Flame spread over thin fuels in actual and simulated microgravity conditions

Combustion and Flame 156 (2009) 1214–1226

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Combustion and Flame www.elsevier.com/locate/combustflame

Flame spread over thin fuels in actual and simulated microgravity conditions S.L. Olson a,∗ , F.J. Miller b , S. Jahangirian c , I.S. Wichman c a b c

NASA Glenn Research Center, Mail Stop 77-5, 21000 Brookpark Rd., Cleveland, OH 44135, USA San Diego State University, Dept. of Mechanical Engineering, San Diego, CA 92182, USA Michigan State University, 2555 Engineering Bldg., East Lansing, MI 48824, USA

a r t i c l e

i n f o

Article history: Received 7 October 2008 Received in revised form 15 December 2008 Accepted 24 January 2009 Available online 24 February 2009 Keywords: Flame spread Microgravity Thin fuel Near-limit Narrow channel Flamelet

a b s t r a c t Most previous research on flame spread over solid surfaces has involved flames in open areas. In this study, the flame spreads in a narrow gap, as occurs in fires behind walls or inside electronic equipment. This geometry leads to interesting flame behaviors not typically seen in open flame spread, and also reproduces some of the conditions experienced by microgravity flames. Two sets of experiments are described, one involving flame spread in a Narrow Channel Apparatus (NCA) in normal gravity, and the others taking place in actual microgravity. Three primary variables are considered: flow velocity, oxygen concentration, and gap size (or effect of heat loss). When the oxidizer flow is reduced at either gravity level, the initially uniform flame front becomes corrugated and breaks into separate flamelets. This breakup behavior allows the flame to keep propagating below standard extinction limits by increasing the oxidizer transport to the flame, but has not been observed in other microgravity experiments due to the narrow samples employed. Breakup cannot be studied in typical (i.e., “open”) normal gravity test facilities due to buoyancy-induced opposed flow velocities that are larger than the forced velocities in the flamelet regime. Flammability maps are constructed that delineate the uniform regime, the flamelet regime, and extinction limits for thin cellulose samples. Good agreement is found between flame and flamelet spread rate and flamelet size between the two facilities. Supporting calculations using FLUENT suggest that for small gaps buoyancy is suppressed and exerts a negligible influence on the flow pattern for inlet velocities 5 cm/s. The experiments show that in normal gravity the flamelets are a fire hazard since they can persist in small gaps where they are hard to detect. The results also indicate that the NCA quantitatively captures the essential features of the microgravity tests for thin fuels in opposed flow. Published by Elsevier Inc. on behalf of The Combustion Institute.

1. Introduction For several decades, the science of flame spread over solid materials has been of interest to researchers, accident investigators, building code authors, vehicle designers, insurance companies, and a variety of other professionals who have responsibility for fire safety. Flame spread is by nature complicated due to the coupled physical processes involved, and a rich literature has developed describing experiments, theories, and numerical modeling efforts aimed at understanding the effect of the numerous important variables. In order to generalize the results, classifications (e.g., thermally thick vs. thin materials) and simplified theories and apparatuses for certain limiting cases have been developed. In this research, we focus on an important but less-studied area within flame spread — that of a flame forced to spread in a confined space. This geometry has important implications for

*

Corresponding author. Fax: +1 (216) 433 8050. E-mail address: [email protected] (S.L. Olson).

fire safety in normal gravity. For this purpose, we built and tested a new experimental apparatus (a Narrow Channel Apparatus, or NCA) which allows well-controlled experiments to be conducted by varying three important variables in this regime: oxygen concentration, flow velocity, and heat loss. In this work, we also show via comparison with drop tower experiments that the NCA is well suited to study flame spread in simulated microgravity. Most previous studies of flame spread have been conducted in open environments, where the fuel and flame are not in proximity to other surfaces, and where the flow is strongly driven by buoyancy. This geometry represents a wall or various objects burning in a room or in the open environment. However, some recent experimental flame spread studies have treated constrained geometries and have demonstrated the appearance of complicated flame spread and flame behaviors [1–3]. These behaviors occur in what are referred to as “near-limit” conditions1 [4] in which the flame is forced into a transitional behavior. The type (or class) of

1 The designation “near-limit” indicates limiting conditions such as poor oxygen delivery or large heat loss from the flame, both of which weaken it.

0010-2180/$ – see front matter Published by Elsevier Inc. on behalf of The Combustion Institute. doi:10.1016/j.combustflame.2009.01.015

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Nomenclature C F loss g h L NCA O2 p q R S /V T V blow V buoy V diff Vf V flow V therm Vy x y Yi ZGRF

heat capacity, J/g K fractional heat loss, Eq. (3) gravity level, 1g = 9.8 m/s2 , 0g = 0 m/s2 gap spacing, cm, variable length of flame cylinder, cm Narrow Channel Apparatus, Fig. 1 oxygen pressure, atm heat flux, W/cm2 , 0 = adiabatic radius of flamelet, cm surface to volume ratio temperature, K fuel surface blowing velocity, cm/s buoyancy-induced velocity, cm/s diffusive velocity, cm/s flame spread rate, cm/s forced flow velocity, cm/s thermal expansion velocity, cm/s velocity in the y direction, cm/s axis along the fuel surface, cm axis normal to the fuel surface, cm mass fraction of species ‘i’ Zero Gravity Research Facility

flame spread examined in this work involves spread in very narrow gaps or channels. In narrow gaps, the flame becomes “near-limit” because it usually suffers large heat losses to the nearby walls. A second way to produce near-limit conditions is to reduce the oxygen inflow to levels low enough to starve the flame of oxygen. A motivation for our research is that “near-limit” conditions are achieved in the most insidious and deadly fires. One of these fires, for instance, caused the crash of the 1998 Swissair Flight 111. The fire originated behind the cockpit bulkhead inside the in-flight entertainment system due to a wire arcing event. Metalized polyethylene terephthalate (MPET)-covered insulation blanket was ignited and a creeping flame spread along it in a narrow gap. The burn patterns on the recovered pieces were consistent with a small, weak flame that slowly spread driven by low velocity ventilation flows between the walls. Releases of smoke had the crew concerned, but they were unable to pinpoint the origin. Eventually, the near-limit flame breached a silicone vent cap, allowing a much greater airflow in the narrow gap, leading to a rapidly growing and spreading flame. By the time the crew realized the full extent of the fire, it was too late and soon thereafter the aircraft could no longer respond to commands from the cockpit. The flight crashed into the Atlantic Ocean while attempting an emergency landing at Halifax International Airport, killing all 229 passengers aboard [5]. Other examples exist of such flames in small gaps (in the presence of wire bundles) or in regions where materials are in close proximity, such as inside a wall or between folds of cloth. As will be shown in this article, the narrowness of the channel suppresses most of the gravitationally-induced buoyant flow caused by the flame. Since buoyant flow is minimized in narrow gaps or channels, microgravity near-limit flame spread (which is an acknowledged space-fire hazard [6]) can be tested in normal gravity on earth by using a narrow-channel apparatus (NCA) of the kind employed in the present research. Previous microgravity results [7–14] have been limited to thin solids that burn rapidly (in under 5 s), or a few small samples flown on the Space Shuttle or a sounding rocket [15]. Thus, the present research has developed

