THE EFFECTS OF NON-UNIFORM SURFACE REGRESSION ON THE 

STABILITY AND SPREADING OF A PMMA BOUNDARY LAYER FLAME 

NEAR THE EXTINCTION LIMIT

Chuka C. Ndubizu (cndubizu@castor.nrl.navy.mil), Geo Centers Inc. 

Ramagopal Ananth (rananth@castor.nrl.navy.mil) and Patricia A. Tatem 

Navy Technology Center for Safety and Survivability 

Naval Research Laboratory 

Washington DC 20375 

ABSTRACT 

This paper focuses on the effects of moving boundary on the stability of a boundary layer 

flame over poly methylmethacrylate. Experiments were conducted with air (less than 

19.4% oxygen (by volume)) and free stream velocity of 87 cm/s. At these conditions the 

flame retreated from the leading edge after ignition and stabilized downstream 

establishing a quenching distance. The results show that the flame could not sustain 

within the quenching distance when the surface was flat, molten and pyrolyzing but will 

sustain and spread upstream after the surface has solidified. This is possible because of 

the creation of a stabilizing valley on the solidified surface as a result of surface 

regression. It appears that the valley helped stabilize the flame, perhaps by creating a 

stagnation/re-circulating zone where the Damkholer number is increased. Thus, moving 

boundary effects could significantly enhance flame stability and spread and may make it 

difficult to extinguish the flame. 

INTRODUCTION 

Boundary layer-type flames are prevalent in wall fires, ceiling fires, and wind-driven fires 

on flat surfaces such as floors and roofs. The suppression and extinction of such fires 

present a challenge because of the proximity of the condensed fuel to the flame. The rate 

of burning depends on the heat feedback to the condensed fuel and in boundary layer 

flames this is highest in the leading section where the flame is closest to the surface and 

decreases with the stream-wise distance from the leading edge. In boundary layer 

combustion of non-charring solids like Polymethyl methacrylate (PMMA), the solid 

surface regresses as the sample burns and forms a valley near the flame leading edge. 

Near the extinction limits, chemical kinetics effects dominate over transport effects and 

depending on the initial value of the Damkholer number, Da, the boundary layer flame 

can be anchored away from the fuel leading edge, creating a quenching distance 

(sometimes referred to as “extinction distance”), where combustion cannot be sustained. 

For a flat surface, it has been established [1-3] that the flame cannot spread upstream and 

the quenching distance remains constant with time. 

This paper will present results of experiments that demonstrate the effects of moving 

boundary on the stability and upstream spreading of a boundary layer flame over PMMA. 

It will show that the flame could not sustain within the quenching distance when the 

surface was flat, molten and pyrolyzing but will spread upstream (decreasing the 
quenching distance) after the surface has solidified. The implication of this is that the

moving boundary effects would enhance flame stability and make it more difficult to 

suppress the flame.

EXPERIMENTAL 

The key components of the experimental setup consist of a 15-cm2 cross-sectional wind 

tunnel, a PMMA sample holder mounted on a MiniTec  sliding mechanism and a

thermocouple mounted on computer controlled Velmex X-Y unislides (Fig.1). The wind 

tunnel has a 36 X 45 X 61 cm plenum at one end into which an Ametek RJ054  variable 

speed blower pumps air. Air from the blower is mixed with a known flow of nitrogen 

before the mixture flows into the plenum. Pressure build-up in the plenum drives the flow 

of the oxidizer through the wind tunnel and hence the effects of the blower on the flow 

are minimized. The flow velocity in the wind tunnel is selected by adjusting the speed of 

the blower. The oxygen concentration in the airflow is continuously measured by 

sampling gas from the wind tunnel and measuring the concentration of the sample in a 

Beckman  Industrial oxygen analyzer Model 755. The burning sample is positioned

outside the tunnel at the center of the tunnel exit. This makes it easier for the

thermocouple to be moved freely in and out to measure temperatures. 

