### 7.18.1. Formation Mechanisms

The formation of NOx is a complicated process involving several different mechanisms that are termed:

- Thermal NO

- Prompt NO

- Fuel Nitrogen

- N2O

- Reburn (destruction of NO)

Reactions for the first three formation paths (thermal, prompt and fuel) and for NO reburn are predefined in the `REACTIONS` database. It is possible to add reactions for other mechanisms, or modify the provided mechanisms, using the Reaction details view in CFX-Pre (or manually in the CCL commands file).

#### 7.18.1.1. Thermal NO

The thermal NO mechanism is a predominant source of NOx in gas flames at temperatures above 1800 K. The NO is formed from the combination of free radical O and N species, which are in abundance at high temperatures. The two-step mechanism, referred to as the Zeldovich mechanism, is thought to dominate the process:

| (7–109)

| (7–110)

In sub or near stoichiometric conditions, a third reaction may be important:

| (7–111)

When this step is included with the first two, it is referred to as the extended Zeldovich mechanism.

The rates of each of these three reactions (using the subscripts 1,2,3 to describe the three reactions) are expressed as [43]:

| (7–112)

| (7–113)

| (7–114)

When multiplied by the concentrations of the reactants, they yield rates in terms of , which can be converted to a volumetric mass source term.

The first step tends to be rate limiting, producing both an NO and N radical species. The N radical is assumed to be oxidized by reaction Equation 7–110 in the Zeldovich mechanism and also by reaction Equation 7–111 in the extended Zeldovich mechanism. Either way, these second oxidation reactions are assumed to be fast and if Reaction Equation 7–109 occurs, then two NO molecules will be formed. The thermal NO formation in , , is therefore related to the rate of reaction Equation 7–109:

| (7–115)

| (7–116)

Here, denotes the molecular mass of NO. Thus, if the molar concentrations [O] and [N2] of O radicals and N2 are known, the thermal NO mechanism can be calculated.

When using the Laminar Flamelet model, almost always the O radical concentration can be taken without further assumptions from the solution because the model predicts it directly. However, when using the Eddy Dissipation model (EDM) and/or the Finite Rate Chemistry model (FRC), O radical concentrations usually are not known directly but must be derived from other quantities. Here, the O radical concentration is estimated from the molecular oxygen dissociation,

| (7–117)

(Westenberg, 1975):

| (7–118)

By substitution, the effective source term for NO then reads:

| (7–119)

| (7–120)

#### 7.18.1.2. Prompt NO

At temperatures lower than 1800 K, hydrocarbon flames tend to have an NO concentration that is too high to be explained with the Zeldovich mechanisms. Hydrocarbon radicals can react with molecular nitrogen to form HCN, which may be oxidized to NO under lean flame conditions.

| (7–121)

| (7–122)

The complete mechanism is very complicated. However, De Soete (see also Peters and Weber, 1991) proposed a single reaction rate to describe the NO source by the Fenimore mechanism,

| (7–123)

| (7–124)

and denote molar mass of NO and the mean molar mass of the mixture, respectively. The Arrhenius coefficients depend on the fuel. (De Soete, 1974) proposed the following values:

Methane fuel

| (7–125)

Acetylene fuel

| (7–126)

#### 7.18.1.3. Fuel Nitrogen

The fuel nitrogen model assumes that nitrogen is present in the fuel by means of HCN. HCN is modeled to either form or destroy NO depending on the local conditions in the mixture, with HCO acting as an intermediate species. The mechanism consists of three reaction steps:

1. HCN-NO formation:

2. HCN-NO destruction:

3. HCO oxidation:

The reaction rates in [mol/s] for the reactions are, respectively:

| (7–127)

where

| (7–128)

| (7–129)

where denotes the molar fraction of and denotes the mean molar mass of the mixture.

#### 7.18.1.4. NO Reburn

Under fuel rich conditions, when the amount of oxygen available is not sufficient to oxidize all of the fuel, the excess fuel may lead to reduction of NO. This process can be described by a global reaction:

| (7–130)

Note that this is only a global representation; the physical process actually occurring is much more complicated. The real process involves many intermediate components appearing during combustion of the fuel, such as CHx radicals, which attack the NO.

