Effect of non-equilibrium thermochemistry on Pitot pressure measurements in shock tunnels (or: Is 0.92 really the magic number?)

Pitot pressure is the most common measurement in high total enthalpy shock tunnels for test condition verification. Nozzle calculations using multi-temperature non-equilibrium thermochemistry are needed in conjunction with Pitot measurements to quantify freestream properties. Pitot pressure is typically matched by tuning the boundary layer transition location in these simulations. However, non-equilibrium thermochemistry effects on the Pitot probe are commonly ignored. A computational study was undertaken to estimate the effect of non-equilibrium thermochemistry on Pitot pressure and freestream conditions. The test flow was produced by a Mach 7 nozzle in a reflected shock tunnel for air at a relatively low total enthalpy of 2.67 MJ/kg. Three different thermochemical models (equilibrium, finite-rate chemistry and two-temperature thermochemistry) were employed to compute flow variables at the nozzle exit and Pitot probe. Pitot pressures from these simulations were compared against those obtained via experiments. The results show a departure from the commonly utilized C of 0.92 in the reduced Rayleigh-Pitot equation form for high Mach numbers. Additionally, calculations were done with a sweep of free-stream conditions and resulting in values for one- and two-temperature models to use in future shock tunnel studies. Overall, our results show that the influence of finite-rate thermochemistry should be taken into account, even at relatively low flow enthalpies.