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## Statistical methods for the analysis of DSMC simulations of hypersonic shocks

In this work, statistical techniques were employed to study the modeling of a hypersonic

shock with the Direct Simulation Monte Carlo (DSMC) method, and to gain insight into how the

model interacts with a set of physical parameters.

Direct Simulation Monte Carlo (DSMC) is a particle based method which is useful for

simulating gas dynamics in rarefied and/or highly non-equilibrium flowfields. A DSMC code

was written and optimized for use in this research. The code was developed with shock tube

simulations in mind, and it includes a number of improvements which allow for the efficient

simulation of 1D, hypersonic shocks. Most importantly, a moving sampling region is used to

obtain an accurate steady shock profile from an unsteady, moving shock wave. The code is MPI

parallel and an adaptive load balancing scheme ensures that the workload is distributed properly

between processors over the course of a simulation.

Global, Monte Carlo based sensitivity analyses were performed in order to determine

which of the parameters examined in this work most strongly affect the simulation results for

two scenarios: a 0D relaxation from an initial high temperature state and a hypersonic shock.

The 0D relaxation scenario was included in order to examine whether, with appropriate initial

conditions, it can be viewed in some regards as a substitute for the 1D shock in a statistical

sensitivity analysis. In both analyses sensitivities were calculated based on both the square of the

Pearson correlation coefficient and the mutual information. The quantity of interest (QoI)

chosen for these analyses was the NO density profile. This vector QoI was broken into a set of

scalar QoIs, each representing the density of NO at a specific point in time (for the relaxation) or

a specific streamwise location (for the shock), and sensitivities were calculated for each scalar

QoI based on both measures of sensitivity. The sensitivities were then integrated over the set of

scalar QoIs to determine an overall sensitivity for each parameter. A weighting function was

used in the integration in order to emphasize sensitivities in the region of greatest thermal and

chemical non-equilibrium. The six parameters which most strongly affect the NO density profile

were found to be the same for both scenarios, which provides justification for the claim that a 0D

relaxation can in some situations be used as a substitute model for a hypersonic shock. These six

parameters are the pre-exponential constants in the Arrhenius rate equations for 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.

After identification of the most sensitive parameters, a synthetic data calibration was

performed to demonstrate that the statistical inverse problem could be solved for the 0D

relaxation scenario. The calibration was performed using the QUESO code, developed at the

PECOS center at UT Austin, which employs the Delayed Rejection Adaptive Metropolis

(DRAM) algorithm. The six parameters identified by the sensitivity analysis were calibrated

successfully with respect to a group of synthetic datasets. / text

Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2012-05-5384 |

Date | 25 June 2012 |

Creators | Strand, James Stephen |

Source Sets | University of Texas |

Language | English |

Detected Language | English |

Type | thesis |

Format | application/pdf |

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