14.1.1.

Overview
emission consists of mostly nitric oxide ( ), and to a lesser degree nitrogen dioxide ( )
and nitrous oxide ( ). is a precursor for photochemical smog, contributes to acid rain, and
causes ozone depletion. Thus, is a pollutant. The ANSYS Fluent model provides a tool
to understand the sources of production and to aid in the design of control measures.

14.1.1.1. NOx Modeling in ANSYS Fluent

The ANSYS Fluent model provides the capability to model thermal, prompt, and fuel
formation, as well as consumption due to reburning in combustion systems. It uses rate
models developed at the Department of Fuel and Energy at The University of Leeds in England,
as well as from the open literature. reduction using reagent injection, such as selective
non-catalytic reduction (SNCR), can be modeled in ANSYS Fluent, along with an
intermediate model that has also been incorporated.

To predict emissions, ANSYS Fluent solves a transport equation for nitric oxide ( )
concentration. When fuel sources are present, ANSYS Fluent solves additional transport
equations for intermediate species ( and/or ). When the intermediate model is
activated, an additional transport equation for will be solved. The transport equations
are solved based on a given flow field and combustion solution. In other words, is
postprocessed from a combustion simulation. It is therefore evident that an accurate combustion
solution becomes a prerequisite of prediction. For example, thermal production
doubles for every 90 K temperature increase when the flame temperature is about 2200 K.
Great care must be exercised to provide accurate thermophysical data and boundary condition
inputs for the combustion model. Appropriate turbulence, chemistry, radiation, and other
submodels must be employed.

To be realistic, you can only expect results to be as accurate as the input data and the selected
physical models. Under most circumstances, variation trends can be accurately predicted,
but the quantity itself cannot be pinpointed. Accurate prediction of parametric trends
can cut down on the number of laboratory tests, allow more design variations to be studied,
shorten the design cycle, and reduce product development cost. That is truly the power of the
ANSYS Fluent model and, in fact, the power of CFD in general.

14.1.1.2. NOx Formation and Reduction in Flames

In laminar flames and at the molecular level within turbulent flames, the formation of can
be attributed to four distinct chemical kinetic processes: thermal formation, prompt
formation, fuel formation, and intermediate . Thermal is formed by the oxidation
/
of atmospheric nitrogen present in the combustion air. Prompt is produced by high-speed
reactions at the flame front. Fuel is produced by oxidation of nitrogen contained in the fuel.
At elevated pressures and oxygen-rich conditions, may also be formed from molecular
nitrogen ( ) via . The reburning and SNCR mechanisms reduce the total formation
by accounting for the reaction of with hydrocarbons and ammonia, respectively.

Important: The models cannot be used in conjunction with the

premixed combustion model.

/
14.1.2. Governing Equations for NOx Transport
ANSYS Fluent solves the mass transport equation for the species, taking into account
convection, diffusion, production, and consumption of and related species. This approach is
completely general, being derived from the fundamental principle of mass conservation. The effect
of residence time in mechanisms (a Lagrangian reference frame concept) is included through
the convection terms in the governing equations written in the Eulerian reference frame. For
thermal and prompt mechanisms, only the species transport equation is needed:

(14–1)

As discussed in Fuel NOx Formation, the fuel mechanisms are more involved. The tracking
of nitrogen-containing intermediate species is important. ANSYS Fluent solves a transport
equation for the , , or species, in addition to the species:

(14–2)

(14–3)

(14–4)

where , , , and are mass fractions of , , , and in the gas

phase, and is the effective diffusion coefficient. The source terms , , , and

are to be determined next for different mechanisms.

Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Release 19.0 - © ANSYS, Inc. All rights reserved.

/
14.1.3. Thermal NOx Formation
The formation of thermal is determined by a set of highly temperature-dependent chemical
reactions known as the extended Zeldovich mechanism. The principal reactions governing the
formation of thermal from molecular nitrogen are as follows:

(14–5)

(14–6)

A third reaction has been shown to contribute to the formation of thermal , particularly at near-
stoichiometric conditions and in fuel-rich mixtures:

(14–7)

14.1.3.1. Thermal NOx Reaction Rates

The rate constants for these reactions have been measured in numerous experimental
studies [47], [140], [336], and the data obtained from these studies have been critically
evaluated by Baulch et al. [31] and Hanson and Salimian [176]. The expressions for the rate
coefficients for Equation 14–5 – Equation 14–7 used in the model are given below. These
were selected based on the evaluation of Hanson and Salimian [176].

= =

= =

= =

/
In the above expressions, , , and are the rate constants for the forward reactions

Equation 14–5 – Equation 14–7, respectively, and , , and are the corresponding

reverse rate constants. All of these rate constants have units of m3/mol-s.

The net rate of formation of via the reactions in Equation 14–5 – Equation 14–7 is given by

(14–8)

where all concentrations have units of mol/m3.

To calculate the formation rates of and , the concentrations of , , and are required.

14.1.3.2. The Quasi-Steady Assumption for [N]

The rate of formation of is significant only at high temperatures (greater than 1800 K)
because fixation of nitrogen requires the breaking of the strong triple bond (dissociation
energy of 941 kJ/mol). This effect is represented by the high activation energy of
reaction Equation 14–5, which makes it the rate-limiting step of the extended Zeldovich
mechanism. However, the activation energy for oxidation of atoms is small. When there is
sufficient oxygen, as in a fuel-lean flame, the rate of consumption of free nitrogen atoms
becomes equal to the rate of its formation, and therefore a quasi-steady state can be
established. This assumption is valid for most combustion cases, except in extremely fuel-rich
combustion conditions. Hence the formation rate becomes

(14–9)

14.1.3.3. Thermal NOx Temperature Sensitivity

From Equation 14–9 it is clear that the rate of formation of will increase with increasing
oxygen concentration. It also appears that thermal formation should be highly dependent on
temperature but independent of fuel type. In fact, based on the limiting rate described by ,

the thermal production rate doubles for every 90 K temperature increase beyond 2200 K.

