Transonic Viscous-Inviscid Interaction over Airfoils for Separated Laminar or Turbulent Flows

A new technique is presented for the calculation of the interaction of the inviscid external flow and the separated boundary layer in the case of the transonic flow over airfoils. A finite-difference method is used for the boundary-layer solution. On the forward portion of the airfoil the boundary-layer equations are solved for a given pressure distribution boundary condition, while on the rear portion of the airfoil and beyond, where separated flow occurs, the equations are solved for a given displacement thickness distribution boundary condition. The inviscid transonic flow solution and the boundary-layer solution are matched by a local point relaxation algorithm, incorporating the two methods of boundary-layer equations solution. Results are obtained for separated laminar, transitional, and turbulent flows on circular-arc airfoils at zero angle of attack. These results are in good agreement with available experimental data. The effects of Reynolds and Mach numbers are also examined. Nomenclature Cf = skin friction coefficient = r^/O.Sp ^ U2* Cp = pressure coefficient = (p-p00)/Q.5p00U2^ cp = specific heat constant at constant pressure D = doublet strengt