Symbols

D

ε ∞ 

π ρ σ τ

diffusion coefficient, cm2 /s emissivity far field value preheat length ahead of the flame leading edge, cm pi, 3.14159 . . . density, g/cm3 Stefan–Boltzmann constant, W/cm2 K4 fuel half-thickness, cm

Subscripts a cyl d f flm i max min rad s u

ambient cylinder downward facing fuel flame feedback, including gas-phase conduction and flame radiation, Eq. (2) species index maximum value minimum value radiative heat loss, Eq. (1) surface sphere upward facing

normal gravity test methods that can simulate burning behaviors in prospective extraterrestrial environments [16]. The research to be described here addresses flame and “flamelet” spread over thermally-thin fuels [3,17–25] in actual and simulated reduced buoyancy conditions. By “flamelet,” we mean small, 3-D flames that are formed when a wide, 2-D flame front weakens to the point where it can no longer be sustained, and breaks up into individual flames separated by distinct gaps of non-burning material [3]. The use of the term “flamelet” to describe the break up of a laminar flame has historical roots [26]. In our experiments, we varied three contributors to flamelet formation, which are controlling variables in real fires in confined spaces. The first contributor is ambient oxygen concentration. Reducing the oxygen concentration weakens the flame, making it more susceptible to quenching. The second contributor is the flow velocity of the incoming oxidizer. Because flames have been shown to preferentially spread upstream in a low velocity flow in microgravity (i.e. opposed flow) [13], we have chosen a range of low opposed flows for our study. If the velocity is sufficiently high, the flame front is uniform. If it is too low, the flame may not receive sufficient oxygen for combustion [9]: at low enough flow rates it may break into flamelets or extinguish. Thus, flow velocity and oxygen concentration are related, in that each controls the amount of oxidizer reaching the flame, but in addition the flow contributes to convective heat loss from the flame. The third contributor to flamelet formation is heat loss to a nearby object. A metal or other substrate placed behind the thermally-thin test sample draws thermal energy, weakening the flame and making it more likely to fragment. A thick sample (which we did not employ in this study) serves as its own heat sink by conducting heat into the interior of the solid. This article is organized so that this introduction is followed by Section 2 on the experimental procedure for both the experiments in the normal gravity Narrow Channel Apparatus (NCA) and the microgravity tests in the NASA drop facilities. The experimental results and the data gathered from both sets of tests as well as flame spread rate results are shown in Section 3, followed by

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(a)

(b) Fig. 1. Schematic of the Narrow Channel Apparatus (NCA). (a) Flow enters the left side through holes in the tube, and is distributed in the plenum section, straightened through screens and honeycomb, and then enters the test section. The flow exhausts from the right plenum. (b) Side view of test section, showing the thin fuel suspended in the center of the narrow channel.

a scaling analysis in Section 4, which is performed to determine the characteristic magnitudes of the various velocity sources in the NCA. In addition, an analysis is presented of the heat losses from the flame/flamelets to the surface and surroundings. Section 5 discusses the flammability map that can be constructed from the data followed by a discussion of results in Section 6 and conclusions in Section 7. 2. Experimental procedure 2.1. Normal gravity experiments — the narrow channel apparatus Inspired by the work of Zik [2,27,28], we developed a Narrow Channel Apparatus (NCA) to study the phenomenon of flamelet spread in narrow gaps that have suppressed-buoyancy, high heat loss conditions [3,17–25]. This apparatus, shown schematically in Fig. 1a, reduces buoyant convection by limiting the channel vertical gap height (Fig. 1b) to a value where vertical cellular flow caused by a hot source is small compared to the horizontal (streamwise) forced flow. This horizontal convective flow is forced through the narrow flow duct at a controlled low speed between the copper bottom plate and the quartz top plate, with the sample held midway between the plates (Fig. 1b). Tests can be done in either an upward facing orientation where the sample is viewed from above (quartz window on top, copper on the bottom), or the downward facing orientation, where the sample is viewed from below (copper on the top, quartz window on the bottom). Ignition occurs at a high flow (∼20 cm/s), followed by a linear flow ramp down (∼0.5 cm/s2 ) to either a fixed flow for steady spreading at that flow, or a continuous very slow ramp down rate (∼0.03 cm/s2 ) until extinction occurs. Results from both types of tests are reported here. A color digital video image is recorded for each test, imaging through the quartz window onto the surface of the fuel sample. All video records from the normal gravity (upward facing or downward facing) and microgravity tests are analyzed using NASA’s

Spotlight software [29]. The analysis includes flame/flamelet spread rate, flamelet size, and burned fraction. 2.2. Microgravity experiments — drop tower wind tunnel rig Microgravity experiments were conducted in a low-speed wind tunnel drop rig [9] in the NASA Glenn Research Center’s 5.18 s Zero Gravity Research Facility (ZGRF). The flow system provided opposed flow velocities ranging between 1 and 15 cm/s at atmospheric pressure through the 20 cm diameter by 48 cm long test section. The sample holder, shown in Fig. 2, was suspended in the center of the test section, and consisted of a copper substrate (painted black) suspended vertically a controlled distance (range 1–8 mm) behind the Whatman 44 ashless filter paper fuel sample, which was 12 cm wide in most tests. The fuel sample was mounted on a thin mica frame to reduce conductive losses to the holder. The space between the sample and the substrate was open at the bottom so that the oxidizer flows over both sides of the sample, with the flow behind the sample exiting a cutout in the holder above the igniter wire. Ignition in these experiments was achieved just prior to the drop in normal gravity using a 29 gauge Kanthal wire, tensioned with spring steel arms that keep the wire taut and straight, and resistively heated using a constant current of 4 amps. Contact with the samples was uniform across the downstream end of the sample, with no air gaps or pressure against the paper. This ensured uniform ignition across the sample. Ignition in normal gravity generally occurred within 5 s for paper and 10 s for PMMA. During each test, the flow was first allowed to fully develop. The sample was then ignited in normal gravity so that a uniform 2-D flame front could be established. Once stable flame propagation was observed and the flame spread away from the igniter (∼5–10 s), the experiment package was released. Two on-board video cameras captured the flame before and during the drop, one from the side and one from the top. At the end of the drop, the chamber was evacuated to extinguish the flame.

