Modeling Uncertainties in Direct Simulation Monte Carlo Calculations of Hypersonic Leading-Edge Flow

摘要

The effects of uncertainties in the gas-surface and intermolecular interaction models on a hypersonic boundary-layer development are investigated by propagating these uncertainties through direct simulation Monte Carlo calculations of Mach 10 and 20 flows. The model input uncertainties considered are the momentum accommodation coefficient in the Maxwellian gas-surface interaction model, surface temperature and the viscosity exponent in the variable hard sphere molecular model. The effects of the input uncertainties are quantified by computing produced uncertainties in the flowfield temperature, flovefield density, surface shear, pressure, and heat flux. A nonintrusive generalized polynomial chaos expansion is used to propagate the uncertainties; reconstruct the probability density functions; and calculate the mean, standard deviation, and skew ness of the output variables. It is shown that the polynomial chaos expansion with just three flowfield samples can propagate uncertainties with an accuracy equivalent to Monte Carlo methods with 10 million samples. The uncertainty analysis shows that the surface fluxes and the flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient uncertainty than surface temperature or 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 a 31% uncertainty at Mach 20. This input uncertainty results in 22 and 28% uncertainties in the surface fluxes at the two Mach numbers. The produced uncertainties generally increase with Mach number, and the effect of introduced uncertainty diminishes away from the leading edge.