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TheeffectofpressureandoxygenconcentrationonthecombustionofPMMAARTICLEinCOMBUSTIONANDFLAMEAUGUST2013ImpactFactor:3.08DOI:10.1016/j.combustflame.2013.02.019

CITATIONS2

5AUTHORS,INCLUDING:

JamesG.QuintiereUniversityofMaryland,CollegePark127PUBLICATIONS1,976CITATIONS

SEEPROFILE

RichardE.LyonFederalAviationAdministration114PUBLICATIONS1,842CITATIONS

SEEPROFILE

F.J.DiezRutgers,TheStateUniversityofNewJersey56PUBLICATIONS132CITATIONS

SEEPROFILE

Availablefrom:JamesG.QuintiereRetrievedon:12October2015

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074r, At

Received 30 May 2012Received in revised form 25 October 2012Accepted 12 February 2013Available online 28 March 2013

tions was performed. The work was motivated by the importance of these effects on re safety in the avi-3

Burning characteristics and rates at high altitude locations (local

bility of solid materials. Similarly, the role of local oxygen concen-tration is extremely important to the burning of solid materialsdue to their strong dependence on oxygen concentration at theame zone [3]. Since the burning of these solids occurs in a diffu-sion ame mode, oxygen transport is often one of the major factorsinuencing ignition criterion and the sustainment of combustion[4,5]. Therefore, pressure and local oxygen concentration are bothexpected to signicantly inuence the ammability of solid

als have focused on ignition criterion and burning rate. Experi-n a reduction inhen compatudies per

in laboratory low-pressure environments have shown a tefor a sample to ignite earlier and at lower ignition energilower pressure. Ignition studies using piloted ignition at rpressure, performed by McAllister et al. [4] and Wang et al. [6],showed a decrease in time to ignition with decreasing pressure.It was observed that as the pressure is reduced, the ignition timedecreased, reached a minimum, and then increased until ignitiondid not occur [4], suggesting a competition between transportand chemical rates.

Another factor inuencing the ignition and burning rate ofsolid combustibles is the interaction between the ame heat ux

Corresponding author.

Combustion and Flame 160 (2013) 15191530

Contents lists available at

n

eviE-mail address: diez@jove.rutgers.edu (F.J. Diez).pressure is up to 35% less than sea level) and the pressurized cabinof a cruising aircraft (at 10 km altitude the local ambient pressureis 0.26 atm) play an important role in characterizing the amma-

ments at high altitude conditions have showignition delay time of solid materials (wood) wsimilar experiments at sea level [6]. In addition, s0010-2180/$ - see front matter 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.combustame.2013.02.019red toformedndencyes andeducedPressure and buoyancy effects on the ammability and burningcharacteristics of solid materials have been previously extensivelyexplored in low gravity and micro-gravity environments. These re-sults have been directly applied to re prevention and re-ghtingstrategies on spacecraft systems [1,2]. However, res can also oc-cur in low pressure environments associated with high altitudelocations and inside sub-ambient pressurized compartments.

planes cruising a high altitude. Although the combined effects ofpressure and local oxygen concentration on solid material amma-bility are not well understood, reduced burning rates under certaindepressurization conditions could allow for more time for the ef-cacy of other re-ghting techniques or to allow for safer landingprocedures.

Prior studies in reduced-pressure ammability of solid materi-Keywords:Combustion of polymersPMMALow pressureBurning rateTime to ignitionFlammability

1. Introductionation industry. Measurements were obtained in a mass loss calorimeter inside a large 10 m pressurevessel capable of reaching pressures as low as 0.1 atm. The PMMA ammability was characterized bymeasuring the burning rate and the time to ignition of small test samples. These were ignited and burnedunder different external heat uxes, total pressures and oxygen concentrations. The combined effects ofpressure and oxygen concentration on the burning rate, combustion ow eld, and ignition were evalu-ated. Results showed that at low pressure, the burning rate was less intense with a decrease in the massloss rate. However, the reduction in pressure caused a shortened ignition delay time. Experimental mea-surements were compared with a simple analytical model showing good agreement. The results alsoshow how pressure and oxygen concentration contributed to the heat transfer from the ame. The modelrevealed that a single function in oxygen and pressure could account for both ame radiative and convec-tive effects. As a result, a power law t was obtained for the relation of the combined pressure and oxygeneffect on the burning rate. This correlation shows a good agreement with the measurements and predictsthe burning rate behavior for the full range of pressure and oxygen tests.

2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

materials. For practical application, depressurization and nitrogenenrichment are both possible re-combating procedures for cargoArticle history: An experimental study of the ammability properties of PMMA at low pressures and oxygen concentra-The effect of pressure and oxygen concenof PMMA

Mariusz Zarzecki a, James G. Quintiere b, Richard E. LaDepartment of Mechanical Engineering, Rutgers University, Piscataway, NJ 08854, USAbDepartment of Fire Protection Engineering, University of Maryland, College Park, MD 2c Fire Safety Branch, Federal Aviation Administration, William J. Hughes Technical Cente

a r t i c l e i n f o a b s t r a c t

Combustio

journal homepage: www.elsation on the combustion

n c, Tobias Rossmann a, Francisco J. Diez a,

2, USAlantic City International Airport, NJ 08405, USA

SciVerse ScienceDirect

and Flame

er .com/locate /combustflame

l viscosityq density material burnt

and(radiation and convection) with the ame zone. Tewarson [3]showed an increase in ame heat ux with a corresponding in-crease in pressure and oxygen concentration above ambient. Wanget al. [6] on the other hand showed that the mass loss rate of woodat high altitude (Lhasa, 3650 m) was greater than that at low alti-tude (Hefei, 50 m). In addition, the ame shape can be highly inu-enced by the reduction in buoyancy for reduced pressure ames as

Nomenclature

A bounding surface of the gasCp specic heatCHF critical heat uxD diameterGr Grashof numberhc convective heat transfer coefcientk conductivity material burntl characteristic lengthlm,e mean beam lengthL heat of gasicationLf ame heightLFL lower ammability limit concentration_m00ig mass ux at ignitionNu Nusselt numberp pressure_q00e incident external radiative ux from the heater_q00ext applied external heat ux_q00f ;c convective heat ux_q00f ;r incident ame radiative heat ux to the material_q00py pyrolysis energy ux_q00rr re-radiation heat ux from the surfacer stoichiometric fuel to oxygen mass ratios length of one side of square sample

1520 M. Zarzecki et al. / Combustionhas been shown previously in microgravity environments [7,8] andlow pressure environments [9,10]. This alteration of the ameshape can strongly affect both heat loss through convection andheat feedback to the ame zone through radiation.

