ABSTRACT 
 
 
 
 
Title of Document: FORWARD HEATING IN WIND-DRIVEN 
FLAMES 
  
 Wei Tang, Doctor of Philosophy, 2017 
  
Directed By: Associate Professor Michael J. Gollner 
Department of Fire Protection Engineering 
 
 
 
Wildland fires pose a significant threat to the environment and society at large. The large 
number of unknowns makes wildland fire predictions much harder than those typically 
encountered within the built environment, especially under the influence of wind. The 
spread rate of a fire depends largely on forward heating from the flame to unburnt fuels, 
however few measurements of heat fluxes from wind-driven flames exist. In wildland fires, 
the intermittent nature of flame is also thought to be uniquely important to the flame spread 
process. In this work, both averaged and time-dependent aspects of the flame are studied, 
including the total heat flux distribution on the downstream surface, flame extension and 
attachment, and frequencies of intermittent flame movements. Correlations of these 
properties, dependent on both fire size and ambient wind, will provide a means to describe 
the thermal exposure during fuel heating and ignition in wind-driven wildland fires. This 
data will provide a basis for both understanding and model development for wildland fire 
spread as well as provide a dataset for future numerical validation of computational fluid 
dynamic models.  
  
Detailed laboratory experiments were performed on line fires under forced flow with a 
variety of ambient wind velocities and fire sizes. Local heat fluxes were measured onto a 
nearly adiabatic surface downstream of a line burner. The downstream heat flux 
distribution was correlated as a piecewise function with the local Richardson number in 
two regimes, the first with higher heat fluxes, where the flame remained attached the 
downstream surface and the second with a steeper decay of heat fluxes. This observation 
was further corroborated by analysis of side-view images of the flame, which showed the 
attachment location was linearly correlated with the location where the Rix equaled unity.  
The flame forward pulsation frequency and the flame-fuel contact frequency were also 
extracted. Scaling analysis indicates that they can be well correlated with Fr, Q*, and local 
Rix respectively. The location of maximum pulsation frequency, xmax, for each burner/wind 
configuration was also obtained using the VITA technique. Further study indicates that xmax 
can be well estimated using mean flame properties. 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
FORWARD HEATING IN WIND-DRIVEN FLAMES 
 
 
 
By 
 
 
Wei Tang 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2017 
 
 
 
 
 
 
 
 
 
 
  Advisory Committee: 
Professor Michael J. Gollner, Chair 
Professor Elaine Oran, Dean’s Representative 
Professor Arnaud C. Trouvé  
Professor Peter B. Sunderland 
Professor Andre W. Marshall 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
© Copyright by 
Wei Tang 
2017 
 
 
 
 
 
 
 
 
 
ii 
 
 
 
DEDICATONS  
 
 
 
To my girlfriend Shaoli Lin, and my family, who keeps me motivated and is always there 
for me.  
iii 
 
ACKNOWLEDGEMENTS 
 
Three years ago, when I first set foot on to the United States and came to the University of 
Maryland, I did not know that three years would pass so fast. But I have always been so 
lucky. Throughout all these years studying and doing research at universities, I have met 
the most dedicated advisors and the best colleagues and the most wonderful friends in the 
world, without whose help and guidance, this dissertation would never be possible. 
First and foremost, I need to thank my advisor, Dr. Michael J. Gollner, who I think is not 
just one of the best professors, but one of the best person I have ever known. He impressed 
me with his dedicated work ethic, during this past 3 years, he has always been there 
throughout any difficulty I have met in the research. He has showed tremendous patience, 
even at the times when I felt very frustrated and had no clue how to proceed. It's been an 
absolute pleasure and honor to work with him and there is just so much to learn from him 
that 3 years seems not enough. Michael will remain as my mentor and advisor for life. I 
am forever thankful to all he has done to help and support me during my time at the 
University of Maryland.  
I also would like to thank my committee members, Dr. Elaine S. Oran, who is serving as 
the Dean’s Representative. Dr. Oran is such a knowledgeable and such a kind person that 
almost all the Ph.D. students in the Department of Fire Protection Engineering will invite 
her to be their committee member. Sorry Dr. Oran, there’s just so much work for you, 
because we love you so much.  
I also would like to thank Dr. Arnaud Trouve for all his help and support during the course 
of my Ph.D. Dr. Trouve has always provided some of the best advice in terms of doing a 
iv 
 
detailed experimental work. His critical thinking from a modeler’s perspective has been a 
great addition to this research work. 
Thanks are also due to Dr. Sunderland and Dr. Marshall, for both serving on my dissertation 
committee and being so insightful and helpful during my dissertation proposal. Thank you 
so much for sparing your time reading and reviewing this manuscript. It’s been just great 
to work with some of the leading experts in Fire Protection Engineering. 
My colleagues and friends at the FPE department have made my life here so meaningful 
and colorful that I will never forget. Colin Miller helped me so much in my research and 
experiments that sometimes his own work was delayed. He is such a cool and nice guy that 
I have never seen him get angry at anyone or anything. He bought me my first beer in the 
U.S, and I brought him some little gifts when I return from China. We have worked together 
and gone to the gym together, he has been my best friend to date. My interactions with 
Ajay Singh, Daniel Gorham, Haiqing Guo, Xuan Liu, Zhao Zhao, Salman Verma, Cong 
Zhang, Yan Ding, Xiaoyue Pi, Nate May, Raquel Hakes, Sara Caton, Ali Tohidi, Pietro 
Maisto, Sriram Bharath, Lin Jiang, Kun Zhao, Yu Hu, Qiong Liu, Xinjie Huang, Dennis 
Kim, Zhengyang Wang, Wuquan Cui, Eric Link, Matthew Weston-Dawkes have been very 
joyful and I am forever grateful to all the help you have given me. 
Also, special thanks to the other professors in our department, Dr. James Milke, Dr. 
Stanislav Stoliarov, and our department’s coordinators and technicians, Mary Lou, Sharon 
Hodgson, Olga Zeller, Christine O'Brien for all your help, you made our research much 
easier. 
v 
 
I owe my heaviest debt to my family, my father, my mother, my sister, and my brother, 
who have always unwaveringly supported me no matter what, and who have always 
accompanied me throughout my life. I am so grateful to the help and trust you have given 
me. 
Last but not least, I want to thank Shaoli Lin for showing up in my life and being my 
girlfriend and my love. Thank you for always standing by my side and adding all those 
“flavors” to our life. 
Financial support for this work was provided by the USDA Forest Service Missoula Fire 
Sciences Laboratory and National Fire Decision Support Center under collaborative 
agreement 13-CS-11221637-124 and the National Science Foundation under Grants no. 
1554026 and 1331615. 
 
 
 
 
 
 
 
 
vi 
 
Table of Contents 
List of figures ............................................................................................................... ix 
List of tables ............................................................................................................... xiii 
Nomenclature ............................................................................................................. xiv 
Chapter 1: Introduction ................................................................................................. 1 
1.1 Wildland Fire Spread Modeling.......................................................................... 1 
1.2 The Structure of Wild-Blown Flames ................................................................. 3 
1.3 Outline of the Dissertation .................................................................................. 4 
Chapter 2: Literature Review ........................................................................................ 6 
2.1 Wildland Fire Spread Modeling.......................................................................... 6 
2.2 Flame Dynamics ................................................................................................. 8 
    2.3 Heat Flux Distribution ...................................................................................... 10 
2.4 Flame Pulsations and Movement ...................................................................... 14 
2.5 Flame Extension and Flame Attachment .......................................................... 16 
2.6 Summary ........................................................................................................... 19 
Chapter 3: Experimental Facility and Instrumentation ............................................... 20 
3.1 Wind Tunnel Setup ........................................................................................... 20 
3.2 Gas Burner ........................................................................................................ 22 
3.3 Velocity Characterization ................................................................................. 22 
3.4 Temperature Measurements and Traverse System ........................................... 27 
3.5 Total Heat Flux Gauge ...................................................................................... 28 
vii 
 
3.6 Radiometer ........................................................................................................ 30 
3.7 Digital Camera .................................................................................................. 31 
3.8 Data Acquisition Systems ................................................................................. 31 
3.9 Experimental Conditions .................................................................................. 32 
Chapter 4: Heat Flux Analysis .................................................................................... 37 
4.1 Total Heat Flux Distribution ............................................................................. 37 
4.2 Richardson Number Analysis ........................................................................... 42 
4.3 Non-dimensional Heat Flux and Correlations .................................................. 49 
4.4 Discussions and Conclusion ............................................................................. 55 
Chapter 5: Flame Fluctuations and Attachment Length ............................................. 57 
5.1 Measurement Methodology .............................................................................. 57 
5.2 Maximum Flame Pulsation Location ................................................................ 62 
5.3 Flame Attachment Length................................................................................. 70 
5.4 Discussions and Conclusion ............................................................................. 74 
Chapter 6: Flame Intermittent Frequencies ................................................................ 76 
6.1 Flame Forward Pulsation Frequency ................................................................ 78 
6.2 Flame-fuel Contact Frequency .......................................................................... 84 
6.3 Discussions and Conclusion ............................................................................. 91 
Chapter 7: Conclusions ............................................................................................... 94 
Chapter 8: Future Work .............................................................................................. 96 
Published Journal/Conference articles ........................................................................ 98 
viii 
 
Appendix A: Convective and radiative heat flux ...................................................... 100 
Bibliography ............................................................................................................. 104 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ix 
 
List of Figures 
 
Figure 1. Diagram of a wind-blown flame illustrating regions existing along the surface 
as well as movements that occur within the flame. ...................................................... 3 
Figure 2. Wildland fire triangle (fuel, weather, and topography) and a representative 
schematic of fire propagation [14]. ............................................................................... 7 
Figure 3. An illustration of flame dynamics and the resulting instabilities from 
experiments performed by Finney et al. [10] are shown. A number of both streamwise 
and spanwise instabilities are shown to form which force flames and hot gases through 
“troughs” in the flame zone to intermittently heat unburned fuels ahead of the flame 
front. .............................................................................................................................. 9 
Figure 4. Comparison of wind-driven fire behaviors with that under quiescent conditions 
(from Rothermel [16-18]). .......................................................................................... 10 
Figure 5. Photo of the wind tunnel apparatus ............................................................. 21 
Figure 6. Schematic including dimensions of the wind tunnel [52] ........................... 21 
Figure 7.  Hot wire anemometer used in his study [78 dantec]. ................................. 23 
Figure 8. Measurement locations for wind profile measurements. ............................. 24 
Figure 9.  Low velocity (1.12 m/s) profile with height over the surface. ................... 25 
Figure 10. High velocity (2.15 m/s) profile with height over the surface. ................. 25 
Figure 11. Turbulence intensity profile with height and downstream distance over the 
surface (1.12 m/s, low wind case) ............................................................................... 26 
Figure 12. Turbulence intensity profile with height and downstream distance over the 
surface (2.15 m/s, high wind case).............................................................................. 27 
Figure 13. Thermocouple and mount used in temperature measurements [79]. ......... 28 
x 
 
Figure 14. The Vatell total heat flux gauge and amplifier used in experiments [80]. 29 
Figure 15.  The calibration used for the Vatelle total heat flux gauge in the cone 
calorimeter. ................................................................................................................. 29 
Figure 16. Schematic of the Medtherm radiometer used from the manufacturer [81].31 
Figure 17. National Instrument data acquisition systems used in the study [82] ....... 32 
Figure 18.  Experimental setup downstream of the tunnel outlet ............................... 34 
Figure 19. Heat flux data taken on 11 cm downstream averaged for 6.3 kW, 9.5 kW fire 
size, 1.14 m/s, 1.62 m/s wind speed scenarios for a period of 150 s. ......................... 38 
Figure 20. Comparison of heat flux profiles for different wind velocities and fire sizes39 
Figure 21. Experimental photos showing different flame shapes under wind ............ 40 
Figure 22. Heat flux distribution under low wind velocities ...................................... 42 
Figure 23. Vertical temperature profile taken 16.5 cm downstream of the trailing edge of 
the burner, with a fire size of 9.5 kW and a wind velocity of 1.91 m/s ...................... 44 
Figure 24. Heat flux distribution under high winds (1.62 and 1.91 m/s) .................... 46 
Figure 25. Heat flux distribution under high winds (2.14 and 2.45 m/s) .................... 47 
Figure 26. Local Rix number under high winds (1.62 and 1.91 m/s) .......................... 48 
Figure 27. Local Rix number under high winds (2.14 and 2.45 m/s) .......................... 49 
Figure 28. Local Rix number with local heat flux (9.5 kW, 1.91 m/s) ........................ 51 
Figure 29. Local Rix number with local heat flux (7.9 kW, 2.14 m/s) ........................ 52 
Figure 30. Comparison of dimensionless downstream location at Rix =1 with the peak 
heat flux value ............................................................................................................. 53 
Figure 31. Dimensionless local total heat flux with local Rix. .................................... 55 
xi 
 
Figure 32.  Flame location between two time steps in a forced flow experiment. The 
flame attachment location (xa) is measured from the downstream edge of the burner to 
edge of the flame within the attachment region. ......................................................... 58 
Figure 33. Flame image processing based on luminosity ........................................... 59 
Figure 34. A side-view of mean flame properties including the flame height Hf, flame 
length Lf, maximum frequency location xmax, mean flame attachment length xa, horizontal 
flame length xf and flame tilt angle 𝜃 ......................................................................... 60 
Figure 35. Fluctuating flame extension with time ...................................................... 61 
Figure 36.  Probability Density Function (PDF) of normalized flame position ......... 62 
Figure 37.  Horizontal flame length versus the location of maximum frequency, xmax65 
Figure 38.  Histograms of flame extension length, xa for a 25×5 cm
2 burner. ........... 66 
Figure 39.  Probability of normalized flame attachment length, 
aa xx / for different fire 
sizes and wind velocities. ............................................................................................ 68 
Figure 40.  The variance, σ2 of the normalized flame attachment length, 
aa xx / , from 
Gaussian curve fits versus Fr2/3/Q*. ............................................................................ 70 
Figure 41. Averaged flame image from experimental pictures .................................. 71 
Figure 42. Averaged flame images under different wind velocities show the attachment 
length (Lattach) of the flame to the surface with scales. Regions between the two blue 
dashed lines represent the burner depth, while the red solid lines, which are 5 mm in 
height, represent the flame attachment length measured along the downstream surface.
..................................................................................................................................... 72 
Figure 43. 

