Non-monotonic dependence of the bow shock stand-off distance on the velocity of a CO2 flow about a sphere

A non-monotonic dependence of the bow shock stand-off distance around a spherical body recently observed in ballistic range experiments in CO2 is explained by a qualitative theoretical analysis and confirmed numerically. The analysis is based on the estimation of the average density in the shock layer with the Rankine–Hugoniot relations on the normal shock for chemically frozen and chemically equilibrium limits using a simplified chemistry model. The analysis reveals that a maximum of the density ratio across the shock and, therefore, a minimum of the stand-off distance as functions of the flight velocity are normally observed in CO2 and other gases, such as additionally considered N2, both in frozen and equilibrium flows. The low dissociation energy of CO2 results in relatively low flight velocities (around 5 km/s) at which the extrema are observed. It makes the effect more readily detectable in experiments in CO2 than in the Earth's atmosphere gases. The results of numerical simulations of the CO2 flow by solving the Navier–Stokes equations agree well with the ballistic range experiments and fully support the results of the theoretical analysis.