Another important parameter that characterizes material am-mability is ame spread. Most of the research on ammability ofcombustible solids in reduced pressure environments has involvedame spread measurements [1115]. The results show that at re-duced pressure the ame spread decreases, with the exception ofinsulated wires, where the effects were negligible [13]. NASAresearchers studied the effects of velocity on the extinguishmentof PMMA samples, in a low pressure and low gravity environment[15] and concluded that the rate of depressurization would affectthe ame spread and burning rate of the sample. Again, couplingbetween the buoyancy induced ow and the kinetics gave rise toa non-monotonic dependence of the burning rate with pressure.Recently, NASA has developed an equivalent low stretch apparatus(ELSA), which can be used to study the effects of buoyancy on con-vective cooling by varying the ame stretch rate [16] to examinethe effect of local quenching rates.

Soot radiation also plays an important role in the complexfeedback heat transfer of the ame. The production of soot in aame contributes to an increase in ame heat ux through there-radiation of energy from the soot particles back to the burningsample. Studies done at pressures above atmospheric suggest anincrease in soot formation with an increase in total pressure[6,17,18]. The studies also suggest that below atmosphericpressure the ame might produce less soot, causing the radiativecomponent of the ame heat ux to decrease.

Prior studies on solid combustible ammability in low-pressureenvironments have previously been limited to ignition delay andame spread experiments. Limited data is available for mass lossmeasurements under steady burning in reduced pressure or re-duced oxygen concentration environments. Prior experimentalwork using mass loss calorimeters has shown good correlation be-tween steady burning mass loss rates with piloted ignition andame-spread data [19,20]. In addition, external heat ux has alsobeen extensively used as a combustion promoter for solid materi-

r StefanBoltzmann constants transmissivity of the ame between the heater and the

materialTf ame temperatureTf,crit adiabatic ame temperature at LFLtig ignition time delayTv material surface vaporization temperatureT1 ambient temperatureTRP thermal response parameterV volume of the gasXr ame radiative fractionYO2 ;1 ambient oxygen mass fraction

Greek symbolsDhc heat of combustionDhpy energy per unit mass loss to vaporize the solidef ame emissivityjf absorption emission coefcient

Flame 160 (2013) 15191530als to enhance gasication and ignition [21,22]. The purpose of thecurrent work is to experimentally obtain mass loss measurementsduring the burning of a solid combustible (PMMA) at low pressuresand oxygen concentrations using a mass loss calorimeter. The dataare then correlated with a theoretical analysis to model the behav-ior of the res in the experiments. This coupling of the analysiswith the experimental data elucidates where the pressure and oxy-gen concentration effects contribute most strongly to the variationof ignition and steady burning rates of the sample.

2. Experimental setup and procedure

All the tests were performed in the pressure modeling facility atthe FAA tech center (Atlantic City, NJ). This facility can simulate thepressure observed at different altitudes up to 14,600 m. The facilityincludes a 10 m3 pressure vessel, capable of reaching pressures of0.1 atm, a data feedthrough system for both temperature andimaging, and rapid internal access through a sealed end-cap door.The internal pressure is monitored using a pressure transducer,connected to a control module that can indenitely maintain aconstant pressure within 0.007 atm for a given test. The controlmodule uses a three-way proportional value which allows air tobe removed by a vacuum pump during the tests to maintain a con-stant system background pressure. Further, a constant air ow ratethrough the vessel of 7 0.5 l/s (lps) was maintained for all thetests to provide an independent air source for the combustionexperiments. Therefore, the environment in the test chamber couldbe independently controlled through the gasses supplied to themass loss calorimeter and the externally applied pressure set inthe pressure vessel.

e am

M. Zarzecki et al. / Combustion andTo closely control the amount of oxygen available to the poly-mer sampling during the burning, all the measurements are per-formed inside a smaller container placed inside the pressurevessel. This container shown in Fig. 1 is 76.2 cm tall with a cross-sectional area 62.5 62.5 cm2. Through the use of the externallyapplied constant air ow, the oxygen concentration can be variedlocally inside the container, without the need to ll the entire pres-sure vessel. The airow enters through the bottom of the containervia a 12.7 mm diameter pipe perforated every 1 cm to create a uni-form updraft. The air exits the container through the top via a7.62 cm exhaust port pipe, expelling the exhaust gas into the insideof the pressure vessel. To avoid exhaust gas air recycling, a verysmall positive pressure difference exists between the smallerchamber and the pressure vessel during the tests to shield the test

Fig. 1. (a) Front and (b) side view of the calorimeter and enclosure (used to control ththrough the top.environment from the conditions in the larger pressure vessel. Thesupplied air, after it has passed through the smaller container, isthen removed via a vacuum pump to the outside. The air enteringthe internal container is maintained at a specied oxygen concen-tration, YO21, that ranged from 12% to 21% depending on the partic-ular tests as shown in Table 1. The required oxygen concentrationfor each test is obtained by mixing the house air with nitrogen toproduce the required gas mixture. The system is capable of reliablyproducing and maintaining oxygen concentrations in nitrogenfrom 21% to 10% by volume. The diluent nitrogen was produced

Table 1List of test conditions.

Test conditions Values

Pressure (atm) 0.18,0.37,0.46,0.68,0.82,1Oxygen concentration (%) 12,14,16,18,21External heat ux (kW/m2) 10,12,16,25,50,72Inlet air temperature (C) 25Air ow rate through pressure vessel (l/s) 7Polymer sample thickness (mm) 6 (10,12,16,25 kW/m2)

24.4 (50 kW/m2)28.58 (72 kW/m2)

Polymer sample area (m2) 0.01Distance between heater and sample surface (cm) 6Distance between igniter and sample surface (cm) 1.3using a Floxal nitrogen generation system manufactured by AirLiquide.

Several time-resolved measurements were made within thesmaller chamber to characterize the burning of PMMA. The mostimportant of these measurements made inside the pressure vesselis performed with a mass loss calorimeter (GovMark cone calorim-eter meeting ASTM E 1354 standards) [34]. This particular conecalorimeter offers a high-accuracy load cell with 0.01 g resolution,5 kW Inconel heater, spark igniter, and automated heat ux set-tings. The mass loss calorimeter was placed inside the containerand allows for the measurements of the instantaneous sampleweight during combustion in a controlled (xed pressure and oxy-gen concentration) environment. A cone heater in the calorimeteris used to provide uniform radiant heat to the polymer sample sur-

ount of oxygen). Air is fed in through the bottom of the enclosure and exhausted out

Flame 160 (2013) 15191530 1521face. Considering that the heater takes some time to reach steadystate, a shutter built into the calorimeter between the sampleand the heater reduces the heat transfer to the sample before themeasurements through radiative shielding, allowing for a betterdetermination of initial test conditions. To further reduce thispre-test radiative heat transfer for these experiments, the shutterwas moved one centimeter closer to the sample, and the samplewas held 6 cm below the cone heater. The calorimeter shutterwas operated remotely via a hydraulic actuator. The same actuatorwas used to move the igniter into position at the beginning of eachcombustion test.