1xRi
L  with dimensionless flame attachment length 

attachL where error bars 
shown represents variation in the chosen threshold heights ....................................... 74 
xii 
 
Figure 44.  Flame location between two time steps in a forced flow experiment ...... 78 
Figure 45.  Fluctuating heat flux signals over time .................................................... 79 
Figure 46.  Level-crossing frequency and Probability Density Function (PDF) shows the 
flame locations on the downstream surface (7.9 kW, 2.45 m/s) ................................. 80 
Figure 47.  Forward pulsation frequency with different wind velocities and fire size 81 
Figure 48.  Flame forward pulsation frequencies are found to scale with Fr1/2/Q*1/4 . 84 
Figure 49.  Heat flux raw data at 11 cm, with 9.5 kW fire size, 1.91 m/s wind velocity, 
and frequency spectrum obtained from FFT ............................................................... 86 
Figure 50. Comparison of frequency obtained from the FFT for different wind velocities.
..................................................................................................................................... 86 
Figure 51. Local flame fuel contact frequency for 7.9 kW under different wind velocities
..................................................................................................................................... 87 
Figure 52. Non-dimensional frequency 

Cf  versus local Rix ..................................... 91 
Figure 53. Temperature distribution on the downstream board with fire size 7.9 kW, wind 
velocity 2.14 m/s ....................................................................................................... 101 
Figure 54. Interpolation of the temperatures measured above the downstream surface102 
Figure 55. Temperature gradient at the surface ........................................................ 103 
 
  
xiii 
 
 
List of tables 
Table 1. Vatell heat flux gauge specifications from the manufacturer [80]. .............. 30 
Table 2. Experimental conditions (I) .......................................................................... 35 
Table 3. Experimental conditions (II) ......................................................................... 36 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
xiv 
 
Nomenclature 
f : Frequency (Hz) 
Ff : Flame forward pulsation frequency (Hz) 
Cf  : Flame-fuel contact frequency (Hz) 

Cf : Non-dimensional flame-fuel contact frequency (-) 
D: Pool fire diameter (m) 
Fr: Dimensionless Froude number (-) 
g: Gravitational acceleration (m/s2) 
St: Dimensionless Strouhal number (-) 
px : Burning (pyrolysis) region (m) 
 xq f  : Heat flux distribution at x location (kW/m2) 
fx : Flame region (m) 
a: Constant in equation (5) (-) 
n: Constant in equation (5) (-) 
A, B, C: Constants in equation 32 (-) 
cp: Specific heat (kJ/kgK) 
Hf : Flame height (cm) 
L: Burner characteristic length/hydraulic diameter (m) 
Lf : Flame length (cm) 
Q : Heat release rate (kW) 
Q : Dimensionless heat release rate (-) 
0T : Ambient temperature (K) 
xv 
 
fT : Flame temperature rise over ambient (K) 
windU : Wind velocity (ms-1) 
u : Characteristic fuel velocity based on mass loss rate (ms-1) 
V: Buoyant flame velocity (ms-1) 
xa: Flame extension location (cm) 
ax : Average flame extension location (cm) 
xf : Horizontal flame length (cm) 
xmax: Location of maximum frequency (cm) 
θ: Flame tilt angle (deg) 
σ2: Variance of flame extension (-) 
0 : Air density (kg/m3) 
L: Downstream location (m) 
L*: Dimensionless downstream location (-) 
L : Characteristic length scale (m) 
S: Surface area of burner (m2) 
P: Perimeter of the burner (m) 
Grx: Local Grashof number (-) 
 : Thermal expansion coefficient (1/K) 
Th: Hot fluid temperature (K) 
T : Ambient temperature (K) 
 : Viscosity (m2/s) 
Rex: Local Reynolds number (-) 
xvi 
 
b: Constant chosen as 2 in equation (12) (-) 
Rix: Local Richardson number (-) 
Tf : Flame temperature (K) 

1xRi
L : Dimensionless location where Rix=1 (-) 

peakL : Dimensionless location where peak heat flux is observed (-) 
*
fq : Dimensionless heat flux (-) 
A: Atwood number (-) 
a : Density of air (kg/m
2) 
pc : Specific heat capacity of air (J/kgK) 
cflq ,  : Convective heat flux (kW/m2) 
rflq ,  : Radiative heat flux (kW/m2) 
rrsq ,  : Re-radiation heat flux (kW/m2) 
wk : Conductivity (W/m•K) 
 : Stephan-Boltzmann constant (kgs-3K-4) 
DH: Hydraulic diameter (m) 
S: Area of the burner top surface (m2) 
P: Perimeter of the burner top surface (m) 
Lattach: Flame attachment length on the downstream surface (m) 

attachL : Dimensionless flame attachment length (-) 
h: Convective heat transfer coefficient (W/(m2K)) 
T’: Temperature gradient (K/m) 
m  : Mass burning rate (kg/m2s) 
xvii 
 
u : Non-dimensional wind velocity (-) 
VITA: Variable-Interval-Time-Average  
PDF: Probability Density Function 
IR : Reaction intensity 
w : The wind coefficient 
s : The slope coefficient 
b : Oven-dried bulk density 
 : Effective heating number 
igQ : Heat of pre-ignition 
 
 
 
 
 
 
 
 
 
 
 
 
 
1 
 
Chapter 1: Introduction 
Despite many years of study, mankind’s understanding of wildland fires is still incredibly 
limited. The large scale and destructive nature of these fires makes them both important 
for society and incredibly difficult to study. Generally, wildland fires can occur or progress 
between two stages, from desirable natural fires that have occurred over the landscape for 
millennia and second, unwanted wildland fire disasters, wildfires. Wildfires as a disaster 
are a growing concern around the world. They pose a significant threat not only to the 
natural landscape, but also to surrounding environments and populations via smoke and 
other effluents, downstream effects such as erosion and floods, and the destruction of 
properties and threat to life in the Wildland-Urban Interface (WUI) [1, 2]. Many factors, 
most importantly deficient fuel management practices, the movement of persons into the 
WUI, and a changing climate have caused an explosive growth in the budget for wildland 
fire suppression in the United States. Unfortunately, these factors are predicted to get worse 
over the coming decades, necessitating research that may mitigate future disasters [3]. 
1.1 Wildland Fire Spread Modeling 
Accurately modelling the spread of wildland fires has become a key goal for the fire 
research community [4]. Wildland fire modeling is now used for a number of essential 
purposes including fire risk mapping, fire management, suppression planning and, in a 
limited sense, active fire suppression. In the future, accurate predictions of ongoing 
wildfires will be an essential source of data for fighting fires. It will be possible, for 
instance, to calculate what the chance of a fire spreading towards a community is, 
predicting the largest possible extent, when and where it might endanger firefighters, better 
predict the most cost-effective prescribed burning locations and improve fire suppression 
2 
 
and evacuation strategies. While current models can do some of this, they are limited by 
inaccuracies both in the model and input data [5, 6]. While there are many efforts under 
way to improve input data, future predictions in time will remain severely limited if the 
physical model for fire spread is incorrect. 
The dynamics of wind-driven fires, especially those resembling a line fire configuration 
similar to spreading wildland fires have not been well documented, instead focusing on 
their steady or averaged characteristics [7]. While Albini studied the response of a 
spreading fire to a non-steady wind [8, 9], he did not account for fluctuations produced by 
the flame front itself or the effects of these motions on unsteady heating. Recent results by 
Finney and Cohen et al [10, 11] have revealed the influence of intermittent convective 
heating on wildland flame spread due to the small diameter of wildland fuels which are 
incredibly sensitive to rapid convective heating and cooling but have a low response to 
radiation due to a low surface to volume ratio. Despite this recent discovery, no work has 
yet addressed the intermittent effects of heating from wind-blown flames. 
Information on steady and intermittent heating and flame-movement will help us to 
understand how fuel downstream of the flame front will be heated as a function of time 
and thus fill in an important part of the puzzle of how wildland fires spread. The convective 
heating found in previous studies from Finney et al. [4] were hypothesized to appear from 
buoyant instabilities in the fire itself. Similar behavior has been observed in laboratory-
scale fires with steady gas burners [12], indicating this may be a reasonable configuration 
from which to study the intermittent behavior of wind-blown flames. 
 
 
3 
 
1.2 The Structure of Wild-Blown Flames 
 
A detailed look at the structure of wind-blown flames reveals that there are a variety of 
structures and regions which vary in both time-dependent and averaged characteristics. 
Figure 1 shows an image of a wind-blown flame from a stationary burner that at first 
appears attached along the downstream surface, but eventually lifts into a tilted flame. In 
this work, three regions will be defined to describe this region. First, a flame attachment 
region exists where the flame is visibly forced to attach the surface, occurring for some 
distance downstream of the burner since the wind momentum overpowers buoyancy from 
the flame. As the flame moves forward, buoyancy increases in proportion to the wind 
momentum and the flame enters a transitional, “intermittent” region, where the flame 
fluctuates between competition with wind momentum and flame buoyancy. After this 
region, the flame is finally lifted due to the dominant role of buoyancy which grows with 
distance as distribute reactions continue to occur within the flame. 
Forward pulsation
Upward pulsation
Wind 
 
Figure 1. Diagram of a wind-blown flame illustrating regions existing along the surface 
as well as movements that occur within the flame. 
Flame attachment Intermittent Lifted region  
Flame-fuel contact 
4 
 
In the process of the flame moving forward, a two-directional fluctuating behavior is 
anticipated, also indicated on Fig. 1. One is forward pulsation, where the flame 
intermittently flickers forward onto the downstream surface ahead of the flame front. In a 
spreading fire scenario, this may potentially reach more unburnt fuels and heat them, albeit 
for short times. This likely occurs due to a competition between momentum-driven wind 
and a counter-clockwise recirculation zone at the flame front, a buoyant instability similar 
to puffing pool fires, or a combination of the two. The other is intermittent contact, which 
appears most rapid in the region between the attached flame length and the lifted region. 
The up-and-down motion of the flame here is most likely due to a local buoyant instability 
and might subject to change along the downstream distance. Separately measuring these 
two components will help to determine the influence intermittent heating has in each of the 
mentioned regions. Flame forward pulsation and intermittent contact will play a significant 
role in the ignition of unburnt fuels within the flame’s reach in wind-driven fires. 
1.3 Outline of the Dissertation 
In this study, a stationary, non-spreading fire configuration will be used to study wind-
driven fire spread as it allows for a thorough statistical analysis of the flame structure and 
its intermittent behavior. Long-duration experiments provide a large sample size and more 
control over variations in experimental parameters, such as decoupling the heat-release rate 
of the fire from flow conditions, unachievable in spreading fires. The flame zone depth in 
the direction of fire spread can also be carefully adjusted via the size of a burner. 
Experiments are conducted at laboratory scale, where control of the experiments is more 
tractable and they can be taken over long times to develop a statistical view of the flame 
and its movement.  
5 
 
First, total heat flux measurements on a nearly adiabatic surface downstream of a burner 
are used to correlate the heat flux distribution there for a variety of fire sizes and forced air 
flow velocities. The data is evaluated versus a local Richardson number to describe how 
heat fluxes change downstream in both attached and lifted scenarios. Next, a time-
dependent view of the extension of the flame is extracted from side-view images with a 
focus on the flame attachment length. Locations of maximum forward flame pulsation 
frequency are then related to correlations of mean flame properties. A statistical view of 
the flame is also presented, dependent on both wind speed and fire size. Finally, the 
frequency of forward flame pulsations extracted from side-view images of the flame and 
frequencies of flame-fuel contact measured using a high-frequency heat flux gauge on the 
surface are measured and analyzed using previous scaling laws.  
Using this stationary configuration, the intermittent behavior of the flame, including its 
motion and heating to the fuel surface will be quantified. These experiments represent a 
first step toward understanding the behavior of larger (and more complex) spreading 
wildland fires, providing a framework from which to study the movements of larger fires 
in the future.  
 
  
6 
 
Chapter 2: Literature Review 
2.1 Wildland Fire Spread Modeling 
In the wildland fire research community, it’s well known that there are several factors that 
control wildland fire spread, namely the fuel, weather, and topography, shown in Figure 2. 
These three factors are the main forces that have been found to affect wildland fire spread. 
In the 1970’s Rothermel [13] developed a semi-empirical correlation to estimate the 
forward rate-of-spread (ROS) based on laboratory experiments, 
                                               
 
igb
swR
surface
Q
I
ROS

 

1
   ,                                         (1) 
where the ROS is the steady, forward rate of spread of a fire, IR is the reaction intensity,   
the propagating flux ratio, w the wind coefficient, s the slope coefficient, b the oven-
dried bulk density,  the effective heating number, and 
igQ  the heat of pre-ignition. 
Essentially, the numerator describes the amount of heat released by the fire (IR) and how 
much of that is propagated forward to unburned fuels ( ), adjusted by factors for wind and 
slope. The denominator then describes how much heat is required to ignite unburned fuel.  
 
 
 
7 
 
  
Figure 2. Wildland fire triangle (fuel, weather, and topography) and a representative 
schematic of fire propagation [14]. 
While this formulation was a huge leap at the time, it has a number of substantial 
limitations. The model is not perfect, there are many aspects of wildland fire spread that 
have not been incorporated into the model. First and foremost, the model is not entirely 
physically based and relies on correlations at laboratory scale that may or may not scale to 
large scale. For example, the model assumes that the fuels are uniformly distributed, which 
is not often the case in real wildland fires spread. The model also treats flame spread to be 
steady and uniform in one direction only. In reality, fires accelerate and spread laterally 
(flanking spread) as well, however the model ignores all time-dependent effects including 
the natural instabilities of the flame and its interactions with the wind. This model was 
simply a correlation to the observed wildland fire phenomena, and most of the data they 
used came from lab tests and prescribed burning. What we are trying to do in this 
dissertation is to further investigate processes which are incorporated into this model, 
particularly under wind-driven scenarios, so that they can be added into future models for 
wildland fire spread.  
 
8 
 
 
2.2 Flame Dynamics 
Recent studies of spreading fires in the 3×3 m wind tunnel at the Missoula Fire Science 
Laboratory have revealed coherent structures that form in the stream-wise direction of the 
flow as well as span wise fluctuations that propagate to the downstream edge of the flame 
zone contributing to fuel heating [15], shown in Figure 3. The highly spatially-uniform fuel 
beds used in these experiments allowed for the observation of these structures with more 
repeatable results than previous efforts. The results suggest that flame spread in fine fuel 
beds is driven by non-steady convective heating and intermittent flame contact on fuel 
particles. These heating characteristics were measured using micro thermocouple arrays 
and high speed video. The unsteady flame front, however, made it difficult to carefully 
study these properties, such as a statistical analysis of these features which appear 
stochastically in the flow. A technique is therefore needed that could study these new 
instabilities and other general structures of propagating wildfires in a small-scale 
configuration that can be utilized over long times. Because of the intermittent behavior of 
wind-driven fires, the average and time-dependent properties of flame, including the heat 
transfer to the unburnt fuels, flame extension and intermittent pulsation frequencies, will 
also be affected.  
9 
 
 
Figure 3. An illustration of flame dynamics and the resulting instabilities from 
experiments performed by Finney et al. [10] are shown. A number of both stream-wise 
and span-wise instabilities are shown to form which force flames and hot gases through 
“troughs” in the flame zone to intermittently heat unburned fuels ahead of the flame 
front. 
 
 
10 
 
Several early studied on flame spread revealed that wind can change the flame shape and 
thus the flame-fuel interaction significantly, shown in Figure 4 [16-18]. In wind-driven 
fires, flames tend to be elongated and forced to attach to the fuel bed surface. Flames and 
the fuel will intermittently interact with each other due to the fluctuating nature of the 
flame. Compared to conditions under stagnant conditions, heat transfer from the flame to 
the unburnt fuel in wind-driven fires may change, for example, convection will play an 
important role as the flame is forced down and intermittently contacting the fuel, thus 
modifying the heat flux distribution on the downstream surface, which will largely 
determine the ignition process of the unburnt fuels, changing the spread rate.  
 
Figure 4. Comparison of wind-driven fire behaviors with that under quiescent conditions 
(from Rothermel [16-18]). 
 
