Computer simulation of transonic flow past airfoils with boundary layer correction

A computer program has been developed to solve the compressible flow equation for the velocity potential. The exterior of the airfoil is mapped onto the unit circle and the flow is computed on a grid in the circle plane. A relaxation method using backward differencing in the flow direction at supersonic points permits solutions for large supersonic areas. The pressure distribution resulting from the flow becomes the input to the von Karman momentum equation which when integrated gives the displacement thickness. This displacement thickness is smoothed and added to the airfoil to account for the turbulent boundary layer. The boundary layer correction is computed iteratively with the flow. Results from this program and test data agree well.