This is an Accepted Manuscript of an article published by Taylor & Fran- cis in Combustion Science and Technology on 26 Feb 2023, available at: https://doi.org/10.1080/00102202.2023.2182201. Fractal Based, Scale-adaptive Closure Model for Darrieus–Landau Instability Effects on Large-scale Hydrogen-air Flames Dario Zivkovic a and Thomas Sattelmayer a a Chair of Thermodynamics, Technical University of Munich (TUM), Boltzmannstr. 15, Garching, Germany ABSTRACT Darrieus–Landau (DL) instability is an essential driving mechanism behind flame ac- celeration, especially in absence of turbulence. Effectively quiescent initial conditions are particularly relevant for explosion safety in various process facilities or parts of nuclear power plants. Large-scale industrial facilities pose a considerable challenge for numerical modeling via CFD since applying methods that rely on resolving the internal flame structure to predict the flame dynamics is well outside the limits of today’s computational resources. Therefore, in present work, a new scale-adaptive URANS (Unsteady Reynolds-Averaged Navier–Stokes) model for sub-grid closure is introduced. It is aimed at modeling the effects of the Darrieus–Landau instability at a significantly reduced computational cost. Model validation was performed using lean and stoichiometric hydrogen deflagration experiments at medium (∼ 1m) and large (∼ 10m) geometric scales. KEYWORDS Darrieus–Landau instability; Fractal flame speed model; Sub-grid closure; Reynolds-Averaged Navier–Stokes (RANS); Industry-scale flame propagation; 1. Introduction A possibility of flame acceleration is a key concern for safety of nuclear, or various process and chemical plants, as it can lead to high pressure loads and significant damage. If specific conditions are met, flame acceleration can lead to deflagration- to-detonation transition (DDT) with severe consequences. In the event of a reactor accident, a large amount of flammable gas can be produced—mostly hydrogen. The safety strategy is to avoid creation of a flammable mixture, but if such a mixture nevertheless forms, avoiding flame acceleration becomes critical (Benta¨ıb et al., 2015). Flame instabilities are an important mechanism of flame acceleration. Here the focus will be on the Darrieus–Landau (DL) hydrodynamic instability, which emerges as an effect of gas expansion due to heat release (Matalon, 2018). The resulting wrinkling of the flame front, in turn, increases the reaction rate—creating a self-accelerating feedback loop that grows the flame radius exponentially in time (Liberman, 2021)—a process that is present in all premixed combustion. Consequently, the DL instability is ubiquitous for hydrocarbon mixtures (Bradley et al., 2001; Bauwens et al., 2015; Kim et al., 2015b), as well as hydrogen (Kim et al., 2013, 2015b,a; Bauwens et al., 2017) and hydrogen-carbon monoxide (Jiang et al., 2020) mixtures—with the latter two being of particular interest in the nuclear safety domain. Furthermore, the emergence of flame instability occurs for both lean (Bauwens et al., 2017; Kim et al., 2013, 2015b) and rich (Kim et al., 2013, 2015a) compositions alike, once flame reaches a critical CONTACT Dario Zivkovic. Email: dario.zivkovic@tum.de