2.3 Heat Flux Distribution 
 
The heat flux downstream from a burning fire has often been of interest to fire safety 
researchers because this heating is known to govern a fire’s rate of spread [19]. 
Formulations [20] describing the rate of flame spread often requires input of the heat flux 
to unburned fuel ahead of the burning (pyrolysis) region, px , the distribution of this heat 
11 
 
flux (as it may not be constant),  xq f  , and the length of this region (nominally the flame 
height minus the pyrolysis height, pf xx  ). While these features have been somewhat 
well studied in upward configurations over a vertical wall, where buoyancy and spread 
occur in the same direction [21-23], little information is available in wind-driven 
configurations where fire-driven buoyancy and wind-driven momentum compete [24]. 
These configurations are vitally important to understand the dynamics of spreading 
wildland fires [25], tunnel fires [26] and mine fires [27]. While some of these 
configurations occur in a closed (bounded) configuration, e.g., a tunnel, the dynamics of 
these process are still relatively translatable, except in the regime where the top surface 
begins to influence the flame. While many studies of flame spread have used a constant 
value for the heat flux distributed to the surface of the unburnt region [28, 29], more 
detailed measurements in vertical configurations have shown that this is only a coarse 
approximation that introduces significant errors. In reality, the heat flux to the unburnt area 
is often in the form of parabolic or exponentially-decaying profile [30–32]. 
Spreading fires are difficult to study because the flame moves as a function of time, often 
accelerating, making it challenging to measure important features such as downstream heat 
fluxes. Experiments with real fuels are also complicated because external conditions such 
as ambient winds or slope not only affect the spread rate, but also the burning rate of the 
fuel, modifying the downstream flame length and heat fluxes. In order to decouple and 
simplify the problem, a gas burner is often used to represent the pyrolyzing region, px , 
which then remains stationary with a fixed burning rate over time. This technique has 
previously been used to study flame spread over fabrics [33] and sloped surfaces [34, 35], 
however little information is available in the literature for a forced-flow configuration [36]. 
12 
 
Certainly, a forced-flow configuration will be more complicated, not only because of a 
competition between buoyancy and momentum, but also because it is difficult to define the 
flame length, fx , as the flame lifts away from the surface of the fuel, but technically is 
present. The stationary gas-burner configuration will enable measurements of heat fluxes 
from the flame to a nearly-adiabatic downstream surface over long times, resulting in 
averaged profile of the flame behavior and how it would affect flame spread.  
Heat fluxes from both spreading and stationary fires in upward [37-39], sloped [40, 41] 
and forced-flow configurations [42-44] have been measured in the past using various 
techniques. Because the flame spread process is incredibly complex, most formulations 
simplify the spatial dependence of the heat flux ahead of px  as a constant [45-46] or as a 
power-law or exponential function of downstream distance [47]. Markstein and de Ris [48] 
fit this dependence for upward and inclined line burners to simulate flame spread over 
fabric as a decaying power law function, here represented as  
                                                              npf xxaxq /  ,                                                            (2) 
where x is the downstream distance from the upstream edge of the fuel, px  is the pyrolysis 
length and a and n are constants fit to the data [48]. In a study by Gollner et al., the exponent 
n was found to vary between -2 to -7 for different inclined angles of thermally-thick PMMA 
[30], but to the best knowledge of the author, no values have been presented in the literature 
for forced-flow flames. 
Heat fluxes to the downstream surface can be divided into two components, convective, 
and radiative. The energy balance at the surface for a steady burning can be written as [49-
51]: 
13 
 
                                              
rrsrflcflf qqqq ,,,                                                           (3) 
where 
  
0, )(  ywcfl
dy
dT
kq , and )( 44,  TTq wrrs  .  
Thus  
                                   )()( 44,0   TTq
dy
dT
kq wrflywf  ,                                            (4) 
where 
cflq ,  , rflq ,  , rrsq ,   are the convective heat flux received by the surface, radiative heat 
flux received by the surface and re-radiation heat flux from the surface to the ambient, 
respectively. The convective heat flux can be approximated close to the fuel surface as 
0, )(  ywcfl
dy
dT
kq , which is the gas phase convective heating assuming the Chilton-
Colburn extension to the Reynolds analogy near the fuel surface [52]. Re-radiation from 
the surface to the ambient can be evaluated from the wall and ambient temperatures. The 
total heat flux to the surface can thus be described as the sum of the convective and 
radiative component of the flame. For small-scale laminar experiments over liquid fuels, it 
has been reported that the convective heat flux is relatively high, contributing 85% of the 
total heat flux [52]. While the absolute value of the convective heat flux will eventually 
reach a relative plateau downstream, radiation will continue to increase as the flame sheet 
thickens. It has also been observed that the radiative component of the total heat flux will 
decrease to some degree with an increase in wind speed. As found in the work of Singh et 
al. [52], the radiative heat flux is 28% and 20% of the total incident heat flux for ambient 
velocities of 0.79 and 2.06 m/s, respectively for PMMA burning cases, because when the 
14 
 
wind velocity is high, it pushes the flame to attach the board surface and the local 
temperature gradient is increased, causing the local convective heat flux to increase, too. 
The heat flux from the flame to the unburnt fuel surface is closely related to fuel heating 
and ignition and thus fire spread. The heat flux distribution in vertical wall fires have been 
studied extensively, however information regarding the heat flux on the downstream 
surface in a wind-driven fire scenario has not been clearly investigated. This information 
has strong implication on the wildland fire spread as the heat to the unburnt fuels controls 
the flame spread. 
2.4 Flame Pulsations and Movement 
 
The “puffing” phenomenon of pool fires has been relatively well studied, with a universal 
scaling law of the frequency of flame pulsations being well correlated with the diameter of 
the burner. The results from Cetegen [53, 54], Rasbash [55], and Hamins [56] on circular 
pool fires indicates the pool fire puffing involves a strong coupled interaction between a 
generated toroidal vortex, formed a short distance above the surface of the fuel, and the 
perturbations it supplies to the flow field in the vicinity of the flame surface. Experiments 
have been conducted using circular burners with a wide range of diameters, including both 
gaseous and liquid fuels. Measurements of fluctuations were performed to study the 
influence from various parameters to the flame behavior, such as heat release rate effects 
and disturbances introduced around fires.  
Cetegen [54] and Hamins [56] noted that the pool fire puffing frequency, f is relatively 
insensitive to the heat release rate of the fire, but is closely related to the diameter of the 
diameter of the pool, D, expressed as  
                                                  
2/1 Df .                                                        (5) 
15 
 
Scaling relationships between these quantities have also been proposed, among which the 
Froude number,  
                                                       
gD
UFr
2
  ,                                                     (6) 
which characterizes the inertial force over the gravity force, and the Strouhal number,  
                                                        St = fD/U,                                                                  (7) 
which characterizes oscillating flow mechanics or vortex shedding, have been most 
commonly used [57]. Here, U represent the characteristic velocity and g represents the 
acceleration due to gravity. For pool fires, the characteristic length is often the diameter of 
the pool and velocity the fuel velocity at the surface, approximated from the burning rate. 
Based on Eq. 5, a relationship between St and Fr can be formed, 
                                  
2/1
2/12/1
~~/ 



 Fr
U
D
U
DD
UfDSt .                                       (8) 
Most of the existing literature on pool fire puffing fits both the diameter and St-Fr scaling, 
however all of these results have investigated fire behavior under stagnant conditions [58-
60]. Some results have extended scaling from pool fires to line fires [61, 62], however these 
have not addressed the puffing phenomena, which has also been observed for wildland 
fires, over a broad range of scales [63]. For smaller fires, a “flickering” instability at a 
higher frequency than “puffing” is also formed at the top of small flames [64]. When a fire 
is influenced by a perpendicular wind, e.g. during a wildland fire, it is easily observed that 
the wind will also significantly affect the movement of the flame and influence the 
frequency by which the flame extends forward of the mean flame zone, reaching the 
unburnt area, but these motions have not been thoroughly described. 
16 
 
More recent studies on stagnant pool fire puffing behavior have also been conducted under 
various ambient conditions. For instance, Tang and Hu [65] studied puffing from pool fires 
with different burner sizes and aspect ratios in normal and sub-atmospheric environments. 
They noticed the puffing frequency will increase with burner aspect ratio, and reaches a 
relative constant with different ambient pressures. Abe [66] studied the influence of gravity 
on the puffing frequency, finding that the puffing phenomenon was suppressed under low 
gravity and that the puffing frequency under low-gravity environments cannot not 
summarized by previous correlations. His results were summarized by a relationship 
between the Strouhal-Froude number as St=0.577Fr-0.502. Different fuel types were also 
tested in the study of pool-fire puffing behavior [67] and it was noticed that the fuel type 
does not have much impact on the puffing frequency and puffing intensity.  
The intermittent behavior of flames in wind-driven fire spread would certainly differ from 
puffing under stagnant conditions. Because wind is introduced, perpendicular to the 
upward movement of the buoyant flow, it will push the flame to move in the span-wise 
direction, with flame buoyancy pushing the flame upward. Thus, in wind-driven fires, 
flame pulsations can be divided into two directions, upward, primarily driven by buoyancy, 
and forward in the wind direction, driven primarily by momentum supplied by the wind. 
There may of course be many interactions between these two modes, however both are 
ultimately the outcome of these competing mechanisms and will be studied separately here.   
2.5 Flame Extension and Flame Attachment 
 
The geometry of flames under various configurations have been studied extensively, 
however most research addresses flames under quiescent ambient conditions. Under these 
stagnant conditions, the flame height is the same as the flame length, often also the most 
17 
 
important length scale in characterizing the geometry of the flame. Thomas found the flame 
height is well correlated with the burning rate and fire diameter for different fuels [68]. 
Heskestad [69, 70] later proposed a widely-used correlation for flame height, based on a 
wide variety of fire sources, 
                                                           02.17.3 5/2*  Q
D
H  ,                                              (9) 
where H is flame height, D is fire source diameter, and 
*Q  is the dimensionless heat release 
rate, defined as 
                                                          
5
*
gDTc
Q
Q
apa

  .                                              (10) 
Here, Q  is the heat release rate of the fire, a  is the density of ambient air, pc the specific 
heat capacity, and aT  the temperature of ambient air in Kelvin. 
In a wind-driven fire, flames will be tilted toward unburnt fuel to form an angle from the 
vertical. The flame will also be “stretched”, and grow longer along the surface. A reduction 
in the overall length may also occur due to better mixing with air, especially at higher 
velocities. The flame extension or flame drag behavior by the wind has not been 
investigated thoroughly. Hu et al [71] studied the flame extension behavior of circular pool 
fires under wind, considering air mixing, and developed a correlation to predict the flame 
extension length, 
                          )(48.202.17.3
,2
25/2*





Oa
O
fgfuel
Cf
Y
M
HM
Hs
gd
u
Q
D 
 ,                 (11) 
where 
f  is the flame extension length, u is the wind speed, D is the pool diameter, s is 
the molar stoichiometric oxygen to fuel ratio, CH  is the heat of combustion of the fuel, 
18 
 
fuelM  and 2OM is the molecular weight of the fuel and oxygen, fgH  is the effective heat 
of evaporation, a is the air density, and ,2OY is the oxygen mass percentage concentration 
in ambient air. Here, the flame extension length in wind-driven fire cases has been shown 
to not only be a function of heat-release rate, but also wind velocity, fuel type and the rate 
of mixing with air. 
In a wildland fire scenario, the flame length has been shown to have a strong relationship 
with the fire spread rate since it provides information on the potential distance the flame 
can convectively heat unburned fuels (a forward heating length), although this relationship 
is much more complex than the simple relationship presented by Byram [72].  In wildland 
fire spread the flame attachment length on the downstream surface, or the flame drag length 
[73, 74] is important in determining this forward heating length. This phenomenon has 
been observed for a long time. Several equations based on laboratory pool fire experiments 
have been proposed to describe this phenomenon. Wellker and Sliepcevich [75] correlated 
the flame attachment length against the Froude number of the wind (Frw), 
                                             
48.0
21.01.2 







a
V
WFr
D
DD


,                                                 (12) 
where V , a are the density of fuel vapor at the boiling point and ambient air respectively, 
D is the diameter of the pool, and D  is the flame attachment length on the surface. Raj 
[76] further proposed  
                                            
5.0
5.0 1375.2 







a
V
WFr
D
D


,                                              (13) 
based on a combination of data from Welker [75] and Raj [76] to predict the attachment 
length in a wind-driven fire.  
19 
 
Flame attachment along a downstream surface has also been observed during spreading 
fires, such as the study by Apte et al. [77] which investigated large-scale wind-driven fire 
spread over a larger thermally-thick slab of polymethyl methacrylate (PMMA) in a mine 
tunnel. The flame and, therefore, attachment was generally divided into regimes of 
attached, boundary-layer like flame spread and lifted, plume-like behavior where the flame 
was lifted and tilted some angle from the surface of the fuel. These distinctive regions are 
formed due to the competing mechanisms of momentum from the wind and buoyancy from 
the flame. In this study, we will also define an intermittent attached region which occurs 
between the attached and lifted regions.  
2.6 Summary 
Based on the literature review, intermittent flame behavior in wind-driven fires is not yet 
well understood. While heat flux distributions have been well-studied in a vertical wall 
configuration, little information is available when the flame is driven by wind. Some 
information on flame shapes, including the flame height and flame length under stagnant 
and some wind-driven conditions have been studied, however there is much left to be 
understood. This information will be important to develop a physical model of wind-driven 
wildland fire spread. 
 
 
  
20 
 
Chapter 3: Experimental Facility and Instrumentation 
A wind tunnel apparatus was used, which mainly includes a blower, gas burner, and a test 
section. A description of the apparatus, instrumentation and experimental procedures are 
provided below. 
3.1 Wind Tunnel Setup 
A specially-designed wind tunnel was used at the University of Maryland to conduct 
forced-flow fire experiments. The structure and dimensions of this lab-scale tunnel can be 
seen in Figs. 5 and 6 [12, 52, 78-81]. Revisions were made to the wind tunnel to facilitate 
our measurements. At one end of the tunnel, a 100×75×100 cm plenum with an EBM 
blower (G3G250-MW72-01) with a maximum flow rate of 1200 cfm was connected to 
pressurize the plenum. A pulse-width modulation controller allowed for precise control of 
the wind blowing without generating significant perturbations to the air flow. The 
pressurized air then travels through a 30.48×30.48 ×122 cm straight tunnel before 
reaching the test section. A set of fine turbulence reduction screens and 5 cm thick 
honeycombs with 0.3 cm diameter holes were built and installed within the tunnel. The 
final piece of the wind tunnel setup is the exhaust duct (tunnel), from which the uniform 
and steady wind travels and provide wind to the test section.    
 
21 
 
    
Figure 5. Photo of the wind tunnel apparatus 
 
Figure 6. Schematic including dimensions of the wind tunnel [52] 
22 
 
 
3.2 Gas Burner 
Two gas burners, previously designed and built by Gorham [12] and Singh [52], were used 
to simulate wind-driven fires. The 6.5 cm tall burners were 25×5 cm2 and 25×10 cm2 
wide, built with thick galvanized steel. They were built with a 2 cm tall plenum and had 
4.5 cm of fine sand placed on top of a fine mesh to distribute the fuel. Propane gas enter 
the sand burner through 0.6 cm diameter NPT bulkhead fitting on the bottom side of the 
burner plenum. The fire size of the tests can be controlled by the mass flow rate of the 
propane, controlled using an Alicat MCR-100SLPM-D mass flow controller. The fire sizes 
of the tests ranged from about 3 to 15 kW. 
3.3 Velocity Characterization 
The ambient wind velocity coming out the tunnel was measured using a Dantec Dynamics 
hot-wire anemometer system. The hot-wire anemometer used here can be seen in Fig. 7. 
Note that the single-direction hot-wire anemometer is fragile, records at high frequency, 
and is very sensitive to ambient conditions. Extra care needs to be taken when making the 
measurement using this device. The maximum sampling frequency of the hot-wire 
anemometer is to 1000 Hz, and the maximum ambient temperature it can withstand it 150 
C. Before performing experiments the hot-wire anemometer is calibrated in a controlled 
Poiseuille flow against a known hand-carry anemometer, with the wind speed during 
calibration ranging from 0 to about 3 m/s, which covers the wind speed range that was used 
during experiments. 
23 
 
 
Figure 7.  Hot wire anemometer used in his study [82]. 
 
The ambient wind velocity in our experiments ranged from about 0.5 to 2.5 m/s. The 
velocity profile and corresponding turbulence intensities of the wind (ratio of the root-
mean-square of the deviation of the wind velocity to the mean velocity) were characterized 
and checked every time in the ambient flow before taking experimental measurements. 
Two ambient velocity conditions were characterized for these experiments, a low wind 
speed at 1.12 m/s, and a high wind speed at 2.15 m/s. The measurement locations used are 
shown in Fig. 7. For each of the two wind conditions characterized, 5 different downstream 
locations were measured, starting from the leading edge of the metal sheet, where the 
incoming wind flow first reaches the test surface, which is labelled as 0 cm in Fig. 8, and 
then 4 more vertical lines were taken every 10 cm along the downstream surface. At each 
measurement location, measurements were taken along a vertical line, starting from 2 mm 
24 
 
above the surface, at an interval of 0.5 mm up to 20 mm above the surface. At each 
measurement location, data were taken for 30 seconds and the averaged velocity was 
calculated. The velocity data are shown in Figs. 9 and 10. The bulk velocity can be 
estimated from the two figures above the boundary layer thickness. The data shows that 
the ambient velocity is very uniform and steady above the boundary layer thickness.  
 
Figure 8. Measurement locations for wind profile measurements. 
 
 
25 
 
Figure 9.  Low velocity (1.12 m/s) profile with height over the surface. 
 
Figure 10. High velocity (2.15 m/s) profile with height over the surface. 
The turbulence intensity of the ambient flow was also recorded to provide more 
information on ambient boundary conditions. Figures 11 and 12 show the turbulence 
intensity for the two wind velocities mentioned above, measured at different downstream 
locations along a vertical line above the board surface. It can be seen that, for the most part, 
the turbulence intensity is well controlled below 2%, with several points approaching as 
high as 5%, where these locations are close to the board surface and surface roughness 
within the boundary layer makes the turbulence intensity increase. It is also found that, 
when the wind velocity is high, the turbulence intensity increases a little bit higher than the 
low velocity ones, but the wind profile remains very uniform and the turbulence intensity 
26 
 
very low in the central core of the tunnel exit, which provides a steady wind profile for our 
experiments, shown in Figs. 11 and 12. 
 
