Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 12, No. 3, 2024 

 

6 

Numerical	Study	on	Flame	Geometric	Characteristics	of	
Ammonia-Fueled	Small	Boiler	
Kunfeng Sun1, * 

1School of Smart Energy & Environment, Zhongyuan University of Technology, Zhengzhou, China 
*Corresponding author: Kunfeng Sun (Email: skf0558@sina.com) 

 

Abstract: Amidst global efforts to cut carbon emissions, the carbon-neutral fuel sector is at a crossroads of opportunity and 
challenge. The pursuit of clean, sustainable energy alternatives is critical. Ammonia, with its zero-carbon and hydrogen-rich 
profile, is emerging as a promising clean fuel, yet its combustion behavior in industrial boilers demands further study. This paper 
presents a numerical analysis of the flame geometry characteristics of ammonia combustion at an equivalence ratio of 1. The 
study delineates the dimensions of the flame, specifically its diameter and length, offering valuable insights that can inform the 
design of industrial boilers. This research contributes to the broader understanding of ammonia's role in the transition towards 
more sustainable energy solutions in industrial settings. 

Keywords: Ammonia, Numerical simulation, Boiler, Geometric characteristics. 
 

1. Introduction 
The extensive utilization of fossil fuels has resulted in a 

significant escalation of carbon dioxide emissions, thereby 
intensifying the greenhouse effect. Consequently, there is an 
urgent need to ameliorate the detrimental environmental 
consequences of carbon emissions. To this end, the scientific 
community is vigorously pursuing sustainable and renewable 
energy alternatives  [1, 2] . Among these, hydrogen energy 
has garnered considerable interest due to its inherent 
cleanliness, yet the challenge of its safe and practical storage 
must be surmounted to realize a global hydrogen economy  
[3] . 

Ammonia, as an emerging energy vector, has increasingly 
piqued interest owing to its distinctive advantages. It is 
characterized as a "zero-carbon hydrogen-rich" clean energy 
source with the potential to supplant fossil fuels [4] . Despite 
its toxicity, ammonia is less prone to ignition compared to 
hydrogen and gasoline. The merits of ammonia include its 
established industrial production processes, its amenability to 
storage and transportation, and the fact that its combustion 
yields only nitrogen and water, thereby achieving zero carbon 
emissions. Furthermore, ammonia boasts a high hydrogen 
content, making it an efficient hydrogen carrier. Its low 
liquefaction pressure at room temperature facilitates storage 
and transportation, and its volumetric energy density 
surpasses that of hydrogen, rivaling that of gasoline and diesel. 
It also exhibits a high octane rating and superior anti-knock 
properties [5] . 

Nevertheless, the use of ammonia as a fuel is not without 
its challenges. These include potential instability during 
combustion and the risk of high NOx emissions upon burning 
[6] . Additionally, the combustion characteristics of ammonia 
in various combustion apparatuses are a subject of ongoing 
research. The objective of this study is to investigate the flame 
geometry of ammonia combustion in small-scale boilers 
through numerical simulation. This research aims to provide 
a scientific foundation and technical guidance for the 
integration of ammonia into power generation equipment. 

2. Problem Description 

2.1. Computation Domain and Mesh 

This article utilizes a burner shown in Figure 1. 
Considering the symmetry of the burner chamber, the 
computational domain is simplified into a two-dimensional 
axial symmetry model. The overall dimensions of the burner 
are a length of 4000mm and an inner diameter of 500mm. The 
two-dimensional mesh is made up of 46700 elements, this 
mesh criterion was taken from Ref[19]. The computational 
model is illustrated in Figure 1. 

 

 
Figure	1. Schematic of the burner chamber	

2.2. Theoretical Background  
Numerical calculations of combustion require fundamental 

control equations, including the continuity equation, 
momentum conservation equation, energy conservation 
equation, and chemical species transport equation [7,8, 9] . In 
this study, for the combustion in a gas boiler, the Navier-
Stokes (N-S) equations are employed to describe fluid flow, 
the RNG  k-epsilon (k-e) equations are utilized as the 
turbulence model, and the non_premix model is adopted as 
the combustion model. Radiation calculation adopts DO 
model [8] .The SIMPLE algorithm is used as the pressure-
velocity coupling method. The discretization of each equation 
adopts a second-order precision format. 

