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JOURNAL OF RESEARCHof the National Bureau of StandardsVolume 82, No.2, September-October 1977

Static Pressure Measurements of Enclosure FiresB. J. McCaffrey and J. A. Rockett

Institute for Applied Technology, National Bureau of Standards, Washington, D.C. 20234(July 5, 1977)

Some enclosure-fire s ta tic pressure measurements are presented for both full and scale model rooms and arecompared with the present hydraulics-orif ice f low model for f ire induced flows into and out of enclosures . Resultsindicate that the vertical pressure differential (enclosure to ambient) follows the expected hydrostatic distributionquite well and accurately reflects the doorway inflow and outflow gas velocities.Measurement of ceiling and floor differential pressure using different numbers of gas burners yields insightinto gross plume entra inment and illus trates how the neutral plane and thermal discontinuity vary with upper gastemperature. Corre la ting upper gas temperature with fire s ize and enclosure height makes it possible to predict atwhat heat release rate a given enclosure might become fully involved, i. e ., by using the temperature at which thethermal discontinuity approaches the floor.In terms of present f ire plume modeling large entrainment coeff icients (0.3-0.4) are required in order toreproduce the enclosure flows for both the small and large scale results. A noted deficiency in the plume modelappears in the small scale results where the data suggest that the entrainment should exhibit a much strongerdependence on the fuel injec tion rate than that predicted by the theory.Key words: Buoyancy pressure; enclosure fires; entrainment; fire induced flows; models; physical scale; plumes.

Nomenclature 1. Introduction

Subscripts

AoCDCpDFrgHHokemNptJ.p

QrTAT

Pw

0, AMB0, OUTi, inf

door opening area (m2)orifice discharge coefficientgas specific heat (J/kg' K)height of thermal discontinuity above floor (m)plume Froude number = u1fg'Yogravitational acceleration (9.8 m/s2)height of enclosure (m)height of door opening (m)entrainment coefficientgas/air flow rate (kg/s)height of neutral plane above floor (m)pressure (torr, N/m2)pressure difference, enclosure to ambient = P-PAMB(torr, also given as N/m2)heat release rate (kW)radial distance from plume axisgas temperature (Oe, K)temperature difference CC)gas burner flow velocity (m/s)gas/air velocity (m/s)door opening width (m)entrained flow in plume (kg/s)gas burner flow rate = Pf7Trf>Ufheight above floor (m)radius of gas burner (m)distance above or below neutral planegas density (kg/m3)fuel property defined by equation (9)

Ambient propertiesoutflowing gasinflowing airfuel

Present enclosure-fire modeling incorporates a hydraulicsorifice approach for calculation of the flow in and out of theopening [1, 2, 3].1 Due to the hot gases present in the upperportion of the room a pressure difference with respect to theambient hydrostatic pressure is developed across the openingwhich is responsible for driving the flow. The gas in theroom is assumed stationary and the flow rate is determinedusing Bernoulli's equation with an appropriate orifice coefficient. Additionally the gas flow in and out of the enclosureis coupled via entrainment of the fire plume. Figures 1 and2 illustrate these ideas schematically. A step function fortemperature with the thermal discontinuity being D metersabove the floor is commonly assumed and used since itleads to integrals expressible in closed form. However, anytemperature distribution can be handled by direct numericalintegration. The ambient pressure is simply hydrostatic,i. e., - P ogy, and the enclosure pressure is made up of twopieces one above and one below D as indicated. The upperportion is hydrostatic but with a different slope, -pgy, andmust intersect the ambient at N, the neutral plane height. Ndemarks the interface between the incoming and the outgoinggas, i.e., v = O. The upper portion is continued down to Dafter which the slope must abruptly change to accommodatethe ambient density. The driving force is the differencebetween the enclosure and the ambient pressure and isshown as tJ.p in figure 2 together with an idealized velocityprofile at the exit. In reality the flow field will be morecomplex near the door with entrainment and possible recirculation occurring near the shear region.Enclosure models incorporating the above hydraulicscheme have been reasonably successful as regards grossfeatures of the burning behavior of compartments [2]. However, the weaker areas where more work is required will be

I Figures in brackets indicate the l iterature references at the end of this paper.

