the upstream influence of the pressure field only. Thus the equations are partially-parabolized by the solution procedure, rather than by neglecting terms.

Predictions are compared with experimental data and with results obtained using the standard first-order interacting boundary layer formulation for a symmetric section and an aft-loaded section. An important feature of these comparisons is that the computational grid, numerical algorithm, and turbulence models are identical for all of the cases compared. Consequently, the effects of the higher-order terms can be studied separately from the influence of these factors.

The results show that the higher-order terms do not significantly affect airfoil lift and moment predictions in fully-attached, incompressible flow. However, the higher-order calculations lead to an increase in the predicted profile drag, particularly at high values of lift coefficient. The interactive procedure involving second-order approximations to the viscous equations and matching conditions provides accuracy comparable to that of the partially-parabolized Navier-Stokes formulation with a level of computational effort which is comparable to that of the standard first-order procedure.