# Systematic validation of non-equilibrium thermochemical models using Bayesian inference

## Abstract

The validation process proposed by Babuška et al. [1] is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. [2], Marrone and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radiative heat flux, QoI, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably largemore »

- Authors:

- NASA Glenn Research Center, OAI, 22800 Cedar Point Rd, Cleveland, OH 44142 (United States)
- Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 306 Talbot Lab, 104 S. Wright St., Urbana, IL 61801 (United States)
- Département de mathématiques et de génie industriel, Ecole Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montréal, QC, H3C 3A7 (Canada)

- Publication Date:

- OSTI Identifier:
- 22465659

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 298; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; CALIBRATION; ELECTRIC ARCS; EXPERIMENTAL DATA; HEAT FLUX; MATHEMATICAL SOLUTIONS; SHOCK TUBES; STATISTICS; STOCHASTIC PROCESSES; THERMAL EQUILIBRIUM; THERMOCHEMICAL PROCESSES; VALIDATION

### Citation Formats

```
Miki, Kenji, Panesi, Marco, E-mail: mpanesi@illinois.edu, and Prudhomme, Serge.
```*Systematic validation of non-equilibrium thermochemical models using Bayesian inference*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2015.05.011.

```
Miki, Kenji, Panesi, Marco, E-mail: mpanesi@illinois.edu, & Prudhomme, Serge.
```*Systematic validation of non-equilibrium thermochemical models using Bayesian inference*. United States. doi:10.1016/J.JCP.2015.05.011.

```
Miki, Kenji, Panesi, Marco, E-mail: mpanesi@illinois.edu, and Prudhomme, Serge. Thu .
"Systematic validation of non-equilibrium thermochemical models using Bayesian inference". United States. doi:10.1016/J.JCP.2015.05.011.
```

```
@article{osti_22465659,
```

title = {Systematic validation of non-equilibrium thermochemical models using Bayesian inference},

author = {Miki, Kenji and Panesi, Marco, E-mail: mpanesi@illinois.edu and Prudhomme, Serge},

abstractNote = {The validation process proposed by Babuška et al. [1] is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. [2], Marrone and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radiative heat flux, QoI, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.},

doi = {10.1016/J.JCP.2015.05.011},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 298,

place = {United States},

year = {2015},

month = {10}

}