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(a)

Fig. 2. Sample holder used in Zero Gravity Research Facility tests, which hangs vertically in the test section. Flow enters from the bottom. The ashless filter paper sample is taped (black strips) to a mica sheet that is spaced a few mm (variable) above a copper substrate that is painted black to absorb the radiation from the flame and burning surface.

3. Results 3.1. Flame character in the narrow channel apparatus Flames spreading across samples held in the center of this apparatus (as shown in Fig. 1b) break up into flamelets just as the microgravity flames described in the next section. However, we have time to observe the spread across the entire sample that took almost 250 s for the case shown in Fig. 3a, instead of only a few seconds as in the microgravity tests. For this test, the sample was ignited at 8 cm/s. The flow was then ramped down to 4 cm/s at a rapid rate of 0.5 cm/s2 to reach the flamelet regime, followed by a slow ramp to 2 cm/s at a rate of 0.03 cm/s2 . The flamelets continued to spread in the 2 cm/s air flow. As they approached the end of the sample, the air flow was quickly ramped back up (not shown) and the flamelets merged into a single flame front. A gap spacing of 5 mm (i.e. h = 1 cm in Fig. 1b) on both sides of the sample was used to mimic the heat loss from the microgravity test in which a substrate at 2.5 mm existed on only one side of the sample. A detailed analysis has shown that there is extensive order in the seemingly random patterns [3,22–25]. This analysis also showed that the flamelet phenomenon is not an ‘instability’ consisting of a transitional state heading to extinction, but that the flamelet state is steady in terms of persistence, spread rate, fraction of sample burned, etc. Thus, the flamelet regimes in our flammability maps are a stable, near-limit, multidimensional flame adaptation to the limiting oxygen environment. For the test from Fig. 3a with steady air flow at 2 cm/s, the burned fraction of the sample was measured in the NCA, as shown in Fig. 3b (where heat loss is proportional to inverse spacing, e.g. two sided heat loss = 1/5 mm + 1/5 mm = 1/2.5 mm one sided heat loss for drop tests). Once breakup occurs, the overall burned fraction drops as the flow ramps from 4 cm/s to 2 cm/s (in ∼60 s). It subsequently stabilizes to ∼62%, maintaining that value for a ∼150 mm burn length.

(b) Fig. 3. (a) Flamelet tracks on the filter paper in the normal gravity NCA, illuminated with green LEDs. The uniform flame consumes the entire sample (black solid area at the left side of the image) and then breaks up into ∼10 flamelets as the flow is reduced. The unburned paper between flamelets appears green, while the flamelet tracks are black. The flamelets are the luminous tips at the ends of the branching pattern. (b) Burned fraction of the sample 1g NCA test shown in (a) for a 2 cm/s air flow and a 5 mm gap on both sides of the sample. The burned fraction remains steady within oscillations caused by local bifurcations and extinctions until the flow is suddenly turned up and then off, causing extinction.

In contrast to the steady flow test shown in Fig. 3, Fig. 4 shows the burned fraction from a continuous ramp-down test in the NCA. The burned fraction data, plotted on the left vertical axis, decrease fairly linearly with flow once breakup occurs. The burned width per flamelet (∼2R) is determined by dividing the total burned width by the number of flamelets, shown in the inset versus flow velocity with a polynomial fit used for the calculation. The mm burned per flamelet, plotted on the right vertical axis, also decreases fairly linearly with flow velocity, even accounting for the changing number of flamelets (also shown on the right vertical axis). 3.2. Flame character and flamelet formation in microgravity Shown in Fig. 5 is the transition from a 1g uniform flame front to flamelets in microgravity under weak forced convection. A black

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Fig. 4. Burned fraction and width burned (in mm) per flamelet for a continuous ramp-down test in the NCA with 5 mm gap spacing in air. Also shown is how the population of flamelets varies with flow velocity, which is needed to determine the mm burned per flamelet from the fraction of the sample burned data. Note the burned fraction in this rampdown test at 2 cm/s agrees with the steady burned fraction data from Fig. 3b.

Fig. 6. Flamelets develop across a 15 cm wide PMMA sample during a 5.18 s drop. After formation, the two flamelets continue to oscillate laterally for the remainder of the drop. One oscillation prior to breakup is shown in single frame increments. The dynamic flashings of the edges of the flame are captured as horizontal stripes (i.e. rapid motion during only one video field) just before breakup into flamelets.

Fig. 5. Sequence of images from a drop experiment showing flame transition from a uniform flame to a corrugated flame (1.25 s) to seven flamelets evenly spaced along the front. The Whatman 44 filter paper sample is 12 cm wide. Time is measured from the start of the drop. Test conditions were air at 8 cm/s, substrate distance 2.5 mm.

copper substrate behind the sample provided the additional heat loss to trigger the formation of flamelets. A stable, uniform, propagating 2-D flame was established over the sample in normal gravity prior to the drop. As the drop proceeded, the flame became

dimmer and thinner, and then formed a corrugated leading edge wave (see Fig. 5, 1.25 s). After ∼1 s elapsed time, the flame broke into uniformly spaced flamelets. Seven flamelets formed and survived to the end of the drop. Smolder spots were also evident as glowing orange char fragments, see Fig. 5. We also produced flamelets using 0.6 mm thick PMMA fuel for several drop tests under similar airflow conditions in microgravity. Shown in Fig. 6 are two flamelets of similar size formed across a 15 cm wide PMMA sample. These flamelets are wider than seen in Fig. 5, but that may be due to the longer solid phase response time of this thicker material, since they resemble the double-wide flamelets seen early in the transition of Fig. 5 (1.25–2.65 s). The flamelets persisted with increasing amplitude oscillations for the last few seconds of the drop. These oscillations were at ∼4 Hz with a lateral motion increasing up to 4 cm (orthogonal to the direction of spread). The oscillations are interpreted as gas phase flame propagation through a regenerating premixed layer as the flamelet slowly shrinks in size, exposing the still-pyrolyzing fuel.

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Fig. 7. Flame breakup into flamelets during the 5.2 s drop shown in Fig. 5. The initial flame breaks up quickly (∼1 s) into fragments that are <4 cm wide. These fragments subsequently break up into flamelets, whose characteristic length scale is on the order of 1 cm.

Fig. 8. Flame area tracking with time, showing flame breakup and average flamelet radius after stabilization for the drop shown in Fig. 5.

