# NOx Formation Mechanism and Emission Prediction in Turbulent Combustion: A Review
###### Abstract  
The field of nitric oxide (NOx) production combined with turbulent flow is a complex issue of combustion, especially for the different time scales of reactions and flow in numerical simulations. Around this, a series of approach methods, including the empirical formula approach, the computational fluid dynamics (CFD) approach coupling with an infinite rate chemical reaction, the chemical reaction networks (CRNs), and the CFD approach coupling with CRNs, were classified, and we discussed its advantages and applicability. The empirical-formula approach can provide an average range of NOx concentration, and this method can be involved only in special scenarios. However, its simplicity and feasibility still promote practical use, and it is still widely applied in engineering. Moreover, with the help of artificial intelligence, this method was improved in regard to its accuracy. The CFD approach could describe the flow field comprehensively. In compliance with considering NOx formation as finite-rate chemical reactions, the NOx concentration distribution via simulation cannot match well with experimental results due to the restriction caused by the simplification of the combustion reaction. Considering NOx formation as a finite-rate chemical reaction, the CRNs approach was involved in CFD simulation, and the CRNs approach could forecast the NOx concentration distribution in the flow field. This article mainly focuses on the simulation method of nitric oxide (NOx) production in different combustion conditions. This review could help readers understand the details of the NOx formation mechanism and NOx formation prediction approach. n pacs: 02.20.-c, 07.63.  
time, the amount of nitrogen oxide (NOx) generation would not reach an equilibrium state after leaving the combustion chamber, NOx could still continue to be generated, and the concentration of each component associated with NOx could continue to change. The key point of approach to predict nitric oxide (NOx) emissions should be coupled with the temperature and flow field. This also makes it difficult to predict the rate of nitric oxide (NOx) production. In addition, nitric oxide (NOx) emissions were affected by the turbulent state and fuel type [4]. With the development of Sustainable Aviation Fuel (SAF), the change in fuel composition affects its physical and chemical properties, in turn affecting its atomization performance [5]. Reforming the atomization of droplets for liquid fuels has a significant impact on emission performance, including nitrogen oxides and particulate matter emissions. In earlier studies, the level of nitric oxide (NOx) emissions could be estimated roughly through empirical formulas [6]. The main idea is to treat the rate of reactant formation as an average constant dependent on the operating conditions. Even though this method could be applied to special scenarios, such as the gas turbine cycle analysis and preliminary design frameworks, its simplicity and feasibility still make it become a common way in practical use. In recent years, artificial intelligence and neural networks have been applied to predict nitric oxide (NOx) emissions to improve accuracy [7; 8; 9], but they still have drawbacks, such as the simplicity of the application scenarios and the huge amount of data that should be given to train the model. With the development of computers and the computing method, the capability and reliability of computational fluid dynamics (CFD) in combustion performance are well-known to use in NOx prediction [10]. In general, the computational fluid dynamics (CFD) method could describe the flow in detail and also solve the fuel oxidation process, which is considered as an infinite rate of chemical reaction. However, compared with the fuel oxidation process, the production of nitric oxide (NOx) is a finite-rate process, which means that the integration of the source item is complex. It is essential in a turbulent combustion regime to introduce a combustion model, which determines the reaction rate in the reacting flow [11].