Shock Polars for Dissociating Gases

The hodograph or polar diagram for oblique shock waves is generalized to the case of dissociating diatomic gases, assuming either a chemically frozen flow or complete thermochemical equilibrium behind the shock. A dissociated ambient gas condition is treated also. Several examples of the shock-polar diagram with dissociation are constructed for hypersonic shock Mach numbers. It is shown that in the presence of equilibrium dissociation the detachment point can occur at a slightly supersonic post-shock velocity, in contrast to the subsonic condition prevailing in perfect gas flow. It is shown also that large degrees (>25%) of ambient dissociation yield post-shock dissociation levels that are considerably less than the preshock value over a significant portion of the shock polar. Nomenclature a = speed of sound HD = dissociation energy h = specific enthalpy M = Mach number p = static pressure RM = molecular gas constant T = temperature U = streamwise velocity component V = normal velocity component a, = atom mass fraction /3 = enthalpy coefficient Y = specific heat ratio 7 = effective specific heat ratio [Eq. (19)] 7 = frozen specific heat ratio 6 = flow angle fj, = Mach angle p = density cr = shock angle Subscripts