These experiments showed that flamelets are not unique to cellulosic or charring fuels. Fig. 7 shows the time history of the flame width during the drop, where each flamelet’s width was tracked with time. In this test (which is the same test shown in Fig. 5), the initially uniform flame broke into increasingly smaller pieces in the first few seconds of the drop. By the end of the drop, seven flamelets of 10 mm average width were spreading across the 120 mm wide cellulose sample (60% of the sample width burning). This burned fraction is in good agreement with the NCA test with the same heat loss shown in Fig. 3b. We analyzed the breakup time for a wide range of conditions, and found that 1–2 s was typical for the initial large scale breakup. The subsequent breakups were most frequently splitting of flame segments into halves, as seen in Fig. 5 (compare 1.25 s to 2.65 s, for example). Measuring the total flame projected area (as seen from the top view camera) as a function of time reveals the flame response to the drop. Fig. 8 shows that the top view thresholded flame area initially increased as the flame briefly expanded when the buoyant flow was abruptly stopped. Then the area decreased rapidly to a much smaller value as the flame broke up. The average flamelet size (total area/7 flamelets) and total flame area stabilized for the

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latter part of the drop (i.e., the final ∼3 s). The average flamelet radius for paper tests is determined from the area assuming the flamelet is a circle (see Fig. 5). The flame area measured above can be used to evaluate the surface to volume ratio (S / V ) for an ideal cylindrical flame (i.e. uniform flame) compared to the nearly spherical flamelets. The effective radius shown in Fig. 9 is based on the flame area A flame measured in Fig. 8. Prior to flame breakup, the radius of the cylinder is calculated by assuming the flame projected area is a rectangle of L = 12 cm sample width, A flame = L2R cyl and solving for the radius R cyl . After flame breakup, the radius of the seven flamelets is calculated by assuming the flame projected area is divided evenly into seven circles, A flame = 7π R 2sphere . These two effective radii, R cyl and R sphere , are used to estimate the surface to volume ratio for the flame. For a cylinder, the S / V = 2π R cyl L /π R 2cyl L, which simplifies to 2/ R cyl . For a sphere, the S / V = 4π R 2sphere /(4/3)π R 3sphere , which simplifies to 3/ R sphere . Thus, for equal effective radii for the two geometries, the surface to volume (S / V ) ratio for the sphere to the cylinder is expected to be 3/2. However, the data in Fig. 9 shows that the surface to volume ratio is about 2.5 for the cylinder until breakup, and then the S / V ratio increases to 7.5 for the spherical geometry. This threefold increase in S / V ratio is enhanced by a more than doubling of the effective radius for the flamelets over a comparable cylinder, as shown in Fig. 9. The increase in S / V ratio enhances the oxygen transport to the flamelets through the flame surface while focusing the heat release in a small volume, which then can provide sufficient heat flux to the unburned fuel beneath. This allows the flamelets to survive on the margins of flammability. They have only been observed on the oxygen-transport limited side of the flammability boundary [9], never on the blowoff side of the flammability boundary. Thus, the flamelet’s multidimensional adaptation extends the material’s flammability beyond the uniform flame extinction limit. Flamelet sizes were measured during numerous drop tests with a 5 cm/s air flow at one atmosphere pressure. Shown in Fig. 10 is the flamelet radius trend observed as substrate distance (abscissa) is varied. As heat loss increases (smaller substrate gap), the flamelet radius decreases in a linear trend. The error bars represent the 95% confidence bounds on the data, and the number inside each data symbols indicates the number of flamelet measurements used in the analysis. These values agree with the range of 1g flamelet sizes measured in Fig. 4, so flamelets in 1g are of similar sizes as flamelets in 0g. 3.3. Flame spread rate The flame and flamelet spread rates are determined from the color video surface view of each test. Frame-by-frame tracking of the blue leading edge of the flame (or flamelet) provides position vs. time data from which we can determine its spread rate. Spotlight software [29] tracks the flame in each digitized video frame with a user-defined intensity threshold. A relative position versus time plot from the drop test shown in Fig. 5 is shown in Fig. 11. The average 1g and 0g spread rates are determined from the slopes of the position time data for each flamelet and then averaged. Prior to time zero the flame is spreading downward in normal gravity at an average rate of 0.24 cm/s, and the data shown are measured across this uniform flame at the locations where the seven flamelets stabilize. At time zero the package is dropped, resulting in some scatter in the data as the buoyant flow dies away and the flame adjusts. The position vs. time line again becomes linear after ∼1 s into the drop, indicating steady spreading after transition from 1g burning to microgravity burning. The average spread rate for the flamelets, however, is 63% slower at 0.09 cm/s.

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Fig. 9. Surface-to-volume ratio based on the measured effective radius as a function of time during the drop experiment also shown in Figs. 5, 7, and 8. The calculation of the effective radius, surface, and volume are based on a cylinder prior to flame breakup and based on a sphere after flame breakup.

Fig. 11. Relative position–time track from the same drop test shown in Fig. 5 (with 8 cm/s air, 2.5 mm gap, 7 flamelets numbered from left to right in image). Each flamelet is tracked along a vertical line based on where the flamelets end up being positioned. In 1g, the flame is a uniform flame, but the flame is tracked along this vertical line through the 1g to 0g transition and flamelet development. The relative flame position data are spaced out by 0.3 cm for clarity. Fig. 10. Flamelet size as a function of substrate distance (i.e., gap spacing) in microgravity.

In the NCA, tests were run either with a steady air flow velocity with an analysis similar to that above for the microgravity cases, or with a continuous ramp down of velocity. Fig. 12 shows the position versus time data, velocity history, and resultant flamelet spread rate as a function of time for two flamelets tracked in a continuous rampdown test. To determine the flamelet spread rate from position–time data, we smooth and then differentiate the data. Exponential smoothing is used to reduce random fluctuations in time series data to provide a clearer view of the true underlying behavior. The smoothed data was differentiated using a Savitsky–Golay algorithm which performs a local polynomial regression around each point. Interestingly, despite the fact

that forced flow velocity linearly decreases from 100 s to the end of the test, the flamelet spread rate plateaus at a fairly constant spread rate. We have demonstrated that this plateau is due to a critical heat flux for ignition [3] that defines a minimum flame spread rate. Instead of spreading more slowly, the flamelet compensates for the reduced air velocity by shrinking in size (shown in Fig. 4) and focusing the reduced heat release from the flamelet onto a smaller surface area to maintain the critical heat flux for ignition. Extinction occurred at 0.6 cm/s air velocity. Spread rates for the NCA were measured for both steady flow (constant spread rate) and a linearly decreasing flow to extinction (rampdown transient test), where the spread rate is obtained by differentiating the position vs. time curve. As shown in Fig. 13, the flame and flamelet spread rates for the NCA agree well with Zero

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Gravity Research Facility (ZGRF) data for a comparable 2.5 mm substrate gap, although the NCA data seems slightly to the left of the ZGRF data, possibly due to residual buoyant flows of ∼1 cm/s. The NCA and ZGRF data are both shifted to the right compared to flight experiment data with minimal heat loss [13], but the trends are the same. In the uniform flame regime, for flows less than ∼15 cm/s [9], the flame spread rate decreases with decreasing forced flow. In the transition region (shaded area), where breakup occurs into flamelets, there is significant scatter in the spread rates depending on whether the transition has occurred or not. After transition to flamelets, the plateau in spread rate is observed that is attributed to a critical heat flux for ignition requirement [3]. While some flamelets extinguish at a few cm/s, they can survive for extended periods of time even at very low velocity flows (<1 cm/s). 4. Analysis 4.1. Scaling analysis In the NCA, there are at least five velocities that can be used in a scaling analysis. As depicted in Fig. 14, these are V flow , V buoy , V therm , V diff , and V blow . Our scaling analysis evaluates the magnitudes of these characteristic velocities for typical conditions in the NCA. The scaling analysis is carried out by performing numerical simulations of narrow channel duct flows over short heated

Fig. 12. Position–time track, velocity history, and spread rate from a NCA continuous ramp-down test in air with 5 mm gaps on either side of fuel sample. Two flamelets are tracked as shown.

