Analytical Models for Shocks in Compressible Flow

The tools for computational flow analysis have become relatively mature tools using powerful computers and reliable software based on the equations of fluid motion. The tasks of shape design may be solved using optimization strategies requiring suitably parameterized boundary conditions, converging toward improved results after a more or less lengthy iterative procedure, depending on available computer power. In this situation analytical models frequently are not seen useful anymore for the acceleration of design processes in aerospace technology. We therefore question the usefulness of the classical knowledge base using mathematical modeling for compressible flow. This contribution is pleading for a modern view on flow models, with a timely extension by computer aided animation of complex flow patterns. The understanding of local shock dynamics via analytical model functions has clarified some seemingly contradictory requirements in the past, but nowadays computerized mapping techniques and suitable fast visualization will do this job even with a strong educational effect. Some examples for the local and global structure of transonic shock waves, as well as using new models of supersonic shock waves for configuration design will be illustrated. Such models give valuable hints for a suitable configuration parameterization incuding target pressure distributions for inverse design without an excessive number of optimization runs