The polymer material used for the burning test is optically clearpoly(methyl methacrylate) (PMMA) [Plexiglass-G, Modern Plas-tics]. The sample preparation included placing the PMMA into asteel sample holder where the back-side of the sample is insulatedusing a high-temperature thermal ceramic insulator (Kaowoolboard, 50 mm). The samples were 10 10 cm2, with a 6 mm thick-ness. The samples were further wrapped in aluminum to preventany spillage of the melted PMMA pool, which would alter theboundary conditions associated with sample heating. Initially,the sample was placed on the load cell with the heater was turnedoff. The pressure vessel was then closed and equilibrated to the setpressure. At this point, the cone heater was then brought to the de-sired heat ux condition with the shutter closed. When a test is ini-tiated, the shutter to the cone heater is opened, radiating theappropriate surface heat ux onto the sample, simultaneously withthe locating of the igniter above the sample centerline. This

synchronization of events allowed for accurate determination ofthe sample ignition delay times. The recorded ignition times wereshown not to be very sensitive to igniter position through varyingthe igniter position at several pressures.

Tests were performed at different applied external heat ux val-ues, _q00ext , ranging from 10 to 72 kW/m

2 as shown in Table 1. Forhigher heat uxes, steady burning was not achieved for a 6 mmsample thickness. In those cases, steady burning was obtained byincreasing the sample thickness to 25.4 mm for 50 kW/m2, and31.8 mm for 72 kW/m2. Once the sample was placed on the loadcell, the system was inaccessible for the duration of the test. Alltests were monitored via a closed circuit TV system, and recordedwith a commercial FS100 Canon camera. The experimental setup isshown in Fig. 1. For oweld characterization, both the still camera(providing still color images) and the video system (providinginformation about ow-eld instability and transients) proved ex-tremely useful in delivering visual information which assisted inthe interpretation of the combustion oweld.

For each burn test condition discussed in this paper, the exper-imental condition was repeated six times in the mass loss calorim-eter with identical system pressures and ambient oxygenconcentrations. It was determined that the repeated testing of a

single set of initial conditions resulted in a variation for the massux measurements of 1 g/m2 s, and a variation for the time toignition of 30 s. The test conditions included external heat uxesfrom 1072 kW/m2, oxygen concentrations from 1221%, andpressures from 0.18 to 1 atm. A summary of test conditions is givenin Table 1.

3. Experimental results

Video recordings provided direct observation of the ame shapeand color during the PMMA ammability study. Some typicalimages of burning PMMA samples are shown in Fig. 2 where noexternal heat ux was applied and the oxidizer mole fractionwas maintained at 21% for the various atmospheric pressure condi-tions. The images show substantial differences in ame height,ame color, and ame shape as a function of external pressure.In terms of luminescence from the ame, the ame color changedfrom a bright yellow at standard pressure to a dim blue color atlow pressures with an associated reduction in the ame luminos-ity. This change in ame color and overall luminous intensity is re-lated to both the amount of soot generated from the PMMA

ux afun

1522 M. Zarzecki et al. / Combustion and Flame 160 (2013) 15191530Fig. 2. Typical images of burning PMMA samples for 21% O2 with no external heat images show substantial differences in ame height, ame color, and ame shape as alegend, the reader is referred to the web version of this article.)Fig. 3. Typical images of burning PMMA samples for 21% O2 and a large external hpplied showing ames at (a) 1 atm, (b) 0.68 atm, (c) 0.47 atm and (d) 0.18 atm. Thection of external pressure. (For interpretation of the references to color in this gureeat ux applied of 50 kW/m2 showing ames at (a) 0.48 atm and (b) 0.18 atm.

oxidation and the features of the buoyancy induced oweld,which changes as the overall gas density varies with pressure.

The images in Fig. 2 also show a clear decrease in ame lengthwith a decrease in pressure. This is primarily due to the reducedmass ux in lower pressure environments (due to the lower oxi-dizer density) such that the ame can only be sustained close tothe surface. Since the ame evolution is a balance between themass transfer from the PMMA surface and the heat transfer fromthe ame, as the mass ux is reduced due to lower densities, themass loss rate (and thus the ame length) is similarly affected.

The effects of a reduced pressure environment on the amecan be modulated by exposing the sample to large external heatuxes (effectively increasing the ame heat transfer back to thePMMA, enhancing the overall mass loss from the surface). Whenthe sample was exposed to a large external heat ux, such as50 kW/m2 in Fig. 3, the mass ux from the surface was markedlyincreased. As this ux is increased, the aspects of the higher pres-sure ame (yellowish ame color, larger ame height, and buoy-ancy dominated ow) can be recovered at lower pressureconditions. This effect can also be seen down to the lowest pres-

ig

[25]. This decrease in ignition delay time is expected as an increasein external heat ux enhanced the mass transfer at the PMMA sur-face, leading to quicker production of ammable mixtures at theignition location.

Time to ignition values were obtained experimentally for all thetest conditions in Table 1 (range of pressures, external heat uxes,and oxygen concentrations). These results are shown as a functionof pressure in Fig. 6 for the ve external heat ux conditions im-posed in this study. Each test condition was repeated six times toreduce the experimental uncertainty with both the average valueand the standard deviation shown in Fig. 6. The results show aweak dependence of time to ignition with pressure at the lowerrange of the externally applied heat ux conditions. This weakdependence then disappears as the heat ux is further increased,and the time to ignition is essentially independent of pressureabove an external heat ux of 16 kW/m2. Due to the nonlinear ef-fect of the external heat ux on the ignition delay time, the errorbars on the higher heat ux conditions are much wider, whilethe repeated lower heat ux tests showed a much smaller variationin ignition times. These experiments suggest that the effect of pres-

M. Zarzecki et al. / Combustion andsure used in this study (comparing Figs. 2d to 3b) where a weak,blue triangular ame at low pressure is enhanced to a higherluminosity, larger, and more buoyant ame by the applicationof the large external heat ux. Figure 3 shows that ames withapplied external heat uxes are much wider and sootier thanthose with no external heat ux, especially evident at lowpressures.

Using the pressure vessel system to control the external pres-sure and oxygen mole fraction, a typical test run involves measur-ing the mass loss rate from the burning sample with the mass losscalorimeter as a function of time. Typical results are shown inFig. 4. The raw mass loss data was smoothed using a linear 21-point SavitzkyGolay lter to reduce measurement and readoutnoise. During the test runs, the mass loss rate can be classied intothree regions: the rst region is where the re is growing (asshown by the increase in the mass loss rate); the second regionshows steady burning as the mass loss rate in constant in time;the third region is where the sample is being consumed, and thereis a loss of available reactants to the ame zone, the ame decays(as shown by the decrease in the mass loss). The critical mass uxis obtained from an average of 20 unltered measurement pointscorresponding to 20 s of data, just before the sample ignited. Also,a steady burning region was reached for all test conditions. Early

Fig. 4. Typical measured mass loss rate as a function of time from the PMMAburning sample for 0.68 atm and 21% O2 at 16 kW/m2 external heat ux. Results are

smoothed using a linear 21 point SavitzkyGolay lter to reduced measurementand readout noise. Steady state is observed between t 400 s and t 700 s.results showed that for the PMMA sample thicknesses used, steadyburning could not be achieved, due to the very high mass loss ratesand limited sample sizes. Thus, for the larger external heat uxes,thicker PMMA samples were used to ensure that steady burningwas achieved during the test time.