Figure 11. Turbulence intensity profile with height and downstream distance over the 
surface (1.12 m/s, low wind case). 
 
27 
 
 
Figure 12. Turbulence intensity profile with height and downstream distance over the 
surface (2.15 m/s, high wind case). 
 
3.4 Temperature Measurements and Traverse System 
R-type thermocouples with Pt/Pt-13% Rh are used here for temperature measurement. Two 
wire diameters, 50 and 75 µm, with bead diameters 100 and 150 µm, respectively are used 
[83]. The small diameters of the R-type thermocouples made high-resolution 
measurements possible. Also, disturbances to the flame and the radiation loss correction 
from the thermocouple bead are minimized. A schematic figure of the thermocouple used, 
including a connector, ceramic tube and thermocouple bead are shown in Fig. 13. In our 
28 
 
tests, to apply a radiation correction to our temperature data, both 50 and 75 µm diameter 
thermocouples were used. A transverse system was also used to obtain accurate positioning 
and incremental movement of the thermocouples. Two computer-controlled Velmex X-Y 
unislides allowed the thermocouple to move in two directions with a maximum spatial 
resolution of 1.5 µm.  
 
Figure 13. Thermocouple and mount used in temperature measurements [83]. 
 
3.5 Total Heat Flux Gauge 
A Vatell water-cooled total heat flux gauge [84] (model HFM1000-0) was used in our tests 
to measure the total heat flux distribution on the downstream surface of wind-driven line 
fires. Before taking measurements, the heat flux gauge was calibrated against a NIST-
traceable Medtherm incident heat flux sensor in the cone calorimeter. The result of the 
calibration can be seen in Fig. 15. An amplifier was also used to process the data output 
before being recorded by the data acquisition system. The total uncertainty for a single heat 
flux sample acquired with this water-cooled heat flux gauge is found to be less than 3%. 
The fitting equation for calibration between the heat flux and the voltage output gives an 
adjusted R2 higher than 99.99%. Additional product details are shown in Table 1.  
29 
 
 
Figure 14. The Vatell total heat flux gauge and amplifier used in experiments [84]. 
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
0
10
20
30
40
50
 
 
x: voltage
y: heat flux
R
2
=0.99993
y=5.35965+23.3273x
H
ea
t 
fl
u
x
(k
W
/m
2
)
Voltage (mV)
Equation y = a + b*x
Adj. R-Square 0.99993
Value Standard Error
A Intercept 5.35965 0.05838
A Slope 23.32073 0.06562
 
Figure 15.  The calibration used for the Vatell total heat flux gauge in the cone 
calorimeter.  
 
30 
 
 
Table 1. Vatell heat flux gauge specifications from the manufacturer [84]. 
Product details Vatell HFM 1000-0  
Output signal Linear output 
Sensor coating Pyromark 1200, 0.95 emissivity 
Repeatability  0.5% 
Resistance (at 24℃) 3690 ohm 
 
3.6 Radiometer  
In order to measure radiation from the flame to the downstream surface, a water-cooled 
Medtherm Schimdt-Boelter radiometer (model NO. 64O-10SB-22) was used [85]. The 
radiometer was pre-calibrated with a water temperature at 29.4℃, with a 3% uncertainty, 
about 95% confidence level. Calibration was performed in compliance with ISO/IEC 
17025, ANSI/NCSL Z540-1 and MIL-STD-45662A to Medtherm PI-20 with traceability 
to the National Institute of Standards and Technology. A sapphire purge window was also 
used to avoid soot from the flame clouding on the radiometer surface. The full-scale output 
level was 9.59 mV at 100 kW/m2 with responsivity 0.0959 mV per kW/m2. The maximum 
non-linearity of the gauge is about 2% of the full range, and repeatability within 0.5%. A 
schematic of the radiometer sensor is shown in Fig. 16. The diameter of the sensor 2.5 cm 
with sapphire window installed on top. The standard window is at 150o view angle. Two 
water tubes, each with diameter 0.32 cm were connected to the sensor to provide cooling 
effect to the gauge when working with heat sources. A 0.32 cm diameter gas purge tube 
was also connected to the gauge to blow nitrogen along the sensor surface. 
31 
 
 
Figure 16. Schematic of the Medtherm radiometer used from the manufacturer [85].  
 
3.7 Digital Camera 
A Nikon D7000 digital SLR camera (4,928 × 3,264 pixels) was used to capture flame side-
view images during tests. A MATLAB program is then used to process the images to obtain 
an averaged image. The camera was set up to perpendicular to the side of the test section 
in order to capture the whole flame. Averaged flame images are determined by a 50% light 
intensity threshold, and the flame attachment length on the downstream surface is 
determined based on the distance between the flame and the downstream surface. 
3.8 Data Acquisition Systems 
A Compact DAQ USB chassis with C-series I/O modules from National Instruments were 
used in tests for velocity, temperature, and heat flux measurement input and output. For 
temperature measurements, the voltage signal from the thermocouple was acquired, 
conditional and digitized through a NI-9214, which is a 24-bit high density 16-channel 
thermocouple input module with a 0.02℃ measurement sensitivity. A built-in cold-junction 
compensation circuit is provided in the NI 9214. In addition to the cold-junction 
compensation system, the NI 9214 also has an extra, internal-only channel known as the 
32 
 
auto-zero channel, from which an offset error can further be eliminated to provide more 
accurate measurements. 
The NI 9214 module is used for thermocouple and heat flux measurements, however, for 
hot wire wind velocity measurements at high frequencies, an NI 9239 module needs to be 
implemented, which is 4-channel, 24-bit C Series analog input module and comes with a 
channel-to-channel isolation and built-in signal conditioner. Figure 17 shows a view of the 
NI-cDAQ 9178, NI 9124, and NI 9239 C-series modules. 
LabVIEW is used for continuous data acquisition, with different scripts prepared for 
temperature, velocity, and heat flux measurements. The scripts also provide readings of the 
data, such as maximum value, minimum value, mean value, standard deviations, and 
turbulence intensity. 
 
Figure 17. National Instrument data acquisition systems used in the study [86]. 
 
3.9 Experimental Conditions 
Tests were conducted in the large fire lab at the University of Maryland to study the heat 
flux and temperature distribution of wind-driven line fires. For heat flux measurements, 
the water-cooled Vatell heat flux gauge was used, with a measurement range from 0-100 
kW/m2 and a response time of 1 kHz. A ceramic fiber insulation board (Superwool board 
33 
 
pre-painted with matte black high temperature paint) with dimensions of 45×90×2.5 cm3 
was used to hold the gas burner and provide a surface over which to take measurements. 
The heat flux gauge was inserted into pre-drilled holes and kept flush with the surrounding 
insulation board to measure the total heat flux received by the surface downstream of the 
burner. The heat flux gauge was calibrated against a known incident heat flux gauge, with 
calibration results showing a measured uncertainty less than ±3%. Heat fluxes were 
averaged over 200 s for each test point. The spacing between adjacent holes on the 
insulation board for the heat flux gauge was 5.5 cm measuring up to 33 cm downstream. 
The first measurement point could only start as close as 5.5 cm away from the trailing edge 
of the burner due to the configuration of the burner and gauge water-cooling system. Each 
heat flux test was repeated three times and an averaged value is taken as the final 
measurement data. The wind velocity in the experiments ranged from about 0.5 m/s to 2.5 
m/s. Three different fire heat release rates, 4, 5 and 6 liter per minute (lpm) of propane gas 
flow were employed for the experiments, corresponding to 6.3, 7.9 and 9.5 kW fire sizes. 
A schematic of the test section is shown in Fig. 18. 
34 
 
 
Figure 18.  Experimental setup downstream of the tunnel outlet. 
 
Local flame temperatures were also measured using R-type thermocouples traversed via 
an X-Y unislide from the surface of the heat flux gauge to the thermal boundary layer above 
the flame. The first measurement point in one vertical line is the insulation board surface, 
measuring vertically above that at 1 mm intervals. In one vertical direction line, there are 
nearly 20 measuring points, up to the flame height. Voltage signals from the thermocouples 
were acquired, conditioned and digitized through a National Instruments NI 9214, averaged 
35 
 
at each point for 60 s. All tests were repeated 3 times to ensure repeatability. Table 2 shows 
the experimental conditions used. 
 
Table 2. Experimental conditions (I) 
 
Fire size (kW) Wind velocity 
(m/s) 
Downstream heat 
flux locations (cm) 
Thermocouple locations 
above the surface (mm) 
6.3 
7.9 
9.5 
0.87 
1.14 
1.37 
1.62 
1.91 
2.14 
2.45 
5.5 
11 
16.5 
22 
27.5 
33 
 
0 
2 
4 
6 
8 
… 
20 
 
A side-view camera was also used to capture flame images. Pictures are averaged, a 
threshold applied to distinguish flame vs. no flame and the flame attachment length on the 
downstream surface determined as the distance between the burner trailing edge to the 
location where the distance between the flame and the surface reaches 5 mm using a custom 
MATLAB script was used, applying different thresholds (1, 2, 4, 6 mm) to test the validity 
of the method. No variations of the trend were observed, though the absolute values shift 
slightly.  
In another set of experiments, different burner geometries, wind velocities and fire heat 
release rates were used to study fluctuations of the flame with wind. The experimental 
setup was very similar to Fig. 18 but without the heat flux gauge and thermocouple 
measurements. The main methodology used there was image analysis. High-speed 
36 
 
videography was used to capture digital images of the flame in all configurations from a 
side view. The camera used was high-speed Casio EFX-1, recording at 120 frames per 
second with a 640×480 pixel resolution. The experimental conditions are listed in Table 3.  
Table 3. Experimental conditions (II) 
 
Burner dimensions 
(cm2) 
Heat-release rate 
(kW) 
Free-stream wind velocity (m/s) 
25×5 
2.38 1.11, 1.39, 1.61, 1.89, 2.11, 2.36 
3.21 1.11, 1.39, 1.61, 1.89, 2.11, 2.36 
4.96 
1.39, 1.61, 1.89, 2.11, 2.36, 2.55, 2.65, 
2.75 
6.86 1.61, 1.89, 2.11, 2.36 
25×10 
4.87 0.95, 1.09, 1.45, 1.78, 1.59, 2.06 
7.30 0.95, 1.09, 1.45, 1.78, 1.59, 2.06 
 
30×25 
4.38 0.223, 0.447, 0.67, 0.894, 1.11 
6.32 0.223, 0.447, 0.67, 0.894, 1.11, 1.34 
8.76 0.223, 0.447, 0.894, 1.11, 1.34 
  
  
37 
 
Chapter 4: Heat Flux Analysis 
4.1 Total Heat Flux Distribution  
In this chapter, the total heat flux distribution obtained under different fire and wind 
conditions are presented and correlated against a parameter representing the influence of 
fire-induced buoyancy and wind-driven momentum. The parameter, namely the local 
Richardson number (Rix), is proposed to scale with heat flux data. A piece-wise function 
of the non-dimensional heat flux versus the local Rix can then be used to predict the heat 
flux in wind-driven fires. Some future work to be done in this area is also discussed. 
Figure 19 shows heat flux data collected at the same point (11 cm downstream surface) 
averaged for 150 s for 4 different sets of experiments, with 2 two fire sizes, 6.3 kW and 9.5 
kW, and 2 wind velocities, 1.14 m/s and 1.62 m/s. The average data will be used in later 
analysis. It is clear that, when the wind velocity is high, the heat flux is quite stable with 
few fluctuations, while on the other hand, the heat flux data varies more with a low wind 
velocity. It is speculated that, when the wind speed is high, most of the flame is forced to 
attach to the surface, and the heat flux gauge is fully covered within the stable flame region, 
thus the heat flux data received is reflecting the stable flame movement. When the wind 
speed is low, only a small portion of the flame is attached to the surface, and heat flux 
gauge is within the unstable flame region, thus the data fluctuates a bit more. 
 
38 
 
-20 0 20 40 60 80 100 120 140 160 180 200
5
10
15
20
25
4.22
7.17
21.5
 
 
 6.3 kW, 1.62 m/s
 6.3 kW, 1.14 m/s
 9.5 kW, 1.62 m/s
 9.5 kW, 1.14 m/s
H
ea
t 
fl
u
x
 (
k
W
/m
2
)
Time (s)
23.75
 
Figure 19. Heat flux data taken on 11 cm downstream averaged for 6.3 kW, 9.5 kW fire 
size, 1.14 m/s, 1.62 m/s wind speed scenarios for a period of 150 s. 
 
In order to quantify the total heat flux in a somewhat universal manner, the local distance 
where each heat flux was measured was first normalized [87, 88]. The distance along the 
downstream surface from the trailing edge of the burner is denoted here as L, which is 
normalized by dividing by the burner hydraulic diameter, DH, which for a rectangular 
burner, is defined as four times the area over the perimeter [89], 
                                                         HDLL /
*                                                               (14) 
                                                        PSDH /4                                                             (15) 
39 
 
Here, S is the area of the burner, P is the perimeter, and L* is the non-dimensional 
downstream distance.  
A significant difference was observed between the heat flux distribution profiles of the 
high and low wind velocities. For low velocities, buoyancy dominates the flame shape and 
only a small portion of the flame was observed to attach to the surface ahead of the burner. 
Because the nearest heat flux gauge is located 5.5 cm from the burner edge, the peak heat 
flux, which we later show occurs at this transition point, is not picked up, instead only 
resolving the downstream decaying heat flux profile in the thermal plume, where the flame 
has already lifted off from the surface.  This is seen in Fig. 20, where the heat flux decays 
from approximately 10 kW/m2 to 0, following a power-law decay like Eq. 2. 
1 2 3 4
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
 0.87m/s, 6.3 kW
 0.87m/s, 7.9 kW
 0.87m/s, 9.5 kW
 
 
 2.14m/s, 6.3 kW
 2.14m/s, 7.9 kW
 2.14m/s, 9.5 kW
H
e
a
t 
F
lu
x
 (
k
W
/m
2
)
Dimensionless downstream location L
*
=L/D
H
  
Figure 20. Comparison of heat flux profiles for different wind velocities and fire sizes. 
40 
 
 
On the other hand, when the wind velocity is high enough, the flame starts to transition 
from a buoyancy-dominated to a momentum-dominated regime, remaining attached to the 
downstream surface for considerably longer distances. This momentum-dominated regime 
can also be seen in Fig. 21, where the heat flux to the downstream surface first increases to 
a peak value, then decreases with downstream distance. This makes sense for these smaller, 
convectively-dominated flames, where the location of closest attachment occurs at a certain 
distance downstream of the burner, followed by a decay in the remaining attached flame. 
This work will focus on finding the location where this heat flux value reaches its 
maximum and the implications of this location, as it may indicate transition from a 
momentum to buoyancy-dominant regime. 
Distinct differences can also be observed from the flame images. Following Fig. 21 is a 
comparison of the flame images under 0.87 m/s and 2.13 m/s wind velocities, 
corresponding to the heat fluxes shown in Fig. 20. The differences between the two flame 
shapes are clear as the wind velocity goes from low to high. 
 
Figure 21. Experimental photos showing different flame shapes under wind.  
 
7.9 kW, 0.87 m/s 5 cm 7.9 kW, 2.14m/s 5 cm 
41 
 
Further analysis of the heat flux data shows that, when the wind velocity is relatively low, 
the heat flux distribution follows a power law, as has been reported in previous literature 
[90],    npf xxaxq / . The fitted constants a and n are shown in Fig. 22 for each test. 
Unlike previous results for upward or inclined flame spread, where the exponent, n varied 
from -2 to -7, here the exponent was closest to -1 for low velocities. This corresponds to a 
heat flux value roughly inversely proportional to the downstream distance. The constant A 
in front of the equations also varies between tests, which corresponds to different fire sizes. 
Based on these results, it can be inferred that, the larger the fire size, the higher the constant 
A will be, being proportional to the change in fire size. The fitted equations in Fig. 22 have 
an adjusted R2 value not less than 0.98, which means the fitted equations match the 
measured data well. 
 
42 
 
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0
1
2
3
4
5
6
7
8
9
10
q=3.3L
*-1.32
, R
2
=0.99
q=4.9L
*-1.25
, R
2
=0.98
q=6.0L
*-1.1
, R
2
=0.98
 
 
 0.87m/s, 6.3 kW
 0.87m/s, 7.9 kW
 0.87m/s, 9.5 kW
H
e
a
t 
F
lu
x
 (
k
W
/m
2
)
Dimensionless downstream location L
*
=L/D
H
  
Figure 22. Heat flux distribution under low wind velocities. 
 
