Numerical prediction of turbulent boundary layer development on a two-dimensional curved wall

A finite difference method for calculating the flow and boundary layer development on a two-dimensional convex wall, i.e., a curved surface such as an airfoil, is presented. Governing partial differential equations are defined for a coordinate system with no lateral transfer of mass, and a solution is sought in terms of the momentum. Modification of the technique to account for turbulent flows by modelling the effective viscosity as a combination of the laminar and turbulent components is demonstrated. A tridiagonal matrix algorithm is employed to solve the implicit forms of the finite difference equations. The model predictions for the flow over a curved body are compared with wind tunnel data for a curved wood surface instrumented with pitot tubes. It is found that the procedure is valid in cases of adverse pressure gradients.