Model Uncertainties in a Sharp Leading-Edge Hypersonic Boundary Layer

The effects of uncertainties in the gas-surface interaction and intermolecular interaction models on the hypersonic boundary layer development are investigated using the non-intrusive generalized polynomial chaos method. In particular, uncertainties in the surface shear stress, normal stress, heat flux, flowfield temperature and density resulting from uncertain viscosity exponent, surface temperature and accommodation coefficient are considered. The polynomial chaos expansion approach is used to reconstruct the probability density function, calculate mean, standard deviation and skewness of the dependent variables from the DSMC calculations. The uncertainty analysis shows that surface fluxes and flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient than surface temperature or viscosity exponent uncertainty. Nomenclature a n = gPC coefficient f z = PDF of the independent variable f y = PDF of the dependent variable I = order of the Gaussian expansion N = order of the gPC expansion N s = number of samples T w = wall temperature w i = Gaussian weight x = spatial coordinate in the downstream direction y = independent variable studied Y = DSMC output z = independent random variable in the [-1,1] interval Z = independent random variable with an arbitrary interval α τ = momentum accommodation coefficient γ = skewness of the dependent variable λ = Mean Free Path (MFP) σ = standard deviation of the dependent variable ψ n = orthogonal polynomial of order n ω = viscosity exponent in VHS model 1 Graduate Student, AIAA Student Member.