The flow remains isentropic before the occurrence of Mach Disk and Barrel shocks, as the entropy increases across these flow features.  The entropy rise in the convergent nozzle would be negligible when compared with that across the shocks.  Hence in the region bounded by the barrel shocks and Mach Disk the isentropic flow assumptions may be justified.

I would check the pressure along the converging nozzle and see if it is close to what is expected from the isentropic flow model.

The previous answers are very correct. If you can trascurate the diffusive terms, i.e. the system can be described by the Euler equations, you can say that the supersonic expansion is isentropic. However in eqs. 1-6, there is another approximation: the isentropic coefficient is a constant. For Argon, if the reservoir temperature is not too high, the assumption can be considered valid. For a molecular gas this is not true. In the reservoir due to the high pressure the plasma is in equilibrium and while in the expansion region the system is far from equilibrium, and therefore the determination of gamma is not straightforward.  Moreover the definition of gamma should contain also the compressibility coefficient. Look the references below.

Electronic excitation and isentropic coefficients of high temperature planetary atmosphere plasmas

G Colonna, A D’Angola, M Capitelli

Physics of Plasmas (1994-present) 19 (7), 072115, 2012

Numerical methods to solve Euler equations in one-dimensional steady nozzle flow

G Colonna, M Tuttafesta, D Giordano

Computer physics communications 138 (3), 213-221, 2001

a very simple technique, take a pitot tube and check the total pressure variation. No matter what kind of flow it is supersonic or subsonic.