NOx

NOx concentration is usually low compared to other species in combustion systems. As a result, it is generally agreed that NOx chemistry has negligible influence and can be decoupled from the main combustion and flow field calculations.

NOx Thermal

The NOx Thermal model solves the transport equation for NO with the thermal source term ${\dot{\omega }}_{{NO}_{X,therm}}$

Formation of nitric oxide during combustion of hydrocarbons is temperature-dependent for the NOx Thermal model. It is produced by the reaction of atmospheric nitrogen with oxygen at elevated temperatures.

Thermal NOx is formed by high temperature oxidation of atmospheric nitrogen. For thermal nitric oxide, the principal reactions are generally recognized to be those proposed by the following three extended Zeldovich mechanisms:

The rate constants for these reactions have been measured in numerous experimental studies, and the data obtained from these studies has been critically evaluated by Baulch et al. [775]. The expressions for rate coefficients of reactions are given below (in units of ${\text{m}}^3{\left(\text{kmol}\right)}^{-1}{s}^{-1}$ ):

where $k_1$ , $k_2$ and $k_3$ are the forward rate constants and $k_{-1}$ , $k_{-2}$ and $k_{-3}$ are the backward rate constants for NOx reactions, respectively. The rate of formation of NOx is significant only at high temperatures since the thermal fixation of nitrogen requires the breaking of a strong N2 bond. This effect is represented by the high activation energy of the first reaction of the mechanism, which makes this reaction the rate-limiting step of the Zeldovich mechanism.

which can be simplified further to the expression:

If both the NOx Thermal and NOx Prompt models are activated, then the net production rate of NOx is the sum of the thermal and prompt NOx.

NOx Prompt

The formation of prompt NOx involves complex reactions with many intermediate species such as CH, CH2, HCN, CN, and others. These complex mechanisms are simplified to a global rate.

For most hydrocarbon fuels, the production rate of prompt NOx is taken from the global kinetics parameters derived by De Soete [776] and represented by the following equations:

Where ${M_w}_{{NO}_X}$ is the molecular weight of NOx and $k_r$ is the rate constant given by:

If both the NOx Thermal and NOx Prompt models are activated, then the net production rate of NOx is the sum of the thermal and prompt NOx.

NOx Fuel

When using the Lagrangian phase models—Liquid Fuel NOx or Coal Fuel NOx—these source terms are derived as shown below.

Liquid Fuel NOx

For liquid fuel, the only source of nitrogen is the evaporating fuel. The intermediates formed can be HCN or NH3. The fuel can also form NO through other pathways. There is also a possibility that N2 is formed as one of the intermediate species. The following figure shows the possible routes.

For multi-component droplets such as ${C_x{H}_{y}N}_z+H_{2}O$ , you identify the fuel species. Only the fuel ${C_x{H}_{y}N}_z$ source is needed.

$$\begin{array}{c}{\dot{\omega }}_{HCN,\text{produced}}=\frac{\left({\dot{\omega }}_{\text{fuel}}\right)\left(Y_N\right)\left(cf\right)\left(Z_{HCN}\right)\left({M_w}_{HCN}\right)}{\left({M_w}_N\right)\left(V\right)}\\ {\dot{\omega }}_{NH3,\text{produced}}=\frac{\left({\dot{\omega }}_{\text{fuel}}\right)\left(Y_N\right)\left(cf\right)\left(Z_{NH3}\right)\left({M_w}_{NH3}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}$$

(3633)

where ${\dot{\omega }}_{\text{fuel}}$ is the rate of evaporation of liquid fuel [kg/s], $V$ is the cell volume, and $cf$ is a correction factor for fuel NOx.

${\dot{\omega }}_{NO,\text{produced}}$ consists of NO produced from the fuel directly and/or NO produced by the oxidation of HCN/NH3:

$$\begin{array}{c}{\dot{\omega }}_{NO,\text{produced}}={\dot{\omega }}_{NO,\text{direct}}+{\dot{\omega }}_{NO,\text{oxidation}}\end{array}$$

(3634)

$$\begin{array}{c}{\dot{\omega }}_{NO,\text{direct}}=\frac{\left({\dot{\omega }}_{\text{fuel}}\right)\left(Y_N\right)\left(cf\right)\left(Z_{NO}\right)\left({M_w}_{NO}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}$$

(3635)

There are four types of reactions:

$$\begin{array}{c}HCN+O2\left(R_{1-HCN}\right)leadsto{NO}_{production}\\ HCN+NO\left(R_{2-HCN}\right)leadsto{NO}_{consumption}\\ NH3+O2\left(R_{1-NH3}\right)leadsto{NO}_{production}\\ NH3+NO\left(R_{2-NH3}\right)leadsto{NO}_{consumption}\end{array}$$

(3636)

The kinetics rates are obtained from De Soete [776].

