Unsteady Flame Spread in...

2515

Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 2515–2524

INHERENTLY UNSTEADY FLAME SPREAD TO EXTINCTION OVER THICKFUELS IN MICROGRAVITY

ROBERT A. ALTENKIRCH,1 LIN TANG,1 KURT SACKSTEDER,2 SUBRATA BHATTACHARJEE3

and MICHAEL A. DELICHATSIOS4

1School of Mechanical and Materials Engineering

Washington State University

Pullman, WA 99164, USA2NASA Lewis Research Center

Cleveland, OH 99135, USA3Department of Mechanical Engineering

San Diego State University

San Diego, CA 92182, USA4Renewable Resources Associates

Lexington, MA 02173, USA

Results of an experiment for flame spread over thick PMMA in a quiescent, 50% O2 in N2, 1 atm,microgravity environment recently obtained aboard space shuttle mission STS 85 are described. Previousexperimental results indicate that the spread process is unsteady with the spread rate decreasing with time.Although experiment time in the earlier experiments was insufficient to determine if steady spread isestablished or extinction occurs, computational modeling predicts extinction.

The sample length was extended over that of the earlier experiments to determine the ultimate fate ofthe flame. Flame imaging shows that following ignition, the flame leading edge spreads at a continuallydecreasing rate for approximately 180 s, ceases to progress forward, and then retreats in the oppositedirection for approximately an additional 360 s, at which time flame extinction occurs. Computationalmodeling, including gas and fuel surface radiation, captures the observed behavior, which is predicted forall oxygen concentrations up to pure oxygen at 1 atm.

In the presence of a flow, a thin heated layer in the solid develops quickly with the heat transfer drivingvaporization and steady spread, while in the quiescent environment, a heated layer of substantial thicknessdevelops over time while the flame spreads, unsteadily, more slowly. As a result, radiation is important,and the length-scale characteristic of the temperature field in the gas is decreased in comparison to themass diffusion scale, which grows with time. Ultimately, the mismatch in scales results in the flame beingin a region to which oxygen is unable to diffuse at a sufficient rate, and the flame extinguishes. Such self-extinction at microgravity has implications for fire safety considerations in spacecraft.

Introduction

Following ignition of the flat surface of a combus-tible solid, flame spreading ensues. On the Earth,buoyancy induces a flow, which opposes the spreadof the flame. The ratio of radiation heat transfer fromthe gas to the solid to the conduction heat transfer,Rg 4 [( /kg)( 1 1)/( 1 )](ag/Vg)2,43a 4a frT T T Tg P ` f vf

(where aP is the Planck mean absorption coefficient)and the ratio of the reradiation from the surface tothe conduction heat transfer back to the surface, Rs

4 [( /kg)( 1 1)/( 1 )](ag/Vg), depend3 4e rT T T Ts ` v f v

inversely on the gas velocity Vg through the diffusionlength scale ag/Vg such that with buoyancy, thespread process is conduction dominated [1,2]. In theabsence of gravity where Vg becomes the flamespread rate Vf , with respect to the flame, these ratiosare driven to be large, and radiation is important.

Radiative effects tend to reduce the thermal scaleover which temperature changes occur to drive theresulting ratios toward unit order where radiativeand conduction effects may be balanced, for exam-ple, Rs 4 1, and steady spread may be possible [3,4]for certain configurations.

For sufficiently thin fuels, the heat transfer backto the surface is used to vaporize the fuel and drivethe spread process toward a spread rate that is largeenough that conduction heat transfer is dominant,and radiation can be viewed as a perturbation thathas an influence. For example, for spread over thincellulosic sheets, increases in pressure tend to de-crease the optical depth of the gas, that is, absorptioncoefficient times thermal length, which, because ra-diation is not dominant but is a perturbation, can beapproximated by the diffusion length. The decreasein the optical depth derives from the decrease in the

2516 MICROGRAVITY COMBUSTION

TABLE 1Description of the generic terms of equation 1

Equation f Cf s-f

Continuity 1 0 0

x momentum u l]P

1]x

y momentum v l]P

1]y

Species: fuel yF k/cg

Ta,c21B q y y exp 1c g F 0 5 6T

Species: oxygen yO k/cg ss-FSpecies: nitrogen yN k/cg 0

Energy: gas phase T k/cg

10 4 4{Dh s- ` q- 1 4a (T 1 T )}c F ign P `

cg

Energy: solid phase Ts ks/cs

q-ign

cs

diffusion length with increasing pressure, and theradiative loss from the flame is decreased, resultingin an increase in spread rate with increasing pressure[4].

