Jump conditions across normal shock waves in pure vapour–droplet flows

Abstract

Closed-form analytical jump conditions across normal shock waves in pure vapour–droplet flows have been derived for different boundary conditions. They are equally applicable to partly and fully dispersed shock waves. Collectively they may be called the generalized Rankine–Hugoniot relations for wet vapour. A phase diagram is constructed which specifies the type of shock structure obtained in vapour–droplet flow given some overall parameters. It is shown that in addition to the partly and fully dispersed shock waves that are possible in any relaxing medium, there also exists a class of shock waves in wet vapour in which the two-phase relaxing medium reverts to a single-phase non-relaxing one. An analytical expression for the limiting upstream wetness fraction below which complete evaporation will take place inside a shock of specified strength has been deduced. A new theory has been formulated which shows that, depending on the upstream wetness fraction, a continuous transition exists for the shock velocity between its frozen and fully equilibrium values. The mechanisms of entropy production inside a shock are also discussed.