DOI: 10.3303/CET24112037 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 21 April 2024; Revised: 14 May 2024; Accepted: 15 July 2024 
Please cite this article as: Ab Aziz N.S., Md. Kasmani R., Rosli N.R., 2024, Correlation of Projected Flame Height for Impinging Horizontal Jet 
Flames, Chemical Engineering Transactions, 112, 217-222  DOI:10.3303/CET24112037 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 112, 2024 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Selena Sironi, Laura Capelli 

Copyright © 2024, AIDIC Servizi S.r.l. 
ISBN 979-12-81206-13-7; ISSN 2283-9216 

Correlation of Projected Flame Height for Impinging 

Horizontal Jet Flames 

Nur Shahidah Ab Aziza,*, Rafiziana Md. Kasmanib, Nor Roslina Roslia 

a School of Chemical Engineering, College of Engineering, Universiti Teknologi MARA, Malaysia 
bDepartment of Energy Engineering,  Faculty of Chemical and Energy Engineering, Universiti Teknologi Malaysia, Malaysia 

 shahidah_aziz@uitm.edu.my 

Horizontal jet flame is said to be among the most dangerous types of fire considering a possible impingement 

effect on nearby facilities. Numerous studies have been conducted and assessed for geometrical flame features 

of jet flames as it imposed dangers where nearby equipment is included. However, data on flame height are 

often missing considering the effects may be deteriorative in the presence of nearby equipment. This study was 

carried out by using propane as fuel and the jet fire was released from a circular nozzle (diameter of 7.15 mm 

and 9.8 mm). The purpose is to determine a suitable correlation to be used to predict the flame extension length 

in the case of an impingement scenario. A review of the literature revealed that existing correlations are 

inapplicable to impinging jet fires. This study offers a better correlation which used elliptical flame shape 

assumption as a basis. A new correlation was suggested based on the experimental condition which is  

𝐻𝑝

𝑑
~31.4 [

[
1

9
𝐿𝑝−𝑓𝑟𝑒𝑒

3−(
1

3
𝐷3𝑙𝑛

𝐿𝑝−𝑓𝑟𝑒𝑒

𝐷
+

1

9
𝐷3)]𝑢

1

9
𝐿𝑝−𝑓𝑟𝑒

3√𝑔𝐷
]

1/2

. 

1. Introduction 

Aging gas pipeline installation for energy transportation is one of the main concerns in structural integrity. Any 

corrosion of the pipeline surface and external impact may cause an unintended release of high-pressure 

transported material and a sudden catch with an ignition source could result in jet fire. The jet flame 

characteristics including flame geometrical features, temperature profile, and radiant heat flux have been 

investigated for decades. In earlier research, the vertical displacement (projected flame height) of a horizontal 

jet flame was not always taken into account. The projected flame height was measured vertically from the nozzle 

to the farthest point that could be seen as shown in Figure 2. 

 

 Figure 1 Projected flame height of horizontal jet flames 

It was reported that with a known projected flame height data of free jet fire release, one could utilise it to 

estimate the likelihood of impingement area for any nearby plant installations (Ramirez-Camacho, Pastor, Casal, 

Amaya-Gomez, & Munoz-Giraldo, 2015). The initial work of Smith, Periasamy, Baird, and Gollahalli (2006) 

computed the flame dimension, including the flame height, using the image that was recorded to determine the 

vertical displacement. The profile values of velocity and mixture characteristics decrease with the jet distance 

Hp 

217



as the jet exits the nozzle. As a result of these reductions, buoyancy forces as well as other elements such as 

regional temperature and concentration differences began to predominate (Winters, 2009). The equations that 

are based on experimental observation for flame height estimation are then further explored by other authors 

that indicate parameters such as the exit diameter, ambient and fuel density, flame exit velocity and heat release 

rate are among the parameters quantified (Changchun et al., 2019; Ekoto, Ruggles, Creitz, & Li, 2014; Fang, 

Zhang, & Hu, 2023; Kim, Yang, Kim, & Won, 2009; Liu, Delichatsios, & Hu, 2019; Vijayan, Sajeevan, Thampi, 

& Palacios, 2024; Zhou et al., 2020). It is also revealed that the same parameters hold an important role in the 

flame-impinging scenario with the addition of nozzle-object separation distance (Wang et al., 2023). In addition, 

the flame morphology was analyzed in terms of receiving heat load and thermal stress over the impacted object. 