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sections of the duct lower surface. These heated duct wall sections (we use L = 0.5 cm length of surface heated to 1500 K) simulate the flamelets, see Fig. 15. The strong local lower-wall heating produces thermal expansion and, in 1g, vertically directed buoyant flow. Our model does not consider lower surface blowing (i.e., mass addition from thermal decomposition of the sample) although we estimate V blow and V diff . Three inflow speeds are used: V flow = (5, 10, 20) cm/s. The simulations are 2-D, hence the duct is assumed infinitely wide. Simulations are conducted for zero gravity and normal earth gravity. The simulation employs the FLUENT code, version 6.2.16 [30]. The inflow air enters the narrow channel 5 cm upstream of the hot spot leading edge. The flat inflow velocity profile evolves into a parabolic profile by the time it reaches the hot spot. No-slip conditions are applied along the channel surfaces. The constant pressure outflow condition is applied at the channel exit 6 cm downstream of the hot spot trailing edge. For the energy equation: the inflow has constant (ambient) temperature; the outflow has zero temperature gradient; the hot spot temperature is 1500 K; the lower surfaces upstream and downstream of the hot spot are insulated; the top surface was insulated (zero normal gradient), except for a comparison test with constant temperature (300 K). Under most flow conditions the differences caused by changing

Fig. 13. Flame spread rate over Whatman 44 filter paper in air as a function of flow velocity. NCA data with a 5 mm gap on either side of the sample. ZGRF data with a 2.5 mm gap on one side of sample, for a comparable total heat loss.

Fig. 14. Definition of the various velocities that occur in the NCA. The sample is placed between top (quartz) and bottom walls. Inflow is left to right, while the flamelet moves right to left. In this picture, gravity vector points downward; buoyant velocity is upward.

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Fig. 15. Schematic of geometry of numerical simulation used for velocity scale analysis. The channel height used was h = 5 mm, and the hot spot was also 5 mm centered at x = 0. Flow velocity (5, 10, 20 cm/s) and gravity level (0g , 1g ) were varied.

the top-surface boundary condition from T = 300 K to zero heat flux (q = 0) are negligible. For the lower-speed inflows the condition T = 300 K changes the buoyant flow slightly. When the inflow speed is higher (between 10 and 20 cm/s) the difference in the flow fields between the two sets of boundary conditions is small. Thus, we consider only q = 0 at the top channel wall. The characteristic magnitudes of V buoy and V therm are determined by comparing the velocity distributions for zero and normal gravity for identical V flow and h values. The velocity distributions are evaluated along imaginary lines in the duct: two horizontal lines at (1/3)h and (2/3)h and two vertical lines located at the middle of the heated section simulating the flamelet (x = 0), and at x = 2.5 mm behind the downstream edge of the heated section, respectively. These locations are illustrated in Fig. 15. Shown in Fig. 16a is V y as a function of x at y = (1/3)h; results at y = (2/3)h are qualitatively similar. This figure shows that at zero gravity there is no downflow upstream of the flame, while at normal gravity there is a small amount of downflow for the lowest value of the in-flow velocity (5 cm/s); otherwise, there is not a substantial difference between normal and zero gravity profiles. The results also clearly show that the largest and smallest values of V y along these lines are always of greater magnitude for the higher flow velocity values. Although these extrema increase with V flow the increase is not linear. The relationship is demonstrated for the zero gravity case in Fig. 16b. The 2nd order fit through the data points yields a negative coefficient for the quadratic term. This indicates that as the forced flow is increased it gradually overcomes the flow due to thermal expansion (since there is no buoyant flow in zero gravity). Note that the reason the thermal expansion velocity increases at all as the forced flow velocity is increased is due to the fact that the heated section maintains a constant temperature, so that more thermal energy enters the flow as the velocity is increased. Fig. 17 shows the vertical version of Fig. 16 at x = 0. The velocities are of the order of approximately 1 cm/s. At V flow = 10 and 20 cm/s the normal and zero gravity vertical velocities are essentially identical, the maximum difference being ∼0.2 cm/s. At an inflow of 5 cm/s, however, buoyancy plays a significant role and shifts the peak of the velocity a lower height in the channel and raises the maximum value. In Fig. 18, the maximum and minimum V y differences [ V y (1g ) − V y (0g )] are examined along the line y = (1/3)h. The quantity [ V y (1g ) − V y (0g )] in Fig. 18 is interpreted as the buoyant velocity. When g = 0 there is only thermal expansion: at normal gravity there is also buoyant flow. The magnitude of the buoyant velocity is larger at the lowest forced flow rate, and drops as the forced flow is increased. Negative values indicate the down-flow that is seen in the 1g case ahead of the heated section.

(a)

(b) Fig. 16. (a) Numerical predictions of the vertical velocity component along the line y = (1/3)h for three values of the in-flow velocity at both normal and zero gravity. (b) Maximum vertical velocity component for three values of the in-flow velocity at y = (1/3)h and y = (2/3)h for zero gravity conditions.

The inset to the graph shows the maximum and the minimum buoyant velocity as a function of forced flow, along with their difference. Here we note that the difference in the extrema approaches zero as the forced flow is increased. Contrasting Figs. 16 and 18, the thermal expansion velocity effect drops slowly as the forced flow velocity is increased, while the buoyant velocity drops more rapidly. At 10 cm/s forced velocity, for instance, the maximum buoyant velocity is less than 1 cm/s, while the maximum thermal expansion velocity is 1.5 cm/s. Both are about 10% of the forced flow velocity. For V blow a different approach is used. Here, a Stefan flow is used to scale V blow . First, we assume that D f ∼ 0.3 cm2 /s for a fuel vapor of moderate molecular weight at ∼400 ◦ C, a reasonable near-surface fuel temperature. Then, with P a = 1 atm the fuel partial pressure gradient may be estimated as 1–0/0.2 cm = 5 atm/cm using pure fuel at 1 atm at the fuel surface that is totally consumed in the flame 2 mm above the fuel. We find the result V blow ≈ (D f / P a ) d P f /dy ∼ (0.3/1)5 = 1.5 cm/s. Thus, V blow is substantially smaller than, V flow . For a V flow value of approximately 10 cm/s, V blow is between 10 and 20% of this value.