14.1.3.4. Decoupled Thermal NOx Calculations

To solve Equation 14–9, the concentration of atoms and the free radical will be required,
in addition to the concentration of stable species (that is, , ). Following the suggestion by
Zeldovich, the thermal formation mechanism can be decoupled from the main combustion
/
process by assuming equilibrium values of temperature, stable species, atoms, and
radicals. However, radical concentrations ( atoms in particular) are observed to be more
abundant than their equilibrium levels. The effect of partial equilibrium atoms on
formation rate has been investigated [330] during laminar methane-air combustion. The results
of these investigations indicate that the level of emission can be under-predicted by as
much as 28% in the flame zone, when assuming equilibrium -atom concentrations.

14.1.3.5. Approaches for Determining O Radical Concentration

There has been little detailed study of radical concentration in industrial turbulent flames, but
work [113] has demonstrated the existence of this phenomenon in turbulent diffusion flames.
Presently, there is no definitive conclusion as to the effect of partial equilibrium on
formation rates in turbulent flames. Peters and Donnerhack [380] suggest that partial equilibrium
radicals can account for no more than a 25% increase in thermal and that fluid dynamics
has the dominant effect on the formation rate. Bilger and Beck [39] suggest that in
turbulent diffusion flames, the effect of atom overshoot on the formation rate is very
important.

To overcome this possible inaccuracy, one approach would be to couple the extended Zeldovich
mechanism with a detailed hydrocarbon combustion mechanism involving many reactions,
species, and steps. This approach has been used previously for research purposes [326].
However, long computer processing time has made the method economically unattractive and
its extension to turbulent flows difficult.

To determine the radical concentration, ANSYS Fluent uses one of three approaches—the
equilibrium approach, the partial equilibrium approach, and the predicted concentration
approach—in recognition of the ongoing controversy discussed above.

14.1.3.5.1. Method 1: Equilibrium Approach

The kinetics of the thermal formation rate is much slower than the main hydrocarbon
oxidation rate, and so most of the thermal is formed after completion of combustion.
Therefore, the thermal formation process can often be decoupled from the main
combustion reaction mechanism and the formation rate can be calculated by assuming
equilibration of the combustion reactions. Using this approach, the calculation of the thermal
formation rate is considerably simplified. The assumption of equilibrium can be justified
by a reduction in the importance of radical overshoots at higher flame temperature [112].
According to Westenberg [530], the equilibrium -atom concentration can be obtained from
the expression

(14–10)

/
 With included, this expression becomes

(14–11)

where is in Kelvin.

14.1.3.5.2. Method 2: Partial Equilibrium Approach

An improvement to method 1 can be made by accounting for third-body reactions in the

dissociation-recombination process:

(14–12)

Equation 14–11 is then replaced by the following expression [520]:

(14–13)

which generally leads to a higher partial -atom concentration.

14.1.3.5.3. Method 3: Predicted O Approach

When the -atom concentration is well predicted using an advanced chemistry model (such
as the flamelet submodel of the non-premixed model), [ ] can be taken simply from the local
-species mass fraction.

14.1.3.6. Approaches for Determining OH Radical Concentration

ANSYS Fluent uses one of three approaches to determine the radical concentration: the
exclusion of from the thermal calculation approach, the partial equilibrium approach,
and the use of the predicted concentration approach.

14.1.3.6.1. Method 1: Exclusion of OH Approach

In this approach, the third reaction in the extended Zeldovich mechanism (Equation 14–7) is
assumed to be negligible through the following observation:

This assumption is justified for lean fuel conditions and is a reasonable assumption for most
cases.
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 14.1.3.6.2. Method 2: Partial Equilibrium Approach

In this approach, the concentration of in the third reaction in the extended Zeldovich
mechanism (Equation 14–7) is given by [32], [529]:

(14–14)

14.1.3.6.3. Method 3: Predicted OH Approach

As in the predicted approach, when the radical concentration is well predicted using an
advanced chemistry model such as the flamelet model, [ ] can be taken directly from the
local species mass fraction.

14.1.3.7. Summary
To summarize, the thermal formation rate is predicted by Equation 14–9. The -atom
concentration needed in Equation 14–9 is computed using Equation 14–11 for the equilibrium
assumption, using Equation 14–13 for a partial equilibrium assumption, or using the local -
species mass fraction. You will make the choice during problem setup. In terms of the transport
equation for (Equation 14–1), the source term due to thermal mechanisms is

(14–15)

where is the molecular weight of (kg/mol), and is computed from

Equation 14–9.

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14.1.4. Prompt NOx Formation
It is known that during combustion of hydrocarbon fuels, the formation rate can exceed that
produced from direct oxidation of nitrogen molecules (that is, thermal ).

14.1.4.1. Prompt NOx Combustion Environments

The presence of a second mechanism leading to formation was first identified by Fenimore
[127] and was termed “prompt ”. There is good evidence that prompt can be formed in
a significant quantity in some combustion environments, such as in low-temperature, fuel-rich
conditions and where residence times are short. Surface burners, staged combustion systems,
and gas turbines can create such conditions [26].

At present, the prompt contribution to total from stationary combustors is small.

However, as emissions are reduced to very low levels by employing new strategies (burner
design or furnace geometry modification), the relative importance of the prompt can be
expected to increase.

14.1.4.2. Prompt NOx Mechanism

Prompt is most prevalent in rich flames. The actual formation involves a complex series of
reactions and many possible intermediate species. The route now accepted is as follows:

(14–16)

(14–17)

(14–18)

(14–19)

A number of species resulting from fuel fragmentation have been suggested as the source of
prompt in hydrocarbon flames (for example, , , , ), but the major contribution
is from (Equation 14–16) and , via

/
 (14–20)

The products of these reactions could lead to formation of amines and cyano compounds that
subsequently react to form by reactions similar to those occurring in oxidation of fuel
nitrogen, for example:

(14–21)

14.1.4.3. Prompt NOx Formation Factors

Prompt formation is proportional to the number of carbon atoms present per unit volume
and is independent of the parent hydrocarbon identity. The quantity of formed increases
with the concentration of hydrocarbon radicals, which in turn increases with equivalence ratio.
As the equivalence ratio increases, prompt production increases at first, then passes a
peak, and finally decreases due to a deficiency in oxygen.