For thick fuels, the situation is somewhat differentin that following ignition, heat transferred back tothe surface is needed to heat a substantial layer ofthe solid in depth, such that the flame spread rate ismuch slower than that for thin fuels. The character-istic heating time is approximately as/ , which, for2V

f

PMMA from typical spread rates at microgravity [6],can be on the order of 100 s. The spread rate de-creases, approximately in proportion to 1/ [6],t!which enhances the radiative effects, resulting forthe conditions considered here in an inability of theflame to reach and maintain a steady spread.

Computational modeling carried out to comple-ment the earlier experiments on the space shuttlefor flame spread over thick PMMA in a quiescentenvironment predicts that the ultimate fate of theflame is extinction rather than steady spread [6]. Amismatch between the thermal scale in the gas,driven by radiation, and the species diffusion scale,driven by mass diffusion, develops such that thehigh-temperature regions of the flame are ultimatelylocated in a region to which oxygen cannot be sup-plied at a sufficient rate to sustain reaction, and ex-tinction occurs. Here we describe an experiment forspread over thick PMMA conducted on space shut-tle mission STS 85 on 9 August 1997 for a longenough period, in contrast to the earlier experiment,to demonstrate the veracity of the predicted extinc-tion. The result of extinction for spread over thickfuels provides direction for the practical problem ofmaterials selection and fire suppression for space-craft.

Modeling

Computational Model

The model has been described elsewhere [4–9]. Itconsists of the unsteady, two-dimensional, energy,momentum, and species equations in the gas,

](qf) ](quf) ](qvf) ] ]f` ` 4 Cf5 6]t ]x ]y ]x ]x (1)

] ]f` C ` s-f f5 6]y ]y

where the different terms are explained in Table 1,and the energy equation in the solid. The momen-tum source terms are written in incompressible formas a simplification because the additional viscousterms present, in principle, in compressible flows arerather unimportant in these slow flows with surfaceblowing [9].

The flame spreads from left to right in the x di-rection, and y is normal to the fuel surface, mea-sured from the insulated back of the fuel slab.Boundary conditions for the rectangular computa-tional domain surrounding the fuel slab and the gasphase in which the flame spreads are the same asthose used earlier [6], namely, ambient conditionsupstream, zero gradient conditions downstream, am-bient pressure downstream and above with nochange in normal velocity in the normal directionabove, and interfacial energy and species balances.

The Planck mean absorption coefficient aP, cal-culated from the method of Global Energy Balance[4,8], considering CO2, H2O, methylmethacrylatevapor, and the temperature distribution in the flame,accounts for reabsorption of radiation despite theapparent thin optical limit of the radiation source

UNSTEADY FLAME SPREAD IN MICROGRAVITY 2517

Fig. 1. Computed position versus time for the 2-D com-putation model for spread over a 59.9-mm-long PMMAsample, 6.35 mm wide by 3.18 mm thick as a function ofvolumetric concentration O2 in N2 at 1 atm. Upstream anddownstream inert surfaces aluminum.

term. The fraction of gas radiation fed back to thefuel surface f, as well as surface reradiation, is in-cluded. Typical values of f are 0.08 for the resultspresented here.

In addition to the conservation equations, theequation of state for density, a square-root depen-dence of viscosity and thermal conductivity in thegas on temperature, and a pyrolysis formula basedon negligible surface regression, constant solid den-sity, and first-order kinetics [10] are used to com-plete the formulation. The pyrolysis law (equation 2)is one that accounts for the mass transfer of fuel atthe surface from the solid to the gas, with the re-maining solid being inert, but it does not describeadditional detailed phenomena such as bubbling ofthe solid in-depth, the transformation of the solid toa liquid prior to gasification, etc.

0.5P M l k T` `q 4 ; 4 4 1 2RT l k Tr r r

1/22q T B ks s p sm8 4 5 60T [3.615Dh ` 4.605c (T 1 T )]a,p v s s `

Ta,p• exp 1 (2)1 22Ts

The properties are ones used before [6] and arelisted in the nomenclature. The set of equations issolved numerically using the SIMPLER algorithm[11].

