Viscous-inviscid interaction schemes for external aerodynamics

For aerofoils a calculation, which involves the coupling of the external inviscid flow with the viscous flow in the boundary layer and the wake, still provides a worthwhile alternative to the solution of the ‘time-averaged’ Navier-Stokes equations. Classical viscous-inviscid interaction methods which can be extended to include flows with separations and significant pressure gradients across the boundary layer are described. Basic theoretical principles of interactive methods in two dimensions are discussed. The extension of the classical methods leads to generalisations of the concept of displacement thickness and the momentum integral equation. The boundary conditions for the equivalent inviscid flow (EIF) are also described and these also include the effect of normal pressure gradients. An integral method based on the lag-entrainment method for the calculation of the turbulent boundary layer is described. The correlations associated with the method are extended to include separated flow. Two methods of solving the boundary-layer equations through a separation region are described: the inverse method and the quasi-simultaneous method. Principles of techniques for coupling the flows are described and the properties of the direct, fully inverse, semi-inverse and quasi-simultaneous methods are discussed. Results from a method for incompressible flow about a stalled aerofoil, a method for compressible flow about a high-lift aerofoil and a method for compressible flow about a transonic aerofoil are compared with experimental results. The current situation regarding the development of viscous-inviscid interaction methods is briefly summarized and future possibilities are considered.