This part is however out of the scope of this paper. This study focuses on the projected flame height as 

influenced by variations in the release rate and separation distance of nozzle-impinged objects.  A series of 

experiments with fuel jet velocities ranging from 17 to 42 m/s were carried out using propane as fuel released 

from a circular nozzle with diameter of 9.8 mm and 7.15 mm in quiescent atmospheric conditions to analyse the 

flame height. 

2. Methodology 

2.1 Experimental facility  

A pressurized gas supply consisting of propane was connected through a flexible high-pressure hose to a 10-

inch diameter pipe, where the gas is temporarily stored upon release and lit. The gas released was controlled 

using a mass-flow controller (Alicat MCR-500) installed together with a solenoid valve and a check valve to 

prevent gas backflow. The nozzle used was circular with a diameter of 9.8 mm and 7.15 mm. All instrumentation 

and measurement apparatus were checked and connected to the data acquisition system (NI 9213 with 16-

Channel ±78 mV, 24 Bit and 75 S/s aggregate was plugged into cDAQ-9178 chassis) upon the gas release. 

The data were acquired through LabVIEW Signal Express at 1s of sampling interval. A total of 24 tests were 

conducted at six different release conditions. Each test was repeated at least four times to ensure data 

uniformity. An anemometer was utilized to record the atmospheric conditions data. A schematic diagram of the 

experimental apparatus can be found in Ab Aziz and Md. Kasmani (2022). 

2.2 Image processing and data fitting 

Geometrical flame features that were observed in this study were the projected height (Hp).  The video was 

recorded using the Nikon D90 SLR camera featuring a CMOS image sensor with 1,280 x 720 resolutions. The 

lens used, the AF-S DX NIKKOR 18-105mm f/3.5-5.6G ED VR, was pre-processed using MATLAB Image 

Processing Toolbox. The method of image analysis was simplified as follows; (1) Videos were rendered to 

100fps (2) a hundred images for each test run were selected to be analyzed (3) Each image was processed 

using MATLAB Image Processing Toolbox in which raw RGB image was converted to grayscale image and 

adjusted to reduce the intra-class variance of grayscale image (4) Local thresholding method was used to 

convert the grayscale image to a binary image (5) The flame edge was determined using Sobel edge detection 

method (7) the flame image were combined and intermittency method was used where flame height were 

defined at the probability of 0.5 based on appearance probability contour (Laboureur, Gopalaswami, Zhang, Liu, 

& Mannan, 2016; Liu et al., 2019). Meanwhile, the regression fitting was used to observe the relationship 

between the y and x-axis factors. 

3. Results and Discussion 

Figure 2 shows the measured flame height at various strain rates (ue/d). The evolution of flame height can be 

observed in two categories, free jet fire release (see Figure 2a) where no obstacle was present downstream of 

the jet release, and impinging jet release (see Figure 2b) where the impinging area was the head of the 

cylindrical vessel. It can be seen that the flame height increased as the release rate increased for free jet fire 

release (JFF) until it reached a point of strain rate where it was observed the flame height was decreased. The 

results for JFF are in good consistent with the previous findings by Changchun et al. (2019); Liu et al. (2019); 

Zhou et al. (2020) as presented in Figure 2a. In contrast to the previous scenario, impingement conditions 

resulted in a continuous increase in flame height with rising release velocity. The flame turned radially upwards 

and downward when it touched the surface. The releasing momentum sets the length of the radial displacement. 

As a result, the flame height increases as the release momentum increases, which is consistent with prior 

research on jet impingement by Xiaochun Zhang et al. (2017). It can be observed too that the projected flame 

height for the impingement scenario is higher than the free jet flame (see data for JFF and JFI_9.8a). The 

explanation is as follows: The free jet fire scenario (JFF) experiences higher air entrainment compared to 

impinging jet (JFI_9.8a), which is consistent with findings from a prior study of impinging jet on the inclined 

218



tunnel (Kong, Wang, Cong, Liu, & Zhu, 2019). Other studies of air entrainment with sidewalls near the jet flame 

have also validated that air entrainment is inversely proportional to flame geometry (Tao, Shen, & Zong, 2016). 