The sample holder is made of a 1.5-mm-thick aluminum plate (18.5 cm x 19 cm) brazed 

onto a 10 cm x 8 cm x 2.1 cm deep cup, which holds the PMMA sample. This provides a 

4-cm lip in the leading section and a 5-cm lip in the other three sides. At the measurement 

location, the holder is positioned with its leading edge against the tunnel exit at the center 

of the channel (Fig.1). A thin strip of quartz glass is placed between the PMMA sample 

and the walls of the holder on all the four sides to prevent molten PMMA from sticking

on the walls of the sample holder. The sample and holder sit on a platform mounted on a 

slide mechanism such that the sample can be ignited under the radiant panel located about 

50 cm downstream from the tunnel exit and quickly moved to the tunnel exit after 

ignition. The test samples are 7.7 X 9.5 cm and are made from Cyro Acrylite GP  sheet 

nominally 2.54 cm thick. The incoming oxidizer velocity is measured at the exit of the

tunnel (measurement location) using a hot wire anemometer. More details of the setup are 

described in [4]. 

Air with reduced oxygen (between 19.4 ± 0.1 % and 18.8 ± 0.1 % by volume) flows 

through the wind tunnel with an exit velocity of 87±1 cm/s at the center. With U∞ = 100 

cm/s, Kodama et al. [3] predicted a mass fraction of 18% at the lean extinction limit. 

Thus, these experiments were conducted near the flame extinction limits. The sample 

surface is ignited by uniform radiation from a radiant panel at the ignition location and

the flame retreats downstream soon after it is moved to the exit of the tunnel (Fig.1). An 

R-type thermocouple, 75 μm in diameter, is quickly lowered into the molten layer as the 

flame retreats. The thermocouple continuously measures the temperature of a point on the 

molten/solidifying layer within the quenching distance as the flame stabilizes 

downstream and as the stable flame spreads upstream within the quenching distance. To 

reveal the sample surface 

2
Motorized unislides 

Air

Radiant 

Panel 

Initial quenching distance

Flame

Wind Tunnel

thermocouple 

Sample holder 

(PMMA sample 

inside) 

Test Location Ignition Location 

Figure 1: Schematic of the experimental setup illustrating the process of establishing 

the quenching distance on the PMMA sample surface 

profile at the relevant times in the experiment, separate tests were conducted, where the 

flame was extinguished as it is retreating (stage 1), as it stabilizes (stage 2) and after it 

spreads upstream for some time (stage 3). 

RESULTS AND DISCUSSIONS 

To establish a boundary layer flame over the entire PMMA sample, the surface is heated

under a radiant panel far downstream, where the air velocity is significantly smaller than 

at the exit of the tunnel, Fig.1. It is important to ensure that the entire surface is 

pyrolyzing as indicated by intense bubbling before the flame is ignited. After ignition, the 

sample is quickly moved to the exit of the tunnel. 

3
Figure 2a shows the flame as the sample was being brought to the exit of the wind tunnel. 

It shows a relatively smooth flame near the leading edge region, which gets wrinkled and 

unsteady downstream. The wrinkling could be as a result of the movement or as a result 

of buoyancy effects, since the plate surrounding the sample was still very hot, having 

been heated by the radiant panel. The buoyancy effects die down as the metal lip cools to 

ambient within a short time. Figure 2a shows that the flame covers the entire sample, 

including the leading edge region, implying that this region is molten and pyrolyzing at 

this stage. The fuel surface sticks out of the sample holder by about 1 to 2 mm so that the 

surface does not regress below the metal lip during the test, preventing the formation of 

an artificial trough. 

 

Shortly after the flame gets to the exit of the channel, where the velocity is significantly

higher than at the ignition location, the boundary layer flame is dislodged from the 

sample leading edge and starts retreating downstream (Fig. 2b) The leading edge of the 

flame was observed to oscillate back and forth over the molten surface of PMMA as it 

retreats from the sample leading edge, similar to what Kodama et al. [3] observed. For the 

purposes of discussion we define this state where the flame was dislodged from the 

sample leading edge and was retreating downstream as stage 1. The thermocouple, which 

is about 15 mm downstream from the sample leading edge along the centerline, is quickly 

lowered into the molten surface at this stage. Figure 2b shows the thermocouple passing 

through the retreating bluish flame and one can see that the surface is still relatively flat

at this stage. This will be shown more clearly later. Soon the leading edge of the flame

stops oscillating and anchors at some distance (quenching distance) from the sample 

leading edge. Thereafter, a small step is formed at the location of the flame leading edge 

and the flame starts to spread upstream (stage 2). In this test, where the air has 19.4% 

oxygen the quenching distance was about 20 mm. 