The stoichiometric coefficients for fuel, carbon dioxide and water vapor are fuel-dependent. For a given fuel they can easily be derived from the element balance. For methane, the global NO reburn reaction is:

| (7–131)

The reaction rate will be fuel dependent. For coal volatiles, the reaction rate defaults to:

| (7–132)

The same reaction rate is applied for the predefined NO reburn reaction for methane.

#### 7.18.1.5. Turbulence Effects

The above reaction rates are applicable to laminar flow, premixed chemistry. In turbulence systems, fluctuations can have a dominant impact on the NO formation rate. For both the thermal and prompt NO mechanisms, there is a strong dependence of the rates on the temperature due to their high activation energy. Thus, temperature fluctuations, particularly positive fluctuations, can dramatically increase the NO formed in flames. These temperature fluctuations are included in CFX using a statistical approach.

In order to determine the mean rate for NO formation, a presumed probability density function (presumed PDF) method is used to compute the weighted average of the reaction rate:

| (7–133)

This integration is carried out separately for each reaction step. For simplicity, the subscripts (thermal or prompt) have been omitted. The integration range for temperature, , is the range of temperatures occurring. The default for NO reactions is the range [300 K; 2300 K], but this may be modified by you on a per reaction scope.

The probability density function (PDF) is computed from mean temperature, , and the variance of temperature, . The shape of is presumed to be that of a beta function (-function):

| (7–134)

Where:

| (7–135)

and:

| (7–136)

For vanishing temperature variance (vanishing temperature fluctuations), the beta function is approaching to a single Dirac peak (delta-function). In the limit, the integrated reaction rate is the same as for that for the standard Arrhenius rate. For very large fluctuation, the beta function goes towards a double Dirac peak, and for small to medium temperature variance the shape of the PDF is similar to that of a Gaussian distribution.

Arrhenius reaction rates integrated over a PDF for temperature is not limited to NO formation but may be used for any reaction.

#### 7.18.1.6. Temperature Variance Equation

For the temperature variance, , that is needed from constructing the probability density function (PDF) used for the temperature integration, the following transport equation is solved:

| (7–137)

Default values for the model coefficients are and .

The above equation is missing some physical aspects namely the production of temperature fluctuations due to heat release by chemical reaction. Heat release is fluctuating, too, because of turbulent fluctuations of the reactants. However, in the current model temperature variance is only needed as input to another model: The construction of a probability density function with presumed shape. For this purpose, the above equation provides sufficient accuracy.

For convenience of setting up a case, the temperature variance equation can be run without specifying BC or IC data. In the first release, these are not offered by the user interface (CFX-Pre). If absent, zero fluctuations are assumed at inlets, openings and walls with specified temperature. At walls with specified heat flux or transfer coefficient, the default BC for temperature variance is zero flux.

#### 7.18.1.7. Model Control

Because the model for NO formation is implemented by means of `REACTION` objects, you have full control of all aspects of the model. CFX provides the same flexibility for the NO model as for the generic combustion and reaction system.

##### 7.18.1.7.1. Adjusting Model Coefficients

It is possible for a user to modify any coefficient of the NO model. Because the NO formation reactions are defined by means of `REACTION` objects, they may be edited either in CFX-Pre in the CCL Editor or in the CCL text file (commands file).

The model parameter that is most likely to need adjusting is the temperature integration range for the presumed PDF. It is specified by the `Lower Temperature` and `Upper Temperature` parameters. These appear in the `FORWARD REACTION RATE` object when Option is set to `Arrhenius with Temperature PDF`. The predefined reaction schemes come with the range set to the interval [300 K, 2300 K]. It is recommended that you adjust this to the maximum temperature range occurring. For many systems, this temperature range is defined by the minimum inlet temperature and the adiabatic flame temperature.

##### 7.18.1.7.2. User Defined NO Formation Mechanisms

The NO formation model can be extended to a user's specific needs by adding appropriate reactions for NO, for example, fuel nitrogen or the N2O reaction path. The procedure is the same as for any other reaction. A user probably may want to chose the `Arrhenius with Temperature PDF` option for reactions rate in order to account for turbulent fluctuations of temperature.

It is also possible to select each NO formation path individually (thermal, prompt, fuel nitrogen, reburn, or possibly user defined). Simply add only those reactions to the mixture material that you want to account for.

Release 18.2 - © ANSYS, Inc. All rights reserved.