Two configurations are considered computation-ally that are identical to the experimental configu-ration for an earlier experiment on STS 63, someresults from which were presented earlier as well [6],and STS 85, each for PMMA at 50% O2 in N2 at 1atm pressure. For STS 63, a 25.4-mm-long sampleof PMMA was embedded flush with an inert surface.

The downstream inert surface, behind the ignitionend, is 4 cm long, and the upstream inert surface,toward which the flame is spreading, is 23.46 cm.For both configurations, both the ends, sides, andbottom of the fuel sample are insulated with theequivalent of a layer of Fiberfrax insulation [6,12],taken computationally to be adiabatic. The compu-tation is performed over a 30-cm-long (x direction)by 20-cm-high (y direction) domain. The ignitionpower input per unit volume is 2.2 2 108 W/m3,which when multiplied by the ignition volume re-sults in 2.4 W of ignition power, which correspondsapproximately to the experimental input. This powerinput is continued until flame ignition occurs, whichis usually at approximately 1.8 s, at which time it isshut off. For STS 85, a 59.9-mm-long sample is used.The downstream inert surface is 4 cm long, and theupstream surface is 20.01 cm long.

Computations on several grids for STS 63 wereperformed to ensure grid-independent results, thegrid chosen being 140 (x nodes) 2 52 (y nodes) with8 y-direction nodes in the solid. Along the y direc-tion, the grid step size is 0.625 mm from the fuelsurface into the gas to y 4 10 mm. After 10 mm, apower-law variation for grid distribution to the topof the domain is used. The grid distribution alongthe x direction consists of a step size of 1.74 mmfrom x 4 0 to x 4 4 cm (downstream inert surface),followed by a step size of 0.283 mm to x 4 6.54 cm(fuel sample), and then followed by a power-law vari-ation to the right-hand side of the domain (upstreaminert surface) [13]. The time step ranged from 0.05to 0.5 s, and the relative convergence criterion forall field variables was 0.005. The grid for simulatingthe STS 85 experiment is the same in the y direction.Along the x direction, there are 175 nodes consistingof a step size of 1.74 mm from x 4 0 to x 4 4 cm,then 0.283 mm to x 4 7.54 cm followed by thepower-law variation to the right side of the domain.

Model Results

In Fig. 1, we show x-t leading edge trajectories,the leading edge being the location of the peak heatflux, with the origin being the left edge of the fuelsample, for the two-dimensional spread problemoutlined earlier for spread over PMMA, 3.18 mmthick, insulated on the back side, at 1 atm with theupstream and downstream inert surfaces being alu-minum. The sample length and grid configuration isthe STS 85 one. For all O2 concentrations, essen-tially the same transient behavior is predicted, thatis, initially decreasing spread rate, cessation of for-ward spreading, for some conditions substantial re-treat of the leading edge, then extinction.

The maximum distance of spread increases withincreasing O2 concentration, and the amount of timebetween when the flame reaches its maximum dis-tance of progression and extinction decreases with


Fig. 2. Computed temperature contours for the 2-Dmodel with added gas-phase conduction heat loss for 3-Deffects for flame spread over a 59.9-mm-long PMMA sam-ple, 6.35 mm wide by 3.18 mm thick for 50% O2 at 1 atm.(a) is at 2.1 s, (b) at 141 s, (c) at 414 s, (d) at 484 s, and(e) at 555 s. Outermost contour is 750 K with temperatureincreasing in 150 K increments moving inward toward theflame.

increasing O2 concentration. The latter behavior oc-curs because the Planck mean absorption coefficientincreases with increasing O2 concentration, 4.1 m11

at 40% O2 to 8.4 m11 at 100% O2 at the point ofmaximum spread distance, because of the increasein CO2 production, which increases the radiative lossfrom the gas and hastens extinction. For the 50% O2case, the optical depth, computed as the Planckmean absorption coefficient times the thermallength, when the flame is at 2.07 cm after 414 s (seeFig. 1) is 0.15, which is typical of values for the com-putations here.

