Flowfield Uncertainty Analysis for Hypersonic CFD Simulations

Uncertainty quantification (UQ) in the hypersonic flow regime offers valuable information to determine physical models in need of improvement and to assist in design of vehicles and flight experiments. Here we present results of UQ analysis based on polynomial chaos method to determine flowfield and surface heat flux uncertainty under typical blunt-body re-entry conditions. The NASA Langley code, LAURA, was used for axisymmetric CFD calculations of chemically reacting hypersonic flow over FIRE-II configuration. A third order polynomial chaos (PC) method using the Gauss-Hermite quadrature was applied for determining probability density functions and moments of output quantities. Input parameters such as freestream density, velocity, and temperature were varied and the propagation of their corresponding uncertainties on output properties of interest through the flowfield were studied. An order of magnitude increase in surface heat flux uncertainties was observed for an input freestream velocity uncertainty of ±100 ft/s, or 0.29%. This parameter thus has the greatest sensitivity to variations, and conversely the freestream temperature has the least sensitivity. Nomenclature H n Hermite polynomial of order n j number of collocation points per dimension k order of PC expansion n order of accuracy for PC and Hermite polynomials N number of samples P total number of points in PC expansion ˙ q heat flux (kW/m 2) T translational temperature (K) V velocity (m/s) w weight corresponding to abscissa x input parameter value Y output value from solver ¯ Y mean output value uncertainty ξ Gaussian random variable μ mean ρ density (kg/m 3) σ standard deviation Ψ random basis function Subscript i collocation point index