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27 

 

 

 

Article 

Properties of turbulent non-premixed 

methane/air flames in a miniature-scale swirl 

burner under different coaxial airflow swirl 

numbers  
Soroush Sheykhbaglou*1 

1School of Mechanical, Aerospace, and Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), 

No. 350, Hafez Ave, Tehran, Iran 

A R T I C L E   I N F O 
 

Article history: 
Received 24 August 2022  
Received in revised form 
24 September 2022 
Accepted 30 September 2022 
 
Keywords: 
miniature swirl burner, flame lift-off, 
flame characteristics,  
intermittency distribution,  
Otsu threshold, flame pulsating displacement 
 
 
*Corresponding author 
Email address:  
soroush.sheykh@aut.ac.ir  

 

 
DOI: 10.55670/fpll.fuen.2.1.5 

A B S T R A C T 
 

This study investigates the dynamics and properties of non-premixed 
methane/air flames under three swirl numbers by segmenting flame images 
using the Otsu thresholding technique. Under three operating conditions, the 
lean blow out (LBO) and flame length, lift-off height, maximum width, flame 
angle, and flame pulsing displacements in terms of flame center of gravity, 
length, and width are measured and compared. A high-speed camera is used to 
record video of flames, and the image processing of frames collected from a 
high-speed video was accomplished by using the intermittency distribution 
method to quantitatively compare flame attributes. The findings show that 
increasing the swirl number from 0.5 to 0.7 generally has an unfavorable 
effect on the LBO at given fuel flow rates, and the LBO of flames under 35° (0.6 
swirl number) and 40° (0.7 swirl number) swirlers has decreased up to about 
15% and 40%, respectively when compared with a 30° swirler (0.5 swirl 
number). Additionally, observations indicate that the flame length (𝐿) and lift-
off height (𝐿𝑂) drop as the swirl number rises, although the flame width (𝑊) 
and angle (𝛼) show an ascending tendency. Besides, flame lift-off reveals an 
increasing-decreasing trend with an increment in the airflow, and flame length 
decreases as the airflow rate increases. It was also observed that flame 
pulsating displacements in terms of center of gravity (𝛿𝐶𝐺), length (𝛿𝐿), and 
width (𝛿𝑊) increases with an increase in the fuel flow rate, and as the swirl 
number is increased, 𝛿𝐶𝐺  and 𝛿𝐿 lessens, while 𝛿𝑊 increases. 

 

 

 
1. Introduction 

Image segmentation is a key step that enables feature 

extraction and identification in the field of image analysis 

and processing. Several techniques are used to perform the 

segmentation task: (1) threshold-based methods, (2) edge-

based methods, (3) region-based methods, (4) clustering-

based methods, (5) partial differential equation-based 

methods, and (6) artificial neural network-based methods 

[1]. Thresholding-based approaches are the most often used 

segmentation techniques among them because they are 

straightforward, simple to grasp, and easy to use [1, 2]. 

Combustion device design must take into account aspects 

such as flame form and size [3]. Threshold segmentation of 

pictures from photography and high-speed video recordings 

is a cheap and efficient way to obtain flame characteristics. 

Several relevant studies to obtain flame characteristics from 

image processing can be found in [4-12], which are generally 

based on the intermittency distribution approach. The flame 

height and lift-off of propane turbulent jet diffusion flames 

attenuated by carbon dioxide at ambient temperature and 

pressure were studied by Tao et al. [9]. They discovered that 

when 𝐶𝑂2 concentration increases, and the flame height 

drops. Additionally, it was shown that when 

𝐶𝑂2 concentration rises, the flame lift-off height also rises. 

 

 

Future Energy 

Open Access Journal 

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February 2023| Volume 02 | Issue 01 | Pages 27-37 

Journal homepage: https://fupubco.com/fuen 

 

 

ISSN 2832-0328 

mailto:soroush.sheykh@aut.ac.ir
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S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

28 

 