Figure 3a shows the flame in stage 2, anchored about 5 mm downstream from 

thermocouple. While the leading edge of the flame was retreating, the molten polymer

was exposed to ambient air and was cooling down slowly. The melt has 1600 times

smaller thermal diffusivity than the hot gas adjacent to the surface; therefore it takes a 

long time to cool down. Consequently, the surface could still put out a significant 

amount of fuel vapor during the transient stabilization process. In the present experiments

the reaction rates (∝ 1/time) are lowered by the presence of nitrogen and the flow rate is

increased as the sample is brought to the exit of the channel. Therefore, the Damkholer 

number Da, which is flow time/reaction time, decreases as the flame is brought to the

tunnel exit and this causes the flame to retreat and stabilize after a quenching distance. 

In boundary layer flames, the heat feedback to the surface is largest near the leading edge 

of the flame where the boundary layer thickness is smallest and decreases with streamwise distance. Since the surface regression rate is roughly proportional to the heat 

feedback, regression rate is non-uniform along the surface, being highest near the flame 

leading edge. Therefore, as time progresses, the shape of the surface changes as the 

depth and shape of the valley or a step formed near the flame leading edge increases and 

changes. The flame appears to anchor behind the step. With time, it was observed that 

the leading edge of the flame and valley move upstream decreasing the quenching 

4
(a)

(b)

Figure 2: (a) Picture of the flame as it is being moved to the measurement location, 

flame anchored at the sample leading edge. (b): Flame dislodged and retreating 

downstream soon after it gets to the measurement location. 

5
(a)

(b)

Figure 3: (a) Flame stabilized about 5mm downstream of the thermocouple location. 

(b): Flame spread upstream up to the location of the thermocouple 

distance. Figure 3b shows a picture of the flame several minutes later (stage 3) as it 

approaches and engulfs the thermocouple, which was located 5 mm upstream from where 

the flame stabilized. It also shows that the surface is no longer flat and the edge of the 

valley has moved past the thermocouple toward the leading edge. The flame could now 

6
sustain behind the step at a location where it could not sustain before while the surface 

was flat (stage 1). The surface profile at the various stages will be shown more clearly

later. The above observations suggest that the formation of a step stabilizes the flame and 

enables it to spread counter-currently as in Fig. 3b. It is well established in literature that

flame is stabilized behind a step and this has been used extensively in burner design [5]. 

These experiments were repeated numerous times with various initial quenching 

distances established with various combinations of flow velocity and oxygen 

concentration and each time the flame was observed to spread upstream decreasing the

quenching distance. Therefore, one can infer that the moving boundary effects lead to 

step formation, which was critical for the lean limit flame stabilization and spread. The 

flame could not sustain on the hot melt surface due to too low Da but was able to sustain

on a cooler solid surface due to the moving boundary effect, which helped to increase the 

Da. 

The time-dependent thermocouple data (uncorrected for radiation) measured as the flame 

retreats and then spreads upstream (Figures 2 and 3) are shown in Fig. 4. The first 

several data points on the left hand side of the curve were taken during stage 1 as the 

flame was retreating and the thermocouple was passing through it (Figure 2b). A fairly 

rigid thermocouple (75 μm diameter) was used to ensure that the bead goes into the 

melt/froth layer. The thermocouple was lowered into the melt until the bead, goes 

through the melt/froth layer and the thermocouple starts to bend. The thermocouple was 

moved slowly through the retreating flame to show that the surface was gasifying at this 

location, producing hot gases and yet the flame could not be sustained there. PMMA is 

known to pyrolyze at temperatures of the order of 650 to 700 K [6,7]. Furthermore, the 

pyrolysis rate drops by a factor of 100 as the temperature drops by about 60 K, since 

PMMA pyrolysis has high activation energy. Therefore for the purpose of this discussion 

we defined pyrolysis zone as 600 to 700 K-temperature range in Fig. 4. Therefore, the 

thermocouple is assumed to be in the PMMA condensed phase when it reads 

temperatures below 600 K. During this time the thermocouple readings represent real 

time changes in the temperature inside the condensed phase at the thermocouple location. 

