## 2 Numerical Simulation Model  
In the Oxy-fuel combustion process, the combustion reaction becomes very complicated owing to the coupling effects of chemical kinetics, molecular diffusion, and turbulent transport. However, as a basic component of non-premixed flame structure, laminar counterflow diffusion flame is widely used in the study of combustion mechanism, which can also analyse and reveal the effects of diffusion, transport, and chemical reactions on the combustion process in detail. Figure 1 schematically shows the structure of a typical counterflow diffusion flame system. Fuel and oxidant are injected from different nozzles to form a stable axisymmetric diffusion flame. Various reactants enter the flame surface through molecular diffusion to participate in the combustion reaction. The complete mathematical description of the counterflow diffusion flame (including mass, momentum, energy, composition equation, and the boundary conditions on the fuel side and oxidizer side) can be found in the works of [23; 32]. The OPPDIF [33] code was used in the current study to solve the mathematical equations of the counterflow diffusion flame. The convection term adopts the upwind difference scheme, and the multi-component diffusion and thermal diffusion models are used to calculate the diffusion coefficient. The adaptive refinement grid is applied in the calculation process, and the damped Newton method is used to solve the equation. The relative and absolute errors of the iteration process are less than \(10^{-6}\). The GRI-Mech 3.0 [34] mechanism was selected as the reaction mechanism, which contains 53 species and 325 elementary reactions including the NO\({}_{\mathrm{X}}\) formation, and is also the most popular mechanism for CH\({}_{4}\). In order to ensure the stagnation surface of the counterflow flame does not deviate from the centre of the fuel and oxidizer nozzles, the calculation limits the two opposing gases to satisfy the momentum balance equation [34]:  
\[\rho_{o}V_{o}^{2}\ =\ \rho_{F}V_{F}^{2} \tag{1}\]  
The global strain rate \(\alpha_{s}\) is defined as follows [23]:  
\[\alpha_{s}\ =\ \frac{2(-V_{O})}{L}\left[1+\frac{V_{F}}{(-V_{O})}\sqrt{\frac{ \rho_{F}}{\rho_{O}}}\right] \tag{2}\]  
where the subscripts '\(O\)' and '\(F\)' stand for oxidizer and fuel flow streams, respectively. \(\rho\) and \(V\) represent the density and the velocity of the flow streams, respectively. \(L\) is the distance between the fuel and oxidizer nozzles, which is specified as 4 cm. For Equations (1) and (2),  
Figure 1: The configuration of the counterflow flame. only considering the absolute value of the velocity, the expressions of the velocity on both sides can be expressed as follows:  
\[|V_{F}|\ =\ |V_{o}|\sqrt{\frac{\rho_{o}}{\rho_{F}}} \tag{3}\]  
\[|V_{O}|\ =\ \frac{\alpha_{S}L}{4} \tag{4}\]  
The counterflow diffusion flame of CH\({}_{4}\) versus O\({}_{2}\) or \(\beta\)CO\({}_{2}\)/(1 - \(\beta\))O\({}_{2}\) (\(\beta\) is defined as CO\({}_{2}\) dilution ratio) with six CO\({}_{2}\) dilution ratios, 0-50% (10% as steps), was conducted. The pressure range is 1 atm to 5 atm, and the global strain rate \(\alpha_{s}\) is set to be 10 s\({}^{-1}\), 30 s\({}^{-1}\), or 50 s\({}^{-1}\). The inlet temperature of both the fuel and the oxidizer was specified as 300 K. The velocities of both sides were decided by Equations (1)-(4), and can be seen in Appendix A. The temperature distribution is the most basic flame characteristic of the counterflow diffusion flame, and it can be regarded as the most basic performance of other flame characteristics (flame front position, generation of thermal NOx, generation of important intermediate components). Therefore, the flame temperature has been selected as the target parameter of the current analysis. Guided by the research goals of this article, the author introduces three groups of artificial species to distinguish the chemical effect, thermal effect, and transport effect of CO\({}_{2}\) on the flame temperature, which is similar to the isolate strategy proposed by [PERSON] et al.