# NOx Formation Mechanism and Emission Prediction in Turbulent Combustion: A Review
## 6 Turbulent Combustion Simulation Approach
### CFD with Different Combustion Models
#### 6.2.2 Combustion Models with Detailed Mechanisms  
Following the last section, another approach is through the joint probability density method. The joint probability density function not only contains composition but also could be combined with velocity or velocity-frequency. The main advantage of the PDF conservation equation is that the chemical reaction item is only related to the chemical variable, and no turbulence combustion model needs to be introduced. Therefore, PDF conservation equations can handle arbitrarily complex chemical reaction models. For instance, through the pure-composition PDF method to evaluate NOx production, [PERSON] [83] applied the PDF/Mixture fraction combustion model to provide more accurate results for the fuels that are a mixture of gases and more practical. [PERSON] [12] simulated a swirling flame of synthetic fuel combustion. By applying a composition PDF transport model to simulate finite-rate kinetic effects in reacting flow, this model not only could calculate the production of CO and NOx but also could be applied to simulate flame extinction and ignition. The main advantage of a PDF model is the possibility of obtaining an accurate value of NOx emission. The root-mean-square error of NOx emission is about 6% between the experiment and CFD calculation. Also, [PERSON] et al. [84] applied a joint velocity-composition-turbulence-frequency probability density function method to calculate the production of a series of piloted-jet non-premixed methane flames. There are 19 species and 15 reactions, including NO formation. Compared with the experimental data of flames D and E, the NO mass fractions conditioned on mixture fraction at different axial locations showed agreement with the experimental data in the whole range, but in some locations, a slightly underpredicted phenomenon occurred. [PERSON] et al. [85] also used a detailed zero-dimensional velocity-composition-frequency transported probability density function model (0D-VCF-tPDF) for numerical simulation, and the NOx mechanism was used in the chemical model. Compared with the 3D-CFD method, the 0D-VCF-tPDF method showed similar accuracy in the field of the predicted normalized engine-out NOx; the coefficient of determination is 0.867 to 0.866, respectively. The composition PDF method has greater advantages in the fields of finite chemical rate and NOx production issues, but it has a large amount of computation, especially for its Monte Carlo method to solve the PDF equations. Usually, this method would be very expensive in the calculation field, needing a computation time of about two orders of magnitude greater than that for a PDF with a fast chemistry model [86]. Another method that allowed for finite chemistry is the EDC combustion model. The EDC model could be applied to overcome the drawbacks of the EBU model, which could consider the complex chemistry reaction. [PERSON] et al. [87] applied the standard \(k-\varepsilon\) model and the EDC combustion model with GRI-Mech 2.2 to predict the NOx emission of a moderate and intense low-oxygen dilution (MILD) combustion of natural gas. The simulation results showed a common tendency and small deviations with the experimental data at the different traverses. However, because of the integration to calculate the chemical composition equations within each cell, the calculation of this method is enormous [88], and it increased with the species numbers [89]. The CMC model is promising for predicting NOx emissions [90]. [PERSON] et al. [91] combined the \(k-\varepsilon\) model and SIMPLE method with an elliptic-type CMC model to predict flow characteristics, conditional averaged temperature, and NO concentration with detailed mechanisms of the fuels. Reasonable agreement between experiments and predictions was obtained, which further confirmed the CMC model's applicability in predicting the species concentration and temperature in turbulent non-premixed combustion.