Using the mass loss rate curves for various environments, sev-eral key combustion parameters can be extracted. The time to igni-tion (or ignition delay time) is a relevant parameter fordetermining the ammability of the sample. This parameter canbe considered a sum of three distinct steps that help contributeto the delay of ignition. Initially the solid has to be heated to a highenough temperature to cause the evolution of pyrolysis gases to begiven off. The second step involves the transport of the fuelthrough the boundary layer and the mixing of the fuel with the oxi-dizer. The last step involves the time it takes for the mixture to sus-tain propagation from the electric arc pilot. Since the mainobjectives of the study are to determine the effect of low-pressureenvironments and normal to low oxygen concentrations, ignitiontimes were determined from the greatest change in mass loss ratecorrelated with the observance of ame by recorded video data.Once the individual ignition times were achieved, they were nor-malized and collapsed by plotting them versus the external heatux as shown in Fig. 5 for ambient pressure conditions. The timeto ignition should scale as t1=2 with increasing external heat ux

Fig. 5. Ignition times normalized and plotted versus the external heat ux for 1 atmand 21% O2. The experimental results are tted by the theoretical model in Eq. (4)(CHF = 8.2 kW/m2).

Flame 160 (2013) 15191530 1523sure on time to ignition is negligible at sufciently high heat uxesand hence can be neglected.

and Flame 160 (2013) 15191530Fig. 6. Experimentally obtained time to ignition values as a function of pressure for

1524 M. Zarzecki et al. / CombustionFor characterization of the pressure effects on steady burning,the experimentally measured mass loss rate can be plottedagainst the external heat ux applied as shown in Fig. 7. The re-sults show the expected scaling that the surface mass ux is di-rectly dependent on the external heat ux. The externallyapplied heat ux increases the surface heat transfer rate, increas-ing the volatilization rate of the fuel and counteracting the radi-ative and convective heat losses from the ame oweld. Themeasurements at low external heat ux up to about 16 kW/m2

have a stronger dependence on pressure than at higher externalheat uxes where the experimental data show little effect ofthe pressure in the chamber. This may be explained by the com-petition between the heat losses and ame heat feedback mech-anism at the polymer surface. At higher external heat uxes, theheat transport to the surface is in excess of that which is natu-rally generated from the ame, resulting in larger vaporizationrates. This larger mass loss rate then feeds into stronger amebehavior (as clearly shown in Fig. 3a and b) where a stronglybuoyant structure is noted in reduced pressure environments,where before a weaker diffusional type ame is evident (Fig. 2cand d). In addition, ame luminosity is also signicantly largersuggesting changes in the soot production levels.

test conditions in Table 1 at 21% oxygen concentration. The analytical model , Eqs.(4) and (12), shows a good t at higher heat uxes and can be used to explain theexperimental measurements.

Fig. 7. Experimentally measured mass loss rate as a function of external heat ux at21% oxygen concentration for characterization of the pressure effect on steadyburning. Results are compared to the analytical model in Eq. (13) to help explain themeasurements.A clearer picture of the effect of pressure on the mass loss ratecan be gained by directly plotting mass ux versus external pres-sure, as shown in Fig. 8. The mass ux decreases with pressure aswas shown in Fig. 7, but now we can more clearly see its depen-dence. For a constant externally applied heat ux, the mass uxdecreases signicantly with decreasing pressure. This is due tothe reduction of two main ame heat feedback mechanisms withdecreasing pressure. The rst is the convective heat ux at thesurface. Here, the reduction in gas density and well as the shiftin the oweld from a buoyancy-induced ow to a diffusionalow act to modulate the convective heat transfer back to the sur-face. Similarly, the radiant heat ux also decreases with decreas-ing pressure due to reduced soot production and ameluminosity. Furthermore, the experimental results show thatdependence of the mass ux on pressure decreases at the higherapplied external heat uxes, with essentially no pressure depen-dence when the external heat ux approaches 75 kW/m2. At suf-ciently high external heat ux, the losses in convection andradiative feedback from the natural ame at lower pressure con-ditions are mitigated.

Fig. 8. Measured steady burning mass ux as a function of pressure for differentexternal heat uxes at 21% oxygen concentration. Results are compared to theanalytical model in Eq. (13) to help explain the measurements.Oxygen mass fraction was varied independently with systempressure to determine the effect of a reduced oxidizer environmenton burning and mass loss rate. The experimental measurementsshowing the effect of oxygen mass fraction on the mass loss rateare presented in Fig. 9. The measurements show a decrease in mass

Fig. 9. Measured steady burning mass ux as a function of oxygen mass fraction fordifferent pressures at a constant heat ux of 16 KW/m2. Results are compared to theanalytical model in Eq. (13) to help explain the measurements.

ux for all pressures tested when the oxygen mass fraction isdecreased. The reduction in mass ux with oxygen mass fractionis similar at all the pressures used in this study, with a slightlystronger correlation at higher pressures. As the oxygen mass frac-tion is reduced, the convective heat transfer and radiative feedbackmechanisms to the ame surface are reduced due to the reductionin fuel burned (leading to smaller ames and less ame luminos-ity). It should be noted that the results at P = 0.18 atm in Fig. 9are only available for oxygen concentration at or aboveYO2 ;1 0:16 since sustained ignition was unattainable below thatvalue. Lower ammability limits were not thoroughly exploreddue to the difculty of maintaining steady aming combustion atthese conditions, thus these data do not extend to their limitingoxygen mass fractions.

Lastly, the critical mass ux for piloted ignition can be deter-mined by combining the time to ignition data with the continu-ously monitored sample mass ux. The critical mass ux is thenfound from the slope of the mass loss curve just before sampleignition. This critical mass ux is shown in Fig. 10a and b for twodifferent external heat ux conditions. At decreased pressures,the reduction in available oxygen lowers the amount of fuel

4. Analytical model

The theoretical analysis will address ignition and burning rateas a function of external heat ux atmospheric pressure, and oxy-gen. The model specically addresses the burning in the cone cal-orimeter conguration, or one comparable in orientation andsample size. However, the model can be extended to larger poolre orientations. The framework of the modeling follows estab-lished theoretical based correlation techniques using propertyparameters that are derived from data taken at several heat uxes.We will use such data from normal atmospheric conditions of pres-sure (14.7 psi) and oxygen (21%) to derive results at other pressureand oxygen conditions. The modeling approach is supported bystudies from Tewarson et al. [3,5,20,23] and Hamins et al. [24] onpredicting the burning rate of pool res. The basis of the approachfor ignition and burning rate is described in more detail in Quinti-ere [25]. Here, only steady burning will be considered, and kineticeffects in the solid phase are not addressed.