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Fig. 19. Schematic of the system for a surface energy balance. Conduction is implicit in the flame feedback to the fuel surface and does not explicitly appear in the surface energy balance.

beneath the sample). The radiative loss from the fuel for one side of the fuel surface is given by: Fig. 17. Numerical results of vertical velocity component for the six cases along a vertical slice centered above the hot spot at x = 0.





4 q˙ rad = εσ T s4 − T ∞ .

(1)

In this equation, ε is the emissivity of the fuel, σ is the Stefan– Boltzmann constant, and T s is the fuel pyrolysis temperature. For an optically thin flame, in the NCA, T ∞ represents the quartz window or duct bottom temperature; in the ZGRF tests it is the chamber wall or substrate temperature. A surface energy balance [3] describes the flame heat flux to the fuel surface is





4 q˙ flm = εσ T s4 − T ∞ + ρs τs C s

(T s − T ∞ ) . (/ V f )

(2)

In these equations, ρs τs is the area density of the fuel, C s is the fuel heat capacity,  is the preheat length, and V f is the flame spread rate. The loss ratio is defined as F loss =

Fig. 18. Numerical results of the buoyant velocity, calculated as the quantity [ v y (1g ) − v y (0g )] along horizontal slice y = (1/3)h. Inset shows the trend in maximum buoyant flow as a function of forced flow.

It is also possible to evaluate V diff in which constituents (e.g., oxygen) diffuse toward the flame. Here we use Fick’s law: V diff = −D∂ Y i /∂ x. Putting ∂ Y i /∂ x ∼ (0.233–0)/(0.5–0) ∼ 0.5 cm−1 and multiplying by D ∼ 3 cm2 /s (oxygen at flame temperature) gives V diff ∼ 1.5 cm/s, which is of the same order of magnitude as V buoy and V therm . These calculations suggest that when buoyancy is suppressed the other velocities are all of the same order of magnitude. When buoyancy is not suppressed, and the channel is not narrow, even though the forced inflow is reduced the induced V buoy can become of the order of 30 cm/s [31]. This value is large enough to dominate these other velocities and to prevent the appearance of flamelets. This is the case in ordinary flame spread. If, on the other hand, buoyancy is suppressed with a NCA, all of the velocities are of the same order of magnitude as the slow inflow rates. As a direct consequence the flamelet phenomenon occurs. 4.2. Loss ratio analysis The heat flux from the flame to the fuel surface can be compared to the heat loss terms the system must sustain, as shown in Fig. 19, which include surface radiative loss to the ambient and conduction from the flame to the ambient (including the substrate

εσ

( T s4

4 εσ ( T s4 − T ∞ ) . s −T ∞ ) 4 − T ∞ ) + ρs τs C s (T(/ Vf)

(3)

Our analysis assumes the flame is symmetric to both sides of the system (i.e., 2 sided flame with equal conduction to both sides of the fuel surface and both sides of the duct via gas-phase conduction). Since the flame moves, the fuel heatup is important, but the window and substrate are thick enough that they don’t heat up substantially during the spread process and thus their different thermal properties are not significant. The conductive loss to the walls (a function of gap spacing h) is lumped into the lefthand side of Eq. (2) and results in a change in the spread rate V f in the right-hand side of Eq. (2). We note that this theoretical configuration differs from the numerical configuration of the preceding section, in which the flamelet or “hot spot” was placed on the lower (substrate) surface (Fig. 15). Properties used for the analysis are T s = 700 K, T ∞ = 300 K, ε = 0.85, σ = 5.729 × 10−12 W/cm2 K4 , half-thickness ρs τs = 0.00385 g/cm2 , C s = 1.26 J/g K, and  = 0.2 cm based on observations of pyrolysis lengths. Fig. 20 shows this heat loss analysis applied to the flamelet spread data shown in Fig. 12. The loss ratio approaches unity as the flamelet approaches extinction at very low velocity. This indicates that as the flow velocity is reduced, a greater portion of the decreasing flame feedback goes to offset the intrinsic losses from the system (conduction to the channel walls, radiative loss from the fuel surface). At a sufficiently low flow velocity, the flamelet can no longer offset these losses, and the flamelet extinguishes. 5. Flammability maps: the flamelet regime Flamelets have been observed over a range of substrate spacings, flow velocities, and oxygen concentrations in both the ZGRF

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Fig. 20. Loss ratio analysis performed on two flamelets in the NCA test using continuous ramp-down in velocity. The loss ratio approaches a limiting value as the flamelet approaches extinction.

Fig. 21. Flammability map with opposed flow velocity and heat loss as axes, showing good agreement between Zero Gravity Research Facility tests and normal gravity tests in the NCA, both in the ‘u’ = upward facing orientation and ‘d’ = downward facing orientation [23,24]. The flamelet regime is a near-limit zone. 0g data with 0.02 mm−1 spacing is from [13].

tests and the NCA in both the upward facing and downward facing configurations. The test results are used to make maps of the flamelet regime, which invariably occurs at the edge of flammability. These maps resemble others [3,7–9], but provide new details of the flamelet regime on the low flow side of the extinction boundary. The exact microgravity borders may be shifted slightly relative to the NCA due to residual buoyancy on the order of 1 cm/s in the NCA relative to the ZGRF.

Fig. 22. Flammability map for filter paper with oxygen concentration and flow velocity axes for 2.5 mm substrate spacing in Zero Gravity Research Facility tests, and a 5 mm spacing on each side in the NCA as a comparable heat loss. This map shows boundaries between uniform/corrugated flames, flamelets, and the extinction boundary for both microgravity and NCA tests.