4.2 Richardson Number Analysis 
What is clear from previous studies is that, when an external ambient flow is applied over 
a fire, natural convection from buoyancy and forced convection from the wind will both 
play a role in the shape of the flame and, consequently, the heat flux from the flame to 
surrounding unignited fuels. As the velocity of the wind is increased, a considerable portion 
of the heat flux from the flame will be received by the downstream surface because the 
flame will “tilt” or “attach” closer to that surface, increasing both convective heat transfer 
due to its closer location and radiative heat transfer due to its improved view factor. Apte 
[91] et al. studied wind-driven flame spread in an enclosed tunnel over PMMA, clearly 
43 
 
delimitating attached and plume flow regimes, however they were not able to draw larger 
conclusions as the flame spread and accelerated as a function of time [92]. Similarities can 
be seen, however, in combined forced and natural convection over a hot plate as our small-
scale experiments are mostly dominated by convective heat transfer [93-95]. For these 
problems, the Grashof,  
                                                 
2
3

 xTTg
Gr hx
                                                        (16) 
and Reynolds numbers, 
                                                    

Ux
x Re                                                                    (17) 
have been used to described both heat transfer and transition problems in flames and hot 
plates, where hT  is the hot gas temperature, T is the ambient temperature, x is downstream 
distance along the plate, g the acceleration due to gravity, U  the ambient velocity,   the 
thermal expansion coefficient, and  the kinematic viscosity of the ambient air. For flow 
over a hot plate, the relative role of buoyant and inertial forces has been divided into three 
regions based on the value of a correlating parameter, b
xxGr Re/ . It is noticed that several 
different values for the numerator, b have been selected in previous literature to describe 
flow over hot surface. For example [96], they chose b to be either 1.5 or 2.5 based on the 
geometry of the flow scenarios. 
In this work, b = 2 is chosen to describe the competition between forced and natural 
convection, taking the more common form of a Richardson number,  
                                               
 
,
Re 22 U
xTTgGr
Ri
f
x
x
x



                                                     (18) 
44 
 
where instead of using 
hT , the temperature of the hot gases, the highest local flame 
temperature, 
fT is used to describe the temperature difference which drives buoyancy. The 
local flame temperature was obtained by interpolating available temperature data in one 
vertical direction (nearly 20 points).  These temperatures are found by applying a fit to the 
profiles of temperature and then interpolating the resulting equation to find the maximum 
temperature. Figure. 23 shows the measured local maximum flame temperature. This figure 
shows the temperature data obtained at a downstream location 16.5 cm from the trailing 
edge of the burner, with a fire size 9.5 kW and wind velocity 1.91 m/s. First, a best-fit 
equation is found for the existing dataset, then it is interpolated to find the highest local 
flame temperature. The same method is applied to all the test cases to get the temperature 
information for Rix analysis. 
500 600 700 800 900 1000 1100
0
10
20
30
40
50
60
70
80
 
 
H
ei
g
h
t 
(m
m
)
Temperature (K)
Peak Temp.=1035 K
 
Figure 23. Vertical temperature profile taken 16.5 cm downstream of the trailing edge of 
the burner, with a fire size of 9.5 kW and a wind velocity of 1.91 m/s. 
45 
 
 
The local Rix can then be used to describe this competition within three regimes, dominated 
by, forced convection, mixed convection, and finally natural convection. These regions can 
be expressed as: 
                     







controlledconvectionnatural
convectionmixed
controlledconvectionforced
Rix
10
10~1.0
1.0
                                    (19) 
Mixed convection flows have often been described as dominated by inertial forces when 
Rix <0.1, and by buoyant forces when Rix >10 [97, 98]. For a fire problem under the effect 
of wind, where strong buoyant forces are introduced both due to high temperatures and 
distributed heat release, with relatively low wind velocities, most problems lie in the mixed 
convection region, where Rix is between 0.1 and 10. The details and implications of heat 
transfer modes in this mixed region (0.1< xRi <10) is of particular interest in our case, where 
the transition from an inertial-dominant to buoyancy-dominant regime occurs. Thus, based 
on the temperature information collected from the flame, a local Rix number analysis can 
be performed. This will be used alongside the heat flux distribution to try to indicate a 
threshold for transition, coupled with observation of attached and plume behavior of the 
flame, such as that shown in Fig. 20.  
The heat flux distribution to the surface downstream of the burner under high wind 
velocities is shown in Figs. 24 and 25. A clear transition point can be seen for these heat 
flux distributions. The location for the peak point is moving with increasing wind velocity. 
Since there are a limited number of heat flux data points for each experiment, to find the 
exact position where the local heat flux reaches a maximum, the data must be interpolated 
and fit.  
46 
 
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
5
10
15
20
25
30
 
 
H
ea
t 
F
lu
x
 (
k
W
/m
2
)
Dimensionless Downstream Location L
*
 1.91m/s, 6.3 kW
 1.91m/s, 7.9 kW
 1.91m/s, 9.5 kW
 1.62m/s, 6.3 kW
 1.62m/s, 7.9 kW
 1.62m/s, 9.5 kW
  
Figure 24. Heat flux distribution under high winds (1.62 and 1.91 m/s). 
 
47 
 
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
10
12
14
16
18
20
22
24
26
28
30
32
34
 
 
H
ea
t 
F
lu
x
 (
k
W
/m
2
)
Dimensionless Downstream Location L
*
 2.45m/s, 6.3 kW
 2.45m/s, 7.9 kW
 2.45m/s, 9.5 kW
 2.14m/s, 6.3 kW
 2.14m/s, 7.9 kW
 2.14m/s, 9.5 kW
  
Figure 25. Heat flux distribution under high winds (2.14 and 2.45 m/s). 
 
The local Rix number is also determined here for high wind velocities to describe 
competition between natural and forced convection. The highest local flame temperature 
was used as Tf and the distance L is taken as the characteristic length scale for Rix. From 
Figs. 26 and 27, one can tell that Rix generally increases with non-dimensional downstream 
distance L*, from about 0.3 to 2.5. In order to find the implication of Rix and its influence 
on the heat flux distribution, a detailed analysis is performed. 
48 
 
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
  
 
 
R
i=
G
r/
R
e
2
L
*
=L/D
 1.62m/s, 6.3 kW
 1.62m/s, 7.9 kW
 1.62m/s, 9.5 kW
 1.91m/s, 6.3 kW
 1.91m/s, 7.9 kW
 1.91m/s, 9.5 kW
  
Figure 26. Local Rix number under high winds (1.62 and 1.91 m/s). 
 
49 
 
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
 
 
R
i=
G
r
/R
e
2
L
*
=L/D
 2.14 m/s, 6.3 kW
 2.14 m/s, 7.9 kW
 2.14 m/s, 9.5 kW
 2.45 m/s, 6.3 kW
 2.45 m/s, 7.9 kW
 2.45 m/s, 9.5 kW
  
Figure 27. Local Rix number under high winds (2.14 and 2.45 m/s). 
 
4.3 Non-dimensional Heat Flux and Correlations  
An analysis of the local Richardson number, Rix was performed for the aforementioned fire 
cases. It is found that Rix along the downstream insulation board will undergo a transition 
as the flame grows and spreads downstream. When the flame starts at the burner leading 
edge, Rix is small (Rix<1) as Grx is smaller than Rex, and the flame is forced to the surface, 
indicating that buoyant forces are weaker than the momentum forces introduced by the 
wind. With continued downstream distance and heat-release from the flame, the buoyant 
force increases until it equals the forward momentum forces (Rix=1). After this point, the 
flame becomes buoyantly dominated and appears as an upward plume lifted away from the 
50 
 
fuel surface. In Figs. 28 and 29, Rix and the local total heat flux to the surface are plotted 
against L* for two scenarios, a 9.5 kW fire size under 1.91 m/s wind velocity, and a 7.9 kW 
fire size under 2.14 m/s wind velocity. In both scenarios, the dimensionless location where 
Rix=1 (

1xRi
L ) and where the peak heat flux is observed ( peakL ) appear to occur at the same 
location, shown in Fig030. Then the same method has been applied to all the experimental 
cases investigated. The two key locations, 

1xRi
L and peakL , were noted and tabulated. Figure 
28 then compares the correlation between 

1xRi
L  and peakL . As they are very nearly linearly 
correlated, it shows the location where the buoyant-inertial transition appears also is the 
location of maximum heat flux. This means that when the local Rix reaches unity, or the 
buoyant force equals the viscous force in wind-driven fires scenarios, the local heat flux 
on the downstream surface reaches a maximum. This has strong implications for the fuel 
heating process. A correlation of local heat flux distribution and local Rix will next be 
developed. 
51 
 
0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
 
 Local Ri
x
 
 Heat Flux
L
*
=L/D
H
R
i x
=
G
r x
/R
e
2
x
10
12
14
16
18
20
22
24
26
28
30
32
34
L
*
peak
H
ea
t flu
x
 (k
W
/m
2)
9.5 kW, 1.91 m/s
L
*
Rix=1
Ri
x
=1
 
Figure 28. Local Rix number with local heat flux (9.5 kW, 1.91 m/s). 
52 
 
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
 
 Local Ri
x
 Heat Flux
L
*
=L/D
H
R
i x
=
G
r x
/R
e
2
x
7.9 kW, 2.14 m/s
L
*
Rix=1
L
*
peak
Ri
x
=1
10
12
14
16
18
20
22
24
26
28
30
32
34
H
ea
t flu
x
 (k
W
/m
2)
 
Figure 29. Local Rix number with local heat flux (7.9 kW, 2.14 m/s). 
53 
 
0.6 0.8 1.0 1.2 1.4 1.6 1.8
0.6
0.8
1.0
1.2
1.4
1.6
1.8
 
 
 1.37 m/s
 1.62 m/s
 1.91 m/s
 2.14 m/s
 2.45 m/s
L
*
p
ea
k
  
L
*
 
Rix=1
 
Figure 30. Comparison of dimensionless downstream location at Rix =1 with the peak 
heat flux value. 
 
Looking back to images of the flame in forced and plume-like configurations, the peak heat 
flux observed where Rix=1 seems reasonable as the flame is observed to slightly curve 
before reaching an inflection point where it transitions to a plume-like configuration. This 
inflection point apparently causes significant flame attachment, which most likely results 
in very high convective heat fluxes (only total, radiative plus convective measurements 
were conducted for this study). Figure 31 shows the dimensionless local total heat flux 
*
fq  
plotted against the local Rix, where 
*
fq  is  
                                       AgLTcqq paff  /*                                                            (20) 

  peakRi LL x 1
54 
 
and                                        )/(  TTTA f                                                              (21) 
with 
 TTT f  the difference between the flame and ambient temperature, and a  and 
pc  the density and specific heat capacity of air, respectively. A is an adapted Atwood 
number for ideal gases used in the study of hydrodynamic instabilities in density stratified 
flows, more commonly defined as )/()( 2121  A . The Atwood number is an 
important parameter in the study of Rayleigh-Taylor instabilities, which are believed to be 
important in wind-driven flame spread problems [99].  
A piece-wise function which correlates the non-dimensional heat flux distribution (Eq. 20) 
with the local Rix number was fit to experimental data and can be expressed as: 









103.0
102.0
2.1
25.0
*
xx
xx
f
RiRi
RiRi
q                                                   (22) 
The local total heat flux to the downstream surface can then be correlated between two 
regimes, with a turning point at Rix=1. Before Rix=1, the non-dimensional heat flux 
changes with local Rix as 
25.0* 02.0

 xf Riq , with a R
2=0.93, while when Rix>1, it changes 
as 
2.1* 03.0

 xf Riq , with a R
2=0.9. Both equations provide a relatively good fit to the 
experimental data. Equation (22) is shown as a solid line in Fig. 31, where it can be used 
to estimate the local total heat flux distribution on the downstream surface for a variety of 
ambient flows and fire sizes.  
55 
 
1 2 3 4
0.01
0.1
Ri
x
>1 regionRi
x
<1 region
 
 
 
Figure 31. Dimensionless local total heat flux with local Rix. 
 
4.4 Discussions and Conclusion 
In this chapter, the total heat flux distribution on the downstream surface is investigated in 
wind-driven line fires. It is found that the heat flux distribution profile changes under 
different wind velocity and fire size regimes. When the wind velocity is low, the heat flux 
will decrease with downstream surface, and when the wind velocity is high, local heat flux 
will first rise to a peak value then decrease with downstream distance. The local Richardson 
number is used to fit experimental data and it is found that the location where the local heat 
flux reaches its maximum matches the location where the local Rix number reaches unity. 
This signals a transition point at Rix=1, at which point the local heat flux profile reaches a 
turning point, too. Finally, a piece-wise function is proposed to correlate the non-
2Re/ xxx GrRi 
9.0
03.0
2
2.1*

 
R
Riq xf
*
fq
93.0
02.0
2
25.0*

 
R
Riq xf
56 
 
dimensional heat flux with local Rix number. Information from this chapter on the local 
heat flux distribution could help shed light onto the fuel heating process and fuel ignition 
process in wind-driven wildland fires. 
  
57 
 
Chapter 5: Flame Fluctuations and Attachment Length 
Pulsations, or “bursts” of flame forward beyond a mean flame front have been observed 
for many different fires, however, few if any works in the literature have addressed this 
subject. In this study, a stationary gas burner is used to investigate forward pulsations of 
flames. The flame shape and location of a wind-driven fire are important information as 
they could potentially determine the region where the flame can reach, and thus the pre-
heating area. The flame shape and location are recorded using high-speed side-view video 
and a methodology is applied to study the controlling parameters.  
 
5.1 Measurement Methodology 
A region starting at the downstream edge of the burner and extending fully downstream, 1 
cm above the surface [12], was determined as a region of interest where extension of the 
flame would relate to flame attachment and fuel particle heating, as shown in the dashed 
rectangle in Fig. 32. The flame location was then determined in this region of interest by 
tracking the furthest-most downstream tip of the flame. This location fluctuated in time, 
where it was observed that the flame would pulse downstream, “bursting” into what would 
be the unburned fuel region in a spreading fire experiment. Experimental videos were 
loaded into a MATLAB script for analysis. While the 1 cm height chosen for the region of 
interest is somewhat arbitrary, the results are found to scale regardless of this height, with 
their absolute values adjusting slightly. To eventually connect these results to real wildland 
fire spread, a fuel bed height could be defined for specific scenarios.  
With captured high definition video perpendicular to the flame, the two-dimensional 
intermittent flame behavior and its corresponding characteristic properties is extracted. 
58 
 
This, of course, averages any variability along the width of the flame, however, the flame 
generally seemed to pulsate along its entire width when observed from above, indicating 
that spatial averaging does not induce a large error to the analysis.  
 
Each image in the video was cropped to this same region of interest and then converted to 
a black and white image using a threshold value based on the average light intensity. This 
analysis included taking a number random images from the video and determining the 
flame/non-flame regions based on light intensity for that specific image using a MATLAB 
tool based on Otsu’s method [100]. The result of this light intensity analysis for each image 
was a conversion factor which was averaged from each of the 6 images randomly selected 
from each video. This average conversion factor was used for all images in the video and 
further analysis of the experiment. The flame attachment location (xa) was finally 
determined as the furthest downstream pixel in the region-of-interest that satisfied the 
flame threshold level, as shown in Fig. 32. 
 
 
 
Figure 32.  Flame location between two time steps in a forced flow experiment. The 
flame attachment location (xa) is measured from the downstream edge of the burner to 
edge of the flame within the attachment region. 
t = 1 t = 2 
xa = 20 cm xa = 24cm 
59 
 
 
 
In the image analysis, the threshold was chosen based on the highest level of light intensity 
present in 6 random images. Then this thresholding method is applied to convert the gray-
scale flame images to binary images from black and white, with 1 indicating flame and 0 
indicating non-flame. Average images from one experiment are obtained by dividing the 
summation of all binary matrices by the total number of images. A 50% probability method 
was used to define the average flame shape following Audoin et al. [101], shown in Fig.  
33. The process of image analysis is shown from still flame images obtained in experiments 
to a black-white binary image, and finally to the average flame shape and geometry 
represented by a red line. The average flame shape, including the average flame length 
from the center of the burner to the flame tip (Lf), the flame tilt angel from the from the 
flame tip to the horizontal (θ), and the horizontal flame extension length (xf) were obtained 
using flame outlines from side-view images, illustrated in Fig. 34. 
 