The continuity equation is written in the following form: 

 

0                   (1) 

 



 

7 

Where, 𝜌 is density, 𝑢  are velocity components. 

The momentum equations are written: 

 

𝜇 𝜌𝑢′ 𝑢′ 𝑆   (2) 

 

Where, 𝜇  is Dynamic viscosity, 𝑢′   are fluctuating 
velocity components, 𝑝 is pressure,𝑆  are source terms. 

The energy equation for the Non_Premix combustion 
Model is written[7]: 

 

𝜌𝐻 ∇ ⋅ 𝜌�⃗�𝐻 ∇ ⋅ ∇𝐻 𝑆      (3) 

 

Where, 𝐻 ∑ 𝑌 𝐻   is total enthalpy, 𝑘   is the 
effective conductivity 𝑘 𝑘   , where 𝑘   is the turbulent 
thermal conductivity. 

Turbulence models: 

This study focuses on the combustion of gas boilers, where 
the gas flow inside the furnace is turbulent flow. RNG k- ε 
turbulence model commonly used in combustion calculations, 
these models consist of two equations: turbulent kinetic 
energy equation and dissipation rate equation. The equations 
expression is as follows: 

 
𝝏 𝝆𝒌

𝝏𝒕

𝝏 𝝆𝒌𝒖𝒊

𝝏𝒙𝒊

𝝏

𝝏𝒙𝒋
𝝁

𝝁𝒕

𝝈𝒌

𝝏𝒌

𝝏𝒙𝒋
𝑮𝒌 𝑮𝒃 𝝆𝝐

𝒀𝑴 𝑺𝒌                    (4) 

 
𝝏 𝝆𝝐

𝝏𝒕

𝝏 𝝆𝝐𝒖𝒊

𝝏𝒙𝒊

𝝏

𝝏𝒙𝒋
𝝁

𝝁𝒕

𝝈𝝐

𝝏𝝐

𝝏𝒙𝒋
𝑪𝟏𝝐

𝝐

𝒌
𝑮𝒌 𝑪𝟑𝜺𝑮𝒃

𝑪𝟐𝜺𝝆
𝝐𝟐

𝒌
𝑺𝝐                  (5) 

 

In above equations , 𝑮𝒌 represents the generation of 
turbulence kinetic energy due to the mean velocity gradients, 
𝑮𝒃  is the generation of turbulence kinetic energy due to 
buoyancy, 

𝒀𝒎 represents the contribution of the fluctuating dilatation 
in compressible turbulence to the overall dissipation rate and 
𝑺𝒌, 𝑺𝜺 are user-defined source terms.   𝑪 𝝐 , 𝑪 𝝐  , 𝑪 𝝐 and 
𝝈𝒌 , 𝝈𝝐  are constants.  

The species transport equations are written: 

 
𝝏 𝝆𝒀𝒊

𝝏𝒕

𝝏 𝝆𝒖𝒋𝒀𝒊 𝑱𝒊

𝝏𝒙𝒋
𝑹𝒊 𝑺𝒊            (6) 

 

Where, where 𝑹𝒊 is the net rate of production of species 
by chemical reaction and 𝑺𝒊    is the rate of creation by 
addition from the dispersed phase plus any user-defined 
sources. 𝐽  is the diffusion flux of species i . 

The Favre mean (density-averaged) mixture fraction 
equation is 

𝜌𝑓‾ ∇ ⋅ 𝜌�⃗�𝑓‾ ∇ ⋅ ∇𝑓‾ 𝑆 𝑆   (7) 

where 𝑘  is laminar thermal conductivity of the mixture, 
𝐶  is the mixture specific heat, 𝜎  is the Prandtl number, and 
𝜇  is the turbulent viscosity. 

The source term 𝑆  is due solely to transfer of mass into 
the gas phase from liquid fuel droplets or reacting particles. 
𝑆user  is any user-defined source term. 