About 100 seconds into the test the thermocouple reads the lowest temperature (close to 

400 K). This should correspond to stage 2, when the flame stabilized about 5 mm 

downstream from the thermocouple and it is farthest from the thermocouple. Meanwhile 

a step is formed where the flame stabilized and it starts spreading upstream. As the flame

spreads, heat is transferred from the flame to the solid ahead of the flame front. This

raises the temperature at the thermocouple location from about 400 K to the pyrolysis 

temperature in about 200 seconds as shown in Figure 4. As the flame creeps up to the 

thermocouple location, the polymer pyrolyzes exposing the thermocouple bead to the hot 

gases. Thereafter, the thermocouple measures the hot gas temperatures of the flame. The

valley has now extended beyond the thermocouple location as seen in Fig. 3b (stage 3). 

To examine the surface profiles more closely during each of the three stages described

above, separate experiments were conducted, where the flame was extinguished during 

each stage. The sample was allowed to cool down and was cut stream-wise along the 

centerline to show the surface profile. 

7
0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

0 100 200 300 400 500 600

Time (sec)

Temperature (K) 

Stage 1

Stage 2

Stage 3

Condensed Phase

Gas Phase

Pyrolysis Zone

Figure 4: Time dependent temperature of a point within the quenching distance as 

the flame retreats (stage 1), stabilizes (stage 2) and spreads within the quenching 

distance (stage 3) 

These experiments were performed with 18.8%± 0.1% oxygen concentration so as to 

obtain a significant quenching distance. Figure 5a shows the picture of the surface 

profile as the flame front retreats from the sample leading edge (stage 1). It shows that

the entire surface is flat and that the degree of pyrolysis during the ignition process and 

the short burn time had negligible effect on the shape of the surface. Figure 5b shows the 

surface profile when the flame had just stabilized about 45 mm downstream from the 

sample leading edge. The surface was still nearly flat except for a tiny step at the location

where the flame has just anchored. There, the reaction time is expected to be comparable 

to the flow time. The flame did not stay long enough at this location to create a deeper 

step before it was extinguished. Figure 5b also shows a tiny step formed at the leading 

edge of the sample before the flame was dislodged in this experiment. This tiny step was 

not adequate to stabilize the flame at the leading edge of the sample where the effective 

velocity was higher. At a fixed oxygen concentration and free stream velocity, the flame

stability may depend both on the distance from the leading edge and on the size of the 

8
step for small size step. Therefore, a bigger step than seen in Figure 5b would be needed 

to stabilize the flame within the quenching distance. In Fig. 5c we show a picture of the 

surface profile in an experiment where the flame stabilized and was allowed to spread

upstream for 5 minutes, before it was extinguished (stage 3). In this experiment, the 

flame initially stabilized nearer the sample leading edge than in Fig. 5b, creating an initial 

quenching distance less than 45 mm. This indicates that the length of the quenching

distance can vary between experiments even when the oxygen concentrations are the 

same. Figure 5c shows a bigger valley than in Fig. 5b, indicating that a bigger valley is

needed to sustain the flame as it spreads upstream closer to the leading edge. This is

further illustrated in Figs. 6a, b and c. 

 

Figures 6a, b and c show sample surface profiles in tests with 19.4% oxygen, where the 

flame was allowed to spread upstream for 5, 10 and 20 minutes, respectively. Like the 

flame described in Figs. 3 a and b, the flames in Figs. 6 a-c stabilized about 20 mm 

downstream from the sample leading edge and as the flames spread upstream the valleys

get deeper and broader. The initial point of stabilization (X=20 mm) was exposed to the 

highest flux from the flame for the longest time than any other part of the surface during 

the flame spread process. Therefore, the deepest point (highest regression distance) in 

the valley is expected to occur approximately at the initial point of flame stabilization.