 
Figure 33. Flame image processing based on luminosity 
 
The flame location in the downstream direction, within a region of interest (ROI) 1 cm 
above the flat, inert surface past the end of the burner was then calculated based on whether 
the flame was present using the 50% probability criterion. This was necessary as the flame 
was observed to fluctuate within this region in time, resulting in intermittent flame 
attachment close to the surface.  
60 
 
 
 
 
Figure 34. A side-view of mean flame properties including the flame height Hf, flame 
length Lf, maximum frequency location xmax, mean flame attachment length xa, horizontal 
flame length xf and flame tilt angle 𝜃 
 
The flame pulsation frequency was obtained from the forward flame location as a function 
of time (Fig. 35) using a variable-interval time-averaging (VITA) method [102], following 
the analysis of pulsations from thermocouples in larger scale spreading experiments [10]. 
Level-crossing was only considered for the forward direction, thus only when the flame 
was not at a location in the previous time step, and then appeared at the next time step, was 
it considered a crossing to avoid double-counting. The resulting forward flame pulsation 
frequency was then determined at each downstream location by dividing the number of 
crossings by the total number of frames, multiplied by the frame rate of the video.  
xf
Hf
Lf
xmax = location (max frequency)
θ
xa = location of mean flame 
(attachment) geometry in ROI
max(flame attachment location) min(flame attachment location)
Flame attachment region
Region of interest
61 
 
0 1 2 3 4 5
44
45
46
47
48
50
51
52
53
 
 
F
la
m
e
 e
x
te
n
si
o
n
 d
o
w
n
st
r
e
a
m
 (
c
m
)
Time (s)
 
Figure 35. Fluctuating flame extension with time.                                    
62 
 
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
0
1
2
3
4
5
6
7
 
 
P
D
F
Normalized flame position
32 36 40 44 48 52 56 60 64
0
2
4
6
8
10
12
14
 
 
L
ev
el
-c
ro
ss
in
g
 f
re
q
u
en
cy
 (
H
z)
Flame location downstream (cm)
 x
max
  
Figure 36.  Probability Density Function (PDF) of normalized flame position 
 
 
5.2 Maximum Flame Pulsation Location 
The downstream flame extension within the attachment region fluctuated in time, causing 
intermittent flame contact within the simulated unburnt fuel region. The flame position in 
time was compared to each of these locations and the number of occurrences was tallied. 
The frequency for each location was then determined by dividing the number of crossings 
by the total number of frames analyzed, and multiplying by the frame rate of the video. 
Thus, based on the flame location over time (Fig. 36, top), the level-crossing frequency can 
be extracted for each flame location downstream (Fig. 36, bottom). The maximum flame 
frequency position, xmax was determined using the method described in previous section, 
63 
 
corresponding, for instance, to 46.5 cm in Fig. 36, bottom. The same method was used for 
each fire/wind configuration. This length was observed to be similar to the average flame 
attachment length, which in this experiment was determined by measuring the 
instantaneous attached flame length, xa within a 1 cm tall crop box downstream of the 
burner for each frame and averaging this value.  
The flame forward pulsation frequency, fF may have an effect on the rate of fire spread 
when intermittent heating is important [10]. It would therefore be desirable to know the 
location of maximum frequency, and if that location corresponds to mean flame features 
for which relationships already exist. Using the defined mean flame geometry from Fig. 
32, we can calculate an approximate horizontal flame length, 
                                                   cosff Lx                                                                 (23)  
which provides a reasonable correlation between the flame length and flame tilt angle. This 
has previously proven useful in the study of flame shapes under wind [103]. Assuming the 
centerline of the flame is straight, the flame tilt angle,  , is approximately a function of 
wind velocity, Uwind and a buoyant vertical velocity from the flame V [104, 105], 
approximated as, 
                                                    
windU
V
tan .                                                             (24) 
Based on correlations by Thomas [106] and Rasbash [107], V can be correlated with the 
flame length for vertical fires as, 
                                                5.0
0
)(51.0
T
T
gLV
f
f

  ,                                                     (25) 
64 
 
where g is the acceleration due to gravity, fL is the flame height, fT  is the flame 
temperature rise over ambient, and 0T  is the ambient temperature. Assuming the centerline 
of the flame is approximately a straight line, as illustrated in Fig. 32, 
                   
wind
f
f
U
T
T
gL 5.0
0
)(51.0
tan

 ,             
2
0
26.0
cos
wind
f
f
wind
U
T
T
gL
U


 .                                  (26) 
 
Thus, the flame horizontal length, xf can be re-written as, 
                                
2
0
26.0 wind
f
f
wind
ff
U
T
T
gL
U
Lx


 .                                                           (27) 
Figure 35 shows the relationship between the location of the maximum flame pulsation 
frequency, xmax, with the horizontal flame length, xf. It is found that there is a clear linear 
relationship between the maximum frequency position and the horizontal flame length, 
with an R2 value of about 0.87, which indicates the data fits fairly well with the function. 
Including Eq. (27), we then can develop a relationship between xmax, Lf and θ, which can 
be expressed as 
                          
2
0
max
26.0
74.02.5
wind
f
f
wind
f
U
T
T
gL
U
Lx


 ,                                               (28) 
where Lf and xmax are measured in cm. 
Equation (28), plotted in Fig. 37, describes the relationship between the maximum 
frequency location and the averaged flame shape. The maximum flame pulsation frequency 
is seen to occur in a specific normalized position of wind-blown flames, perhaps indicating 
that there is a location where attachment is most unstable and the flame’s position 
65 
 
fluctuates with time. Using this fit, the location of the maximum flame pulsation frequency 
can be estimated using mean flame properties, particularly the flame length and the wind 
speed, which is useful as these parameters are much easier to measure in spreading flames. 
Continued study using stationary flames such as these may help to further elucidate the 
mechanisms by which these processes occur and improve our understanding of flame 
spread through wildland fuels.  
 
10 15 20 25 30 35 40 45 50 55 60
15
20
25
30
35
40
45
50
 
2
0
26.0 wind
f
f
wind
ff
U
T
T
gL
U
Lx



 
 
 25*5 cm
2
 25*10 cm
2
 30*25 cm
2
M
a
x
im
u
m
 f
re
q
u
en
cy
 l
o
ca
ti
o
n
 x
m
a
x
 (
cm
)
 
Figure 37.  Horizontal flame length versus the location of maximum frequency, xmax 
 
 
Another important question that arises in flame spread is the distance a flame may extend 
forward of the mean flame attachment length, xa. Previous studies have focused only on a 
87.02 R
2
0
max
26.0
74.02.5
wind
f
f
wind
f
U
T
T
gL
U
Lx



66 
 
mean value, however, a statistical understanding of the flame location can provide more 
useful information when fine fuels in wildland are sensitive to fluctuation of the flame.  
 
  
 (a), Q  = 2.38 kW, Uwind = 1.9m/s                                (b), Q  = 5.0 kW, Uwind = 2.65 m/s 
Figure 38.  Histograms of flame extension length, xa for a 25×5 cm
2 burner. 
 
In order to illustrate the periodic movement of the attachment region, probability density 
functions (PDFs) of the normalized flame location versus the probability of the flame 
occurring at that location were created, shown in Fig. 38. The flame locations were 
normalized by the mean flame attachment length, ax , using the methods described above 
where the Gaussian curve-fits for occurrence created such that the area under each curve 
was equal to unity. These PDF’s therefore indicate the probability that the attachment 
region of a flame would extend beyond the mean flame location and vice versa. As shown 
in Fig. 38, both configurations have a 25×5 cm2 burner with 8(a), Q

=2.38kW, Uwind=1.9m/s, 
and gLUFr wind /
2 =4.28; and 8(b), Q =5.0kW, Uwind=2.65m/s and Fr=6.27. 
Figure 39 shows the Gaussian fits to the PDF’s of xa for two different heat-release rates, 
3.2 and 5.0 kW, for a range of wind velocities. It is clear from the Fig. 39 that, for the same 
fire size, an increase in wind velocity will cause the flame to extend increasingly further 
67 
 
from the mean flame position, even when normalized with mean properties. The 
significance of this result is that increasing winds will cause the attachment region of 
flames to extend significantly further into unburnt fuels during flame spread, further 
explaining why periodic bursts of flames may be a significant factor in heating during 
flame spread. 
0.85 0.90 0.95 1.00 1.05 1.10 1.15
0
2
4
6
8
10
12
14
16
18
20
 
 
p
ro
b
a
b
il
it
y
 o
f 
o
cc
u
rr
ec
n
e
Normalized flame extension position
 1.11m/s
 1.39m/s
 1.61m/s
 2.11m/s
Increase in 
wind velocity
 
      (a)  Fire size = 3.2 kW                                                    
68 
 
 
0.85 0.90 0.95 1.00 1.05 1.10 1.15
0
2
4
6
8
10
12
14
16
18
20
 
 
P
r
o
b
a
b
il
it
y
 o
f 
o
c
c
u
r
r
e
n
c
e
Normalized flame extension position
 1.39 m/s
 1.89 m/s
 2.36 m/s
 2.65 m/s
Increase in
wind velocity
 
(b)  Fire size = 5.0 kW 
Figure 39.  Probability of normalized flame attachment length, 
aa xx / for different fire 
sizes and wind velocities. 
The variance of the normalized flame attachment length, aa xx / from Gaussian curve fits, 
σ2, were extracted for each fire case. Increasing values of σ2 indicate an extension of the 
“wings” of the PDF’s as shown in Fig. 39, which represents an increasing probability of 
both up and downstream extensions from the mean flame position. In other words, a large 
σ2 increases the probability of a flame “burst” forward from the mean flame locations. 
69 
 
Further study of the flame extension found that σ2 has a strong correlation with *
3/2
Q
Fr , 
where gLUFr wind /
2  and )/( 5.25.000 LgTcQQ p 
 . *
3/2
Q
Fr has been found to be a good 
indicator of wind-driven flame movement in previous studies [108, 109]. The variance σ2 
first increases with increasing *
3/2
Q
Fr , then reaches a plateau (Fig. 40). This signifies that, 
as the ratio between wind momentum over flame buoyancy increases, the flame extends 
further from the mean flame attachment length, ax . As *
3/2
Q
Fr  continues to increase and 
exceeds about 2.5, the correlation begins to level off, where σ2 is less dependent on the 
ratio. This observation is expected as the flame starts to become fully attached to the surface 
at high wind velocities, reaching a maximum possible extension length with significantly 
less movement from the mean flame location. Eventually at high velocities, the flame will 
start to extinguish at the leading edge, however, this situation was avoided in this study as 
it is not in the same regime as spreading fires. 
 
70 
 
1.0 1.5 2.0 2.5 3.0 3.5
4.0x10
-4
6.0x10
-4
8.0x10
-4
1.0x10
-3
1.2x10
-3
1.4x10
-3
 
 


Fr2/3/Q*
Level offIncrease with Fr2/3/Q*
 
Figure 40.  The variance, σ2 of the normalized flame attachment length, 
aa xx / , from 
Gaussian curve fits versus Fr2/3/Q* 
 
5.3 Flame Attachment Length 
The flame attachment length of a wind-driven fire along the downstream surface is also an 
important parameter in assessing flame spread. It more directly describes the competition 
between natural convection and forced convection, and should correlate with measured 
heat fluxes along the surface for these smaller, convectively-dominated flames. Averaged 
flame images were first obtained using a 50% threshold that was describe in Section 4.1 to 
determine the flame shape. In Fig. 41, we first obtained the averaged flame shape for one 
case from hundreds of separate images. The flame attachment length for each test was 
71 
 
obtained by analyzing averaged side-view images. An intensity threshold determining the 
flame/non-flame region was applied to the images to give iso-contours of the flame shape. 
  
 
Figure 41. Averaged flame image from experimental pictures 
 
After obtaining the averaged flame shape, the flame images are processed in a MATLAB 
program, to get the iso-contour flame images for each case. Figure 42 shows resulting 
averaged flame with different wind velocities for the same fire size. The flame attachment 
length was then defined as the distance between the burner trailing edge to the downstream 
location where the flame contour is 5 mm from the downstream surface. Different threshold 
72 
 
heights were used to determine the flame attachment length (1, 2, 4, 6 mm) to give a 
representation of the potential error seen in Fig. 42. As the wind velocity is increased, the 
distance along which the flame attaches to the surface increases, but does so at a slower 
rate once the flame becomes nearly attached along the surface. This behavior will increase 
heat fluxes to the downstream surface which would, in turn, increase rates of flame spread. 
We measured the flame attachment length using the scales given in the figures. The flame 
attachment length information is then further analyzed and compared with a local Rix 
number used earlier as well as compared to the location where local heat flux reaches a 
peak value. 
 
 
 
 
 
 
Figure 42. Averaged flame images under different wind velocities show the attachment 
length (Lattach) of the flame to the surface with scales. Regions between the two blue 
dashed lines represent the burner depth, while the red solid lines, which are 5 mm in 
height, represent the flame attachment length measured along the downstream surface. 
7.9 kW, 1.91 m/s 
7.9 kW, 2.45 m/s 
5 cm 
5 cm 
5 cm 
Lattach= 4.6 cm 
Lattach= 18 cm 
Lattach= 19.8 
cm 
7.9 kW, 1.14 m/s 
73 
 
The dimensionless flame attachment length, 
attachL was calculated by dividing the 
attachment length by the hydraulic diameter of the burner surface, DH. 

attachL  was then 
plotted against  1xRiL , the dimensionless location where Rix=1, representing nearly equal 
competition between buoyancy and momentum at that point. After plotting the values, 
shown in Fig. 43, a clear linear relationship was found between 
attachL  and 

1xRi
L , 
                                                


  15.055.1 xRiattach LL .                                                                                                  (29) 
Because we can choose different thresholds for determination of the flame attachment 
length, different definitions for 

attachL  could shift the values in Fig. 43 up or down a little 
bit, however the attachment height (5 mm) was varied ±15% to determine the error bars 
shown, which clearly has little effects on the relationship. Therefore, the flame attachment 
length appears to be directly correlated with the location of maximum heat flux, meaning 
that this location corresponds to the transition between where boundary layer to plume like 
burning occurs.  
74 
 
0.6 0.8 1.0 1.2 1.4 1.6 1.8
1.6
1.8
2.0
2.2
2.4
2.6
 
 
 L
*
a
tt
a
ch
 
L
*
Rix=1
L
*
attach
=1.55+0.5L
*
Rix=1
R
2
=0.94
 
Figure 43. 

1xRi
L  with dimensionless flame attachment length 

attachL where error bars 
shown represents variation in the chosen threshold heights. 
 
Following analysis from the previous section where a relationship was found between the 
local Rix number and the location where the local heat flux reaches a peak, the non-
dimensional flame attachment length on the downstream surface, 

attachL  in terms of 

peakL  
is found to be expressed as: 
                                             


  15.055.1 xRiattach LL                                                      (30) 
5.4 Discussions and Conclusion  
In this chapter, the flame shape in wind-driven fire is investigated, with a focus on the 
flame intermittent fluctuation length and flame attachment length on the downstream 
75 
 
surface. An average flame shape was first obtained using image analysis, followed by a 
flame extension length in the region-of-interest tracked using the VITA method. The 
location of maximum flame pulsation frequency was collected and compared with the 
average flame measurements. A correlation was proposed between the flame horizontal 
length and the maximum flame pulsation frequency location and a linear equation was 
found between the two parameters. The variance of the flame fluctuation was been found 
to be related to Fr and the fire heat release rate, Q*. The flame attachment length on the 
downstream surface was also studied, and a linear correlation was found between the flame 
attachment length and the location where the local Rix reaches unity, the location where 
the flame starts to detach from surface shifts a little bit from the location where local heat 
flux reaches a maximum value.  
Information from this chapter on the flame intermittent fluctuation can help shed light on 
the flame intermittent heating behavior. By using some average parameters determined 
from flame measurements, such as the flame length, flame height and flame tilt angle, one 
can estimate the flame fluctuation extension length. The variance of flame fluctuation is 
sensitive to wind velocity and fire heat release rate, which was found to be well correlated 
with *
3/2
Q
Fr . 
  
