# NOx Formation Mechanism and Emission Prediction in Turbulent Combustion: A Review
## 6 Turbulent Combustion Simulation Approach
### CFD with Different Combustion Models
#### 6.2.1 Combustion Models with Fast Chemistry Hypothesis  
The EBU combustion model was effectively utilized to predict the temperature and concentration of key species [69, 70, 71]. The standard EBU combustion model neglects chemical kinetics under the assumption of the reaction rate dictated by the turbulent mixing time scale [72]. [PERSON] and [PERSON] [73] applied the standard \(k-\varepsilon\) model, EBU combustion model, and NOx equilibrium assumption to predict the combustion process and NOx emission on a modified four-cylinder MPFI SI engine. The result showed that the EBU model with global assumption has the least deviations on the NOx emission. However, according to the results figure, it only compared with the result of the 420-degree crank angle, which has few results to prove this model could approach the NOx emission.  
The EDM combustion model is also based on the infinite fast-chemistry assumption. The rate of reactions in EDM depends only on the behavior of the turbulent flow. Moreover, the EDM combustion model only handles the global kinetic mechanisms with a maximum of a few reactions. Hence, the model cannot discriminate between slow and fast chemistry [74]. [PERSON] et al. [75] applied the standard \(k-\varepsilon\) model, the EDM combustion model, and the NOx equilibrium assumption to research the NOx emission of a methane/air diffusion flame. The simulation results showed that increasing the swirl number could reduce exhaust NOx values.  
The PDF method treats the turbulent flow field from a completely random point of view. There are two approaches to determining the PDF in the modeling of a turbulent reacting flow. The presumed PDF method with a fast chemistry assumption could be employed to investigate the reaction-turbulence interactions. The transported PDF method is discussed in the next section.  
[PERSON] et al. [76] and [PERSON] et al. [77] provided a variety of presumed PDF shapes, and the most commonly used method is the form of the beta function. [PERSON] and [PERSON] [78] used the beta function to represent the probability density function containing 10 compounds related to the oxidative decomposition of hydrocarbon fuels. At the same time, the NOx generation rate was calculated with the quasi-steady-state hypothesis. Under the effect of the thermal radiation model, the concentration of NOx prediction reached a value of approximately 9 ppm, in good agreement with the experiment measurements. [PERSON] et al. [79] researched the effect of air turbulence intensity on NO formation in the combustion of mixed hydrogen-hydrocarbon fuel. The turbulence-combustion interaction was chosen as a presumed beta PDF model due to its better results for the turbulent non-premixed reacting flow. The NO concentration increased with the axial distance increasing, and the deviation between the present results and numerical results reached the maximum value at the end of the axial distance, about 160 ppm, approximately 19% of the present results. [PERSON] et al. [80] investigated the effect of air inlet conditions on NOx emission in a co-flowing methane/air diffusion flame. The beta PDF combustion model was applied to simulate the NOx emission. The average NOx emission at the exit of the combustors was 601 ppm, according to the present results, compared with 553 ppm from the other simulation results with similar conditions; thus, this simulation showed a good model validation. A similar method also appeared in [PERSON] et al. [81] and [PERSON] et al. [82].  
These combustion models were built under the assumption of fast chemistry. Because of the combustion models, the NOx approach method was applied to the equilibrium hypothesis. The reason is that the fast chemistry assumption is not compatible with the process of NOx generation.