energies Article Numerical Study of Hydrogen Auto-Ignition Process in an Isotropic and Anisotropic Turbulent Field Agnieszka Wawrzak * and Artur Tyliszczak   Citation: Wawrzak, A.; Tyliszczak, A. Numerical Study of Hydrogen Auto-Ignition Process in an Isotropic and Anisotropic Turbulent Field. Energies 2021, 14, 1869. https:// doi.org/10.3390/en14071869 Academic Editor: Victor Terekhov Received: 25 February 2021 Accepted: 24 March 2021 Published: 28 March 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Armii Krajowej 21, 42-201 Czestochowa, Poland; atyl@imc.pcz.pl * Correspondence: awawrzak@imc.pcz.pl Abstract: The physical mechanisms underlying the dynamics of the flame kernel in stationary isotropic and anisotropic turbulent field are studied using large eddy simulations (LES) combined with a pdf approach method for the combustion model closure. Special attention is given to the ignition scenario, ignition delay, size and shape of the flame kernel among different turbulent regimes. Different stages of ignition are analysed for various levels of the initial velocity fluctuations and turbulence length scales. Impact of these parameters is found small for the ignition delay time but turns out to be significant during the flame kernel propagation phase and persists up to the stabilisation stage. In general, it is found that in the isotropic conditions, the flame growth and the rise of the maximum temperature in the domain are more dependent on the initial fluctuations level and the length scales. In the anisotropic regimes, these parameters have a substantial influence on the flame only during the initial phase of its development. Keywords: hydrogen auto-ignition; isotropic turbulence; anisotropy; LES; Eulerian Stochastic Fields 1. Introduction Turbulent combustion processes exist widely in various technical applications, e.g., gas turbines combustion chambers, burners, car engines. Numerical simulations of turbulent reactive flows are one of the most challenging tasks in contemporary CFD (Computa- tional Fluid Dynamics) both in the academic and industrial science centres. The turbulent flame being the result of the two-way interaction between chemical reactions and turbulent structures is characterized by significant oscillations of all flow variables. The combustion strongly changes the density and viscosity associated with temperature variations and these variables strongly affect the velocity field. The opposite impact is equally important, i.e., the turbulence affects the combustion process by enhancing the convective and diffu- sive mixing mechanisms. In this work we concentrate on the auto-ignition phenomenon for which the mixing process is particularly important, especially in non-premixed condi- tions where the regimes favorable for ignition as well as an initial flame development are conditioned by the mixing intensity [1,2]. Modeling the ignition process is one of the most difficult tasks in CFD research of reactive flows. It requires the use of Direct Numerical Sim- ulations (DNS) or Large Eddy Simulations (LES) with advanced combustion models, e.g., in non-premixed conditions the Conditional Moment Closure (CMC) [3–5], Eulerian stochas- tic fields (ESF) [6–8] and Partially Stirred Reactor (PaSR) type models [9,10] have been proven to predict the ignition process and flame stabilization relatively well. Recently, LES method is used in investigations of very complex combustion problems including the flame initiation by a spark ignition and auto-ignition in gasoline engines [11–13] and combustion instabilities (e.g., thermoacoustic oscillations, blow-off) in liquid-fuelled burners [14,15] or gas turbines [16,17]. In the present work we apply LES to study a very fundamental issue of the auto- ignition process, i.e., we analyze to what extent this phenomenon is influenced by the Energies 2021, 14, 1869. https://doi.org/10.3390/en14071869 https://www.mdpi.com/journal/energies