4.1. Ignition

M. Zarzecki et al. / Combustion and Flame 160 (2013) 15191530 1525needed to reach the lower ammability limit, thereby resultingin a lower critical mass ux at ignition as pressure is decreased,as shown in Fig. 10. Similar observations were made by Ferereset al. in a horizontal, forced convection apparatus [37], indicatingthat the sample material is becoming more ammable at reducedpressures.

The mass ux at ignition appears to have a slightfunctional dependence on the external heat ux, with the higherheat ux values increasing the amount of fuel available throughpyrolysis. The external heat ux also speeds the pre-heating ofthe sample and production of pyrolysis gases effectively reducingthe mass ux required at ignition. In addition, all of the criticalmass ux data tends to follow the computed re pointassociated with self-sustained aming combustion of the sample.Typically, we see that the ashpoint conditions are thosewhere the pyrolysis products achieve a ammable concentration,while the re-point corresponds to the condition where theame is self-sustaining. The re-point typically depends onwhether the heat ux from the ame (or externally applied) issufcient to produce enough pyrolysis gases to sustain amingcombustion.Fig. 10. Measured mass ux at ignition as a function of pressure for 21% O2 and comparedheat ux and for (b) 12W/m2 external heat ux.4.1.1. Ignition delay timeIgnition modeling follows the approach used in ASTM E-1321

with some modication. This is described in detail in Quintiere[25, p. 176187]. It has been found that piloted ignition data forreal materials follows the following behavior, except near the crit-ical heat ux (CHF). The ignition time delay can be related to theapplied external heat ux, _q00ext , as shown in the following equation.

tig TRP_q00ext

21

The Thermal Response Parameter (TRP), coined by Tewarson[20], is a material property combining the ignition temperaturewith the material properties conductivity, density and specic heatas

TRP p4kqcp

12Tig T1; 2

This result can be derived from the heat conduction in a semi-innite solid with linearized surface heat loss in the limit of smalltime or high external heat ux [25].to the pressure-dependent sample ashpoint and repoint for (a) 10 W/m2 external

the surface. Under the conditions specied the CHF can be found by

andCHF rT4ig T41 hcTig T1 _q00py 3

where r is the StefanBoltzmann constant, _q00py pyrolysis energyux, and hc is the convective heat transfer coefcient. The emissiv-ity is taken as unity, as this property is nearly unity for these com-bustion materials and re conditions.

The challenge is to present a unied theory for predicting thetime to ignite that addresses both high and low external heat uxconditions with respect to the CHF. As prior experimental studieshave shown, the TRP material property can be extracted fromexperimental data at small ignition delay times and higher externalheat uxes as it correlates these data very well. Using the experi-mentally derived TRP and theoretically determined CHF, the follow-ing equation is proposed which can be a suitable correlatingfunction of ignition delay times over the entire heat ux range:

CHF_q00ext

1 exp CHFTRP

tig

p 4This equation follows the scaling of ignition delay time in the

limits of both high and low heat ux behavior. However, it shouldbe realized that this equation does not account for kinetic gasphase effects that would especially become signicant at low pres-sure and low oxygen concentrations. Additionally, the pilot mustbe capable of launching a premixed ame to achieve sustainedignition of the material. The reaction rate in the gas phase is mono-tonic with pressure and oxygen by typical Arrhenius kinetics, so atcritically low levels of each, ammability will not occur. These ki-netic effects in the gas phase will retard the ignition time and ulti-mately stop the ignition process. We will not address kineticsexplicitly in the equation for the time to ignite, but can addressit by investigating the critical mass ux needed for ignition.

4.1.2. Critical mass ux for ignitionA theoretical analysis of the critical mass ux at ignition (ash-

point) and at extinction (re point) has previously been put forthby Lyon and Quintiere [26] showing good agreement with polymerdata. The mass ux at ignition can be related to the LFL (as a massfraction concentration) using convective mass transfer theory withequal Prandtl and Schmidt numbers applicable to air:

_m00ig hccp

LFL 5

Drysdale [27, p 88] indicates that the LFL is fairly constant be-low normal atmospheric pressure down to about 0.1 atm(1.5 psi). He also shows that the LFL is fairly constant forThis equation does not accurately represent experimental igni-tion data when the external radiant heat ux approaches the CHF.The CHF can be estimated by computation through an energy bal-ance at the surface of the material just before ignition to a sus-tained ame at very long time. At very long time, the externalheat ux will be the CHF with the material effectively at a uniformtemperature equal to its ignition temperature. There is no heat lossby conduction into the material. Consequently the external heatux is equal to the radiative and convective surface losses andthe energy required to pyrolyze the material to achieve its lowerammability limit concentration (LFL) at the pilot location. Here,no inclusion of surface oxidation is taken, as we assume it willbe small for our application. However, at higher than ambient oxy-gen concentrations, it should be considered as a source of energy to

1526 M. Zarzecki et al. / Combustionoxygen concentrations above that of a normal atmosphereconditions. At lower fuel concentrations, piloted ignition will notbe possible. The lower limit can be estimated using the fact thatit is empirically well known that a critical ame temperature isneeded at the LFL mixture [25, p.104] to create ignition. Thus, theLFL can be written as

LFL R Tf ;critT1 cpdTDhc

cpTf ;crit T1Dhc

6

The critical temperature is commonly taken at 1300 C. Thelower limit as an oxygen mass fraction can be alternatively consid-ered, with the heat of combustion per mass of oxygen taken as13 kJ/g. Using ambient temperature as 25 C, and the specic heatas 1.2 J/g K (1000 C), then

LFLDhc Yo2 ;limDho2 1:53 kJ=g 7It should be recognized that there is a critical energy density

needed for ignition (1.53 MJ/kg 1.1 kg/m3) of 1.68 MJ/ m3. Drys-dale [27, p. 84] cites 2.16 MJ/m3, and Lyon and Quintiere [26] nds1.9 MJ/m3. The differences between these three estimations are inthe empiricism of the various models involved, but many fuels fol-low these typical scaling values. This result also yields an estimatefor the lower limit oxygen concentration, for all fuels, as approxi-mately 0.12 or about 11% oxygen concentration by volume. Wewould expect no piloted ignition below this limit. The other criticalenergy density values would increase this oxygen limit to about12.8 1% by volume.

From the above analysis it follows that the critical mass ux atignition can be estimated from

_m00ig hc1530 K

Dhc8

As this is the condition associated with the ashpoint, using thestoichiometric fuel to air concentration instead of the LFL wouldgive a result close to the re point or sustained ignition. Drysdale[27] showed that the ratio of the LFL to the stoichiometric concen-tration is about 0.55 0.03 for many fuels giving the estimate thatthe mass ux at sustained ignition would then be 1.8 _m00ig . For thisanalysis, we dene the ashpoint as conditions under which thepyrolysis products achieve the LFL, while the re-point corre-sponds to the condition where the ame can sustain itself. There-point is dependent on whether the heat ux from the ameis sufcient in raising the surface temperature, where enoughpyrolysis gases are produced to sustain aming combustion.