As the flame gets closer to the leading edge, it encounters increasing air velocity. 

Therefore, a bigger valley is needed for the flame to be stable. The surface profiles in 

Figs. 6 a-c clearly show increased depth of valley with time that enables the flame to 

sustain and spread. 

The results of these experiments have demonstrated that the formation of a valley

(moving boundary) is critical for the stability and counter-current spreading of a lean 

limit boundary layer flame within the quenching distance. The effectiveness of steps and 

baffles as flame stabilizers have been recognized in the gas turbine industry, where

burner designs exploit the enhanced stability associated with combustion in a recirculation zone [5]. The presence of a step may be advantageous for flame holding and 

stabilization, but it becomes a disadvantage in flame suppression and extinction. 

Takahashi et al. [8] studied the stabilization and suppression of methane flames formed 

behind a step in a wind tunnel. A re-circulation zone was formed behind the step and they 

showed that the minimum mass fraction of the agent required to extinguish the flame

increased with the volume of the re-circulation zone. It is therefore expected that effects 

of moving boundary would reduce the effectiveness of suppressing agents in boundary 

layer fires over non-charring solids. 

9
(a)

Flame anchored here 

(b) 

Flame anchored here

(c) 

Figure 5: Sample surface profiles for tests with 18.8% Oxygen and flame 

extinguished (a) while flame was retreating from the leading edge (stage 1); (b) just 

as flame stabilized (stage 2) and (c) after flame has spread upstream for 5 minutes

(stage 3). 

Figure 6: PMMA Surface profiles after (a) 5 min, (b) 10 min and (c) 20-min burns; 

Tests with 19.4% oxygen; flame spreading within X< 20 mm 

Y

X 

(a)

(b)

(c)

10
CONCLUSIONS 

The results presented above reveal the effects of moving boundary on counter-current 

boundary layer flame spread over a non-charring solid near the flame extinction limits. 

Tests were conducted at low oxygen concentration (≤19.4%) and air velocity of 87 cm/s. 

This created an initial quenching distance (≥20 mm) where the flame could not sustain

while the surface was pyrolyzing and flat. As the flame stabilized, a small step is formed 

under the leading edge of the flame where the heat feedback is the highest. This small

step was observed to grow deeper and bigger with time. The step (valley) appears to have 

played a critical role in the flame stabilization and spread within the quenching distance,

where it could not sustain when the surface was flat. Therefore, the effects of moving 

boundary enhance flame spread and stability significantly and may make it difficult to

extinguish the flame. 

ACKNOWLEDGEMENT 

We acknowledge the contributions of Mr Clarence Whitehurst in these experiments. This 

work was funded by the office of Naval Research, through Naval Research Laboratory 

and Code 334, under the Damage Control Task of the FY01 Surface Ship Hull, 

Mechanical and Electrical Technology Program. 

REFERENCES 

 

1. Fernandez-Pello A.C, Ray S.R and Glassman I. “Flame spread in an opposed 

forced flow: the effects of ambient oxygen concentration” Eighteenth Symposium 

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2. Chen C.H and T’ien J. S “Diffusion flame stabilization at the leading plate of a 

fuel plate” Combust. Sci. Tech. Vol 50 pp283-306 (1990) 

3. Kodama, H Miyasaka, K and Fernandez-Pello, A. C “Extinction and stabilization

of a diffusion flame on a flat combustible surface with emphasis on the thermal 

controlling mechanisms” Combust. Sci. and Tech 54: pp 37-50 (1987) 

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flow boundary layer flame over PMMA” 2nd Joint meeting of the U.S sections of

the combustion Institute Oakland C.A, March 26-28 2001

5. Lafebvre A.H; Gas Turbine Combustion Hemisphere, New York, 1983, p.179 

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numerical study of the thermal degradation of PMMA” Combust. Sci. Tech. 53: 

pp187-201 (1987) 

8. Takahashi F; Schmoll J W; Strader E.A and Belovich V.M “Suppression of a

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pp105-116 (2000)

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