14.1.4.4. Primary Reaction

The reaction described by Equation 14–16 is of primary importance. In recent studies [427],
comparison of probability density distributions for the location of the peak with those
obtained for the peak have shown close correspondence, indicating that the majority of the
at the flame base is prompt formed by the reaction. Assuming that the reaction
described by Equation 14–16 controls the prompt formation rate,

(14–22)

14.1.4.5. Modeling Strategy

There are, however, uncertainties about the rate data for the above reaction. From the reactions
described by Equation 14–16 – Equation 14–20, it can be concluded that the prediction of
prompt formation within the flame requires coupling of the kinetics to an actual
hydrocarbon combustion mechanism. Hydrocarbon combustion mechanisms involve many
steps and, as mentioned previously, are extremely complex and costly to compute. In the
present model, a global kinetic parameter derived by De Soete [104] is used. De Soete
compared the experimental values of total formation rate with the rate of formation
calculated by numerical integration of the empirical overall reaction rates of and
formation. He showed that overall prompt formation rate can be predicted from the expression
/
 (14–23)

In the early stages of the flame, where prompt is formed under fuel-rich conditions, the
concentration is high and the radical almost exclusively forms rather than nitrogen.
Therefore, the prompt formation rate will be approximately equal to the overall prompt
formation rate:

(14–24)

For (ethylene)-air flames,

(14–25)

is 251151 , is the oxygen reaction order, is the universal gas constant, and is
pressure (all in SI units). The rate of prompt formation is found to be of the first order with
respect to nitrogen and fuel concentration, but the oxygen reaction order, , depends on
experimental conditions.

14.1.4.6. Rate for Most Hydrocarbon Fuels

Equation 14–24 was tested against the experimental data obtained by Backmier et al. [19] for
different mixture strengths and fuel types. The predicted results indicated that the model
performance declined significantly under fuel-rich conditions and for higher hydrocarbon fuels.
To reduce this error and predict the prompt adequately in all conditions, the De Soete
model was modified using the available experimental data. A correction factor, , was
developed, which incorporates the effect of fuel type, that is, number of carbon atoms, and the
air-to-fuel ratio for gaseous aliphatic hydrocarbons. Equation 14–24 now becomes

(14–26)

so that the source term due to prompt mechanism is

(14–27)

/
In the above equations,

(14–28)

(14–29)

is 303474.125 , is the number of carbon atoms per molecule for the hydrocarbon
fuel, and is the equivalence ratio. The correction factor is a curve fit for experimental data,
valid for aliphatic alkane hydrocarbon fuels ( ) and for equivalence ratios between 0.6

and 1.6. For values outside the range, the appropriate limit should be used. Values of and
were developed at the Department of Fuel and Energy at The University of Leeds in
England.

Here, the concept of equivalence ratio refers to an overall equivalence ratio for the flame, rather
than any spatially varying quantity in the flow domain. In complex geometries with multiple
burners this may lead to some uncertainty in the specification of . However, since the
contribution of prompt to the total emission is often very small, results are not likely to
be significantly biased.

14.1.4.7. Oxygen Reaction Order

Oxygen reaction order depends on flame conditions. According to De Soete [104], oxygen
reaction order is uniquely related to oxygen mole fraction in the flame:

(14–30)

/
14.1.5. Fuel NOx Formation

14.1.5.1. Fuel-Bound Nitrogen

It is well known that nitrogen-containing organic compounds present in liquid or solid fossil fuel
can contribute to the total formed during the combustion process. This fuel nitrogen is a
particularly important source of nitrogen oxide emissions for residual fuel oil and coal, which
typically contain 0.3–2% nitrogen by weight. Studies have shown that most of the nitrogen in
heavy fuel oils is in the form of heterocycles, and it is thought that the nitrogen components of
coal are similar [215]. It is believed that pyridine, quinoline, and amine type heterocyclic ring
structures are of importance.

14.1.5.2. Reaction Pathways

The extent of the conversion of fuel nitrogen to is dependent on the local combustion
characteristics and the initial concentration of nitrogen-bound compounds. Fuel-bound
compounds that contain nitrogen are released into the gas phase when the fuel droplets or
particles are heated during the devolatilization stage. From the thermal decomposition of these
compounds (aniline, pyridine, pyrroles, and so on) in the reaction zone, radicals such as ,
, , , and can be formed and converted to . The above free radicals (that is,
secondary intermediate nitrogen compounds) are subject to a double competitive reaction path.
This chemical mechanism has been subject to several detailed investigations [327]. Although
the route leading to fuel formation and destruction is still not completely understood,
different investigators seem to agree on a simplified model:

Recent investigations [188] have shown that hydrogen cyanide appears to be the principal
product if fuel nitrogen is present in aromatic or cyclic form. However, when fuel nitrogen is
present in the form of aliphatic amines, ammonia becomes the principal product of fuel nitrogen
conversion.

In the ANSYS Fluent model, sources of emission for gaseous, liquid, and coal fuels
are considered separately. The nitrogen-containing intermediates are grouped as , ,
or a combination of both. Transport equations (Equation 14–1 and Equation 14–2 or
Equation 14–3) are solved, after which the source terms , , and are determined
/
for different fuel types. Discussions to follow refer to fuel sources for and intermediate
, and sources for and . Contributions from thermal and prompt

mechanisms have been discussed in previous sections.

14.1.5.3. Fuel NOx from Gaseous and Liquid Fuels

The fuel mechanisms for gaseous and liquid fuels are based on different physics, but the
same chemical reaction pathways.