4.1.3. Pyrolysis energy uxIn order to compute the CHF, the pyrolysis energy ux is

needed. From the analysis to estimate the critical mass ux at igni-tion, this follows as

_q00py _m00igDhpy 9

where Dhpy is the energy per unit mass loss to vaporize the solid.

4.1.4. Effect of pressure and oxygenTo bring closure to the analysis in predicting the time to ignite,

Eq. (4) can be used to correlate ignition delay times over a wide setof conditions. However, there are several restrictions to its use thatshould be noted. Eq. (4) will not hold below a pressure of approx-imately 0.1 atm due to kinetic rates that will signicantly slow atlow pressures, increasing the time to ignite or rendering the mate-rial nonammable. At oxygen concentrations below about 12%(vol.) no ignition is likely. Additionally, two crucial parameters thatwill affect the time to ignite are the heat of combustion and theconvective heat transfer coefcient. From Eq. (7), as long as the

Flame 160 (2013) 15191530LFL does not vary signicantly (above 0.1 atm and above 12% oxy-gen) the heat of combustion should be invariant. However, the heattransfer coefcient will vary with pressure.

by the ame. The convective heat transfer coefcient is taken as

diameter (D) as the effective diameter of the square (s s) sample,

andIn the present application the combustion environment is acone calorimeter as described in the experimental setup. Liuet al. [28] have measured the convective heat transfer coefcientin a similar cone calorimeter apparatus with varying fan speeds,and have theoretically correlated the heat transfer coefcient sat-isfactorily by considering combined forced and free laminar condi-tions. They nd that hc is 12 2 W/m2 K over a range of heat ux of1535 kW/m2 and airow rates of 1825 g/s at normal atmo-spheric pressure. These experimental results were supported by amix of low velocity forced and free convection theory.

Therefore from laminar free convection theory, e.g. [25, p 250],

Nu Gr1=4hclk ql

2g DTT l

3 1=4

hc q1=2 p1=210

This suggests a pressure dependence on the heat transfer coef-cient without combustion.

Hence, for the same temperature conditions at ignition (or am-ing), the same size material, and with density proportional to pres-sure by perfect gas theory, it follow that the heat transfercoefcient is proportional to pressure to the one-half power. If con-ditions were turbulent, the pressure scaling would shift to the two-thirds power, and in forced ow this would vary as one-half powerfor laminar conditions and one-third power for turbulent condi-tions. In the present application, the one-half power for free andforced conditions per Liu et al. [28] is used to represent the depen-dence of the convective heat transfer coefcient with pressure:

hc 0:012 ppsi14:7 1=2

0:00313ppsi1=2 kW=m2 K 11

It should be noted that the heat transfer coefcient occurring inEqs. (3), (5), (8), and (13) all represent the approximation by Eq.(11), as they are the pure heat transfer value without mass transfer.

4.1.5. Properties for PMMAThe CHF is computed based on an ignition temperature for

PMMA of 275 C, as a best estimate from Babrauskas [29, p.1068]. The heat of pyrolysis is taken from Stoliarov and Walters[30] as 0.87 kJ/g, and the heat of combustion from Tewarson [20]of 24.2 kJ/g. Substituting accordingly in Eq. (3) gives

CHF 4:68 0:934ppsi1=2 kW=m2 12At atmospheric pressure, the CHF is determined to be 8.25 kW/

m2 (see Fig. (5)).

4.2. Steady burning rate

The burning rate model follows the modied B number ap-proach for a stagnant layer with added radiative heat ux consid-erations as explained in Quintiere [25]. Such an approach was usedby Hamins et al. [24] to reasonably predict the burning rate of poolres for a wide range of liquid fuels over diameters ranging fromabout 0.022 m. They used a gray gas model for radiation fromthe ame with a mean beam length to model emissivity, and wewill employ a similar model. In the current application, the cong-uration is a horizontal square sample exposed to radiation from thecone heater. Radiation from the ame and the blockage of externalradiation by the ame to the material is considered. No effect of theradiation blockage due to the fuel pyrolysis gases is considered, asthat effect is lacking in prior experimental or theoretical results to

M. Zarzecki et al. / Combustionaddress. While steady burning is only considered here, the gas-phase heat ux model followed can provide input to a transientpyrolysis model to address transient burning.i.e. D = (2/p1/2)swhere s is the length of one side of the square sam-ple. Consequently,

lm;e 3:623pD=232pD=22

! 0:6D 0:677 s 16

4.2.3. Radiation from ameThe radiant heat ux from the ame is modeled in a similar

fashion with the volume considered as a cylinder of diameter Dand height Lf, the ame height. In this case the mean beam length,lm,f, is given as

lm;f p4D

2LfpDLf 2 p4D2

0:9 Lf =DLf =D 1=2

D

1:01s Lf =DLf =D 1=2

17

Here Lf cannot exceed the vertical duct height of the cone calo-rimeter, as that would limit the vertical ame height.

The incident ame heat ux is given as

_q00f ;r efrT4f T41 18where the emissivity is given asthat measured in the cone calorimeter, as given by Eq. (11). It isconsidered laminar in representation as the ame near its base islaminar in this representation while above it makes a transitionto turbulent ow. The convective heat ux is dependent on bothoxygen concentration and pressure.

4.2.2. Radiation from heaterThe radiation effects are modeled by a homogeneous gray-gas

representation for the ame. The entire gas phase above the mate-rial to the ame tip is considered. The blockage of the radiative uxfrom the heater is determined from the transmissivity given interms of a mean beam length, lm,e.

s ejf lm;e 14The mean beam length is given by [31, p 180].

lm 3:6V=A 15where V is the volume of the gas, A is the bounding surface of thegas,

Here the volume is considered to be a hemisphere with a base4.2.1. B-number theoryUnder steady burning, the net surface heat ux is equal to the

energy ux to vaporize the fuel as modeled by the heat of gasica-tion, L.

_m00L hccp

kek 1

Yo2 ;1Dhc=r1 Xr cpTv T1

_q00f ;r s _q00ext rT4v T41 13

where _q00f ;r is the incident ame radiative heat ux to the material,_q00ext is the incident external radiative ux from the heater, s is thetransmissivity of the ame between the heater and the material,Yox,1 is the ambient oxygen mass fraction Dhc/r is the heat of com-bustion per unit mass of oxygen (13 kJ/g Xr) is the ame radiativefraction, Tv is the material surface vaporization temperature,k _m00cp=hc .