In Fig. 21, the flamelet regime is delineated by flow velocity and heat loss. The latter is inversely proportional to substrate spacing, as shown on the right axis. As the velocity decreases for a given heat loss (moving left on the figure), the flame becomes corrugated, breaks into flamelets, and eventually extinguishes at sufficiently low velocities. For a given velocity (5 cm/s), as the heat loss is increased (substrate spacing reduced, moving up on the figure), the same sequence of events occurs, with eventual extinguishment at sufficiently high heat loss values. Although we did not find the upper absolute heat loss limit in the heat loss plot, the flamelet regime narrows as flow increases, suggesting that the flamelet regime disappears as we undergo transition from the oxygen-transport limited flow regime to the residence time limited flow regime [9]. In addition to the baseline upward facing tests in the NCA, we conducted downward facing tests where the apparatus was turned upside down so that the positions of the copper substrate and quartz viewing window were reversed. The goal of the downward facing tests was to determine whether the gravitational influence in the 1g tests had been eliminated altogether, or whether the reversal of g would manifest itself in a variation in flame behavior. The results shown in Fig. 21 indicate that the flamelet and quenching boundaries are similar, though slightly narrower in the downward facing geometry. These differences indicate a limited role of gravity in the flame behavior. Fig. 22 presents the low flow side of the flammability map in terms of oxygen and opposed flow for a 2.5 mm gap spacing. The ZGRF tests were conducted at fixed flow rates, whereas the NCA tests were conducted in the normal configuration with a linearly decreasing flow velocity (very slow ramp down of 0.03 cm/s2 ). The transition boundaries are represented in Fig. 22. As the oxygen concentration decreases, the flame breaks into flamelets and eventually extinguishes. The flamelet regime becomes increasingly narrow as the flow increases, consistent with Fig. 21. We expect that the flamelet regime will disappear to the right of the minimum in this flammability curve, as above, based on the absence of literature on flamelets in normal gravity (high buoyant flow) experiments. Comparing the two apparatuses, the extinction boundary agrees well, but the uniform/flamelet boundary is shifted to lower flows in the NCA. This shift is attributed to a slight buoyant flow ∼1 cm/s in the NCA that is not present in the ZGRF.

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6. Discussion Flamelets exist on the margins of flammability. They are a multi-dimensional adaptation to enhance oxygen flux to the flame. They have only been observed on the oxygen-transport limited side of the flammability boundary [9], and they occur only under low oxygen flux conditions. The phenomenon extends the material’s flammability beyond the uniform flame extinction limit by increasing the flame surface to volume (S / V ) ratio. The branching response to the limited transport of oxygen is mirrored throughout nature, where organisms circumvent the limitations imposed by passive diffusion by developing higher surface to volume (S / V ) ratios. Examples in nature include lungs, gills, digestive tracts, filter systems, and the brain, where reactive-diffusive ‘Turing’ structures serve to optimize the transport of materials through their surfaces [32]. From a fire safety viewpoint, flamelets are by nature small and hard to detect, since they occur at the limits of extinction. They have been found for opposed flow and concurrent flow under similar low oxygen flow conditions [3]. They can persist indefinitely under the right conditions, and can flare up rapidly into a large fire when the environmental conditions become favorable. See Fig. 23. It is standard practice on US spacecraft for the astronaut crew to turn off the ventilation to help with the extinguishment of a fire, both to eliminate the fresh oxygen supply and to reduce the distribution of the smoke. If some dim, blue, tiny flamelets or smolder spots go undetected until the ventilation system is reactivated, then the sudden increase in flow would allow the enduring flamelets to grow into a large fire very rapidly, posing a significant hazard. This could as well happen in normal gravity, and indeed was thought to be a factor in the Swissair accident [5]. In that case, the fire moved through the cockpit wall and ceiling, and eventually burned through a silicone cap that allowed fresh air into the system whereupon it could grow. Under suppressed buoyancy conditions, we have shown that a uniform flame front becomes corrugated and breaks into separate flamelets as the opposed flow is reduced. Flamelets were found under the same conditions in both the NASA drop facilities and in a NCA which suppresses normal gravity buoyancy, indicating that the NCA provides an environment similar to that in microgravity for this range of tests (thin fuel, heat loss to a mounting structure, opposed flow, etc.). While the ZGRF flamelet observations were limited by the length of the drop (5.2 s), the NCA flamelets persisted for many minutes. We have mapped the flamelet regime in terms of oxygen, flow, and heat loss with good agreement between microgravity and NCA results. Flame spread rates and burned fuel sample fractions agree. The results indicate that the NCA quantitatively captures the essential features of these microgravity tests, and thus provides a new method to study non-buoyant flame spread without the costs of actual low-gravity testing. 7. Conclusions 1. Flame and flamelet spread rates and flamelet size show good agreement between the NCA and the NASA microgravity drop facilities. This suggests that the NCA essentially suppresses buoyancy and in effect produces a low-gravity flame spread environment. The applicability of the “buoyancy free” condition is not restricted to actual microgravity conditions. In fact, flame spread in tight gaps and narrow spaces is an important fire safety challenge in normal gravity conditions. 2. The flamelet regime extends the range of material flammability to lower opposed flow velocities, lower oxygen concentrations, or higher heat loss by increasing the dimensionality of the flame (surface to volume ratio = S / V ) and thus enhancing

Fig. 23. A single flamelet (∼6 mm wide) propagates steadily in an air flow of 0.5 cm/s in the NCA. When the air flow is abruptly increased to 50 cm/s (100×), the flamelet grows 200% in less than 10 s. (Each photograph is 2 s after the preceding one.)

oxygen transport to the flame zone. This was demonstrated in the research and illustrated in Fig. 8, which shows that the ratio of S / V increases by a factor of nearly three times that predicted from geometry. Our analysis showed that this three-fold increase in S / V ratio (i.e., 7.5/2.5 = 3) is cogently explained by noting that the effective radius is doubled while the the-

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4.

5.

6.

S.L. Olson et al. / Combustion and Flame 156 (2009) 1214–1226

oretical (geometric) ratio is only 1.5, whereby 2(1.5) = 3. The S / V ratio increase enhances oxygen transport to the flamelets through the flame surface while simultaneously focusing the heat release in a small volume, which provides adequate heat flux to the unburned fuel beneath. This important mechanism allows the flamelets to survive on the margins of flammability. Experimentally-generated flammability maps were presented that delineate the flamelet and extinction limits for thin cellulose samples in microgravity and in the normal gravity NCA as a function of opposed flow velocity, heat loss, and oxygen concentration. These flammability maps represent comprehensive plots of these three dominant influences on flamelet behavior. A crucial feature of these plots is that the data groups (microgravity drop tests and NCA tests in two facilities) broadly overlap. Thus, the three regions representing flame spread, flamelet spread and extinction generally agree over all classes of tests. This result supports the assertion that the NCA device serves to produce test conditions that can, to a satisfactory degree of accuracy, simulate the conditions achieved in actual microgravity for the opposed flow tests conducted in this work. Two-dimensional FLUENT calculations demonstrate, for small gap heights, that buoyancy is suppressed and has a negligible effect on the flow pattern for inlet velocities 5 cm/s. These calculations suggest that when buoyancy is suppressed or eliminated the other velocities in the system (blowing, thermal expansion, and diffusion) are all of the same order of magnitude, approximately 10–20% of the inflow velocity, and that when the inflow is correspondingly reduced to this level the flamelet phenomenon appears in the experiments. The results indicate that the buoyancy-suppressing NCA quantitatively captures the essential features of these microgravity tests for thin fuels, and thus provides a viable method to study non-buoyant flame spread in a normal gravity laboratory. Although the applicability of 2-D FLUENT simulations to the case of 3-D flamelets is not certain, the current 2-D model represents at present a viable simulation that can be upgraded when a serious numerical effort at full-scale simulation is attempted. NASA’s current method of screening spacecraft materials for fire resistance is the NASA Standard 6001 Upward Flammability Test 1 [33]. However, because of the limited low-gravity testing to date of practical materials, the prediction of material flammability and fire behavior in low gravity still involves uncertainty. Low-gravity testing faces many limitations, including short test time and high cost. The short available test times in ground-based microgravity facilities make it difficult to study the flammability of thick materials or those of low flammability. The NCA, shown here to simulate microgravity conditions, provides an extremely long test time (of the order of minutes to tens of minutes) compared with the few-second time intervals available in ground-based drop facilities. Perhaps the most important long-term impact of this research addresses the fire safety implications of flames and flamelets in narrow spaces, gaps, grooves, and other places in which combustible materials are placed in both high density and close proximity. Examples of fires originating in confined, narrow spaces abound, whether rare and spectacular cases like the Swissair Flight 111 accident of 1998 or simple domestic and industrial electrical or appliance fires originating undetected in tight spaces. In fact, since these flames/flamelets operate or “survive” in near-limit environments, detection is an important practical matter. As demonstrated in this article a miniature flamelet is essentially an active ignition source or pilot flame, which will ignite into full flaming with inflow of fresh oxidizer. Once ignition occurs the flamelet undergoes