For intermediate species HCN:

$$\begin{array}{c}{R}_{1-HCN}=A_{1-HCN}{X}_{HCN}{X}_{O2}^a{e}^{-E_{1,HCN/\left(RT\right)}}\\ R_{2-HCN}=A_{2-HCN}{X}_{HCN}{X}_{NO}^a{e}^{-E_{2,HCN/\left(RT\right)}}\end{array}$$

(3637)

where: $\begin{array}{c}\begin{array}{c}\begin{array}{c}{R}_1,R_2=\text{conversion rates of }HCN\left(S^{-1}\right)\\ X=\text{mole fractions}\end{array}\\ \begin{array}{c}{A}_{1,HCN}=1.0\times {10}^{10}\left(S^{-1}\right)\\ A_{2,HCN}=3.0\times {10}^{12}\left(S^{-1}\right)\end{array}\end{array}\\ E_{1,HCN}=280451.95\text{ J/gmol}\\ E_{2,HCN}=251151\text{ J/gmol}\end{array}$

$X_{O2}\le 4.1\times {10}^{-3}$	$a=1$
${4.1\times {10}^{-3}<X}_{O2}\le 1.11\times {10}^{-2}$	$\begin{array}{c}a=-3.95-0.9\text{ln}{X}_{O2}\end{array}$
${1.11\times {10}^{-2}<X}_{O2}<0.03$	$\begin{array}{c}a=-0.35-0.1\text{ln}{X}_{O2}\end{array}$
$X_{O2}\ge 0.03$	$a=0$

For intermediate species NH3:

$$\begin{array}{c}{R}_{1-NH3}=A_{1,NH3}{X}_{NH3}{X}_{O2}^a{e}^{-E_{1,NH3/\left(RT\right)}}\\ R_{2-NH3}=A_{2,NH3}{X}_{NH3}{X}_{NO}^a{e}^{-E_{2,NH3/\left(RT\right)}}\end{array}$$

(3638)

$\begin{array}{c}\begin{array}{c}\begin{array}{c}{R}_1,R_2=\text{conversion rates of }NH3\left(S^{-1}\right)\end{array}\\ \begin{array}{c}{A}_{1,NH3}=4.0\times {10}^6\left(S^{-1}\right)\\ A_{2,NH3}=1.8\times {10}^8\left(S^{-1}\right)\end{array}\end{array}\\ E_{1,NH3}=133947.2\text{ J/gmol}\\ E_{2,NH3}=113017.95\text{ J/gmol}\end{array}$

From Eqn. (3632):

$$\begin{array}{c}\begin{array}{c}{\dot{\omega }}_{HCN,\text{consumed}}={\dot{\omega }}_{HCN-1}+{\dot{\omega }}_{HCN-2}\\ =-(R_{1,HCN}+R_{2,HCN})\rho \frac{{M_w}_{HCN}}{{\overline{M}}_w}\end{array}\end{array}$$

(3639)

$$\begin{array}{c}\begin{array}{c}{\dot{\omega }}_{NH3,\text{consumed}}={\dot{\omega }}_{NH3-1}+{\dot{\omega }}_{NH3-2}\\ =-(R_{1,NH3}+R_{2,NH3})\rho \frac{{M_w}_{NH3}}{{\overline{M}}_w}\end{array}\end{array}$$

(3640)

From Eqns. Eqn. (3634) and Eqn. (3632):

$$\begin{array}{c}\begin{array}{c}{\dot{\omega }}_{NO,\text{oxidation}}=(R_{1,HCN}+R_{1,NH3})\rho \frac{{M_w}_{NO}}{{\overline{M}}_w}\end{array}\end{array}$$

(3641)

$$\begin{array}{c}\begin{array}{c}{\dot{\omega }}_{NO,\text{consumed}}=(R_{2,HCN}+R_{2,NH3})\rho \frac{{M_w}_{NO}}{{\overline{M}}_w}\end{array}\end{array}$$

(3642)

So putting together all equations:

$$\begin{array}{c}{\dot{\omega }}_{HCN}=\frac{\left({\dot{\omega }}_{\text{fuel}}\right)\left(Y_N\right)\left(cf\right)\left(Z_{HCN}\right)\left({M_w}_{HCN}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}-\frac{(R_{1,HCN}+R_{2,HCN})\rho {M_w}_{HCN}}{{\overline{M}}_w}$$