The conservation equation for the mixture fraction variance 
is : 

∂
∂𝑡

𝜌𝑓 ∇ ⋅ 𝜌�⃗�𝑓 ∇ ⋅
𝑘

𝐶
𝜇
𝜎

∇𝑓  

𝐶 𝜇 ⋅ ∇𝑓‾ 𝐶 𝜌 𝑓 𝑆       (8) 

 

where 𝑓 𝑓 𝑓‾  is the mixture fraction variance . The 
default values for the constants 𝜎 , 𝐶   , and 𝐶   are 
0.85,2.86  , and 2.0, respectively, and 𝑆user   is any user-
defined source term. 

2.3. Boundary and Initial Conditions 
Flow rate and mass flow inlet conditions are selected for 

air inlet, swirling speed also be considered for air flow, 
Turbulent intensity is set to 10%. Under different working 
conditions, the molar ratio of hydrogen in the fuel is shown in 
Table 1. 

Fuel inlet are set to velocity inlet conditions, Turbulent 
intensity is set to 10%，The exit boundary condition is set as 
pressure outlet, Turbulent intensity is set to 2%[20]. 

The circumferential wall is set as a constant temperature 
boundary, and other walls are set as adiabatic boundary. 

 

Table 1. Velocity of fuel flow 

Index Velocity(m/s) Index Velocity(m/s) 
1 35 4 20 
2 30 5 15 
3 25   

3. Chemical-kinetic Modeling 
At present, many mechanisms of ammonia combustion 

have been studied by scholars at home and abroad, including 
the miller model [19], the Konnov [9] model, and the Hadi 
Nozari [10, 11] mechanism model. To study the combustion 
of ammonia at high temperatures and pressures, Song et al. 
[12] proposed an improved mechanism. Following Song's 
mechanism, Otomo et al. [13] developed a newer kinetic 
reaction mechanism, including flame and flame-related 
reactions. Duynslaegher et al. [14] studied GRI [15], San 
Diego [16], Lindstedt [17], etc., and found that Konnov's 
mechanism was consistent under low pressure conditions.  

In order to improve the modeling accuracy, Duynslaegher 
et al. studied a series of mechanisms and obtained a simplified 
mechanism that was in good agreement with the previous 
measurements. 

In this paper, computational simulations were conducted 
utilizing the PFR model (show in Table 2) within the Chemkin 
Pro software suite [18] . 

 

 



 

8 

Table 2. Reaction steps and corresponding rate constant data used in the model Mechanism for NH3/air combustion, 
Parameters for use in the Arrhenius expression 𝑘 𝐴𝑇 exp E/ 𝑅𝑇 , And the coefficients A ,b,E with units in cm, mol, s, 

cal. 

Index Reactions A b E 
1 NH3+M=NH2+H+M 0.920E+16 0 84800 
2 NH3+H=NH2+H2 0.246E+14 0 17071 
3 NH3+O=NH2+OH 0.150E+13 0 6040 
4 NH2+OH=NH+H2O 0.125E+14 0 2200 
5 NH3+OH=NH2+H2 0.325E+13 0 2120 
6 H+HNO=NH+OH 0.200E+12 0.5 1300 
7 HNO+M=H+NO+M 0.300E+17 0 48680 
8 HNO+OH=NO+H2O 0.360E+14 0 0 
9 NH2+HNO=NH3+N 0.500E+14 0 1000 

10 NH2+NO=NNH+OH 0.468E+20 -2.46 1876 
11 NH2+NO=N2+H2O 0.702E+20 -2.46 1876 
12 NH+O2=HNO+O 0.112E+13 0 3250 
13 NNH+M=N2+H+M 0.200E+15 0 20000 
14 NNH+NO=N2+HNO 0.500E+14 0 0 
15 NNH+OH=N2+H2O 0.300E+14 0 0 
16 NH2+NH2=NH3+N 0.630E+13 0 10000 
17 CO+OH=CO2+H 0.151E+08 1.3 -758 
18 H2+OH=H2O+H 0.520E+14 0 6500 
19 H+O2=OH+O 0.719E+17 -0.861 16523 
20 O+H2=OH+H 0.180E+11 1 8826 
21 2OH=O+H2O 0.170E+07 2.03 -1190 
22 H2+M=H+H+M 0.223E+13 0.5 92600 
23 H+OH+M=H2O+M 0.750E+24 -2.6 0 

