### Abstract

First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution for thirty-one parameters focusing on the H
_{2}
O
_{2}
and HO
_{2}
reactions resulting from conditioning on ninety-one experiments. Established literature values are used for the remaining parameters in the mechanism as well as other thermodynamic and transport data needed to specify fluid properties. The samples are computed using an affine invariant sampler starting with broad, noninformative priors. Autocorrelation analysis shows that O(1M) samples are sufficient to obtain a reasonable sampling of the posterior. The resulting distribution identifies strong positive and negative correlations and several non-Gaussian characteristics. Using samples drawn from the posterior, we investigate the impact of parameter uncertainty on the prediction of two more complex flames: a 2D premixed flame kernel and the ignition of a hydrogen jet issuing into a heated chamber. The former represents a combustion regime similar to the target experiments used to calibrate the mechanism and the latter represents a different combustion regime. For the premixed flame, the net amount of product after a given time interval has a standard deviation of less than 2% whereas the standard deviation of the ignition time for the jet is more than 10%. The samples used for these studies are posted online. These results indicate the degree to which parameters consistent with the target experiments constrain predicted behavior in different combustion regimes. This process provides a framework for both identifying reactions for further study from candidate mechanisms as well as combining uncertainty quantification and propagation to, ultimately, tie uncertainty in laboratory flame experiments to uncertainty in end-use numerical predictions of more complicated scenarios.

Original language | English (US) |
---|---|

Pages (from-to) | 305-315 |

Number of pages | 11 |

Journal | Combustion and Flame |

Volume | 205 |

DOIs | |

State | Published - Jul 1 2019 |

### Fingerprint

### Keywords

- Hydrogen kinetics
- MCMC
- Parameter estimation
- Uncertainty quantification

### ASJC Scopus subject areas

- Chemistry(all)
- Chemical Engineering(all)
- Fuel Technology
- Energy Engineering and Power Technology
- Physics and Astronomy(all)

### Cite this

*Combustion and Flame*,

*205*, 305-315. https://doi.org/10.1016/j.combustflame.2019.04.023

**A Bayesian approach to calibrating hydrogen flame kinetics using many experiments and parameters.** / Bell, John; Day, Marcus; Goodman, Jonathan; Grout, Ray; Morzfeld, Matthias.

Research output: Contribution to journal › Article

*Combustion and Flame*, vol. 205, pp. 305-315. https://doi.org/10.1016/j.combustflame.2019.04.023

}

TY - JOUR

T1 - A Bayesian approach to calibrating hydrogen flame kinetics using many experiments and parameters

AU - Bell, John

AU - Day, Marcus

AU - Goodman, Jonathan

AU - Grout, Ray

AU - Morzfeld, Matthias

PY - 2019/7/1

Y1 - 2019/7/1

N2 - First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution for thirty-one parameters focusing on the H 2 O 2 and HO 2 reactions resulting from conditioning on ninety-one experiments. Established literature values are used for the remaining parameters in the mechanism as well as other thermodynamic and transport data needed to specify fluid properties. The samples are computed using an affine invariant sampler starting with broad, noninformative priors. Autocorrelation analysis shows that O(1M) samples are sufficient to obtain a reasonable sampling of the posterior. The resulting distribution identifies strong positive and negative correlations and several non-Gaussian characteristics. Using samples drawn from the posterior, we investigate the impact of parameter uncertainty on the prediction of two more complex flames: a 2D premixed flame kernel and the ignition of a hydrogen jet issuing into a heated chamber. The former represents a combustion regime similar to the target experiments used to calibrate the mechanism and the latter represents a different combustion regime. For the premixed flame, the net amount of product after a given time interval has a standard deviation of less than 2% whereas the standard deviation of the ignition time for the jet is more than 10%. The samples used for these studies are posted online. These results indicate the degree to which parameters consistent with the target experiments constrain predicted behavior in different combustion regimes. This process provides a framework for both identifying reactions for further study from candidate mechanisms as well as combining uncertainty quantification and propagation to, ultimately, tie uncertainty in laboratory flame experiments to uncertainty in end-use numerical predictions of more complicated scenarios.

AB - First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution for thirty-one parameters focusing on the H 2 O 2 and HO 2 reactions resulting from conditioning on ninety-one experiments. Established literature values are used for the remaining parameters in the mechanism as well as other thermodynamic and transport data needed to specify fluid properties. The samples are computed using an affine invariant sampler starting with broad, noninformative priors. Autocorrelation analysis shows that O(1M) samples are sufficient to obtain a reasonable sampling of the posterior. The resulting distribution identifies strong positive and negative correlations and several non-Gaussian characteristics. Using samples drawn from the posterior, we investigate the impact of parameter uncertainty on the prediction of two more complex flames: a 2D premixed flame kernel and the ignition of a hydrogen jet issuing into a heated chamber. The former represents a combustion regime similar to the target experiments used to calibrate the mechanism and the latter represents a different combustion regime. For the premixed flame, the net amount of product after a given time interval has a standard deviation of less than 2% whereas the standard deviation of the ignition time for the jet is more than 10%. The samples used for these studies are posted online. These results indicate the degree to which parameters consistent with the target experiments constrain predicted behavior in different combustion regimes. This process provides a framework for both identifying reactions for further study from candidate mechanisms as well as combining uncertainty quantification and propagation to, ultimately, tie uncertainty in laboratory flame experiments to uncertainty in end-use numerical predictions of more complicated scenarios.

KW - Hydrogen kinetics

KW - MCMC

KW - Parameter estimation

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85064451795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064451795&partnerID=8YFLogxK

U2 - 10.1016/j.combustflame.2019.04.023

DO - 10.1016/j.combustflame.2019.04.023

M3 - Article

AN - SCOPUS:85064451795

VL - 205

SP - 305

EP - 315

JO - Combustion and Flame

JF - Combustion and Flame

SN - 0010-2180

ER -