14.1.5.3.1. Fuel NOx from Intermediate Hydrogen Cyanide (HCN)

When is used as the intermediate species:

The source terms in the transport equations can be written as follows:

(14–31)

(14–32)

14.1.5.3.1.1. HCN Production in a Gaseous Fuel

The rate of production is equivalent to the rate of combustion of the fuel:

(14–33)

where

= source of (kg/m3–s)

/
 = mean limiting reaction rate of fuel (kg/m3–s)

= mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, , is calculated from the Magnussen combustion
model, so the gaseous fuel option is available only when the generalized finite-rate
model is used.

14.1.5.3.1.2. HCN Production in a Liquid Fuel

The rate of production is equivalent to the rate of fuel release into the gas phase
through droplet evaporation:

(14–34)

where

= source of (kg/m3–s)

= rate of fuel release from the liquid droplets to the gas (kg/s)

= mass fraction of nitrogen in the fuel

= cell volume (m3)

14.1.5.3.1.3. HCN Consumption

The depletion rates from reactions (1) and (2) in the above mechanism are the same
for both gaseous and liquid fuels, and are given by De Soete [104] as

/
 (14–35)

(14–36)

where

, = conversion rates of (s–1)

= instantaneous temperature (K)

= mole fractions

= 1.0 s–1

= 3.0 s–1

= 280451.95 J/mol

= 251151 J/mol

The oxygen reaction order, , is calculated from Equation 14–30.

Since mole fraction is related to mass fraction through molecular weights of the species (
) and the mixture ( ),

(14–37)

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 14.1.5.3.1.4. HCN Sources in the Transport Equation

The mass consumption rates of that appear in Equation 14–31 are calculated as

(14–38)

(14–39)

where

, = consumption rates of in reactions 1 and 2,

respectively (kg/m3–s)

= pressure (Pa)

= mean temperature (K)

= universal gas constant

14.1.5.3.1.5. NOx Sources in the Transport Equation

is produced in reaction 1, but destroyed in reaction 2. The sources for Equation 14–32
are the same for a gaseous as for a liquid fuel, and are evaluated as follows:

(14–40)

(14–41)

14.1.5.3.2. Fuel NOx from Intermediate Ammonia (NH3)

When is used as the intermediate species:

/
The source terms in the transport equations can be written as follows:

(14–42)

(14–43)

14.1.5.3.2.1. NH3 Production in a Gaseous Fuel

The rate of production is equivalent to the rate of combustion of the fuel:

(14–44)

where

= source of ( )

= mean limiting reaction rate of fuel (kg/m3–s)

= mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, , is calculated from the Magnussen combustion

model, so the gaseous fuel option is available only when the generalized finite-rate
model is used.

14.1.5.3.2.2. NH3 Production in a Liquid Fuel /

The rate of production is equivalent to the rate of fuel release into the gas phase
through droplet evaporation:

(14–45)

where

= source of (kg/m3–s)

= rate of fuel release from the liquid droplets to the gas (kg/s)

= mass fraction of nitrogen in the fuel

= cell volume (m3)

14.1.5.3.2.3. NH3 Consumption

The depletion rates from reactions (1) and (2) in the above mechanism are the same
for both gaseous and liquid fuels, and are given by De Soete [104] as

(14–46)

where

, = conversion rates of (s–1)

= instantaneous temperature (K)

/
 = mole fractions

= 4.0 s–1

= 1.8 s–1

= 133947.2 J/mol

= 113017.95 J/mol

The oxygen reaction order, , is calculated from Equation 14–30.

Since mole fraction is related to mass fraction through molecular weights of the species (
) and the mixture ( ), can be calculated using Equation 14–37.

14.1.5.3.2.4. NH3 Sources in the Transport Equation

The mass consumption rates of that appear in Equation 14–42 are calculated as

(14–47)

(14–48)

where

, = consumption rates of in reactions 1 and 2,

respectively (kg/m3–s)

/
 = pressure (Pa)

= mean temperature (K)

= universal gas constant

14.1.5.3.2.5. NOx Sources in the Transport Equation

is produced in reaction 1, but destroyed in reaction 2. The sources for Equation 14–43
are the same for a gaseous as for a liquid fuel, and are evaluated as follows:

(14–49)

(14–50)

14.1.5.3.3. Fuel NOx from Coal

14.1.5.3.3.1. Nitrogen in Char and in Volatiles

For the coal it is assumed that fuel nitrogen is distributed between the volatiles and the
char. Since there is no reason to assume that is equally distributed between the volatiles
and the char, the fraction of in the volatiles and the char should be specified separately.

When is used as the intermediate species, two variations of fuel mechanisms

for coal are included. When is used as the intermediate species, two variations of fuel
mechanisms for coal are included, much like in the calculation of production from
the coal via . It is assumed that fuel nitrogen is distributed between the volatiles and
the char.

14.1.5.3.3.2. Coal Fuel NOx Scheme A

The first mechanism assumes that all char converts to , which is then
converted partially to [456]. The reaction pathway is described as follows:

/
With the first scheme, all char-bound nitrogen converts to . Thus,

(14–51)

(14–52)

where

= char burnout rate (kg/s)

= mass fraction of nitrogen in char

= cell volume (m3)

14.1.5.3.3.3. Coal Fuel NOx Scheme B

The second mechanism assumes that all char converts to directly [291]. The
reaction pathway is described as follows:

/
According to Lockwood [291], the char nitrogen is released to the gas phase as
directly, mainly as a desorption product from oxidized char nitrogen atoms. If this approach
is followed, then

(14–53)

(14–54)

14.1.5.3.3.4. HCN Scheme Selection

The second mechanism tends to produce more emission than the first. In
general, however, it is difficult to say which one outperforms the other.

The source terms for the transport equations are

(14–55)

(14–56)

The source contributions , , , and are described previously.

Therefore, only the heterogeneous reaction source, , the char source, ,
and the production source, , need to be considered.