 

5. Results and Discussion 
In this work, a non-premixed combustion model was 

employed to initially derive the PDF average mixing function 
lookup table, as depicted in Figure 2, which illustrates a two-
dimensional schematic diagram. Subsequent numerical 
computations were conducted for five distinct operational 
conditions, each with an equivalence ratio of 1, yielding a 
temperature distribution map of the boiler's thermal field. The 

numerical methodology was utilized to simulate the flame 
structure of ammonia's non-premixed combustion, with 
Figures 3 to 7 presenting the temperature contours. This 
approach aligns with the detailed chemical kinetic modeling 
of ammonia oxidation, as discussed by Otomo et al. , and 
contributes to the understanding of flame dynamics in non-
premixed ammonia combustion systems. 

 

 
Figure 2. PDF average mixing function lookup table 

 
From the PDF lookup table, it can be seen that the 

maximum temperature for ammonia combustion is 
approximately 2000K. From the temperature contour, it can 
be seen that the shape of the flame is similar, but the size is 



 

9 

different. As the power increases, the length and diameter of 
the flame also increase. The contour maps of temperature at 

different powers are shown in Figures 2 to 6. 

 

 
Figure 3. Temperature contour (56kW) 

 
Figure 4. Temperature contour (48kW) 

 
Figure 5. Temperature contour (40kW) 

 
Figure 6. Temperature contour (32kW) 

 
Figure 7. Temperature contour (24kW) 

 
By controlling the boundary conditions, specifically the 

fuel inlet velocity, a range of power outputs is simulated 
within the combustion chamber. The total sensible heat 
transfer rate within the system is meticulously calculated 



 

10 

using the flux report, which facilitates the determination of 
the corresponding power value for each scenario. Utilizing 
the acquired data and cloud map analysis, the flame length 

and flame diameter under these specific operating conditions 
are subsequently calculated. 

 

 
Figure 8. Flame length and burner power correlation curve 

 

 
Figure 9. The relationship between flame diameter and burner power 

 
This comprehensive approach enables the generation of a 

relationship curve between flame length, flame diameter, and 
power output, as illustrated in Figures 8 and Figures 9. Such 
an analysis is crucial for optimizing combustion efficiency 
and can inform strategies for power control in practical 
applications. 

6. Conclusion 
As a carbon-free fuel and an excellent hydrogen carrier, the 

combustion characteristics of NH3 in industrial boiler 
combustion need to be studied in detail. In this paper, the 
turbulent combustion of ammonia in a small boiler is 
numerically calculated by using the PDF model of non-
premixed combustion, and the Chemkin suite PFR ammonia 
combustion mechanism is applied. The combustion 
environment of the industrial boiler was simulated under 
atmospheric pressure conditions, and the grid model was 
established and the grid independence check was carried out 
to determine the appropriate grid model, and the temperature 
fields of ammonia combustion flames of different powers 
under five working conditions were obtained for the 
combustion of ammonia in the air, and the geometric 
characteristics of the flames under different powers could be 
intuitively seen through comparison. 

1) The temperature of ammonia combustion is generally 
low, and the maximum flame temperature is about 2000K. 
Therefore, from an industrial point of view, ammonia-doped 

combustion may be more promising, and this will be 
optimized in the next step. 

2) As the amount and power of fuel increases, the flame 
size increases. 

3) The diameter and length of the flame vary approximately 
linearly at the same equivalent ratio. 

In the future, it is necessary to compare the flame size of 
ammonia combustion under different equivalent ratios, and it 
is necessary to use different ammonia combustion 
mechanisms to compare, so as to obtain more reasonable and 
accurate results to meet the requirements of industrial design. 

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1.977

2.082

2.174

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1.95
2

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