76 
 
 
Chapter 6: Flame Intermittent Frequencies 
Most literature on wind-driven fire spread has focused on steady-state burning 
characteristics of these fires, preferring this time-averaged view of flame tilt angles, 
burning rates and downstream heat fluxes to the more complicated, stochastic movements 
that flames make. The fluctuation of the flame front, however, has recently been 
determined to play an important role in flame spread, in particular for wildland fires. The 
movement of flames therefore may have implications in a variety of wind-driven scenarios, 
wherever flames reside long enough to heat unburnt fuels and thus contribute to forward 
fire spread. While some flame “pulsation” have been studied in the past, such as the 
intermittent “puffing” of pool fires under stagnant conditions, this behavior is different 
from what is observed from wind-driven configurations. The puffing frequency of the pool 
fires has, however, been found to correlate well with the diameter of the fire source. These 
experiments on buoyant plumes suggest that puffing is primarily a result of a buoyant flow 
instability, which involves a strong coupled interaction between the buoyant plume and a 
toroidal vortex formed a short distance above the burner surface. This scaling has also been 
represented as a Strouhal –Froude relationship St ~ Fr-0.5. In wind-driven fires, the pulsation 
of the flame will probably not scale with burner size in the same way as fires under stagnant 
conditions, as the wind velocity, which is a critically important element in the flame 
movement, is not included in the formulation.  
 
In the previous chapter, the local total heat flux distribution on the downstream surface of 
wind-driven line fires was investigated and a local Richardson number ( 2Re/ xxx GrRi  , 
flame buoyancy over wind momentum) was employed to scale the measured non-
77 
 
dimensional heat fluxes. The average flame attachment length was also found to be linearly 
related to the local Rix. Those experiments represented a first step toward understanding 
the behavior of spreading wind-driven fires. However, only time-averaged quantities were 
reported, which would be able to help estimate the amount of heat that can be received by 
the downstream unburnt fuel by a given time, thus helping to further understand the fuel 
ignition and fire spread in wind-driven flames. 
In this study, a stationary, non-spreading gas-burner fire configuration was chosen as it 
allows for a thorough statistical analysis of the flame structure. Long-duration experiments 
allow for a large sample size and more control over variations in experimental parameters, 
such as decoupling the heat-release rate of the fire from flow conditions, unachievable in 
spreading fires. The flame zone depth in the direction of fire spread can also be carefully 
adjusted via the size of the burner. High speed video is useful on these fires to reveal and 
track buoyant instabilities in the fire flow which resemble those appearing in spatially-
uniform fuel beds [10]. The same intermittent movements observed in the fuel bed 
experiments were observed with the stationary burner, but with the ability to collect a larger 
data set. The flame forward and downward pulsation of wind-driven line fires will be 
studied, respectively to shed light into the ignition of unburnt fuels by flame contact and 
thus the fire spread. The flame forward pulsation frequency will be extracted from flame 
videos using the VITA method, while the local flame-fuel contacting frequency on the 
downstream surface will be obtained through a FFT of heat flux sensor data. Scaling laws 
will be developed for these two frequencies respectively and equations will be derived to 
correlate the frequency with related controlling parameters. 
 
78 
 
 6.1 Flame Forward Pulsation Frequency 
The flame forward pulsation was measured for stationary burners under wind. The flame 
location was determined using side-view high speed videos. Each image in the video was 
cropped to the same region-of-interest, a region defined from the downstream edge of the 
burner surface to the end of the image in the downstream direction, with a certain height 
above the surface. This region, in theory, could represent a fuel bed depth in a spreading 
fire (see the dashed rectangle in Fig. 44). Flame images were then converted to greyscale 
images in MATLAB by averaging all three color channels, and a threshold applied to result 
in a black-and-white image of flame and no-flame regions. As shown in Fig. 44, the flame 
position and flame shape are constantly changing when there is a perpendicular wind. The 
flame location is determined in the region of interest by tracking the furthest downstream 
tip of the flame detected from thresholding. This location fluctuates in time and would 
“burst” or quickly enter into what would be the unburnt fuel region, resulting in the 
intermittent heating of unburnt fuels by flame contact. 
 
Figure 44.  Flame location between two time steps in a forced flow experiment 
 
Resultant flame locations as a function of time, shown in Figure 45, were analyzed using 
the VITA method. Level-crossing was only considered in the technique for the forward 
t = 1 t = 2 
xa = 40 cm xa = 45 cm 
79 
 
direction, thus only when the flame was not at a location in the previous time step, and then 
appeared at the next time step, was it considered a crossing to avoid double-counting. The 
resulting flame forward pulsation frequency was then determined at each downstream 
location by dividing the number of crossings by the total number of frames, multiplied by 
the frame rate of the video. For this study, a 1 cm crop box height was used as the region 
of interest, as shown in Fig. 44. Other heights up to 4 cm were also tried, however the 
results were found to follow the same scaling shown here regardless of the height, with 
only their absolute values adjusting slightly. The mean values of the frequency data 
obtained from all the thresholds was used for later analysis. To connect results eventually 
to real flame spread, a fuel bed height will need to be defined for the scenario at hand.  
0 1 2 3 4 5 6
44
45
46
47
48
50
51
52
53
 
 
F
la
m
e
 l
o
c
a
ti
o
n
 (
c
m
)
Time (s)
 
Figure 45.  Fluctuating heat flux signals over time 
 
80 
 
 
Figure 46 shows resultant frequencies following application of the VITA technique. As can 
be seen, the frequency is initially 0 within the continuous flame region nearer to the burner, 
but as the flame intermittently moves forward and backwards, it enters and leaves the 
unburned region producing a parabolic profile of frequencies. A maximum frequency 
therefore occurs between the continuous flame region and the maximum forward extension 
of the flame, indicated in Figure 46. The frequency at this location is used in the analysis 
as a maximum representative frequency of the flame along the surface.  
 
0.4 0.6 0.8 1.0 1.2 1.4 1.6
0
1
2
3
4
5
6
7
 
 
P
D
F
 o
f 
fl
a
m
e 
p
re
se
n
ce
Normalized flame position
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0
2
4
6
8
10
12
14
 
 
L
ev
el
-c
ro
ss
in
g
 f
re
q
u
en
cy
 (
H
z)
Flame location downstream (cm)
Max frequency
 
Figure 46.  Level-crossing frequency and Probability Density Function (PDF) shows the 
flame locations on the downstream surface (7.9 kW, 2.45 m/s) 
81 
 
 
Applying the VITA method to all fire sizes and wind velocities, maximum frequencies are 
extracted, shown in Fig. 47. It shows that the flame pulsation frequency increases relatively 
linearly with the wind velocity, while it decreases with fire size in all the experiments 
tested. The frequencies observed range from less than 10 Hz to about 15 Hz. 
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
9
10
11
12
13
14
15
 
 
 6.3 kW
 7.9 kW
 9.5 kW
F
o
r
w
a
r
d
 p
u
ls
a
ti
o
n
 f
F
 (
H
z
)
Wind Velocity (m/s)
  
Figure 47.  Forward pulsation frequency with different wind velocities and fire size 
 
For the flame forward pulsation frequency, it is thought to be the result of competition 
between the forward momentum of the ambient wind and buoyancy from the flame itself. 
A scaling analysis can be performed, assuming relevant parameters, which reveals two 
primary groups that the forward pulsation frequency is dependent on, the Froude number 
(wind momentum over inertial force) and Q* (buoyancy). A phenomenological explanation 
can be arrived at by first assuming the flame forward-pulsation frequency can be related to 
82 
 
both the ambient wind velocity, u and the flame length, lf, which characterizes buoyancy 
from the fire, as 
                                                               
f
F
l
u
f ~                                                           (31) 
In a wind-driven fire, the flame length has previously been found to be a function of the 
wind velocity and mass burning rate in the form [110, 111],  
                                             
 C
B
a
f
u
gD
m
A
D
l








 



                                          (32) 
where D is the characteristic diameter or length of the burner, m   the mass burning rate 
of the fire, and A, B, and C are constants, previously found to be 62, -0.044, 0.25, 
respectively for gas diffusion flames [111]. A non-dimensional velocity can be defined as 
a ratio of the ambient wind velocity and a characteristic buoyant velocity of the fire,  
                                                 3/1/ aDmg
u
u



                                                    (33) 
where g is the acceleration due to gravity and a  the density of ambient air. Assuming the 
fuel burns completely, m  can be related to the heat-release rate of the fire, Q  as  
                                                  mHQ c  
                                                                (34) 
which provides a more functional and universal parameter from which to define the fire. 
The heat-release rate can be non-dimensionalized as Q  [112] for a fire plume and 
expressed in terms of m   as 
                                           m
gDCT
Q
Q
paa
 

~
5
                                                 (35) 
83 
 
Combining equations (1-5), we arrive at equation (6), which relates the flame forward-
pulsation frequency with the Froude number and the non-dimensional heat-release rate,   
                              2/14/1
2/1
265.0
044.1
~


Q
Fr
Q
Fr
Q
u
fF                                               (36) 
The flame forward pulsation frequency data is then plotted against this parameter derived 
above in Figure 48, and a power-law relationship is found relating them as shown in 
Equation (37), 
                              
35.0
2/1
7.0
4/1
2/1
)(9.12)(9.12


Q
Fr
Q
Fr
fF                                               (37) 
It shows that the correlation between flame forward pulsation frequency and 
2/1
/ QFr can 
be well correlated in an equation, with an R2 very close to 1, indicating an excellent fit. 
Thus with Eq. 37, one can well estimate the flame forward pulsation frequency using more 
basic and more achievable fire parameters and mean flame measurements, including the 
fire heat release rate and Fr number. 
84 
 
0.6 0.8 1 1.2 1.4 1.6
9
10
11
12
13
14
15
 
 
 6.3 kW
 7.9 kW
 9.5 kW
F
o
rw
a
rd
 p
u
ls
a
ti
o
n
 f
F
 (
H
z)
Fr
1/2
/Q
*1/4
f
F
=12.9*(Fr/Q
*1/2
)
0.35
R
2
=0.97
  
Figure 48.  Flame forward pulsation frequencies are found to scale with 
4/1*
2/1
Q
Fr  
 
6.2 Flame-fuel Contact Frequency 
The flame-fuel contact frequency can help determine how much heat flux can be received 
by unburnt fuels ahead of the flame through direct flame contact, which has recently been 
found to be a primary mechanism of ignition of fuels in a wind-driven wildland fire [10]. 
For each of the experimental conditions mentioned in Table 1, raw heat flux signals were 
taken at different locations on the downstream board. The flame-fuel contact frequency can 
be extracted from measured heat flux signals, such as the one shown in Figure 49 (top), by 
applying a FFT which results in a frequency spectrum, on the bottom, which has a peak at 
about 2 Hz. 
85 
 
0 20 40 60 80 100 120 140
21.6
21.8
22.0
22.2
22.4
22.6
22.8
23.0
 
 
9.5 kW, 1.91 m/s
H
ea
t 
F
lu
x
 (
k
W
/m
2
)
Time (s)
 
0 5 10 15 20 25 30 35
0.00
0.01
0.02
0.03
0.04
0.05
0.06
 
 
In
te
n
si
ty
Frequency (Hz)
FFT
 
86 
 
Figure 49.  Heat flux raw data at 11 cm, with 9.5 kW fire size, 1.91 m/s wind velocity, 
and frequency spectrum obtained from FFT 
 
The same method is applied to three cases with different wind velocities but the same fire 
size (9.5 kW) at 11 cm downstream, shown in Figure 50. The FFT is smoothed using a 
Savitzky–Golay filter and the peak intensity used to choose the peak frequency at that 
location. In Figure 49, it can be seen that the flame-fuel contact frequency slightly increases 
with increasing wind velocity, however the intensity of this peak decreases.  
0 2 4 6 8 10 12 14 16 18 20
0.00
0.01
0.02
0.03
0.04
0.05
 
 
In
te
n
si
ty
Flame-fuel contact frequency f
C
 (Hz)
 
 
 
Figure 50. Comparison of frequency obtained from the FFT for different wind velocities. 
 
0 1 2 3 4 5
0.000
0.005
0.010
0.015
0.020
0.025
0.030
 
 
f=2.1 Hz
f=1.5 Hz
In
te
n
si
ty
Frequency (Hz)
 
 
 9.5 kW, 1.62 m/s
 9.5 kW, 1.91 m/s
 9.5 kW, 2.14 m/s
f=1.2 Hz
87 
 
 
The local flame-fuel contact frequency was further plotted for different wind velocities and 
fire sizes. Figure 51 shows one example where the fire size is 7.9 kW, with the local 
frequency at different locations plotted and compared. The figure shows how, for a given 
wind velocity, the local frequency tends to go down with downstream distance from the 
burner.  
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
 
 
 5.5 cm   22 cm
 11 cm    27.5 cm
 16.5 cm  33 cm
F
la
m
e-
fu
el
 c
o
n
ta
ct
 f
re
q
u
en
cy
 f
C
 (
H
z)
Wind velocity (m/s)
7.9 kW
 
Figure 51. Local flame fuel contact frequency for 7.9 kW under different wind velocities  
 
 
Previously, the flame puffing frequency without wind has been found to be only a function 
of burner size. Under wind conditions, however, two directional flame pulsations are 
clearly observed. One is the forward pulsation, where the flame is driven by the wind and 
moves back and forth in the stream-wise direction. The other is the upward pulsation, 
88 
 
which is found to be really a local phenomenon, where flame is touching and transferring 
heat to the local unburnt fuel within the attachment and intermittent regions. This section 
will discuss these two pulsation frequencies and their correlations with related parameters. 
For the local flame-fuel contacting frequency, following our previous work on the local 
heat flux distribution on the downstream surface in wind-driven line fires. The local 
Grashof (   23 / LTTgGr hx  ) and Reynolds ( /Re ULx  ) numbers arise as critical 
parameters describing the flow and heat transfer in our setup, where hT  and T are the hot 
gas and ambient temperatures, respectively, L is the characteristic length, g the acceleration 
due to gravity,   the thermal expansion coefficient, and  the kinematic viscosity of the 
ambient air. The relative role of buoyancy and inertial forces in the flow have been found 
to be well-described by comparing the relative influence of these two parameters, often 
determined to be a
xxGr Re/ , with a varying constant a.   
In a flame scenario with forced air flow, the Richardson number, with the exponent on Rex 
determined as 2, was defined as: 
                                                   
 
22Re U
LTTgGr
Ri
f
x
x
x



                                           (38) 
Ri was used to represents the ratio between natural convection (controlled by the buoyancy 
of the flame) and forced convection (controlled by the forced air flow velocity), and instead 
of using the temperature of the hot gas, the flame temperature
fT was used. The flame was 
then divided into regions to describe flame attachment and liftoff that shown in Eq. 19. 
Inertial forces would be expected to dominate the flame behavior when Rix <0.1 and 
buoyancy forces dominate when Rix >10. However, the details and implications of the heat 
transfer modes in the mixed regions (0.1< xRi <10), where the transition from an inertial-
89 
 
dominant to buoyancy-dominant regime, has not been well studied. Because most fires 
with cross air flow scenarios reside in this region, seen visually with flames that begin 
attached near the surface and tend to “lift off” into a more plume-like scenario downstream, 
study of the fire behavior in this region will help improve understanding of the flame spread 
mechanisms. The Local Rix is calculated using equation 18 and plotted against the 
downstream distance, L. Figures 26 and 27 shows several examples of the local Rix trends 
with downstream distance. An increasing trend is seen with increasing downstream 
distance, although the patterns for different wind cases are different from one another other. 
In Chapter 4, it was found that the local Rix was a good indicator to collapse the local heat 
flux distribution along the downstream surface. Here we also apply this method to the 
frequency study and come up with one way to quantify and predict the local flame-fuel 
contacting frequency trend with local Rix number. 
A non-dimensional flame-fuel contacting frequency 
Cf  is proposed based on a 
characteristic gas fuel flow rate and downstream distance, 
                                             



u
Lf
f CC                                                                       (39) 
                                           3/1/ aDmgu 
                                                              (40) 
where 
Cf is the raw frequency data we obtained from heat flux gauge sensor, 
L  is the 
downstream distance from the measuring point to the leading edge of the burner chosen as 
characteristic length scale, 
u  is the characteristic fuel velocity based on mass loss rate, 
m   is the mass flow rate, D the burner hydraulic diameter, and a  the air density.  
Note that this non-dimensional flame-fuel contact frequency is not a typical Strouhal 
number as has been previously defined in pool fire studies. St-Fr correlations have been 
90 
 
found for pool fire puffing frequencies under stagnant conditions, where only natural 
convection (buoyancy) is controlling the flame behavior, and the length scale chosen for 
the study was pool diameter. This appears to be more of a global instability of the system 
driven by buoyancy. In our study, we introduced forced convection (wind), and the length 
scale is chosen as the distance from the measuring point to the leading edge of the burner, 
where the thermal boundary layer starts to develop. The length scale chosen in this paper 
follows the approach in Chapter 4.1 on the effect of forced and natural convection on heat 
flux distribution in wind-driven line fires.  
In Figure 52, the local Rix is plotted against the non-dimensional frequency. When Rix is 
smaller than 1, 
Cf  does not change much, however after Rix reaches 1, 