The behavior shown in Fig. 1 obtains because ofthe mismatch in the thermal and mass diffusionscales described earlier. For example, for the 50%case, the condition of the STS 63 and 85 experi-ments, the distance along the surface over which theO2 mass fraction changes from 0.1% to 95% of theambient grows from less than 1 cm at 2.1 s to about9 cm at the maximum distance of progression, atwhich time it remains relatively fixed until extinc-tion. At the same time, the distance between themaximum computed temperature and 95% of theambient changes from about 0.5 cm to about 1.5 cmat the same locations. The ratio of the diffusion tothe thermal scale then grows from about 2 to 6 atthe maximum distance of progression, and it contin-ues to increase as the leading edge retreats and theextent of the temperature field shrinks under theinfluence of radiation. Leading edge retreat occursbecause the flame is unable to preheat the virgin fuelahead of it, and it moves toward a region of previ-ously heated fuel that is pyrolyzing until it extin-guishes.

For the results in Fig. 1, the trailing edge of theflame remained pinned at the left edge of the fuel

sample. It would appear that in order to move thetrailing edge computationally, an additional heat-lossmechanism is necessary over and above the radiativelosses. In Fig. 2, we show temperature contours forthe model outlined previously except that a side heatconduction loss in the gas has been added, point bypoint, so that it varies with computational location,the loss being approximately kg(Tf 1 T`)/(ag/Vf )[14]. The resulting heat loss is more than 1 order ofmagnitude smaller than the conduction flux back tothe fuel surface. This small conduction loss thoughis capable of quenching the flame at the trailingedge, resulting in the trailing edge propagating for-ward.

The leading edge shows the same behavior aswithout the additional heat loss. The outermost con-tour in Fig. 2 is 750 K, and the increment from con-tour to contour moving inwardly toward the flame is150 K. The highest temperature at 141 s is 1050 K,and at 555 s, it is 750 K. The x-t trajectory of theleading edge is, for all intents and purposes, thesame in Figs. 1 and 2 for the same condition, al-though the overhang of the temperature field aheadof the peak heat flux used to track the flame in Fig.1 is evident in Fig. 2 in comparing the two figures.

Experiment

Description

The test apparatus was similar to that used in ear-lier experiments [6,12] but with some notablechanges. Here, a single PMMA sample more thantwice the length of the earlier samples was used toobtain observations of the extended flame lifetimepredicted by the numerical results [6]. The sample,59.9 mm long, 3.18 mm thick, and 6.35 mm wide,insulated around all sides and the bottom, was ig-nited using a joule-heated Kanthal wire, located 1.75mm from the end of the sample and energized au-tomatically for 5 s. Six thermocouples, 0.07 mm typeR, were suspended 10 mm above the fuel centerlineat streamwise distances from the ignitor of 5, 10,19.6, 29.2, 38.8, and 48.4 mm.

As before, the experiment was conducted inside a39-L chamber filled before flight with a mixture of50% O2, 50% N2 at 1 atm. At lower oxygen concen-trations, for example, 21%, which might be moretypical of a spacecraft environment, the fuel is onlyflammable if a flow of a few centimeters per secondis provided as might occur from a ventilation system.The flow suppresses radiation sufficiently to allowfor development of a steady spread. Here we areinterested in the quiescent environment in an effortto uncover the physics of the very low velocity en-vironment, the quiescent environment being thelimiting case.

A video camcorder was used to record images of


b

Fig. 3. Digitized image sequence showing side view offlame spreading over PMMA sample (59.9 mm long, 6.35mm wide, 3.18 mm thick) burning in a quiescent micro-gravity atmosphere of 50% O2, 50% N2 at 1 atm. The spa-tial scale origin is attached to the insulated ignitor end ofthe fuel sample. The joule-heated, hot-wire ignitor isshown in (a) at 6 s after ignition. The flame leading edgefirst advances: (b) 66 s, (c) 126 s, and (d) 186 s; then re-treats: (e) 246 s, (f ) 306s, and (g) 366 s. At 420 s afterignition, (h), the flame is noticeably disturbed by the burst-ing of a bubble in the fuel surface. After the disturbance,the leading edge of the flame remains approximately sta-tionary as the flame dims (i) 480 s, (j) 510 s then extin-guishes at 532 s after ignition.

the side view of the sample, showing the flame abovethe fuel in each frame, nominally to reproduce thedomain of the two-dimensional numerical model.The top view, with the fuel behind the flame in eachimage, was recorded using cine film. In earlierflights, cine film was used for both views [6]. Theflight video recording was directly transcribed ontoa laser disk medium on which each frame is individ-ually addressable.