transition into full, active flaming as a nascent fire. This scenario represents the most insidious and deadly feature of such near-limit flames. Acknowledgments This work is supported by NASA Cooperative Agreement NNC04AA50A and NCC31053 with MSU. We thank the ATHINA engineering team, especially Jim Bruewer, and the Zero Gravity Research Facility personnel for their support of this work. Thanks also to Dr. Paul Ferkul for his help with some of the figures. Supplementary material Supplementary material associated with this article can be found, in the online version, at DOI: 10.1016/j.combustflame.2009. 01.015. References [1] S.L. Olson, H.R. Baum, T. Kashiwagi, Proc. Combust. Inst. 27 (1998) 2525–2533. [2] O. Zik, Z. Olami, E. Moses, Phys. Rev. Lett. 81 (1998) 3868–3871. [3] S.L. Olson, F.J. Miller, I.S. Wichman, Combust. Theory Modell. 10 (2) (2006) 323–347. [4] J.S. T’ien, Combust. Flame 65 (1) (1986) 31–34. [5] Transportation Safety Board of Canada, Report Number A98H0003, 1998. [6] R. Friedman, B. Jackson, S. Olson, Testing and Selection of Fire-Resistant Materials for Spacecraft Use, NASA TM-2000-209773, 2000. [7] J.S. T’ien, et al., in: H.R. Ross (Ed.), Microgravity Combustion: Fire in Free Fall, Academic Press, San Diego, 2001, Ch. 5. [8] S.L. Olson, P.V. Ferkul, J.S. T’ien, Proc. Combust. Inst. 22 (1988) 1213–1222. [9] S.L. Olson, Combust. Sci. Technol. 76 (4–6) (1991) 233–249. [10] S. Bhattacharjee, R.A. Altenkirch, Proc. Combust. Inst. 24 (1992) 1669–1676. [11] G. Grayson, K.R. Sacksteder, P.V. Ferkul, J.S. T’ien, Microgravity Sci. Technol. II/2 (1994) 187–195. [12] L. Honda, P.D. Ronney, Combust. Sci. Technol. 133 (1998) 267–291. [13] S.L. Olson, T. Kashiwagi, O. Fujita, M. Kikuchi, K. Ito, Combust. Flame 125 (2001) 852–864. [14] S. Bhattacharjee, R. Ayala, K. Wakai, S. Takahashi, Proc. Combust. Inst. 30 (2004). [15] S.L. Olson, U. Hegde, S. Bhattacharjee, J.L. Deering, L. Tang, R.A. Altenkirch, Combust. Sci. Technol. 176 (2004) 557–584. [16] F.J. Miller, S.L. Olson, S.A. Gokoglu, P.V. Ferkul, Material Flammability Test Methods for Achieving Simulated Low-Gravity Conditions, in: Fifth US Combustion Meeting, San Diego, March 2007. [17] L.M. Oravecz, I.S. Wichman, S.L. Olson, in: Proceedings of the 1999 ASME International Mechanical Engineering Congress and Exposition, HTD-Vol. 364-4, Nashville, November 1999, pp. 183–187. [18] L.M. Oravecz, I.S. Wichman, S. Olson, Space Forum 6 (2000) 253–258. [19] L.M. Oravecz, M.S. thesis, Michigan State University, 2001. [20] I.S. Wichman, L.M. Oravecz-Simpkins, S. Tanaya, Experimental Study of Flamelet Formation in a Hele-Shaw Flow, in: 3rd Joint Mtg. U.S. Sections Combustion Institute, March 2003. [21] I.S. Wichman, R. Vance, Combust. Sci. Technol. 175 (2003) 1807–1834. [22] S.L. Olson, F.J. Miller, I.S. Wichman, Describing Near-Limit Flamelet Fingering Behavior Using Bio-Mathematical Population Models, in: Fourth International Symposium on Scale Modeling, September 17–19, 2003. [23] S.A. Tanaya, M.S. thesis, Michigan State University, 2004. [24] K.L. Aditjandra, M.S. thesis, Michigan State University, 2005. [25] I.S. Wichman, S. Tanaya, K. Aditjandra, L. Yang, S.L. Olson, F.J. Miller, A Simulated Zero-Gravity Flame Spread Apparatus, in: Central States Section of the Combustion Institute Annual Meeting, Cleveland, OH, May 21–23, 2006. [26] G. Böhm, K. Clusius, Z. Naturforsch. 3a (1948) 386; also referenced in B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases, 3rd ed., Academic Press, Orlando, 1987, pp. 326–327. [27] O. Zik, E. Moses, Proc. Combust. Inst. 27 (1998) 2815–2820. [28] O. Zik, E. Moses, Phys. Rev. E 60 (1) (1999) 518–531. [29] R. Klimek, T. Wright, Spotlight Image Analysis Software, 2005, available at http://microgravity.grc.nasa.gov/spotlight/. [30] FLUENT Software, by ANSYS, Inc., http://www.fluent.com. [31] T. Hirano, S.E. Noreikis, T.E. Waterman, Combust. Flame 23 (1974) 83–96. [32] A.M. Turing, Philos. Trans. R. Soc. B (London) 237 (1952) 37–72. [33] D. Mulville, Flammability, Odor, Offgassing, and Compatibility Requirements and Test Procedures for Materials in Environments that Support Combustion, NASA-STD-6001, 1998.