Cf  starts to 
decrease with Rix. A piece-wise function was obtained based on correlated data to describe 
the local frequency trend with Rix. Equation 41 indicates that, in a wind-driven fire, the 
flame-fuel contact frequency before the local Rix reaches 1 will remain unchanged, 
fluctuating around 0.7. After Rix reaches 1, which means natural convection and forced 
convection approximately balance each other, 
Cf
 will decrease with Rix in a power law 
trend as 78.07.0   xC Rif . 
                                       








17.0
17.0
78.0
xx
x
C
RiRi
Ri
f                                              (41) 
91 
 
0.1 1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
f
C
 +
=0.7Ri
x
-0.78
Ri
x
>1
 
 
 5.5 cm    22 cm
 11 cm     27.5 cm
 16.5 cm  33 cm
f C
+
=
f C
L
+
/U
+
Ri
x
=Gr
x
/Re
x
2
Ri
x
<1
f
C
 +
=0.7
  
Figure 52. Non-dimensional frequency 

Cf  versus local Rix 
 
6.3 Discussions and Conclusion 
The flame forward pulsation frequency and local flame-fuel contact frequencies were 
discussed in this section, as they represent two directions of the flame movement in a wind-
driven fire scenario. The flame forward pulsation frequency describes how frequently the 
flame will move back and forth under certain fire sizes and wind velocities, indicating the 
potential of the flame to reach unburnt fuels on the downstream surface. It has been found 
to be the result of competing mechanisms of buoyancy of the flame and the wind 
momentum. A scaling analysis with Froude number and the non-dimensional heat release 
rate has been proposed to correlate the flame forward pulsation frequency. 
92 
 
In order to study the heating process of the fuels under attached and intermittent regions of 
the flame, the local flame-fuel contact frequency has been studied from measured heat flux 
signals. The local flame-fuel contact describes how frequently the flame “touches” the 
unburnt fuel surface under the flame attachment and intermittent regions, shedding light 
on how the unburnt fuels are actually being heated and ignited by direct flame contact, thus 
providing critical information for the prediction of flame spread. This frequency is thought 
to primarily be due to local flame buoyancy, although the distribution of this frequency has 
a relationship with the flame length (the three flame regions mentioned in Fig. 1). A local 
Rix number analysis has been performed to represent the distribution of this frequency, 
following our previous analysis on the local heat flux distribution on the downstream 
surface. 
Experiments were conducted on a variety wind-driven line fires where the intermittent 
behavior of the flame was studied. Both the flame forward-pulsation frequency and flame-
fuel contact frequency were independently measured. Trends in these quantities were 
reviewed and non-dimensional scaling proposed for each. It was found that flame forward 
pulsation frequency Ff , which could indicate the potential of the flame reaching out 
unburnt fuels on the downstream surface, can be well correlated and predicted by a non-
dimensional parameter, 2/1Q
Fr  in a power law trend. The mechanism of this forward 
pulsation has been found to be related to the competition of wind momentum and flame 
buoyancy. For the flame-fuel contacting frequency, which tells the local heating process of 
the flame to the unburnt fuels on the flame attachment and intermittent regions. A piece-
wise function was found between the non-dimensional 
Cf  with local Rix, indicating that 
93 
 
when Rix<1, non-dimensional flame contact frequency Cf  remains approximately 
constant, when Rix>1, it decreases with Rix. The information of flame forward pulsation 
frequency and local flame-fuel contact frequency, and their correlations with concerning 
parameters will help explain the wildland fire fuel ignition and flame spread.  
  
94 
 
Chapter 7: Conclusions  
In this work, a thorough experimental work has been conducted on the wind-driven line 
fires. Detailed information connecting intermittent fluctuations of the flame to fuel heating 
processes have been investigated. The local heat flux distribution on the downstream 
surface, intermittent pulsation frequencies of the flame, the flame extension length and 
flame attachment region have been studied in detail.  
First, the local total heat flux from a wind-driven line fire on the downstream surface was 
found to have different profiles for different wind speeds and fire sizes. When the wind 
speed is low, the heat flux decreases with downstream distance, while with a high wind 
speed, the heat flux first increases to a maximum value, then decreases. The location where 
the maximum local heat flux received by the downstream surface in a forced flow flame 
roughly matches the location where the local Rix =1. The dimensionless local total heat flux 
was then correlated with downstream location in a piece-wise function based on the 
Richardson number, breaking up the correlation between the attached and plume regions. 
The visually-observed flame attachment length was also found for each test, and linear 
correlation was found between this length and Rix. Information between the flame 
attachment length and local Rix are be able to help estimate the downstream location where 
it receives the most heat flux from a turbulent diffusion flame, and also where the flame 
starts to rise up and eventually enter plume region, thus shedding light on flame spread 
mechanisms downstream.  
A time-dependent view of the flame was also taken, observing the flame forward pulsation 
frequency Ff , which indicates the potential of the flame reaching out to unburnt fuels on 
the downstream surface past the average extent of the flame, can be well correlated and 
95 
 
predicted by a non-dimensional parameter, 
2/1Q
Fr , following a power law trend. The 
mechanism of this forward pulsation has been found to be related to the competition of 
wind momentum and flame buoyancy. For the flame-fuel contact frequency, which 
describes the local heating process of the flame to the unburnt fuels within the flame 
attachment and intermittent regions. A piece-wise function was found between the non-
dimensional 
Cf  with local Rix, indicating that when Rix<1, the non-dimensional flame 
contact frequency 
Cf  remains approximately constant and when Rix>1, it decreases with 
Rix. Information on the flame forward pulsation frequency and the local flame-fuel contact 
frequency, as well as their correlations with concerning parameters will be useful in the 
future to develop models for wildland fire fuel ignition and flame spread.  
The extension length of the flame has also been studied as a function of time. For increasing 
ambient wind velocities, flames are found to intermittently extend further downstream 
from the mean flame front, when measured along the surface. This means a longer region 
of flame contact with unburnt fuels would result during flame spread, increasing flame 
spread rates. The maximum frequency position is also found to be linearly related with the 
horizontal flame length along the fuel surface, indicating that periodic properties of the 
flame could be estimated from mean flame measurements and wind speeds. The variance 
(σ2) of the mean flame attachment length is also found to be sensitive to *
3/2
Q
Fr . The 
attachment length and intermittency characteristics of flames are critical factors in heating 
and ignition of fine fuel particles in wildland fires. Further study of the mechanisms leading 
to forward pulsations of the flame front are needed to more carefully determine the 
influence of these mechanisms on flame spread through wildland fuels. 
96 
 
Chapter 8: Future Work 
This study presented a first look at the behavior of stationary wind-driven flames and their 
time-dependent behavior. Based on what was found, there is a large amount of future work 
to explore in the area. First, tests with a large fire size and high wind velocity should be 
introduced, as only small fire sizes (~10 kW) and relatively low wind velocities (~2 m/s) 
have been employed in this project. In real wildland fires, the fire size will be much larger 
and turbulent. The flames in this study are, at best, transitionally turbulent, so this may 
limit their application. Data from larger fire sizes and a range of wind velocities should be 
collected and compared with our existing data, seeing whether the data and experimental 
observations can scale with size. 
The proportion of radiation vs. convection is also an important aspect that should be studied 
for its use in determining future models for flame spread, especially at larger scale. The 
local convective and radiative components can be calculated with either sapphire-window 
radiometers or estimated using the local temperature gradient. This information is 
important in that it will show a more direct picture of the fuel heating process, how much 
of the total heat flux is radiant heat, and how much is convective heat, shedding further 
light onto the heating and ignition of fuels in wind-driven fire spread. 
The mechanisms governing the frequencies observed for both forward pulsations of flames 
and flame-fuel contact are still not fully understood. Preliminary results have already 
shown that the frequency of wind-driven line fires are less than in stagnant situations. But 
the reason for this decrease in frequency is not fully understood. Probing detailed numerical 
simulations of the situations studied and/or development of theory to describe this behavior 
may be useful to further elucidate the mechanisms responsible.  
97 
 
Further improvements to the experiments can also be made. Further characterization of the 
incoming flow may be useful for validation of numerical models. Further aspect ratios of 
the burner would also be useful, but that will require a larger wind tunnel. The resolution 
of the heat flux data may also be improved by employing a smaller diameter heat flux 
gauge.  
In these experiments, flame spread behavior was studied on a flat plane, where the wind is 
flush with the surface. In real wildland fires, there could be many different geometries, for 
example, the flame can spread over an inclined surface, or the flame can spread in canyons. 
The fire behavior in these inclined geometries can be very different compared with flame 
spread over flat surfaces due to changes in entrainment, although the mechanisms may be 
similar. In later experiments, variations of these geometries will be undertaken to gain more 
insight into the processes governing wildland fire spread. 
 
  
98 
 
Published Journal/Conference articles 
1. Wei Tang, Colin Miller, Michael Gollner, Local Flame Attachment and Heat Fluxes 
in Wind-Driven Line Fires, Proceedings of the Combustion Institute, Volume 36, 
Issue 2, 2017, Pages 3253-3261. 
2. Wei Tang, Daniel Gorham, Mark Finney, Sara McAllister, Jack Cohen, Jason 
Forthofer, Michael Gollner, Intermittent heating and flame extension in wind-driven 
fires, Fire Safety Journal, in press. 
3. Colin Miller, Wei Tang, Mark Finney, Sara McAllister, Jason Forthofer, Michael 
Gollner, An investigation of coherent structures in laminar boundary layer flames, 
Combustion and Flame, Volume 181, July 2017, Pages 123–135. 
4. Cong Zhang, Mélanie Rochoux, Wei Tang, Michael Gollner, Jean-Baptiste Filippi 
and Arnaud Trouvé. Evaluation of a data-driven wildland fire spread forecast model 
with spatially-distributed parameter estimation in simulations of the FireFlux I field-
scale experiment, Fire Safety Journal, in press. 
5. Michael Gollner, Colin Miller, Wei Tang, Ajay Singh, Recent developments in 
concurrent flame spread, Fire Safety Journal, in press. 
6. Wei Tang, Mark Finney, Sara McAllister, Michael Gollner, An experimental study 
of the intermittent heating frequencies of wind-driven line fires. Preparing. 
7. Wei Tang, Daniel Gorham, Michael Gollner, Jason Forthofer, Mark Finney, Forward 
pulsation behavior of wind-driven line fires, 9th  U. S. National Combustion Meeting, 
May, Cincinnati, Ohio. 
99 
 
8. Wei Tang, Mark Finney, Sara McAllister, Michael Gollner, An experimental study 
of the flame intermittent frequencies of wind-driven line fires, 10th  U. S. National 
Combustion Meeting, April, College Park, Maryland. 
9. Gollner, M.J., Tang, W., Gorham, D.J., Finney, M.A., McAllister, S., Cohen, J. and 
Forthofer, J., Dynamic Behavior and Structure of Wind Blown Flames, 25th 
International Colloquium on the Dynamics of Explosions and Reacting Systems, 
August 2-7, Leeds, UK, 2015.7-20, 2015. 
10. Cong Zhang, Mélanie Rochoux, Annabelle Collin, Philippe Moireau, Wei Tang, 
Michael Gollner, Evan Ellicott, Arnaud Trouvé. Front Shape Comparison in Data-
Driven Wildland Fire Spread Simulations, 10th U. S. National Combustion Meeting, 
April, College Park, Maryland. 
11. Kun Zhao, Lizhong Yang, Wei Tang, Michael Gollner, Experimental and theoretical 
study on downward flame spread over two parallel PMMA slabs in different pressure 
environments, 10th U. S. National Combustion Meeting, April, College Park, 
Maryland. 
12. Colin Miller, Mark Finney, Sara McAllister, Torben Grumstrup, Evan Sluder, Wei 
Tang, Michael Gollner, Investigating streak-like structures in boundary layer 
combustion via heated plates, 10th U. S. National Combustion Meeting, April, 
College Park, Maryland. 
 
 
100 
 
Appendix A: Convective and radiative heat flux 
In this section, we will discuss the convective and radiative heat flux components from the 
total incident heat flux received by the downstream surface. Radiation can be directly 
measured by a Medtherm radiometer, which is described in previous experimental setup 
part. Convection, however, can be calculated or estimated based on the temperature 
gradient on the board surface.  
                                      
 
f
wfl
fwflcfl，
y
TT
kTThq

                                                (42) 
in which, 
cfl，q  is the gas phase convective heat flux, or we can further estimate the 
convective heat flux as 
                                                  
0, )(  ywcfl
dy
dT
kq .                                                         (43) 
To calculate the convective heat flux, fine resolution temperature profiles near the 
insulation board surface can be measured. For example, for one measuring location with 
one wind velocity and fuel flow rate, six points were measured in a vertical direction with 
0.4 mm in spacing. An average temperature data was taken for three repeated 
measurements. Figure 53 below shows the temperature profile for a given fire case, with a 
fire size of 7.9 kW and wind velocity 2.14 m/s. Here, we can see there is a high temperature 
gradient on the board surface close to the burner, and with further locations away from the 
burner, the temperature gradient decreases. This can be explained by the flame attachment 
process, when the flame is attached the near burner surface and temperature gradient and 
convection at the surface is very high. When the flame lifts up at further downstream 
101 
 
locations, the local temperature gradient becomes less obvious, and convection in that 
region plays less of an important role. 
0 2 4 6 8 10 12
200
400
600
800
1000
1200
 
 
T
em
p
er
a
tu
re
 (
K
)
Vertical location from the surface (cm)
 5.5 cm
 11 cm
 16.5 cm
 22 cm
 27.5 cm
 33 cm
 
Figure 53. Temperature distribution on the downstream board with fire size 7.9 kW, wind 
velocity 2.14 m/s 
The data was further analyzed, interpolating the temperature profile, shown in Figure 54.. 
From this figure, we could also see the temperature gradient difference in the near and far 
locations on the downstream surface. In the near-field of the burner, the local temperature 
gradient is much higher than in the far field.  
102 
 
 
Figure 54. Interpolation of the temperatures measured above the downstream surface 
 
Figure 55 below shows the temperature gradient profile for one case (wind velocity 2.14 
m/s, fire size 6.3 kW, and measurement location 5.5 cm from the trailing edge of the 
burner). It can be seen that a large temperature gradient appears at the board surface. The 
local temperature is first estimated by fitting the data points and a gradient at the surface 
calculated from the derivative of this fit at the board surface,  
                                                     0 yyTT .                                                          (44) 
The local temperature gradient at the surface is about 4.9× 105 K/m and thermal 
conductivity for air at the film temperature, which is the mean temperature of the wall and 
the flame, is estimated as 4.3×10-5 kW/K.m. Thus, the local convective heat flux is  
                                        0, )( ywcfl
dy
dT
kq 21.07 kW/m2                                                 (45) 
Re-visiting the total heat flux data we had from the previous section, we noticed that the 
local heat flux for this fire case are about 26 kW/m2. So, radiation in this region only 
provides less than 20% of the total heat flux. This makes sense for these small, laminar or 
103 
 
transitional flames. Information from previous studies also shows that convection in the 
near-field of the burner field is dominant within the boundary layer for laminar flames [52]. 
0.0 5.0x10
-4
1.0x10
-3
1.5x10
-3
2.0x10
-3
5.0x10
2
5.5x10
2
6.0x10
2
6.5x10
2
7.0x10
2
7.5x10
2
8.0x10
2
8.5x10
2
9.0x10
2
9.5x10
2
1.0x10
3
1.1x10
3
1.1x10
3
1.1x10
3
1.2x10
3
 
 
T
em
p
er
a
tu
re
 (
K
)
Vertical location (m)
 
Figure 55. Temperature gradient at the surface 
  
  mKyTT
y
/109.4 5
0


104 
 
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