For the jet fire impingement scenario, the presence of an object downstream reduces air entrainment, resulting 

in a higher flame height. 

  
(a)  (b) 

Figure 2 Dimensionless flame height against strain rate for (a) free jet fire release (JFF) plotted with previous 

findings ofLiu et al. (2019),Changchun et al. (2019);Zhou et al. (2020) and (b) impinging jet release (JFI) 

The binary images that are shown in Figure 3 (a), (b), and (c) were created from the pre-processed images 

using the MATLAB Image Processing Toolbox. It is evident that, despite the similarity in release flow rate across 

all scenarios, variations in release diameter and nozzle to target distance have a notable impact on the resulting 

flame pattern and dimensions. 

   
(a) (b) (c) 

Figure 3 Pre-processed image of (a) JFI_9.8a and (b) JFI_7.15 (c) JFI_9.8b at similar release flowrate 

The measurement of the flame extension length as it reaches the impingement point was determined by 

quantifying the amount of unburned fuel remaining after impingement, as well as the quantity of unburned fuel 

while moving along the impinging surface. Thus, for an impinging jet, a relationship between the height of the 

flame and the amount of fuel left unburned after the impingement point is represented in Eq (1) (Xiaochun Zhang 

et al., 2017); 

𝐻𝑝

𝐷
~𝑓𝑐𝑛 (

𝑉𝑓𝑢

𝑉𝑓
�̇�) 

(1) 

where Hp is the projected flame height, D is the nozzle-to-object separation distance, Vfu is the flame volume 

portion intercepted by the impinging surface in m3, and Vf is the volume of the free flame in m3. For a horizontal 

and inclined surface, the region where the flame is intercepted, an ideal geometry such as cylinder and ellipse 

was used to represent the flame volume (Qiu, Hu, Chen, & Carvel, 2018; Xiaolei Zhang, Hu, Delichatsios, & 

Zhang, 2019; Xiaochun Zhang, Hu, Zhu, Zhang, & Yang, 2014; Xiaochun Zhang et al., 2017). The following Eq 

(2) and (3) correlate the upward flame height after impingement points for cylindrical and elliptical flame shapes, 

respectively. 

𝐻𝑝

𝑑
~

1

2
[
(𝐿𝑝−𝑓𝑟𝑒𝑒 − 𝐷)𝑢𝑒

𝐿𝑝−𝑓𝑟𝑒𝑒√𝑔𝐷
]

1/2

 (2) 

ue/d ue/d 

H
p
/d

 

H
p
/d

 

219



𝐻𝑝

𝑑
~ [

[
1
9

𝐿𝑝−𝑓𝑟𝑒𝑒
3 − (

1
3

𝐷3𝑙𝑛
𝐿𝑝−𝑓𝑟𝑒𝑒

𝐷
+

1
9

𝐷3)] 𝑢𝑒

1
9

𝐿𝑝−𝑓𝑟𝑒𝑒
3√𝑔𝐷

]

1/2

 (3) 

From the study of Xiaochun Zhang, Hu, Zhu, et al. (2014), the cylindrical flame shape was an ideal assumption 

for a vertical jet impingement on a horizontal ceiling with a wider range of ([(𝐿𝑡 − 𝐷)/𝑑]) from 0 to 14.5 as 

compared to the study  done by You and Faeth (1979) which ranges between 0 to 5.8. In this study, a higher 

range of ([(𝐿𝑡 − 𝐷)/𝑑]) was used to test and extend the previous correlation applicability for larger-scale jet 

impingement release. The range used is between 20 to 110. Higher ([(𝐿𝑡 − 𝐷)/𝑑]) indicates a larger scale of 

impingement release. Based on Figure 4, a comparison was done to fit data in this study with the Eq (2) and Eq 

(3). From both figures, the elliptical flame shape assumption gives a better fit with an R2 value of 0.97. However, 

the data of the release nozzle of 7.15 mm (JFI_7.15) fit the previous correlation of Xiaochun Zhang, Hu, Zhang, 

Yang, and Wang (2014). This is due to the smaller nozzle producing a thinner flame volume visibility, and this 

will influence the flame height (refer to Figure 3). 

