Sound speed isentropic flow

Initial shock-wave overpressure can be determined from a one-dimensional technique. It consists of using conservation equations for discontinuities through the shock and isentropic flow equations through the rarefaction waves, then matching pressure and flow velocity at the contact surface. This procedure is outlined in Liepmatm and Roshko (1967) for the case of a bursting membrane contained in a shock tube. From this analysis, the initial overpressure at the shock front can be calculated with Eq. (6.3.22). This pressure is not only coupled to the pressure in the sphere, but is also related to the speed of sound and the ratio of specific heats. 

Substituting the values of the density ratio in terms of the temperature for isentropic flow and of the velocity in terms of the Mach number and the speed of sound and then eliminating the temperature ratio, we find... 

Experimental investigations of transcritical expansion flows show a pronounced sound speed minimum close to the critical point. Phase changes develop significantly different on subcritical and supercritical isentropes, respectively, although the initial conditions are fairly close to each other. 

The maximum flow is obtained for the reversible adiabatic, that is, isentropic state change. However, for the calculation of this process, the speed of sound has to be evaluated at the conditions in the cross-flow area (index 1) of the valve. For this purpose, an iterative procedure is necessary. The necessary steps are as follows ... 

---