## 1 Introduction  
Oxy-fuel combustion is currently known to have significant advantages over conventional combustion concepts where fossil fuel is oxidized with air, affecting the environment in terms of emission increase of carbon dioxide (CO\({}_{2}\)), NOx formation through the oxidation at high temperature of nitrogen (N\({}_{2}\)) in air. According to the Emission Database for Global Atmospheric Research [1], global emission of CO\({}_{2}\) increased to 35.8 billion tones in 2016, compared to 22.06 billion tones registered two decades ago. The concept of carbon capture and storage (CCS) is actually one accepted strategy towards cleaner combustion of fossil fuels. Three main approaches are currently emerging, namely, pre-combustion capture, post-combustion capture, and during-combustion capture or Oxy-fuel combustion (see in [2]). Thereby, the concept of oxy-fuel combustion has been especially promoted. It is mainly based on replacing the air containing nitrogen with enriched air or pure oxygen as oxidizer, where the resulting flue gas is composed primarily of CO\({}_{2}\) and H\({}_{2}\)O, from which CO\({}_{2}\) can be easily separated, enabling its capture, storage or recycling [2; 3; 4]. The oxy-combustion process is classified as a high thermochemical process with faster chemical reaction and burning velocity when compared to air combustion. Thus, in order to control the flame's temperature, structure and heat transfer, recycled CO\({}_{2}\) is often added to the oxidizer stream as a diluent [3]. With all these challenging changes with respect to the traditional combustion environment, it is essential to better understand the impact of the oxy-fuel conditions on the flow properties and flame characteristics. Relying on numerical investigations, appropriate numerical simulation tools are highly needed. Focusing on the description of complex turbulent flow, the large eddy simulation (LES) technique has proven to be able of to capture very complex turbulent reacting flows better than Reynolds averaging-based numerical simulation (RANS) [5]. Using a LES filter, large turbulent flow structures are classically separated from the unresolved scales. The former are explicitly computed while the unresolved structures need to be modeled by means of sub-grid scale models. The classical LES approach [5; 6; 7] is applied in this paper in conjunction with a tabulated chemistry-based combustion modeling. As the chemistry has to be considered within the LES framework, the integration of the required chemistry equations needs special care, in order to reduce the overall computational cost related with detailed chemistry computations essential for fully describing the chemistry process evolving. That is why various chemical mechanism reductions and chemistry tabulation or storage/retrieval approaches are now available in the literature and widely utilized, as pointed out in [5; 8; 9]. The mathematical procedures do not exclude species. The species concentrations are rather calculated or by tabulating them as functions of a few preselected controlling progress variables. Dealing with tabulated chemistry techniques, the most common methods used in different studies include the intrinsic low dimensional manifold (ILDM) in [10], the reaction-diffusion manifold (REDIM) [11] flamelet/progress variable approach (FPV) in [4; 8], flame prolongation of ILDM (FPI) or flamelet generated manifold (FGM) in [12], and filtered tabulated chemistry for LES (F-TACLES) [9; 13]. Thereby, each chemical look-up table corresponds to one set of boundary conditions in terms of fuel and oxidizer compositions and is mapped by means of a small number of reaction progress variables (RPV). When dilution by burnt gases and heat losses or multiphase phase process effects are to be considered, additional RPV may dramatically increase the size of the tables to be stored, resulting in huge look-up tables.