# Toward a reduced order model of lean H₂ flames using experimental and numerical data

Nicole Junqueira<fnref n="1" />,<fnref n="2" />, Luís Fernando Figueira da Silva<fnref n="2" />, Valéry Morgenthaler<fnref n="1" />

## Abstract

Hydrogen is been considered as an energy carrier and as a hydrocarbon fuel substitute, as it does not produce carbon dioxide when burned with air. Furthermore, lean hydrogen-air flames have the benefit of consuming less fuel and reaching a lower temperature than stoichiometric ones, which reduces the thermal stress on the combustion chambers. However, these lean flames have intrinsic instabilities that require consideration, for safety reasons, before they can be used in practical systems.

Accordingly, the novelty of this work is to use different data sources to create a reduced-order model of a lean flame. In this way, we propose a ROM using high-fidelity simulations and experimental results. Regarding the experimental approach, we consider here the OH* chemiluminescence and the temperature gradient using the schlieren technique. These measurements are performed in a newly developed annular burner, specifically designed to study ultra-lean H₂-air flames, shown in Fig. 1. We use the results of computational fluid dynamics models of these flames to interpret and calibrate the experimental data obtained. This model solves the transport equations of mass, momentum and energy for a reactive mixture considering detailed transport and chemistry descriptions.

Reduced-order models are applied to lower the cost associated of a parametric exploration. Here, these models are created from results (numerical and experimental) that cover the parametric space in terms of Reynolds and Damköhler numbers. Indeed, a model only using the experimental results would have the benefit of having several data points, but it would be poor in information, since there are only two flame properties available. On the other hand, a model using only high-fidelity simulations takes a huge amount of time to generate a dataset to create the model.

In the first part of this work we compare the Schlieren and OH* chemiluminescence results of lean laminar hydrogen/air flames obtained through 1D numerical simulation, 2D CFD simulations, and experimental results.

<footnote n="1">¹ Ansys France</footnote>

<footnote n="2">² Institut Pprime, CNRS, ISAE-ENSMA and Université de Poitiers, France</footnote>
<figure><img src="image_1.png" /><figcaption>Figure 1: A scheme of the annular burner, with the mean measurements of the OH* chemiluminescence (left) and the schlieren imaging (right) [3].</figcaption></figure>

References

[1] Brunton, S. L.; Noack, B. R.; Koumoutsakos, P. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, v.52, n. 1, p. 477–508, 2020. <https://doi.org/10.1146/annurev-fluid-010719-060214>.

[2] Adams, M. et al. Hybrid digital twins: A primer on combining physics-based and data analytics approaches. IEEE Software, v. 39, n. 2, p.47–52, 2022. <https://doi.org/10.1109/MS.2021.3134042>.

[3] Figueira da Silva, L. F. Stochastic characterization of unstable lean hydrogen/air annular premixed flames. Combustion Theory and Modelling. 2023. <https://hal.archives-ouvertes.fr/hal-03728087>.