_Article_  
**Combustion Characteristics of a Non-Premixed**  
**Oxy-Flame Applying a Hybrid Filtered Eulerian**  
**Stochastic Field/Flamelet Progress Variable Approach**  
**[PERSON] 1,2,*, [PERSON] 3, [PERSON] 1,** [PERSON] 2, [PERSON] 1 and**  
**[PERSON] 1,4**  
* Institute of Energy and Power Plant Technology, TU, 64287 Darmstadt, Germany; [EMAIL_ADDRESS] (F.R.); [PERSON]ADDRESS] (J.J.); [PERSON]_ADDRESS] (A.S.)
* Laboratoire EM2C, CNRS, CentraleSupelec, Universite Paris-Saclay, 91190 Gif-sur-yvette, France; [EMAIL_ADDRESS]
* Department of Mechanical Engineering, University of Birmingham, Birmingham B15 2 TT, UK; [EMAIL_ADDRESS]
* Laboratoire de Modelisation Mecanique, Energetique et Materiaux, Institut Superieur des Techniques Appliquees, Nololo, Kinshasa 6534, Congo
* Correspondence: [PERSON]ADDRESS]; Tel.: +49-(61)-511628756 check for updates  
Received: 28 January 2019; Accepted: 19 March 2019; Published: 29 March 2019  
**Abstract:** The oxidation of methane under oxy-fuel combustion conditions with carbon capture is attractive and deserves huge interest towards reducing CO\({}_{2}\) and NOx emissions. The current paper reports on the predictions and analysis of combustion characteristics of a turbulent oxy-methane non-premixed flame operating under highly diluted conditions of CO\({}_{2}\) and H\({}_{2}\) in oxidizer and fuel streams, respectively. These are achieved by applying a novel, well-designed numerical combustion model. The latter consists of a large eddy simulation (LES) extension of a recently suggested hybrid model in Reynolds averaging-based numerical simulation (RANS) context by the authors. It combines a transported joint scalar probability density function (T-PDF) following the Eulerian Stochastic Field methodology (ESF) on the one hand, and a flamelet progress variable (FPV) turbulent combustion model under consideration of detailed chemical reaction mechanism on the other hand. This novel hybrid ESF/FPV approach removes the weaknesses of the presumed-probability density function (P-PDF)-based FPV modeling, along with the solving of associated additional modeled transport equations while rendering the T-PDF computationally less affordable. First, the prediction capability of the LES hybrid ESF/FPV was appraised on the well-known air-piloted methane jet flame (Sandia Flame D). Then, it was assessed in analyzing the combustion properties of a non-premixed oxy-flame and in capturing the CO\({}_{2}\) dilution effect on the oxy-fuel flame behavior. To this end, the so-called oxy-flame B3, already numerically investigated in a RANS context, was analyzed. Comparisons with experimental data in terms of temperature, scalar distributions, and scatter plots agree satisfactorily. Finally, the impact of generating the FPV chemistry table under condition of unity Lewis number, even with CO\({}_{2}\) dilution, was investigated on the general prediction of the oxy-fuel flame structure, stability and emissions. In particular, it turns out that 68% molar percentage of CO\({}_{2}\) leads to 0.39% of CO formation near the burner fuel nozzle and 0.62% at 10 d\({}_{\text{fuel}}\) above the nozzle.  
**Keywords:** oxy-fuel combustion; non-premixed flame; large eddy simulation; filtered Eulerian stochastic field method; flamelet progress variable approach