The rst term on the right hand side is the convective heating

Flame 160 (2013) 15191530 1527ef 1 ejf lm;f 19

pronounced as the predictions by the model. Also the effect of thelarger external heat uxes of 25 kW/m2 and above are not well pre-

andThe ame height is computed as a turbulent ame [32]although the amemay resort to laminar at low pressures. As thereis no clear way to differentiate in this study, we maintain the tur-bulent equation of Heskestad [32]

LfD 15:6

_Qq1T1cp

g

pD5=2

2=5 Yo2 ;1cpT1Dhc=r

3=5 1:02

orLfD 0:23 _Q2=5 14:7p

2=50:233Yo2 ;1

3=5 1:02

20

where _Q _m00s2Dhc in kW, p is pressure in psiIt is seen that both pressure and oxygen affects the ame

height.The effect of pressure also affects the ame absorption coef-

cient as identied by de Ris et al. [33]. They show that it dependson pressure to the second power. Therefore, we represent

jf jo ppo 2 21

where jo and po are the absorption coefcient and pressure at 1atm (14:7 psi)

It is likely that the absorption coefcient also is affected byambient oxygen concentration due to the dependence of soot for-mation on local oxygen. The soot levels would be expected to dropas the oxygen concentration is reduced from normal ambient, butwe will not speculate in including this likely effect.

To complete the model for ame radiation the ame tempera-ture must be estimated. From Quintiere [25, p. 316] the tempera-ture can be computed from

TfT1T1

CT;f 1 XrYo2 ;1Dhc=rcpT1where CT;f 0:50 for cp 1:0 kJ=kg K

Tf T1 65001 XrYox;1 K22

The ame radiative fraction likely is affected by pressure andoxygen, especially as the ame nears extinction due to changesin the soot volume fraction. It is well known that for res over1 m in diameter, the radiation fraction also drops due to sootblockage. The latter does not apply to the present application,and the former cannot be described due to lack of detailed exper-imental data about the soot levels as a function of the conditionsvaried in this study. So in the current application, the radiationfraction will be taken as a constant for a given fuel.

4.2.4. Empirical analysisAs an approximation to Eq. (13), the ame energy balance can

be written as

_m00L _q00ext rT4v T41 _q00f ;c _q00f ;r 23Using simple scaling, we see that the inuence of the convective

ame heat ux on the mass loss rate scales with the square root ofexternal pressure, Eq. (10), and linearly with the oxygen mass frac-tion, Eq. (13). The convective ame heat ux can then be approxi-mated as

_q00f ;c / p1=2Yo2 ;1 24Similarly, for optically thin radiant environments (small jfD), a

ame radiant heat ux scaling can also be derived used Eq. (21), tosee the pressure scaling effect on the ame emissivity, and Eq. (22),to see the oxygen mass fraction effect on the ame temperature.The overall ame radiant heat ux scaling is approximately pro-portional as

1528 M. Zarzecki et al. / Combustion_q00f ;r / p2Y4o2 ;1 25This means thatdicted by the simple model used. The analytical model showing theeffect of oxygen mass fraction on the mass loss rate is presented inFig. 9. The values used for the model in Eq. (13) used in this gureare cp = 1 kJ/kg K, hc = 12W/m2 K, sf = 1.3, Tf = 1300 K, Tv = 648 K,T1 = 300 K, L = 2.2 kJ/g, Xr = 0.34. Although the model has some_m00L _q00ext rT4v T41 functionp1=2Yo2 ;1 26This functionality is investigated for the data as a way to sim-

plify the inuence of pressure and oxygen on the burning rate, atleast where the above approximations are valid.

5. Comparison of measurements with analytical model

In order to compare the experimental measurements to thesimple analytical model proposed, the burning of the samplesneeded to show a steady burning region such as in Fig. 4 whichwas the case for all the runs. The main objective of the experimen-tal study is to determine the sample ignition time and burning ratefor normal to low-pressure environments and normal to low oxy-gen concentrations. To better understand the measured time toignition of the sample, this can be compared with that predictedfrom Eq. (1) in Fig. 5. The good t suggests that the scaling is valid.The parameter TRP is determined from a t to the time to ignitedata at normal pressure. Using Eq. (1), the TRP is found to be238 kW s1/2/m2. However, using a more unied theory that takesinto account the inuence of the CHF at long ignition delay times(Eq. (4)), the relevant TRP is 179 kW s1/2/m2, as shown in Fig. 5.Knowing the TRP, the only unknown parameter left in the analyt-ical model for time to ignition in Eq. (4) is the CHF which containsthe pressure effect. This can be found using Eq. (12) and analyticalmodel prediction for tig can be obtained.

The analytical model for time to ignition previously described inEq. (4) is also shown in Fig. 6 as solid lines. Similar to the experi-ments, the model shows that the effect of pressure is negligibleat high heat uxes and hence can be neglected. At lower levels ofexternal heat ux the convective losses became important asshown for 10 and 12 kW/m2. When comparing the analytical mod-el to the experimental results in Fig. 6, the model works well fortest conditions at the lower heat uxes, but underestimates theignition times for conditions at the higher heat uxes.

The experimental mass loss rate measurements are also com-pared to the analytical model for the burn rate in Eq. (13) inFig. 7. The model can be computed by calculating all the heat uxcomponents from Eqs. (14)(22). The terms not know in theseequations include the soot emitter parameter, and the radiativefraction. These can be obtained from [23,33] to give jf = 1.3 m1

and Xr = 0.34 respectively. Also, the experimental value for thevaporization temperature Tv = 350400 C was obtained from[35] and an average vaporization temperature was used in themodel as 375 C. Last, the heat of gasication is obtained by plot-ting the inverse of the slope of mass ux at ambient condition ver-sus the external heat ux [36], resulting in a value of 2.2 kJ/g.Having estimated values for all the terms in the right hand sideof Eq. (13), the burn rate can be analytically calculated for all thetest conditions used. The model predicts the measurements atlow external heat ux up to about 25 kW/m2 but clearly under-predicts the mass ux at higher external heat uxes where theexperiments show that the effect of pressure is negligible. The ef-fect of pressure on the mass loss rate is also predicted by the ana-lytical model in Fig. 8 although the decrease in mass ux is not as

Flame 160 (2013) 15191530limitations at the lower oxygen mass factions, it captures the trendof the decrease in mass ux for all pressures tested when the oxy-gen mass fraction is decreased.

The critical mass ux determined experimentally can also becompared with the analytical model in Eq. (8) with the heat ofcombustion taken at the re-point, or where aming combustioncan be sustained. The scaling of the critical mass ux at ignitionwith pressure comes largely from the dependence of the convec-tive transfer coefcient, since the LFL and re-point of the sampledo not signicantly vary with pressure over this range [4]. Themodel predicts lower critical mass ux at ignition as pressure is de-creased as shown in Fig 10. At the lowest pressure tests conductedin this study, the critical mass ux data tends to correlate less wellwith the theoretical re-point prediction, consistent with thechemical kinetic timescale becoming longer relative to the convec-tive timescale.When combining the results from Figs. 8 and 9, theyindicate that the mass loss rate scales with pressure and oxygenconcentration. Thus, the mass loss rate measurements are plottedagainst the proposed scaling variable [p1=2YO2 ;1] from Eq. (26) inFig. 11. The scaling suggests that the mass loss rate should be pro-portional to the product of the square root of pressure and oxygen

An experimental study of the ammability properties of PMMA

[1] R. Friedman, Fire Mater. 20 (1996) 235243.[2] C.K. Law, G.M. Faeth, Prog. Energy Combust. Sci. 20 (1994) 65113.

