Viscous-Inviscid Interaction

• Quasi-Simultaneous Method

Veldman recognized the importance of solving simultaneously the viscous and inviscid flow equations. The coupling is advanced station-by-station between a linearized form of the inviscid flow and the boundary layer equations. There are two alternatives, depending on whether the boundary layer equations are solved directly or inversely. For example, the direct solution of the boundary layer equations would lead to a correction formula as

Veldman used a local linearization of the viscous effects on the external inviscid flow from the thin airfoil theory

where is the velocity distribution at the outer edge of the boundary layer in absence of viscous effects, and denote the limits of influence of the viscous correction on the inviscid flow, and is the blowing velocity at the wall.

Eq.15 is formally the interaction law. In fact, it is solved simultaneously with the boundary layer equations, since both and are unknown. Then the method consists in iterating Eq. 15 with the boundary layer equations at the current step, until convergence is achieved. Then the process is advanced.