14.1.5.3.3.5. NOx Reduction on Char Surface

The heterogeneous reaction of reduction on the char surface has been modeled
according to the following [271]:
/
 (14–57)

where

= rate of reduction ( )

= mean partial pressure ( )

= 142737.485

= 230

= mean temperature ( )

The partial pressure is calculated using Dalton’s law:

The rate of consumption due to reaction 3 will then be

where

= BET surface area ( )

= concentration of particles ( )

/
 = consumption ( )

14.1.5.3.3.5.1. BET Surface Area

The heterogeneous reaction involving char is mainly an adsorption process, whose rate
is directly proportional to the pore surface area. The pore surface area is also known as
the BET surface area, due to the researchers who pioneered the adsorption theory
(Brunauer, Emmett, and Teller [63]). For commercial adsorbents, the pore (BET) surface
areas range from 100,000 to 2 million square meters per kilogram, depending on the
microscopic structure. For coal, the BET area is typically 25,000 , which is used
as the default in ANSYS Fluent. The overall source of ( ) is a combination

of volatile contribution ( ) and char contribution ( ):

14.1.5.3.3.5.2. HCN from Volatiles

The source of from the volatiles is related to the rate of volatile release:

where

= source of volatiles originating from the coal particles into the gas
phase (kg/s)

= mass fraction of nitrogen in the volatiles

= cell volume ( )

Calculation of sources related to char-bound nitrogen depends on the fuel scheme

selection.

14.1.5.3.3.6. Coal Fuel NOx Scheme C /

The first mechanism assumes that all char converts to which is then
converted partially to [456]. The reaction pathway is described as follows:

In this scheme, all char-bound nitrogen converts to . Thus,

(14–58)

(14–59)

where

= char burnout rate (kg/s)

= mass fraction of nitrogen in char

= cell volume ( )

14.1.5.3.3.7. Coal Fuel NOx Scheme D

The second mechanism assumes that all char converts to directly [291]. The
reaction pathway is described as follows:

/
According to Lockwood [291], the char nitrogen is released to the gas phase as
directly, mainly as a desorption product from oxidized char nitrogen atoms. If this approach
is followed, then

(14–60)

(14–61)

14.1.5.3.3.8. NH3 Scheme Selection

The second mechanism tends to produce more emission than the first. In
general, however, it is difficult to say which one outperforms the other.

The source terms for the transport equations are

(14–62)

(14–63)

The source contributions , , , , , and are described

previously. Therefore, only the production source, , must be considered.

The overall production source of is a combination of volatile contribution ( ),

and char contribution ( ):

/
 (14–64)

14.1.5.3.3.8.1. NH3 from Volatiles

The source of from the volatiles is related to the rate of volatile release:

where

= source of volatiles originating from the coal particles into the gas
phase (kg/s)

= mass fraction of nitrogen in the volatiles

= cell volume (m3)

Calculation of sources related to char-bound nitrogen depends on the fuel scheme

selection.

14.1.5.3.4. Fuel Nitrogen Partitioning for HCN and NH3 Intermediates

In certain cases, especially when the fuel is a solid, both and can be generated as
intermediates at high enough temperatures [348]. In particular, low-ranking (lignite) coal has
been shown to produce 10 times more compared to the level of , whereas higher-
ranking (bituminous) coal has been shown to produce only [347]. Studies by Winter et
al. [539] have shown that for bituminous coal, using an / partition ratio of 9:1 gave
better predictions when compared to measurements than specifying only a single
intermediate species. Liu and Gibbs [290] work with woody-biomass (pine wood chips), on the
other hand, has suggested an / ratio of 1:9 due to the younger age of the fuel.

/
In total, the above work suggests the importance of being able to specify that portions of the
fuel nitrogen will be converted to both and intermediates at the same time. In
ANSYS Fluent, fuel nitrogen partitioning can be used whenever or are
intermediates for production, though it is mainly applicable to solid fuels such as coal
and biomass. The reaction pathways and source terms for and are described in
previous sections.

/
14.1.6. NOx Formation from Intermediate N2O
Melte and Pratt [316] proposed the first intermediate mechanism for formation from
molecular nitrogen ( ) via nitrous oxide ( ). Nitrogen enters combustion systems mainly as a
component of the combustion and dilution air. Under favorable conditions, which are elevated
pressures and oxygen-rich conditions, this intermediate mechanism can contribute as much as
90% of the formed during combustion. This makes it particularly important in equipment such
as gas turbines and compression-ignition engines. Because these devices are operated at
increasingly low temperatures to prevent formation via the thermal mechanism, the
relative importance of the -intermediate mechanism is increasing. It has been observed that
about 30% of the formed in these systems can be attributed to the -intermediate
mechanism.

The -intermediate mechanism may also be of importance in systems operated in flameless

mode (for example, diluted combustion, flameless combustion, flameless oxidation, and FLOX
systems). In a flameless mode, fuel and oxygen are highly diluted in inert gases so that the
combustion reactions and resulting heat release are carried out in the diffuse zone. As a
consequence, elevated peaks of temperature are avoided, which prevents thermal .
Research suggests that the -intermediate mechanism may contribute about 90% of the
formed in flameless mode, and that the remainder can be attributed to the prompt
mechanism. The relevance of formation from has been observed indirectly and
theoretically speculated for a number of combustion systems, by a number of researchers [25],
[91], [158], [473], [480].

14.1.6.1. N2O - Intermediate NOx Mechanism

The simplest form of the mechanism [316] takes into account two reversible elementary
reactions:

(14–65)

(14–66)

Here, is a general third body. Because the first reaction involves third bodies, the mechanism
is favored at elevated pressures. Both reactions involve the oxygen radical , which makes the
mechanism favored for oxygen-rich conditions. While not always justified, it is often assumed
that the radical atoms originate solely from the dissociation of molecular oxygen,
/
 (14–67)

According to the kinetic rate laws, the rate of formation via the -intermediate
mechanism is

(14–68)

To solve Equation 14–68, you will need to have first calculated [ ] and [ ].