The flame length of buoyant turbulent slot flames was 

examined by Gao et al. [13]. They created a rough prediction 

correlation for the length of the flame. They found that the 

flame length for the buoyancy-dominated and momentum-

dominated flames is proportional to (𝐹𝑟𝑚)1/3 and 
(𝐹𝑟𝑚)0(modified Froude number that shows the relationship 

between initial speed and buoyancy), respectively. Zhou et 

al. [10] analyzed the flame height and lift-off height of 

rectangular fuel jet source fires. The flame buoyancy-

momentum Froude number varied between 0.38 and 3.06. It 

was noticed that as the aspect ratio rises at a certain heat 

release rate, the flame height decreases. Zhang et al. [5] 

examined the features of curving flames in a tunnel model of 

a smaller size. They discovered that the recorded flame 

length under these conditions is almost comparable to that 

of flames in open space. In addition, they offered an 

empirical model for predicting the flame's tilt angle. Ligang 

et al. [14] measured the height of the coal jet flame using 

image processing. Image processing included the ROI (region 

of interest), filtering, grayscale, binarizing, and edge 

detection processes. The height of the flame was seen to 

decrease when the oxidizer temperature and main air 

velocity increased. Since swirl plays a significant role in 

flame stability, swirling flames are often used in practical 

combustion systems such as gas turbine engines and 

industrial burners [15, 16]. It is commonly acknowledged 

that swirl increases the local velocity fluctuations, hence 

increasing the turbulent burning velocity. Moreover, the 

swirl-induced recirculation zone may function as a heat 

source, causing heated products to interact with fresh 

reactants upstream [17]. Because of high energy density of 

hydrocarbon fuels, combustion-based micro-power devices 

are a more attractive option for portable power generation 

than rechargeable batteries [18-22]. In these systems, 

swirling flows are one method for flame stabilization [23-

30]. To the best of authors’ knowledge, there has never been 

research on the effects of swirl number on turbulent flame 

dynamics and characteristics by taking advantage of 

threshold-based image segmentation method. Using the Otsu 

threshold approach, this study compares the properties of 

turbulent swirling flames, including flame length, lift-off 

height, angle, maximum width, and pulsating displacements 

(in terms of flame center of gravity, length, and width), for 

three swirl numbers. 

2. Experimental setup 

Figure 1(a) depicts the experimental setup and flow 

delivery system layout. Air and Fuel are supplied by an air 

compressor and a high-pressure cylinder, respectively, and 

their pressures are then regulated using pressure reduction 

valves. Methane was used as fuel, and AZBIL MPC0020 and 

KOBOLD DMS-5 mass flow controllers with 1% full-scale 

accuracy regulate the flow of air and methane, respectively. 

Images of flames were taken with a Nikon V1 camera in its 

high-speed mode (400 fps) with a resolution of 640 × 240, a 

f-number of F/2.8, and a sensitivity of Hi 1. The miniature-

scale burner employed in this study is illustrated in Figure 

1(b).  The core component of the burner is its axial flat vane 

swirlers which are made of polylactic acid (PLA).  The 

construction of these swirlers was met using additive 

manufacturing techniques, and their geometrical 

characteristics are presented in Table 1. This burner's fuel 

nozzle consists of five 1 𝑚𝑚 holes that are encircled by 

coaxial air. 3D-printed flat vane axial swirler are used to 

swirl coaxial air. Beer and Chigier proposed the following 

equation to get the well-known dimensionless theoretical 

swirl number for a swirler with a constant vane angle  [23]: 

𝑆𝑛 =
2

3

1− (
𝐷ℎ

𝐷𝑠𝑤
)

3

1−(
𝐷ℎ

𝐷𝑠𝑤
)

2 tan 𝜃            (1) 

 

where 𝐷ℎ is the swirler hub diameter, 𝐷𝑠𝑤 is the swirler 

diameter, and 𝜃 is the vane angle from the centerline. 

 

Table 1. Specifications of studied swirlers 

Swirler No. Vane angle, 𝜃, (°) Swirl number, 𝑆𝑛 , (−) 
1 30 0.5 
2 35 0.6 
3 40 0.7 

No. of vanes: 10 
Vane thickness: 0.5 𝑚𝑚 
Hub diameter, 𝐷ℎ: 4.5 𝑚𝑚 
Tip diameter, 𝐷𝑠𝑤: 6.5 𝑚𝑚 
Swirl direction: counter-clockwise 

 

3. Results and discussion 

In this section, the flame lean blowout limits, flame 

characteristics, including flame length, lift-off height, 

maximum width, flame angle, and flame pulsing 

displacements in terms of flame center of gravity, length, and 

width are measured and compared under three coaxial 

airflow swirl numbers and three operating conditions (Table 

2). 

