Elements of Gasdynamics

This chapter deals with inviscid compressible flows of a perfect gas. It starts with an analysis of small perturbations propagating through a gas at rest using piston theory and then turns to integrals of motion, including compressible versions of the Bernoulli equation, entropy conservation law, and Kelvin’s Circulation Theorem. Crocco’s formula, which allows determination of whether a flow is potential in the presence of shock waves, is derived. The theory of characteristics is formulated for two-dimensional potential flows and applied to Prandtl–Meyer flow over a body surface bend and flow past a corner. The formation of shock waves, normal or oblique, is discussed. The shock conditions are deduced and the shock polar, which describes the behaviour of oblique shocks, is introduced. These results are applied to flows past a wedge and a circular cone. Finally, unsteady compressible flows are analysed, in particular shock tubes and blast waves are considered.