The flame progress data were extracted from over15,800 images using an image analysis package de-veloped by NASA [15]. The analysis sequence in-cludes measuring the hue and intensity of each pixelwithin a prespecified portion or window of the imagecontaining the flame. The flame position in that im-age is recorded as the position of the rightmost pixelwhere it attains a predetermined threshold intensity,set here at 29 arbitrary units out of a saturation in-tensity of the digitizing device of 255.

Results and Discussion

Figure 3 shows selected images taken from thevideo recording of the spreading flame. As predictedby the numerical model, the flame leading edge ad-vances at a continuously decreasing rate, stops, re-cedes, and quenches. Late in the experiment, a bub-ble of fuel vapor apparently burst, briefly ejecting ajet toward the flame. This fuel jet is visible in onlytwo video frames (30 frames/s) indicating a maxi-mum duration of less than 1/10 s.

The trailing edge of the flame began over the backend of the sample and moved past and then awayfrom the ignitor during the early phase of the flamelifetime. Later, the trailing edge reversed directionand advanced toward the ignitor. Near the time ofthe bubble disturbance, the trailing edge reaches thevicinity of the ignitor wire. In the original video, theignitor wire appears to reach incandescent tempera-tures very briefly at this point. Thereafter, the trail-ing edge recedes from the ignitor and spreads for-ward upstream at a steady rate.


Fig. 4. Digitized image sequence showing side view ofthe sample ignition. The joule-heated ignitor wire vapor-izes surrounding fuel into a cloud that is shown igniting inthe central image, 0.4 s after the first incandescence of theignitor wire, shown in the top image. Two gas-phase ther-mocouples suspended 10 mm above the fuel surface 5 mmand 10 mm from the ignitor wire in the flame spread di-rection also appear in the central image. The bottom imageshows the first video image of the spreading flame, 6 s afterignition.

Figure 4 shows the ignition sequence of thePMMA sample, which consists of the heating andvaporization of the solid, creating in the quiescentenvironment a cloud of heated fuel vapor that mixeswith the surrounding oxidizer. When the premixedcloud becomes flammable, it ignites and burns rap-idly. After the premixed cloud is consumed, themuch smaller spreading flame, in its early stages, ap-pears and begins to grow.

In Fig. 5, measured positions of the experimentalflames from the current experiment and from theearlier STS 63 experiment conducted in the sametest atmosphere but with a 25.4-mm-long sample [6]are presented along with predictions from the nu-merical model. In the upper panel, the two sets ofexperimental data are compared. In the current ex-periment, with the thermocouples further removedfrom the vicinity of the flame, the flame progressesfaster but finally not as far as the earlier flames.

In the lower panel of Fig. 5, the model predictionsare shown from the two-dimensional model for the25.4-mm-long sample, upper curve, with the inertsurface upstream and downstream of the sample be-ing inert PMMA for this computation, and for the

two-dimensional model for the 59.9-mm samplewith and without the three-dimensional conductionloss term added. The three-dimensional conductionloss term does not materially affect the x-t trajectoryof the leading edge, but it does allow the trailingedge to move computationally.

The leading edge of the flame, both experimen-tally and computationally, progresses farther for theshorter sample, with the leading edge coming closeto the insulated end of the sample, than for thelonger sample. The reason is that the insulated endfor the shorter sample traps the heat transferred up-stream of the flame between the leading edge andthe insulation such that it cannot leak farther up-stream as it can in the longer sample. The result isthat the surface temperature at the position of theinsulation for the short sample is predicted compu-tationally to be 130 K larger than for the longer sam-ple, that is, a predicted surface temperature at the25.4-mm location of 550 K for the short insulatedsample and 420 K for the longer sample, at 430 s. Itis this preheating that allows the flame for theshorter sample to spread farther as energy is drainedupstream for the longer sample. The computed re-sults for the leading edge trajectory compare favor-ably qualitatively with experiment, although thequantitative comparison with the trajectory of STS85 is not as good as it is for STS 63, which may belinked to the trapping effect of the insulation for theshort sample providing some added stability as com-pared to the long sample as extinction is approached.