Table 2. Experimental conditions 

Case 
Airflow rate, 

(𝑠𝑙𝑝𝑚) 

Methane flow rate, 

(𝑠𝑙𝑝𝑚) 

Coaxial airflow swirl 

number, 𝑆𝑛, (−) 

1 3.0 0.100 0.5 

2 3.0 0.150 0.5 

3 3.0 0.200 0.5 

4 3.0 0.100 0.6 

5 3.0 0.150 0.6 

6 3.0 0.200 0.6 

7 3.0 0.100 0.7 

8 3.0 0.150 0.7 

9 3.0 0.200 0.7 

 

3.1 Lean blowout (LBO) limits 

In the present study, flame lean blowout limits are 

determined according to [12, 24]: (1) initially, a sustained 

diffusion flame is produced at a predetermined fuel flow 

rate, while the airflow rate is maintained at its minimum; (2) 

Second, the airflow rate is increased by 0.1 slpm while the 

fuel flow rate stays constant until the flame is extinguished; 

(3) The airflow rate at which the flame blows out 

(extingushes) is the lean blow out limit for the adjusted fuel 

flow rate; (4) This process is performed three times, and the 

average values are provided in this paper. 

 

 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

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(a) 

(b) 

Figure 1. (a) Experimental setup and flow delivery system, (b) miniature-scale swirl burner 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

30 

 

Figure 2(a) compares LBO values for three swirl numbers of 

0.5, 0.6, and 0.7 for methane flow rates ranging from 0.050 

to 0.500 slpm with an increment of 0.050 slpm. It has been 

seen that the equivalence ratio at which the flame blows out 

rises as the fuel flow rate is increased. It has also been seen 

that increasing the swirl number from 0.5 to 0.7 generally 

has an unfavorable effect on the LBO at given fuel flow rates 

(the flame blows out at lower airflow rates or higher 

equivalence ratio). This can be attributed to the following 

factors: (a) interaction between flame base and fuel nozzle 

due to an increase in the recirculation zone; (b) entrainment 

of cold outside air due to the recirculation zone; and (c) 

flame cooling due to an increase in the rate of strain on the 

flame with increasing swirl strength. In order to properly 

examine the impacts of raising the coaxial airflow swirl 

number from 0.5 to 0.7 on LBO, the findings of Figure 2(a) 

are compared to 30° swirler using the following equation: 

Diff in Φ =  
𝛷35° 𝑜𝑟40° 𝑠𝑤𝑖𝑟𝑙𝑒𝑟 − 𝛷30° 𝑠𝑤𝑖𝑟𝑙𝑒𝑟

𝛷30° 𝑠𝑤𝑖𝑟𝑙𝑒𝑟
 ×  100%        (2) 

 

(a) 

 

(b) 

Figure 2. (a) Lean blow out (LBO), (b) percentage difference 

in LBO compared with 30° swirler 

The percentage difference in the equivalence ratio at LBO 

under two swirl numbers is depicted in Figure 2(b). 

Negative and positive values indicate lower and higher 

equivalence ratios for LBO compared to 30° swirler, 

respectively. At two fuel flow rates of 0.050 and 0.100 slpm, 

a 35° swirler produces lower equivalence ratios for LBO. 

However, at fuel flow rates larger than 0.100 slpm, flames 

formed under swirl numbers of 0.6 and 0.7 blow out at 

higher equivalence ratios than flames formed under swirl 

number 0.5. For flames under 35° and 40°, the LBO has 

decreased up to about 15% and 40%, respectively. 

3.2 Flame characteristics 

In this section, the process for measuring is as follows: 

first, the fuel is introduced at predefined flow rates (0.100, 

0.150, and 0.200), ignited, and a sustained diffusion flame is 

created for each swirler; second, the airflow rate is steadily 

raised until it achieves the desired value of 3; then, a Nikon 

V1 is used to record a high-speed video of the formed flame 

at 400 fps for 5 seconds, resulting in 2000 frames. Within the 

scope of this investigation, visual luminosity served as the 

indicator for flame contours. The objective was to more 

clearly depict form variations seen in flame photographs 

(not to get an accurate location of the reaction zone). 

