A finite-difference solution for unsteady wave interactions with an application to the expansion tube

An analytical study of the unsteady wave interaction of a shock wave overtaking a previously initiated shock tube flow has been conducted for a real gas by solving a finite-difference representation of the one-dimensional Navier-Stokes equations. This analysis has been used to determine the effect on the available test time of opening the secondary diaphragm in the expansion-tube operating cycle prior to the arrival of the incident shock wave. Special emphasis is placed on determining expansion-tube test-time limitations resulting from a nonuniform entropy distribution occurring during the early test-gas flow due to the varying Mach number of the incident shock wave as it traverses the expansion fan caused by the preopening process. Time distributions of velocity, temperature, pressure, and entropy at various distances from the diaphragm are presented as a function of the time required to open the diaphragm.