The Saha equation and the adiabatic exponent in shock wave calculations

Abstract

The purpose of this note is to comment on the calculation of equilibrium gas dynamic parameters behind strong shock waves. The writer has been aroused by the appearance of a paper by Guman (1956) presenting a generalized computing scheme for ionizing shock waves in monatomic gases. In that paper the reader is not cautioned about including excited states in the Saha equation for the computation of the degree of ionization behind shock fronts at appropriate temperatures and densities. The same paper treats the adiabatic exponent γ = c_p/c_v as constant across strong shocks when at the same time it is implied that the computing scheme is of general validity. Hence, the unwary reader might attempt to apply the scheme in a regime where γ is not only no longer constant but is no longer a useful quantity for characterizing the shock conditions. Other authors (see, for example, Glass, Martin & Patterson (1953)) characterize flows in which a shock has excited internal degrees of freedom in terms of a variable specific heat ratio when in fact one cannot use this quantity in calculating shock front conditions.