Thresholding-based approach, which is the most common 

segmentation method because of its simplicity, ease of 

understanding, and implementation, is used to extract flame 

contours of an image [1, 2]. The intermittency distribution 

approach is used to examine and compare flame length, lift-

off height, maximum width, and angle. This methodology has 

also been used in other research too [4-6, 9-11, 25].  In this 

procedure, the probability of a flame's existence is 

determined using the following steps: (a) 2000 frames are 

converted to grayscale and then preprocessed; (b) the Otsu 

thresholding algorithm, one of the most common methods in 

combustion, is applied to these grayscale images; (c) the 

thresholded images are binarized; (d) intermittency 

distribution is obtained by averaging the obtained images; 

(e) flame existence probability is obtained using a color bar 

(Figure 3 and the first row of Figure 5); (f) a threshold of 0.5 

is applied to maintain the part with existence probability 

greater than 50%; (g) by converting the image coordinates 

to metric coordinates, flame length, lift-off height, maximum 

width, and angle are obtained (Figure 3). In Figure 4, 

quantitative comparisons of the flame's length (L), lift-off 

height (LO), maximum width (W), and angle (α) are shown 

for three different swirl numbers and operating conditions. 

In these figures, L, LO, and  W are normalized to swirler 

diameter (D_sw). It is observed that the flame length and lift-

off height drop as the swirl number rises, although the flame 

width and angle show an ascending tendency. Additionally, it 

has been shown that raising the methane flow rates causes 

an increase in these variables except for the flame angle. The 

radial mixing of air and fuel is improved and accelerated by 

increasing the swirl number, which also accelerates chemical 

processes. By moving the reaction zone upstream, swirl may 

also extend the residence duration during which reactants 

and products can coexist. As the swirl number rises, fuel can 

also be efficiently entrained. All of these may shorten the 

visible flame length as well the flame lift-off height. In 

addition, when the swirl number is rising, the flame width 

and angle increase because radial mixing is improved and 

the fuel and air mixture is pushed outward.  

 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

31 

 

 

 

 

When the fuel flow rate is increased for swirling 

flames, the entrainment by swirling air diminishes owing to 

accelerated fuel velocity, resulting in more fuel burning in 

diffusion mode by the air from the surroundings. As a 

consequence, the flame lengthens, and its lift-off height 

increases with an increment in the fuel flow rate. On the 

other side, the fuel nozzle geometry may be responsible for 

the rise in flame width and angle with an increase in fuel 

flow rate. It is also observed that the flame lift-off height and 

angle exhibit the least sensitivity to an increase in fuel flow 

rate for a swirl number of 0.7. This is shown in Table 3, 

which was generated using MATLAB's curve-fitting toolbox 

with 95% confidence bounds (linear curve-fitting). 

Table 3. Slopes of linear fitted curves for normalized flame lift-off 

and angle 

Swirl number, 
𝑆𝑛 , (−) 

𝐿𝑂/𝐷𝑠𝑤 versus fuel 
flow rate 

𝛼 versus fuel flow 
rate 

0.5 1.662 −290.2 

0.6 2.123 −273.3 

0.7 0.7077 −189 

 

Figure 5 depicts the mean flame shape (mean of 2000 

frames for each operating condition) and its normalized 

intensity map as a function of the swirl number at 0.200 and 

3 slpm methane and airflow rates, respectively. It has been 

shown that the bottom section of the flame has the greatest 

normalized intensity value, and by raising the swirl number, 

this area expands radially,  the flame's width grows, and its 

length reduces. The mean flame contour (boundary) is 

obtained after applying the Otsu threshold to the grayscale 

mean flame and separating the foreground and background. 
The change of flame shape with airflow rate at a given fuel 

flow rate of 0.200 slpm for a 30° vane angle swirler 

(S_n=0.5) is shown in Figure 6 (single frames from 2000 

frames of each operating condition is presented only). The 

following observations can be made: 

 

 

 

 

 Flame lift-off reveals an increasing-decreasing trend 

with an increment in the airflow rate, and the decreasing 

section corresponds to improved mixing of fuel and air 

because swirl has shown its effect. Flame length is affected 

by the airflow rate increase, and it decreases as the airflow 

rate increases. This is consistent with the findings in [26]. 

For swirling flames, this tendency is the consequence of an 

increase in turbulence intensity with an increase in airflow 

rate, which enhances fuel-air mixing and reduces flame 

length. At airflow rates, when flame lift-off has a declining 

trend, flame width reduces as airflow rate increases. This 

may be described as follows: when the swirl exerts its 

impact, a recirculation zone is created, which recirculates 

fuel and air, so decreasing the flame width. These findings 

are similar to other swirl numbers and operating conditions 

investigated in this research (Table 2). 