It is often assumed that is at quasi-steady-state (that is, ), which implies

(14–69)

The system of Equation 14–68 – Equation 14–69 can be solved for the rate of formation
when the concentration of , , and , the kinetic rate constants for Equation 14–65 and
Equation 14–66, and the equilibrium constant of Equation 14–67 are known. The appearance of
in Equation 14–66 entails that coupling of the mechanism with the thermal
mechanism (and other mechanisms).

= =

= =

In the above expressions, and are the forward rate constants of Equation 14–65 and

Equation 14–66, and and are the corresponding reverse rate constants. The units for

, , and are , while has units of .

/
14.1.7. NOx Reduction by Reburning
The design of complex combustion systems for utility boilers, based on air- and fuel-staging
technologies, involves many parameters and their mutual interdependence. These parameters
include the local stoichiometry, temperature and chemical concentration field, residence time
distribution, velocity field, and mixing pattern. A successful application of the in-furnace reduction
techniques requires control of these parameters in an optimum manner, so as to avoid impairing
the boiler performance. In the mid 1990s, global models describing the kinetics of destruction
in the reburn zone of a staged combustion system became available. Two of these models are
described below.

14.1.7.1. Instantaneous Approach

The instantaneous reburning mechanism is a pathway whereby reacts with
hydrocarbons and is subsequently reduced. In general:

(14–70)

Three reburn reactions are modeled by ANSYS Fluent for :

(14–71)

(14–72)

(14–73)

Important: If the temperature is outside of this range, reburn will not be

computed.

The rate constants for these reactions are taken from Bowman [51] and have units of
:

/
The depletion rate due to reburn is expressed as

(14–74)

and the source term for the reburning mechanism in the transport equation can be
calculated as

(14–75)

Important: To calculate the depletion rate due to reburning, ANSYS

Fluent will obtain the concentrations of , , and from the species
mass fraction results of the combustion calculation. When you use this
method, you must be sure to include the species , , and in your
problem definition.

14.1.7.2. Partial Equilibrium Approach

The partial equilibrium approach is based on the model proposed by Kandamby et al. [219], [11].
The model adds a reduction path to De Soete’s global model [104] that describes the
formation/destruction mechanism in a pulverized coal flame. The additional reduction path
accounts for the destruction in the fuel-rich reburn zone by radicals (see
Figure 14.1: De Soete’s Global NOx Mechanism with Additional Reduction Path).

Figure 14.1: De Soete’s Global NOx Mechanism with Additional Reduction Path

This model can be used in conjunction with the eddy-dissipation combustion model and does
not require the specification of radical concentrations, because they are computed based on
the -radical partial equilibrium. The reburn fuel itself can be an equivalent of , , ,
/
or . How this equivalent fuel is determined is open for debate, and an approximate guide
would be to consider the ratio of the fuel itself. A multiplicative constant of has
been developed for the partial equilibrium of radicals to reduce the rates of and in
the reburn model. This value was obtained by researchers who developed the model, by way of
predicting values for a number of test cases for which experimental data exists.

14.1.7.2.1. NOx Reduction Mechanism

In the fuel-rich reburn zone, the oxidation is suppressed and the amount of formed
in the primary combustion zone is decreased by the reduction reaction from to .
However, the concentration may also decrease due to reactions with radicals, which
are available in significant amounts in the reburn zone. The following are considered to be the
most important reactions of reduction by radicals:

(14–76)

(14–77)

(14–78)

These reactions may be globally described by the addition of pathways (4) and (5) in
Figure 14.1: De Soete’s Global NOx Mechanism with Additional Reduction Path, leading
respectively to the formation of and of minor intermediate nitrogen radicals. Assuming
that methane is the reburning gas, the global reduction rates are then expressed as

(14–79)

(14–80)

where

/
Therefore, the additional source terms of the and transport equations due to reburn
reactions are given by

(14–81)

(14–82)

Certain assumptions are required to evaluate the rate constants , , and and the
factors and . For hydrocarbon diffusion flames, the following reaction set can be

reasonably considered to be in partial equilibrium:

(14–83)

(14–84)

(14–85)

(14–86)

Thus, the rate constants may be computed as

where , , and are the rate constants for Equation 14–76 – Equation 14–78. The
forward and reverse rate constants for Equation 14–83 – Equation 14–86 are – and

– , respectively. In addition, it is assumed that , because the -radical

concentration in the post-flame region of a hydrocarbon diffusion flame has been observed to
be of the same order as [ ]. Finally, the -radical concentration is estimated by
considering the reaction

/
 (14–87)

to be partially equilibrated, leading to the relationship

Values for the rate constants , , and for different equivalent fuel types are given in
Arrhenius form ( ) in Table 14.1: Rate Constants for Different Reburn Fuels [269].
All rate constants have units of , and all values of have units of .

Table 14.1: Rate Constants for Different Reburn Fuels

Equivalent
Fuel Type

-1.54 27977 -3.33 15090 -2.64 77077

-1.54 27977 -3.33 15090 -2.64 77077

-1.54 27977 -3.33 15090 -2.64 77077

0.0 0.0 0.0 -3.33 15090 -2.64 77077

For Equation 14–87,

/
14.1.8. NOx Reduction by SNCR
The selective noncatalytic reduction of (SNCR), first described by Lyon [302], is a method to
reduce the emission of from combustion by injecting a selective reductant such as ammonia
( ) or urea ( ) into the furnace, where it can react with in the flue gas to form

. However, the reductant can be oxidized as well to form . The selectivity for the reductive
reactions decreases with increasing temperature [325], while the rate of the initiation reaction
simultaneously increases. This limits the SNCR process to a narrow temperature interval, or
window, where the lower temperature limit for the interval is determined by the residence time.

14.1.8.1. Ammonia Injection

Several investigators have modeled the process using a large number of elementary reactions.
A simple empirical model has been proposed by Fenimore [128], which is based on
experimental measurements. However, the model was found to be unsuitable for practical
applications. Ostberg and Dam-Johansen [368] proposed a two-step scheme describing the
SNCR process as shown in Figure 14.2: Simplified Reaction Mechanism for the SNCR Process,
which is a single initiation step followed by two parallel reaction pathways: one leading to
reduction, and the other to formation.

