Numerical computations of transonic critical aerodynamic behavior

Abstract

The determination of aerodynamic coefficients by shell designers is a critical step in the development of any new projectile design. Of particular interest is the determination of the aerodynamic coefficients at transonic speeds. It is in this speed regime that the critical aerodynamic behavior occurs and a rapid change in the aerodynamic coefficients is observed. Three-dimensional, transonic, flowfield computations over projectiles have been made using an implicit, approximately factored, partially flux-split algorithm. A composite grid scheme has been used to provide the increased grid resolution needed for accurate numerical simulation of three-dimensional transonic flows. Details of the asymmetrically located shock waves on the projectiles have been determined. Computed surface pressures have been compared with experimental data and are found to be in good agreement. The pitching moment coefficient, determined from the computed flowfields, shows the critical aerodynamic behavior observed in free flights. I. Introduction T HE flight of projectiles covers a wide range of speeds. The accurate prediction of projectile aerodynamics at these speeds is of significant importance in the early design stage of a projectile. The critical aerodynamic behavior occurs in the transonic speed regime, 0.9<M< 1.1 where the aerodynamic coefficients have been found to change by as much as 100%. Of particular interest is the determination of the pitching-moment coefficient since it is used to determine the static stability of the projectile. The critical behavior in this case is usually characterized by a rapid increase in the coefficient followed by a sharp drop. This rapid change in the pitchingmoment coefficient can be attributed in part to the complex