In this investigation, the flame's center of gravity as 

well as its length and width, are used to examine flame 

fluctuations (pulsating displacements). The flame center is 

used to determine the position of the flame as a point 

utilizing the center of gravity concept (mass center in this 

case). Each pixel serves as a local point for calculating the 

mass center, and the intensity of each pixel represents its 

mass [27]. To obtain flame fluctuations, the Otsu threshold is 

used to generate binarized images of 2000 frames for each 

operating condition (boundaries of all 2000 frames are 

shown simultaneously in Figure 7 for methane and airflow 

rates of 0.200 and 3 𝑠𝑙𝑝𝑚, respectively). The mean center of 

gravity (𝑥𝐶𝐺,𝑚𝑒𝑎𝑛 , 𝑦𝐶𝐺,𝑚𝑒𝑎𝑛), length (𝐿𝑚𝑒𝑎𝑛), and width 

(𝑊𝑚𝑒𝑎𝑛) are determined; then, the standard deviation is then 

used to calculate the flame's pulsating displacement in terms 

of the flame's center of gravity, length, and width [28]: 

𝛿𝐶𝐺 = √
∑ [(𝑥𝐶𝐺,𝑖−𝑥𝐶𝐺,𝑚𝑒𝑎𝑛)

2
+(𝑦𝐶𝐺,𝑖−𝑥𝐶𝐺,𝑚𝑒𝑎𝑛)

2
]2000

𝑖= 1

2000
        (3) 

 

 

Figure 3. Definitions of flame length, lift-off height, maximum width, and angle 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

32 

 

(a) 

(b) 

(c) 

(d) 

 

Figure 4. Normalized (a) flame length, (b) lift-off, (c) 

width, (d) angle as a function of swirl number 

 

 

 

𝛿𝐿 = √
∑ (𝐿𝑖−𝐿𝑚𝑒𝑎𝑛)22000

𝑖= 1

2000
    (4) 

 

𝛿𝑊 = √
∑ (𝑊𝑖−𝑊𝑚𝑒𝑎𝑛)22000

𝑖= 1

2000
    (5) 

Where 𝐿𝑖  and 𝑊𝑖  stand for the length and maximum width 
of the 𝑖𝑡ℎ frame, respectively and 𝑥𝐶𝐺,𝑖  and 𝑦𝐶𝐺,𝑖 are the 𝑥 

and 𝑦 coordinates of the 𝑖𝑡ℎ frame’s center of gravity. 

 

Figure 5. Flame existence probability, mean flame, its 

normalized intensity map, and its Otsu threshold versus 

swirl number at fuel and airflow rates of  0.200 and 3 slpm, 

respectively 

 

Figure 6. The change of flame shape with airflow rate at a 

given fuel flow rate of 0.200 slpm for a 30° vane angle 

swirler (Sn = 0.5) 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

33 

 

Figure 7. Fluctuations of flame boundary for methane and 
airflow rates of 0.200 and 3 slpm under three swirl 
numbers (obtained from 2000 frames for each 
experimental condition) 

Figure 1 in Appendix I shows the flame length and width 
difference (𝐿𝑑𝑖𝑓𝑓 =  |𝐿𝑖 −  𝐿𝑚𝑒𝑎𝑛|, 𝑊𝑑𝑖𝑓𝑓 =  |𝑊𝑖 −  𝑊𝑚𝑒𝑎𝑛|) 

over time spanning from 0 to 5 𝑠. Observations reveal that 
when the swirl number rises, the peak values for flame 
length and width differences shift to lower and higher 
values, respectively. On each figure, the mean values of 
these differences are also displayed (𝐿𝑑𝑖𝑓𝑓,𝑚𝑒𝑎𝑛  and 

𝑊𝑑𝑖𝑓𝑓,𝑚𝑒𝑎𝑛). It is observed that as the swirl number is 

increased, 𝐿𝑑𝑖𝑓𝑓,𝑚𝑒𝑎𝑛 and 𝑊𝑑𝑖𝑓𝑓,𝑚𝑒𝑎𝑛  show a decreasing and 

increasing trend, respectively. This is presented 
quantitatively in Figure 2 in Appendix I.  It is also noted 
from Figure 2 in Appendix I that these values (𝐿𝑑𝑖𝑓𝑓,𝑚𝑒𝑎𝑛  

and 𝑊𝑑𝑖𝑓𝑓,𝑚𝑒𝑎𝑛) rise when the fuel flow rate increases. The 

changes of 𝛿𝐶𝐺 , 𝛿𝐿, and 𝛿𝑊 with the swirl number at three 
fuel flow rates are determined and depicted in Figure 3 in 
Appendix I based on the above-mentioned formulae for 
quantifying flame fluctuations. It is noticed that flame 
pulsating displacements in terms of center of gravity (𝛿𝐶𝐺), 
length (𝛿𝐿), and width (𝛿𝑊) increases with an increase in 
the fuel flow rate; although the increase in 𝛿𝐶𝐺  from 0.6 
swirl number to 0.7 swirl number is negligible. 
Additionally, it has been shown that as the swirl number is 
increased, 𝛿𝐶𝐺  and 𝛿𝐿 lessens, while 𝛿𝑊 increases.  

