Boundary layer method for unsteady transonic flow

A numerical method for determination of unsteady loads in a 2-D transonic flow, with the occurrence of a shock wave, on a pitching airfoil is demonstrated. The method implements the Euler equations for inviscid region and integral boundary layer equations for the viscous region near the airfoil. The viscous-inviscid interaction method is employed using the transpiration velocity concept on the airfoil contour. The Euler solution is calculated by using the Van Leer flux-vector splitting method on the body-fitted C-grid. The boundary layer model is calculated applying Drela’s model of integral boundary layer equations for the laminar and turbulent flow. The transition from the laminar to the turbulent flow is predicted by the en method. The viscous-inviscid interaction method is made in the direct mode. The results obtained by this method are comparable with the calculated RANS and experimental results, while time and computational costs were lower than for RANS calculations. Generally, the pressure coefficient distribution results showed good agreement with the RANS and experimental results. The method predicted the position of a shock wave to be slightly shifted towards the leading edge of the airfoil with respect to the position obtained by the RANS and experimental results. This indicates that the boundary layer model has a strong influence on the inviscid part of the flow.