The interpretation of the experimental behavior ofthe leading edge of the flame was given earlier. Localquenching occurs, and the leading edge retreats intoa region of previously heated fuel. For the trailingedge, which moves forward, backward, and then for-ward again before the flame extinguishes, the for-ward motion occurs because of heat loss near thetrailing edge quenching the flame there, whereas thebackward motion is interpreted to occur because thetrailing edge spreads back into previously heatedfuel as the leading edge approaches the trailing edgeto heat the fuel and oxidizer there further while ox-ygen diffuses in. The trailing edge then moves for-ward again because the heat losses at the trailingedge are sufficient to quench the flame there again.Flame extinction occurs abruptly throughout theflame when the streamwise flame length diminishesto approximately 5 mm. Computationally, the trail-ing edge is not predicted to move backward (see Fig.2); the heat losses and three-dimensional effects thatoccur in the trailing edge of the flame are modeledonly approximately.

In Fig. 6, the thermocouple histories are shown aswell as the computed temperatures, for the two-di-mensional model with the three-dimensional heatconduction loss term added, at the thermocouple lo-cations. The accuracy of the thermocouples is 55K. Both experimentally and computationally, as the


Fig. 5. Flame position versustime: experimental results from STS63 and STS 85 and numerical pre-dictions. The upper panel shows theflame leading edge spreading in 50%O2, 50% N2, 1 atm over a 25.4-mm-long sample (two tests during STS63, square symbols) and over a 59.9-mm-long sample (single test duringSTS 85, upper curve of circle sym-bols). The insulated end position at2.54 cm is for STS 63. For STS 85,the insulated end is at 5.99 cm but isnot shown on the figure. The trailingedge position of the STS 85 flame isalso shown as the lower curve of cir-cle symbols. The letters indicate thetime of the corresponding images inFig. 3. The lower panel shows againthe experimental flame leading edge,affected by heat losses attributed tothermocouples, for STS 63 (squaresymbols), numerical predictions“with no loss” (up triangle symbols)for STS 63, “with no loss” for STS 85(down triangle symbols), and with“3-D loss” for STS 85 (diamond sym-bols).

Fig. 6. Thermocouple-measured and computed tem-peratures for STS 85 for five thermocouples located 10 mmabove the fuel surface and at (a) 5 mm from the ignitorend of the sample, (b) 10 mm, (c), 19.6 mm, (d) 29.2 mm,and (e) 38.8 mm.

flame progresses, the extent of the temperature fielddecreases, consistent with the interpretation that theflame is shrinking into a region to which the oxygentransport is diminished [16] as the distance throughwhich oxygen must diffuse grows comparatively withtime until the flame extinguishes. The early spike inthe measured temperatures, rapidly evident for the

thermocouples at 5, 10, and 19.6 mm, is the influ-ence of the ignition phenomenon, which is not cap-tured computationally at such long distances fromthe ignition source.

Conclusions

We have demonstrated experimentally that flamespread over a thick fuel in a quiescent, microgravityenvironment is inherently unsteady, with the ulti-mate fate of the flame being extinction. The extinc-tion occurs because the thermal scale of the flame isdominated by radiation, while the mass diffusionscale is unaffected by radiation. The diffusive scalegrows in time compared to the thermal scale suchthat eventually, oxygen cannot be supplied at a suf-ficient rate, and extinction occurs. Modeling predictsthis behavior for all O2 concentrations up to pureoxygen for spread over PMMA at 1 atm. Implica-tions are that in spacecraft fires, self-extinction willoccur in quiescent, microgravity environments formaterials with substantial thermal mass.

Acknowledgment

We gratefully acknowledge support for this work byNASA through Contract NAS3-23901 and Grant NCC3-354.


Nomenclature

aP planck mean absorption coefficient consider-ing CO2, H2O, and MMA vapor [4,8]