Figure 14.2: Simplified Reaction Mechanism for the SNCR Process

(14–88)

(14–89)

The reaction orders of and at 4% volume and the empirical rate constants and
for Equation 14–88 Equation 14–89, respectively, have been estimated from work done by
Brouwer et al. [60]. The reaction order of was found to be 1 for Equation 14–88 and the

/
order of was found to be 1 for both reactions. As such, the following reaction rates for
and , at 4% volume , were proposed:

(14–90)

(14–91)

The rate constants and have units of m3/mol-s, and are defined as

where J/mol and J/mol.

This model has been shown to give reasonable predictions of the SNCR process in pulverized
coal and fluidized bed combustion applications. The model also captures the influence of the
most significant parameters for SNCR, which are the temperature of the flue gas at the injection
position, the residence time in the relevant temperature interval, the to molar ratio,
and the effect of combustible additives. This model overestimates the reduction for
temperatures above the optimum temperature by an amount similar to that of the detailed
kinetic model of Miller and Bowman [325].

Important: The SNCR process naturally occurs when is present in the

flame as a fuel intermediate. For this reason, even if the SNCR model is
not activated and there is no reagent injection, the natural SNCR process
may still occur in the flame. The temperature range or “window” at which
SNCR may occur is 1073 K < T < 1373 K. If you want to model your case
without using the natural SNCR process, contact your support engineer for
information on how to deactivate it.

14.1.8.2. Urea Injection

Urea as a reagent for the SNCR process is similar to that of injecting ammonia, and has been
used in power station combustors to reduce emissions successfully. However, both
reagents, ammonia and urea, have major limitations as a reducing agent. The narrow
temperature “window” of effectiveness and mixing limitations are difficult factors to handle in a
large combustor. The use of urea instead of ammonia as the reducing agent is attractive
because of the ease of storage and handling of the reagent.

/
The SNCR process using urea is a combination of Thermal DeNOx (SNCR with ammonia) and
RAPRENOx (SNCR using cyanuric acid that, under heating, sublimes and decomposes into
isocyanic acid), because urea most probably decomposes into ammonia and isocyanic acid
[325].

One problem of SNCR processes using urea is that slow decay of , as well as the
reaction channels leading to and , can significantly increase the emission of pollutants
other than . Urea seems to involve a significant emission of carbon-containing pollutants,
such as and .

Also, some experimental observations [415] show that SNCR using urea is effective in a narrow
temperature window that is shifted toward higher temperatures, when compared to Thermal
DeNOx processes at the same value of the ratio of nitrogen in the reducing agent and the in
the feed, , where is defined as the ratio of nitrogen in the reducing agent and in the
feed. The effect of increasing the value is to increase the efficiency of abatement, while the
effect of increasing concentration depends on the temperature considered.

The model described here is proposed by Brouwer et al. [60] and is a seven-step reduced
kinetic mechanism. Brouwer et al. [60] assumes that the breakdown of urea is instantaneous
and 1 mole of urea is assumed to produce 1.1 moles of and 0.9 moles of . The
work of Rota et al. [415] proposed a finite rate two-step mechanism for the breakdown of urea
into ammonia and .

The seven-step reduced mechanism is given in Table 14.2: Seven-Step Reduced Mechanism
for SNCR with Urea, and the two-step urea breakdown mechanism is given in Table 14.3: Two-
Step Urea Breakdown Process.

Table 14.2: Seven-Step Reduced Mechanism for SNCR with Urea

Reaction A b E

4.24E+02 5.30 349937.06

3.500E-01 7.65 524487.005

2.400E+08 0.85 284637.8

1.000E+07 0.00 -1632.4815

1.000E+07 0.00 0

2.000E+06 0.00 41858.5

6.900E+17 -2.5 271075.646

/
Table 14.3: Two-Step Urea Breakdown Process

Reaction A b E

1.27E+04 0 65048.109

6.13E+04 0 87819.133

where SI units (m, mol, sec, J) are used in Table 14.2: Seven-Step Reduced Mechanism for
SNCR with Urea and Table 14.3: Two-Step Urea Breakdown Process.

14.1.8.3. Transport Equations for Urea, HNCO, and NCO

When the SNCR model with urea injection is employed in addition to the usual transport
equations, ANSYS Fluent solves the following three additional mass transport equations for the
urea, , and species.

(14–92)

(14–93)

(14–94)

where , and are mass fractions of urea, , and in the gas

phase. The source terms , , and are determined according to the rate

equations given in Table 14.2: Seven-Step Reduced Mechanism for SNCR with Urea and
Table 14.3: Two-Step Urea Breakdown Process and the additional source terms due to reagent
injection. These additional source terms are determined next. The source terms in the transport
equations can be written as follows:

(14–95)

(14–96)

/
 (14–97)

Apart from the source terms for the above three species, additional source terms for , ,
and are also determined as follows, which should be added to the previously calculated
sources due to fuel :

(14–98)

(14–99)

(14–100)

The source terms for species are determined from the rate equations given in
Table 14.2: Seven-Step Reduced Mechanism for SNCR with Urea and Table 14.3: Two-Step
Urea Breakdown Process.

14.1.8.4. Urea Production due to Reagent Injection

The rate of urea production is equivalent to the rate of reagent release into the gas phase
through droplet evaporation:

(14–101)

where is the rate of reagent release from the liquid droplets to the gas phase (kg/s) and

is the cell volume (m3).

14.1.8.5. NH3 Production due to Reagent Injection

If the urea decomposition model is set to the user-specified option, then the rate of
production is proportional to the rate of reagent release into the gas phase through droplet
evaporation:

(14–102)
/
where is the rate of reagent release from the liquid droplets to the gas phase (kg/s),
is the mole fraction of in the / mixture created from urea

decomposition, and is the cell volume (m3).

