Transonic Flow Calculations

In these lectures I shall attempt to survey some of the principal recent developments in computational aerodynamics. Prior to 1960 computational methods were hardly used in aerodynamic analysis, although they were already widely used for structural analysis. The NACA 6 series of airfoils had been developed during the forties, using hand computation to perform the Theodorsen method for conformal mapping [1]. The primary tool for the development of aerodynamic configurations was the wind tunnel. Shapes were tested and modifications selected in the light of pressure and force measurements together with flow visualization techniques. In much the same way that Michelangelo, della Porta and Fontana could design the dome of St. Peters through a good physical understanding of stress paths, so could experienced aerodynamicists arrive at efficient shapes through testing guided by good physical insight. Notable examples of the power of this method include the achievement of the Wright brothers in leaving the ground (after first building a wind tunnel), and more recently Whitcomb’s discovery of the area rule for transonic flow, followed by his development of aftloaded supercritical airfoils and winglets [2, 3, 4]. The process was expensive. More than 20000 hours of wind tunnel testing were expended in the development of some modern designs, such as the F 111 or Boeing 747. By 1960 it began to be recognized that computers had become powerful enough to make it worth while to attempt calculations of aerodynamic properties of at least isolated components of an airplane. Efficient flight can