Global sensitivity analysis for DSMC simulations of hypersonic shocks

Abstract

Two global, Monte Carlo based sensitivity analyses were performed to determine which reaction rates most affect the results of Direct Simulation Monte Carlo (DSMC) simulations for a hypersonic shock in five-species air. The DSMC code was written and optimized with shock tube simulations in mind, and includes modifications to allow for the efficient simulation of a 1D hypersonic shock. The TCE model is used to convert Arrhenius-form reaction rate constants into reaction cross-sections, after modification to allow accurate modeling of reactions with arbitrarily large rates relative to the VHS collision rate. The square of the Pearson correlation coefficient was used as the measure for sensitivity in the first of the analyses, and the mutual information was used as the measure in the second. The quantity of interest (QoI) for these analyses was the NO density profile across a 1D shock at ∼8000m/s (M∞≈23). This vector QoI was broken into a set of scalar QoIs, each representing the density of NO at a specific point downstream of the shock, and sensitivities were calculated for each scalar QoI based on both measures of sensitivity. Profiles of sensitivity vs. location downstream of the shock were then integrated to determine an overall sensitivity for each reaction. A weighting function was used in the integration in order to emphasize sensitivities in the region of greatest thermal and chemical non-equilibrium. Both sensitivity analysis methods agree on the six reactions which most strongly affect the density of NO. These six reactions are the N2 dissociation reaction N2+N⇄3N, the O2 dissociation reaction O2+O⇄3O, the NO dissociation reactions NO+N⇄2N+O and NO+O⇄N+2O, and the exchange reactions N2+O⇄NO+N and NO+O⇄O2+N. This analysis lays the groundwork for the application of Bayesian statistical methods for the calibration of parameters relevant to modeling a hypersonic shock layer with the DSMC method.