14.1.8.6. HNCO Production due to Reagent Injection

If the urea decomposition model is set to the user-specified option, then the rate of
production is proportional to the rate of reagent release into the gas phase through droplet
evaporation:

(14–103)

where , the injection source term, is the rate of reagent release from the liquid droplets
to the gas phase (kg/s), is the mole fraction of in the / mixture

created from urea decomposition, and is the cell volume (m3).

Important: The mole conversion fractions (MCF) for species and

are determined through the user species values such that if one mole
of urea decomposes into 1.1 moles of and 0.9 moles of , then
= 0.55 and = 0.45. When the user-specified option is

used for urea decomposition, then .

However, the default option for urea decomposition is through rate limiting reactions given in
Table 14.3: Two-Step Urea Breakdown Process, and the source terms are calculated
accordingly. In this case, both values of and are zero.

/
14.1.9. NOx Formation in Turbulent Flows
The kinetic mechanisms of formation and destruction described in the preceding sections
have all been obtained from laboratory experiments using either a laminar premixed flame or
shock-tube studies where molecular diffusion conditions are well defined. In any practical
combustion system, however, the flow is highly turbulent. The turbulent mixing process results in
temporal fluctuations in temperature and species concentration that will influence the
characteristics of the flame.

The relationships among formation rate, temperature, and species concentration are highly
nonlinear. Hence, if time-averaged composition and temperature are employed in any model to
predict the mean formation rate, significant errors will result. Temperature and composition
fluctuations must be taken into account by considering the probability density functions that
describe the time variation.

14.1.9.1. The Turbulence-Chemistry Interaction Model

In turbulent combustion calculations, ANSYS Fluent solves the density-weighted time-averaged
Navier-Stokes equations for temperature, velocity, and species concentrations or mean mixture
fraction and variance. To calculate concentration, a time-averaged formation rate must
be computed at each point in the domain using the averaged flow-field information.

Methods of modeling the mean turbulent reaction rate can be based on either moment methods
[538] or probability density function (PDF) techniques [209]. ANSYS Fluent uses the PDF
approach.

Important: The PDF method described here applies to the transport

equations only. The preceding combustion simulation can use either the
generalized finite-rate chemistry model by Magnussen and Hjertager, the
non-premixed or partially premixed combustion model. For details on these
models, refer to Species Transport and Finite-Rate Chemistry, Non-Premixed
Combustion, and Partially Premixed Combustion.

14.1.9.2. The PDF Approach

The PDF method has proven very useful in the theoretical description of turbulent flow [210]. In
the ANSYS Fluent model, a single- or joint-variable PDF in terms of a normalized
temperature, species mass fraction, or the combination of both is used to predict the
emission. If the non-premixed or partially premixed combustion model is used to model
combustion, then a one- or two-variable PDF in terms of mixture fraction(s) is also available.
The mean values of the independent variables needed for the PDF construction are obtained
from the solution of the transport equations. /
14.1.9.3. The General Expression for the Mean Reaction Rate
The mean turbulent reaction rate can be described in terms of the instantaneous rate and
a single or joint PDF of various variables. In general,

(14–104)

where ,... are temperature and/or the various species concentrations present. is the
probability density function (PDF).

14.1.9.4. The Mean Reaction Rate Used in ANSYS Fluent

The PDF is used for weighting against the instantaneous rates of production of (for
example, Equation 14–15) and subsequent integration over suitable ranges to obtain the mean
turbulent reaction rate. Hence we have

(14–105)

or, for two variables

(14–106)

where is the mean turbulent rate of production of , is the instantaneous molar rate
of production, is the instantaneous density, and and are the PDFs of
the variables and, if relevant, . The same treatment applies for the or source
terms.

Equation 14–105 or Equation 14–106 must be integrated at every node and at every iteration.
For a PDF in terms of temperature, the limits of integration are determined from the minimum
and maximum values of temperature in the combustion solution (note that you have several
options for how the maximum temperature is calculated, as described in Setting Turbulence
Parameters in the User's Guide). For a PDF in terms of mixture fraction, the limits of the
integrations in Equation 14–105 or Equation 14–106 are determined from the values stored in
the look-up tables.

14.1.9.5. Statistical Independence

In the case of the two-variable PDF, it is further assumed that the variables and are
statistically independent, so that can be expressed as
/
 (14–107)

14.1.9.6. The Beta PDF Option

ANSYS Fluent can assume to be a two-moment beta function that is appropriate for
combustion calculations [175], [329]. The equation for the beta function is

(14–108)

where is the Gamma function, and and depend on the mean value of the quantity in
question, , and its variance, :

(14–109)

(14–110)

The beta function requires that the independent variable assumes values between 0 and 1.
Thus, field variables such as temperature must be normalized. See Setting Turbulence
Parameters in the User's Guide for information on using the beta PDF when using single-
mixture fraction models and two-mixture fraction models.

14.1.9.7. The Gaussian PDF Option

ANSYS Fluent can also assume to exhibit a clipped Gaussian form with delta functions at the
tails.

The cumulative density function for a Gaussian PDF ( ) may be expressed in terms of the
error function as follows:

(14–111)

where is the error function, is the quantity in question, and and are the mean
and variance values of , respectively. The error function may be expressed in terms of the
incomplete gamma function ( ):
/
 (14–112)

14.1.9.8. The Calculation Method for the Variance

The variance, , can be computed by solving the following transport equation during the
combustion calculation or pollutant postprocessing stage:

(14–113)

where the constants , , and take the values 0.85, 2.86, and 2.0, respectively.

Note that the previous equation may only be solved for temperature. This solution may be
computationally intensive, and therefore may not always be applicable for a postprocessing
treatment of prediction. When this is the case or when solving for species, the calculation
of is instead based on an approximate form of the variance transport equation (also referred
to as the algebraic form). The approximate form assumes equal production and dissipation of
variance, and is as follows:

(14–114)

The term in the brackets is the dissipation rate of the independent variable.

For a PDF in terms of mixture fraction, the mixture fraction variance has already been solved as
part of the basic combustion calculation, so no additional calculation for is required.