  
(a) (b) 

Figure 4 Dimensionless association between the upward flame height and the ideal flame shape assumption 

(a) cylindrical and (b) elliptical on an impinged surface. 

From Figure 4, a new constant of 31.4 was introduced to give a better fit on the influence of impingement to the 

flame height using an elliptical flame shape  as follows; 

𝐻𝑝

𝑑
~31.4 [

[
1
9

𝐿𝑝−𝑓𝑟𝑒𝑒
3 − (

1
3

𝐷3𝑙𝑛
𝐿𝑝−𝑓𝑟𝑒𝑒

𝐷
+

1
9

𝐷3)] 𝑢

1
9

𝐿𝑝−𝑓𝑟𝑒𝑒
3√𝑔𝐷

]

1/2

 (4) 

It can be said that the flame impingement gave an elliptical flame shape instead of cylindrical and thus, Eq (4) 

could be used to estimate the projected flame height of the impinging jet flame. Further data fitting was done by 

using theoretical assumption as has been done by other previous studies of Kim et al. (2009); Liu et al. (2019) 

by using the following model 

𝑡𝑎𝑛 𝜃 =
1

√
𝜌0

𝜌∞
𝐹𝑟∗

[(
𝑠

𝑑
) + 2𝛽 (

𝑠

𝑑
)

2

+
4

3
𝛽2 (

𝑠

𝑑
)

3

] 
(5) 

Where the tilt angle, 𝜃 at designated coordinates, s were dependent on the exit diameter, d, and modified Froude 

number, Fr*. Thus, the data in this study were also fitted in the Eq (5) and the observation for free jet fire release 

can be seen in Figure 5a while for impingement scenario can be seen in Figure 5b.  

Xcylinder Xellipse 

H
p
/d

 

H
p
/d

 

220



  
(a) (b) 

Figure 5 Graph of predicted against measured value of Hp for (a) free jet fire release (b) impinging jet release. 

In the case of a free jet fire release, it is evident that the flame integral model's theoretical assumption is suitable 

for predicting Hp, as evidenced by an R2 value of 0.97. Conversely, in the scenario of impingement, the R2 value 

is 0.86. In the impinging scenario, the Hp data were compared to the predictions obtained from Eq (4), resulting 

in a higher level of agreement with an R2 value of 0.98 as shown in Figure 6. The aforementioned observation 

provides additional support for the utilization of Eq (4) for the prediction of the flame extension length. In the 

present study, the term "flame height" is employed instead of the conventional term "flame extension length" 

due to variations in orientation compared to previous investigations.  

 

Figure 6 Comparison of predicted and measured values of Hp by employing elliptical flame shape assumption 

for impinging jet fire. 

4. Conclusion 

This paper presents the experimental results that elucidate the fuel velocity and nozzle exit size on the 

anticipated flame height Hp, it was found that the projection was inconsistent or discordant with the actual value. 

Experimental data indicated an initial increase in Hp value followed by a subsequent decline. When the 

separation gap was smaller, the Hp for an impinging scenario was larger. The quantity of unburned fuel would 

influence the Hp since the initial momentum of the discharged fuel is conserved. It is evident that with a greater 

release rate, there is more unburned fuel at the moment of impingement, which results in higher Hp. The Hp 

equation should be utilised with caution because this condition could not be seen using Hp prediction. The 

laminar oscillation field, followed by the turbulent and momentum-dominated zones, interleaves the flow regimes 

as the nozzle exit velocity rises. As proposed, the Eq (4) can be used to correlate the predicted flame height for 

an impingement situation utilizing an elliptical flame shape.  

Acknowledgments 

The authors gratefully acknowledge the financial support provided by the College of Engineering, UiTM.  

 

(Hp)measured (Hp)measured 

(Hp)measured 

(H
p
) p

re
d
ic

te
d

 

(H
p
) p

re
d
ic

te
d

 

(H
p
) p

re
d
ic

te
d

 

221



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	Correlation of Projected Flame Height for Impinging Horizontal Jet Flames