Chapter 3.4 - Theory of Shock Waves: 3.4 Rarefaction Shocks

Abstract

This chapter focuses mainly on the conditions under which rarefaction shocks may form in single-phase fluids and on the local properties of discontinuities. One of the main issues in the theory of gasdynamic shocks is the question of the type of shocks, that is, compression or rarefaction shocks, which can be sustained by a given fluid. The second law of thermodynamics provides a powerful tool to eliminate shocks that are physically impossible. This chapter concentrates on shock formation in the dense gas regime of Bethe-Zel'dovich-Thompson (BZT) fluids. The properties of BZT fluids and the role of the second law in ruling out impossible shocks are treated in discussed. Further, restrictions resulting from the stability condition that requires that the wave speeds immediately upstream/downstream of the shock front must not be larger/smaller than the shock speed is considered. The main emphasis is on rarefaction shocks, the properties of compression shocks is also addressed, the reason being twofold. First, it is found that embedded regions of negative that are a necessary ingredient for the existence of rarefaction shocks strongly affect the behavior of compression shocks. Second, when dealing with general initial and/or boundary value problems, rarefaction and compression shocks may be generated simultaneously and even interact.