M. Zarzecki et al. / Combustion andconcentration. The plot in Fig. 11 shows that the properly normal-ized mass loss measurements lie onto a single line that can be t-ted by a power function of the form y = axn, where a = 64, andn = 1.3 to give

_m00 _q00ext _q00rr

L 64p1=2YO2 ;11:3 27

where _q00rr rT4v T41 is the re-radiation heat ux from the sur-face. This is a simple relation that works for the measurements ofall PMMA samples burned at different pressures, oxygen concentra-tions and external heat uxes. By plotting the y-axis in Eq. (27) as_m00 _q00ext _q00rr=L it allow us to show that the data is independentof heat ux. The only exceptions are the results for external heatuxes above 50 kW/m2 that are not shown since this large externalheat ux dominates the mass loss rate.

The above simple scaling does not include modeling of a nitechemical reaction timescale, which can play an important role inignition and extinction. A Damkohler number could be createdwhich combines the chemical reaction timescale with that fromthe convective heat transfer. At the highest heat ux cases exam-ined in this study, it is possible that the timescale associated withconvective heat transfer combined with the very strong buoyancygenerated in the ame oweld has decreased to be of the sameorder as the fundamental chemical timescale [38]. This introduc-tion of a Damkohler number dependence would allow for theextension of the proposed model to higher heat ux values. At

Fig. 11. Measured mass loss rate plotted as a function of the proposed scaling

variable (p1=2YO2 ;1) from Eq. (26). The scaling suggests that the mass loss rateshould be proportional to the product of the square root of pressure and oxygenconcentration.[3] A. Tewarson, J. Fire Sci. 18 (2000) 183214.[4] S. McAllister, C. Fernandez-Pello, D. Urban, G. Ruff, Combust. Flame 157 (2010)

17531759.[5] A. Tewarson, J.L. Lee, R.F. Pion, Proc. Combust. Inst. 18 (1981) 563570.[6] Y. Wang, L. Yang, X. Zhou, J. Dai, Y. Zhou, Z. Deng, Fuel 89 (5) (2010) 1029

1034.[7] D.L. Dietrich, H.D. Ross, Y. Shu, P. Chang, J.S. Tien, Combust. Sci. Technol. 156

(1) (2000) 124.[8] S.L. Olson, Combust. Sci. Technol. 76 (4) (1991) 233249.[9] J. Kleinhenz, I. Feier, S. Hsu, J. Tien, P. Ferkul, K. Sacksteder, Combust. Flame

154 (2008) 637643.[10] A.E. Frey, J.S. Tien, Combust. Flame 26 (1976) 257267.[11] R. McAlevy, R.S. Magee, Proc. Combust. Inst. 12 (1969) 215227.at low pressures and oxygen concentrations was performed in alarge 10 m3 pressure vessel, capable of reaching pressures as lowas 0.1 atm. The PMMA ammability was characterized by the burn-ing rate and time to ignition of 10 10 cm2 samples. Tests wereperformed at different applied external heat uxes ranging from10 to 72 kW/m2 with burning rates obtained during steady burningfor all cases. Other test conditions included oxygen concentrationsfrom 1221%, and pressures from 0.18 to 1 atm. For each burn testcondition, the experiment was repeated 6 times in the mass losscalorimeter inside the pressure vessel.

Experimental measurements allowed the observation of the ef-fect of pressure and oxygen concentration on the burning rate. Theresults show that at low pressure the burning was less intense,which is shown by the decrease in the mass loss rate. On the otherhand, the reduction of pressure causes the sample to ignite fasterand at a lower critical mass ux, but this is only relevant at low lev-els of external heat ux. In general, the experimental measure-ments showed a good agreement with the power law tobtained for the relation of the combined pressure and oxygen ef-fect on the burning rate. This correlation predicts the burning ratebehavior for the full range of pressure and oxygen measurementsobtained.

Experimental measurements were compared with a simple ana-lytical model. The results show how pressure and oxygen concen-tration contributed to the heat transfer from the ame. Pressureaffects the heat transfer trough the convective heat transfer coef-cient and the effective soot emitter parameter. The convective heattransfer coefcient affects the convective heat losses which arediminished at low pressure, causing the sample to ignite faster.Similarly it explains the decrease in the burning rate through low-ering of the heat feedback mechanism to the sample surface aswell as the decrease in the critical mass ux at ignition throughthe reduction in the available oxygen. The lower oxygen contentthe reduces then ame temperature, thereby lowering the net heatux back to the sample surface.

Referencesthese higher externally applied heat ux values, the ame temper-ature may also be signicantly affected, inuencing the diffusioncoefcient and introducing a Lewis number effect [39]. These high-er order effects may limit the correlation of this model with veryhigh external heat ux cases (as seen and discussed in Fig. 6).Due to these signicant added complexities, we have chosen tolimit the applicability of our model to a lower externally appliedheat ux range where these additional scaling parameters are ofless import.

6. Conclusion

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[20] A. Tewarson, Generation of Heat and Chemical Compounds in Fires, SFPEHandbook of Fire Protection Engineering, third ed., National Fire ProtectionAssociation, 2002, Section 3, pp. 82162.

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Sussex, England, 1993.[26] R.E. Lyon, J.G. Quintiere, Combust. Flame 151 (4) (2007) 551559.

[27] D. Drysdale, An Introduction to Fire Dynamics, third ed., John Wiley & Sons,Ltd., Chichester, UK, 2011.

[28] X. Liu, J.G. Quintiere, Flammability Properties of Clay-Nylon Nanocomposites,DOT/FAA/AR-07/29, Federal Aviation Administration, 2007.

[29] V. Babrauskas (Ed.), Ignition Handbook, Fire Science Publishers/Society of FireProtection Engineers, Issaquah WA, 2003.

[30] S.I. Stoliarov, R.N. Walters, Polym. Degrad. Stab. 93 (2) (2008) 422427.[31] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, third ed., Hemisphere,

New York, 1992.[32] G. Heskestad, Fire Saf. J. 5 (2) (1983) 103108.[33] J. de Ris, P.K. Wu, G. Heskestad, Proc. Combust. Inst. 28 (2000) 27512759.[34] ASTM E 1354, Standard Test Method for Heat and Visible Smoke Release Rates

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[35] T. Kashiwagi, A. Inaba, J.E. Brown, Fire Saf. Sci. 1 (1986) 483493.[36] B.T. Rhodes, J.G. Quintiere, Fire Saf. 26 (3) (1996) 221240.[37] S. Fereres, C. Lautenberger, C. Fernandez-Pello, D. Urban, G. Ruff, Combust.

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1530 M. Zarzecki et al. / Combustion and Flame 160 (2013) 15191530