Quantification of modeling uncertainties in hypersonic non-equilibrium flows

The effects of uncertainties in the gas-surface interaction model, intermolecular interaction model and high temperature reaction rates on the prediction of aerothermodynamic properties of hypersonic flows are studied. The uncertainties in the input parameters are propagated through the Direct Simulation Monte Carlo (DSMC) solutions using the non-intrusive generalized polynomial chaos (gPCE) method. It is shown that gPCE expansion with just three flowfield samples can reconstruct output mean, standard deviation, skewness and probability distribution function with an accuracy equivalent to the Monte Carlo (MC) random sampling methods with ten million samples. Flows generated by hypersonic leading edges and Small Particle Hypervelocity Impact Range (SPHIR) projectiles are considered in this study. In the hypersonic flow leading edge study, the considered input uncertainties are the accommodation coefficient, surface temperature and the viscosity exponent. The effect of the input uncertainties are quantified by computing produced uncertainties in the flowfield temperature, flowfield density, surface shear, pressure and heat flux. It is shown that surface fluxes and flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient than the surface temperature or the viscosity exponent uncertainty. An input uncertainty of 19 % in the accommodation coefficient results in a 20 % uncertainty in the flowfield temperature at Mach 10 and 31 % uncertainty at Mach 20. Uncertainties introduced near the leading edge have greater effect that those introduced further downstream. It is also shown that the effect of most input uncertainties increase with Mach number. Uncertainties in the N2 dissociation reaction rate, O 2 dissociation reaction rate and two NO exchange reaction rates are considered in a Mach 23 flow around a 2 mm SPHIR projectile. This study reveals that the shock front is most sensitive to input uncertainties. In the flowfield, away from the shock front, atomic nitrogen and nitric oxide are most sensitive to uncertainties in the four reaction rates