Bc pre-exponential factor for the gas-phase re-action, 5.928 2 109 m3/kg s

Bp pre-exponential factor for the pyrolysis reac-tion, 2.282 2 109 s11

cg specific heat of the gas, 1.183 kJ/kg Kcs specific heat of the PMMA, 1.465 kJ/kg Kf fraction of gas radiation fed back to the fuel

surfaceLg gas-phase thermal and mass diffusion scale,

ag/Vf , mm9 mass flux, kg/m2 sM` molecular weight, 30 kg/kmolP pressure, atmq9ign ignitor heat flux, W/m2

s stoichiometric air–fuel ratio,/( ), 1.92v8M v8Mo o f f

s-f source term in the conservation equations(see Table 1)

t time, sT temperature of the gas, KTa,c activation temperature of the gas-phase re-

action, 10,700 KTad adiabatic flame temperature for stoichiomet-

ric combustionTa,p activation temperature of the pyrolysis reac-

tion, 15,600 KTr reference temperature,

(T` ` Tad)/2 4 1958 KT temperature measured in the units of T`

u gas velocity in the x direction, m/sv gas velocity in the y direction, m/sVf spread rate, m/sVg gas velocity, m/sx coordinate parallel to the fuel surface, my coordinate perpendicular to the fuel surface,

m

Greek Symbols

a thermal diffusivity, m2/soDhc heat of combustion for the gas-phase reaction,

25,900 kJ/kgfueloDhv heat of evaporation for the pyrolysis reaction,

941.08 kJ/kgfueles radiative emittance of the fuel surface, unityk thermal conductivity of the gas, W/m Kkr reference thermal conductivity of the gas,

0.086 W/m Kks thermal conductivity of the solid phase, 0.188

W/m Kl absolute viscosity of the gas, N s/m2

lr reference viscosity of the gas, 0.675 2 1013

N s/m2

q density of the gas, kg/m3

qs density of the solid fuel, 1190 kg/m3

r Stefan–Boltzmann constant

Subscripts

ad adiabaticF fuelf flameg gas phaseign ignition` ambient conditionsr references solid phasev vaporization

REFERENCES

1. de Ris, J. N., in Twelfth Symposium (International) on

Combustion, The Combustion Institute, Pittsburgh,1969, pp. 241–252.

2. Williams, F. A., in Sixteenth Symposium (Interna-

tional) on Combustion, The Combustion Institute,Pittsburgh, 1977, pp. 1281–1294.

3. Bhattacharjee, S., Altenkirch, R. A., Olson, S. L., andSotos, R. G., J. Heat Transfer 113:670–676 (1991).

4. Bhattacharjee, S., Altenkirch, R. A., and Sacksteder,K., J. Heat Transfer 118:190 (1996).

5. Ramachandra, P. A., Altenkirch, R. A., Bhattacharjee,S., Tang, L., Sacksteder, K., and Wolverton, M. K.,Combust. Flame 100:71–84 (1995).

6. West, J., Tang, L., Altenkirch, R. A., Bhattacharjee, S.,Sacksteder, K., and Delichatsios, M. A., in Twenty-

Sixth Symposium (International) on Combustion, TheCombustion Institute, Pittsburgh, 1996, pp. 1335–1343.

7. Bullard, D. B., Tang, L., Altenkirch, R. A., and Bhat-tacharjee, S., Adv. Space Res. 13-7:171–184 (1993).

8. Bhattacharjee, S. and Altenkirch, R. A., in Twenty-

Third Symposium (International) on Combustion, TheCombustion Institute, Pittsburgh, 1990, pp. 1627–1633.

9. Bhattacharjee, S., Altenkirch, R. A., Srikantaiah, N.,and Vedha-Nayagam, M., Combust. Sci. Technol. 69:1–15 (1990).

10. Lengelle, G., AIAA J. 8:1989–1986 (1970).11. Patankar, S. V., Numerical Heat Transfer and Fluid

Flow, Hemisphere, New York, 1980.12. Vento, D., Zavesky, R., Sacksteder, K., and Altenkirch,

R. A., “The Solid Surface Combustion Space ShuttleExperiment Hardware Description and Ground-BasedTest Results,” NASA TM 101963, 1989.

13. DiBlasi, C., Crescitelli, S., Russo, G., and Fernandez-Pello, A. C., “Prediction of the Dependence on theOpposed Flow Characteristics of the Flame SpreadRate over Thermally Thick Solid Fuel,” Second Inter-

national Symposium on Fire Safety Science, Tokyo, Ja-pan, 1988.

14. Frey, A. E. and T’ien, J. S., Combust. Flame 36:263–289 (1979).


15. Klimek, R. G., Wright, T. W., and Sielken, R. S., “ColorImage Processing and Object Tracking System,” NASATechnical Memorandum, TM107144, 1996.

