Sensitivity Analysis for DSMC Simulations of High-Temperature Air Chemistry

Abstract

This research centers on laying the groundwork for the application of Bayesian statistical methods for the calibration of parameters relevant to modeling a hypersonic shock layer with the Direct Simulation Monte Carlo (DSMC) method. The DSMC method used in this work employs the algorithm of Bird (1994), with modifications to allow integration with sensitivity analysis and Markov Chain Monte Carlo (MCMC) driver codes. The DSMC code was written and optimized with shock tube simulations in mind. Sensitivity analyses have been performed to determine which parameters most affect the simulation results for a 0-D relaxation which is similar in many respects to the relaxation behind a steady 1-D hypersonic shock. Analyses were performed for a pure nitrogen case and for a 5-species air case. The parameters which are most sensitive have been identified for future calibration with MCMC. The current work focuses on sensitivity analysis and on laying the groundwork for future parameter calibration. The DSMC method includes many parameters related to gas dynamics at the molecular level. Examples include elastic collision cross-sections, vibrational and rotational excitation probabilities, reaction cross- sections, etc. In many cases, the precise values of these parameters are not known. Parameter values often cannot be directly measured. Instead they must be inferred from experimental results, and by necessity parameters must often be used in regimes far from where their values were determined. More precise values for some of these important parameters could lead to better simulation of the physics, and thus to better predictive capability for DSMC. In the future Bayesian methods could also be employed to evaluate the plausibility of various models within the context of DSMC simulations. For example, comparisons could be made between the total collision energy (TCE) model for reaction cross-sections which was described by Bird (1994) and used by Ozawa (2008), and the vibrationally favored dissociation model, also described by Bird (1994). Future model development could also be guided by information gleaned from application of Bayesian statistical analysis to existing models. Our current work, however, focuses on using Bayesian methods to provide improved calibrations for models which are already in common use. Obtaining these calibrated parameters is the long-term goal of our work. In approaching that goal, the first step is a sensitivity analysis to determine which parameters most affect the simulation results in a case which is similar to a hypersonic shock. In this work, we have performed a rigorous sensitivity analysis in order to select appropriate parameters for calibration. This will set the stage for eventual calibrations with experimental data from the NASA EAST shock tube (see Grinstead et al., 2008) in future work.