(3643)

$$\begin{array}{c}{\dot{\omega }}_{NH3}=\frac{\left({\dot{\omega }}_{\text{fuel}}\right)\left(Y_N\right)\left(cf\right)\left(Z_{NH3}\right)\left({M_w}_{NH3}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}-\frac{(R_{1,NH3}+R_{2,NH3})\rho {M_w}_{HCN}}{{\overline{M}}_w}$$

(3644)

$$\begin{array}{c}{\dot{\omega }}_{NO}=\begin{array}{c}\frac{\left({\dot{\omega }}_{\text{fuel}}\right)\left(Y_N\right)\left(cf\right)\left(Z_{NO}\right)\left({M_w}_{NO}\right)}{\left({M_w}_N\right)\left(V\right)}\\ +\frac{(R_{1,HCN}+R_{1,NH3}-R_{2,HCN}-R_{2,NH3})\rho {M_w}_{NO}}{{\overline{M}}_w}\end{array}\end{array}$$

(3645)

Coal NOx

Unlike the liquid fuel NOx, coal nitrogen is divided into volatile bound N and char bound N.

$$\begin{array}{c}{\dot{\omega }}_{HCN,\text{produced}}=\begin{array}{c}\frac{\left({\dot{\omega }}_{\text{devol}}\right)\left(Y_{N,\text{vol}}\right)\left(cf\right)\left(Z_{HCN}\right)\left({M_w}_{HCN}\right)}{\left({M_w}_N\right)\left(V\right)}\\ +\frac{\left({\dot{\omega }}_{\text{char-oxi}}\right)\left(Y_{N,\text{char}}\right)\left(cf\right)\left(Z_{HCN}\right)\left({M_w}_{HCN}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}\end{array}$$

(3646)

$\begin{array}{c}\begin{array}{c}{\dot{\omega }}_{HCN,\text{consumed}}=-(R_{1,HCN}+R_{2,HCN})\rho \frac{{M_w}_{HCN}}{{\overline{M}}_w}\end{array}\end{array}$ (as in Eqn. (3639))

$$\begin{array}{c}{\dot{\omega }}_{NH3,\text{produced}}=\begin{array}{c}\frac{\left({\dot{\omega }}_{\text{devol}}\right)\left(Y_{N,\text{vol}}\right)\left(cf\right)\left(Z_{NH3}\right)\left({M_w}_{HCN}\right)}{\left({M_w}_N\right)\left(V\right)}\\ +\frac{\left({\dot{\omega }}_{\text{char-oxi}}\right)\left(Y_{N,\text{char}}\right)\left(cf\right)\left(Z_{NH3}\right)\left({M_w}_{HCN}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}\end{array}$$

(3647)

$\begin{array}{c}\begin{array}{c}{\dot{\omega }}_{NH3,\text{consumed}}=-(R_{1,NH3}+R_{2,NH3})\rho \frac{{M_w}_{NH3}}{{\overline{M}}_w}\end{array}\end{array}$ (as in Eqn. (3640))

Note that the values for $cf$ , $Z_{HCN}$ , $Z_{NH3}$ and $Z_{NO}$ can be specified differently for char and volatile.

$$\begin{array}{c}{\dot{\omega }}_{NO,\text{direct}}=\begin{array}{c}\frac{\left({\dot{\omega }}_{\text{devol}}\right)\left(Y_{N,\text{vol}}\right)\left(cf\right)\left(Z_{NO}\right)\left({M_w}_{NO}\right)}{\left({M_w}_N\right)\left(V\right)}\\ +\frac{\left({\dot{\omega }}_{\text{char-oxi}}\right)\left(Y_{N,\text{char}}\right)\left(cf\right)\left(Z_{NO}\right)\left({M_w}_{NO}\right)}{\left({M_w}_N\right)\left(V\right)}\end{array}\end{array}$$

(3648)

The values for ${\dot{\omega }}_{NO,\text{oxidation}}$ and ${\dot{\omega }}_{NO,\text{consumed}}$ are the same as in Eqn. (3641) and Eqn. (3642). There is some restriction in choosing values for the mass fraction of char $Y_{N,\text{char}}$ and the mass fraction of coal $Y_{N,\text{vol}}$ —they are not independent of each other. You need ultimate and proximate analysis. Ultimate analysis indicates the percentage of elemental N in coal, that is, the mass fraction of N $Y_N$ in dry ash free (daf) coal:

$$Y_N=Y_{N,\text{vol}}+Y_{N,char}$$

(3649)

Proximate analysis provides the mass fractions of vol and char, along with other coal components. Always make sure that Eqn. (3649) is satisfied.