4. Conclusion 
The In this work, turbulent non-premixed methane/air 

flame dynamics, and properties in a miniature-scale swirl 
burner were investigated under three different swirl 
numbers using high-speed video recordings of swirling 
flames. For the measurement of flame length, lift-off height, 
maximum width, and angle, an intermittency distribution 
approach based on the Otsu threshold method for image 
segmentation was used. Furthermore, the flame's center of 
gravity as well as its length and width, are used to examine 
flame fluctuations (pulsating displacements). The following 
are the main conclusions: 
• Increasing the swirl number from 0.5 to 0.7 has an 
unfavorable effect on the lean blowout (LBO) at a given fuel 
flow rate (the flame blows out at lower airflow rates or 
higher equivalence ratio). This can be attributed to the 
interaction between flame base and fuel nozzle due to an 
increase in the recirculation zone, entrainment of cold 
outside air due to the recirculation zone, and flame cooling 
due to an increase in the rate of strain on the flame with 
increasing swirl strength. Additionally, for flames under 35° 
(0.6 swirl number) and 40° (0.7 swirl number) swirlers, the 

LBO has decreased up to about 15% and 40%, respectively, 
when compared with the 30° swirler (0.5 swirl number). 
• Observations indicate that the flame length (L) and 
lift-off height (LO) drop as the swirl number rises, although 
the flame width (W) and angle (α) show an ascending 
tendency. Additionally, it has been shown that raising the 
methane flow rates causes an increase in these variables 
except for the flame angle. Additionally, Flame lift-off reveals 
an increasing-decreasing trend with an increment in the 
airflow rate at a specified methane flow rate, and the 
decreasing section corresponds to improved mixing of fuel 
and air because swirl has shown its effect. Besides, flame 
length is affected by the airflow rate increase, and it 
decreases as the airflow rate increases. For swirling flames, 
this tendency is the consequence of an increase in 
turbulence intensity with an increase in airflow rate, which 
enhances fuel-air mixing and reduces flame length. 
• Flame pulsating displacements in terms of center of 
gravity (δ_CG), length (δ_L), and width (δ_W) increases with 
an increase in the fuel flow rate; although the increase in 
δ_CG from 0.6 swirl number to 0.7 swirl number is 
negligible. Additionally, it has been shown that as the swirl 
number is increased, δ_CG and δ_L lessens, while δ_W 
increases.  

Ethical issue 
The author is aware of and complies with best practices 

in publication ethics, specifically with regard to authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and 
compliance with policies on research ethics. The author 
adheres to publication requirements that the submitted 
work is original and has not been published elsewhere in 
any language. 

Data availability statement 
All data that support the findings of this study are 

included within the article (and any supplementary files). 

Conflict of interest 

The authors declare no potential conflict of interest. 

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S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

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Appendix I 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
(a) 

  
(b) 

  
(c) 

 
Figure 1. Fluctuations of flame length and width differences with time (2000 frames in 5 seconds) for 

methane and airflow rates of 0.200 and 3 slpm under three swirl numbers: (a) 30°; (b) 35°; (c) 40°. 
 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

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(a) 

 
(b) 

 
Figure 2. (a) Ldiff,mean and (b) Wdiff,mean as a function of swirl number at three fuel flow rates of 0.100, 

0.150, and 0.200 slpm at the airflow rate of 3 slpm 
 

 

 

 



S. Sheykhbaglou/Future Energy                                                                                        February 2023| Volume 02 | Issue 01 | Pages 27-37 

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(a) 

 

(b) 

 

(c) 
 

Figure 3. Flame pulsating displacements in terms of (a) center of gravity, (b) length, and (c) width 
as a function of swirl number at three fuel flow rates of 0.100, 0.150, and 0.200 slpm and at the 

airflow rate of 3 slpm 
 