16. Olson, S. L., Combust. Sci. Technol. 76:233–249(1990).

COMMENTS

Howard Baum, NIST, USA. It is hard to see how theexperimental configuration can be analyzed with a two-di-mensional simulation. The fact that the fuel strip is so nar-row compared with its length means that the temperaturewill fall rapidly in the direction transverse to the flow. Thiscooling effect draws in a flow from the side that proceedsup the temperature gradient. This has important combus-tion implications and is impossible in a two-dimensionalscenario.

Author’s Reply. The phenomenon observed, namely, un-steady spread from ignition to extinction, is predicted tooccur using the two-dimensional model described here,with the exception of prediction of movement of the trail-ing edge. It would appear that three-dimensional effectsneed to be accounted for in order to capture the behaviorof the trailing edge, as we have shown here by incorporat-ing, although in an approximate way, three-dimensional ef-fects. Such effects though do not seem to disturb the phys-ics occurring near the leading edge of the flame, which isresponsible for determining the propagation characteristicsof the spreading flames. While three-dimensional effectsare likely to be present throughout the flame, the fact thatqualitatively the basic behavior of the leading edge is cap-tured by a two-dimensional model would suggest that anythree-dimensional effects in that region are not necessaryto understand the essential physics of the unsteady spreadprocess. That this is the case is most likely associated withthe fact that the thermal scale is actually rather small, atleast in comparison to the mass diffusive scale, because ofthe dominance of radiation.

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Kuldeep Prasad, Naval Research Laboratory, USA.

1. In the numerical model, how does the mass pyrolysisrate change as the leading edge and the trailing edgemove closer to the fuel surface?

2. How is the location of the leading edge and trailing edgedetermined numerically?

Author’s Reply.

1. It is difficult to provide a general answer to this questionbecause of the presence of radiation. If the flame wereto move closer to the surface because of an increase inopposing flow, the heat flux to the surface would in-crease. The solid would accommodate the increased fluxthrough an increase in surface temperature. With radi-ation dominant as it is here, movement of the flame tothe surface is accommodated by an increased surface

re-radiative loss and an enhanced gas radiative loss aswell. The result is that the peak surface temperaturedecreases slightly as the flame moves closer to the sur-face over time, as it moves toward extinction.

2. The leading and trailing edges are identified as the lo-cation of the local maxima in heat flux back to the sur-face.

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A. C. McIntosh, University of Leeds, UK. Is there a criti-cal microgravity where this self-extinction of the flameceases to occur? Can this be usefully plotted against otherparameters in the system?

Author’s Reply. Steady spread over thick fuels in down-ward and horizontal (flame on top) configurations is ob-tainable in a quiescent environment in Earth’s normal grav-ity. As the gravity level is reduced, eventually the unsteadybehavior observed and predicted here occurs. Logicallythen, there is some limiting gravity level (g) below whichsteady spread cannot be maintained. The unsteady spreadprocess to extinction occurs because the mass diffusionscale characteristic for oxygen diffusion into and productremoval from the flame grows in time with respect to thethermal scale, which is dominated by radiative effects. Theradiative effects are enhanced, that is, Rg and Rs are madelarger, and Vg decreases in proportion to g1/3 as g is de-creased. Eventually, Rg and Rs are large enough (g is lowenough) that the unsteady process observed here emerges.Through computation or experiment then, the limitinggravity level, appropriately made dimensionless, could bedetermined as a function of the other parameters of theproblem as suggested by the question.

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Sandra Olson, NASA Lewis Research Center, USA.

Could you comment further on the effect of the bubblerupture/vapor jet on the flame stability late in the experi-ment? Do you think a material with a higher “bubblingrate” would show a similar transition to extinction, or wouldthe vapor jetting enable some steady burning state?

Author’s Reply. The bubble rupture late in the experi-ment introduced a perturbation to which the flame re-sponded. As a result, the details of flame evolution to ex-tinction may have been altered some over what they wouldhave been without the disturbance; however, by the time


the disturbance occurred, the driving force for extinctionhad taken the flame close enough to extinction that it isunlikely that the disturbance had any quantifiable effectson overall flame behavior or time to extinction.

The “bubbling rate” question is an intriguing one. It

would seem logical that indeed a higher “bubbling rate”would allow for steady burning, and perhaps spreading, asthe bubbling eventually mimics a jet flame, which is known,under certain circumstances, to burn steadily in micro-gravity.

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