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TD1FIGURE 1. Room geometry.

H

TEMPERATURETo T

PRESSURE LJ.p PoO(l-fHH-N) DOORWAYVELOCITY

o

1o

FIGURE 2. Plots , using a common height scale, to show the interrelation of temperature,pressure difference and doorflow.

difficult to identify until the validity of the flow portion ofthe model is determined. Recent experimental work usingsalt water-fresh water analogs [3] may not be valid forsizeable fires due to the limited density ratios available.Presented here are some measurements of b.p in full-scaleand scale model enclosure burns. Shown will be both verticaldistributions of b.p and b.p as a function of temperature for agiven height. The latter measurements can be used as aguide in assessing the other piece of enclosure modeling,that is, plume entrainment which determines the height ofthe thermal discontinuity.

2. Experimental Apparatus and Procedures2.1. Full-Scale

Complete details of the full-scale experimental facility arecontained in reference [4]. The enclosure dimensions were3.0 X 3.0 X 2.3 m high with a 0.73-m X 1.93-m highdoorway offset to one side; a moveable gas burner providedthe fire source. Static pressure taps were made by insertingcopper tubing through the wall from the outside and positioning them just flush with the inside surface. Type K (0.25mm D), unshielded and unaspirated, thermocouples deter-

mined the temperature at the pressure measuring positioNo radiation corrections were made; the implications ofare discussed in the text. Other tests at NBS, stillprogress and not reported here, show that radiation canquite important to room fire thermocouple readings.differential pressure transducer was located on the floor wone pressure tap positioned outside of the burn-roomaway from the door inflow and shielded from large draThe pressure signal at each height then was the differebetween the room and the ambient pressures at that heigThe pressure taps were located in the doorwall corner excwhere noted. Pressures were measured with a variacapacitance electrical manometer calibrated against a mimanometer water column which can be read fairly accuratto 10-1 N/m2For the smaller fires, the burner, located 0.30 m abthe floor, was usually run for a period of ten minutes,duration of the test; for larger fires the corresponding runntime was shorter. Due to the highly insulated ceilingwalls, a quasi-steady condition was reached quickly.

2.2 ModelMeasurements of b.p across the doorway at the floorceiling of a scale model burn-room were made during

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Q:::140KW

TEMP. a DB-BURNERPRESSURE .TAPS 0

steady operation of up to three Meeker gas burners used forfire simulation. The room was 0.39 m wide by 0.37 m deepby 0.41 m high with a 0.11 m by 0.29 m high doorwayopening located symmetrically in the 0.39 m wall. Thefacility was the same as that used in a recent burn-roomcorridor study [5J except that the corridor was open at bothends allowing the burn-room to interact with the ambient airwithout the additional complexity introduced by a corridor.The burners were located 0.055 m above the floor (exceptwhere noted) and arranged in an approximately triangularfashion around the room. They were separated sufficientlyso as to eliminate plume merging. The pressure taps wereimplanted similar to the full-scale procedure. Upper gastemperature was monitored in the rear of the box at aposition on the centerline 0.37 m high and 0.04 m out fromthe wall. Observations of other thermocouples in the upperportion of the box indicated that the gases were well stirred .3. Results and Discussion

-2

2.0

1.5

! 1.0:I:.5

-I

o

l>P (N/mt)012

a

3 4 5 6 7

[]]3.1. Full-Scale

o -.01 o .01l:>P ; P-PAM

.02 .03(TORR)

.04

Figure 3 shows a typical vertical pressure traverse withthe burner located in the center of the room for two nominallyidentical runs of 140 kW fires. The circles indicate readingswith the pressure and temperature taps in the usual doorwallcorner, and the squares show values taken at an interiorcorner in order to gage any variation due to location of themeasuring station. The slight differences noted are probablymore indicative of the fact that the second run (squares) wasmade immediately after the first, without waiting for theroom to cool, as opposed to a true room non-uniformity. Infigure 4 values of temperature are shown for both the interiorat the pressure taps and for the doorway [4]. No radiationcorrection was made. Note that the interior values approximate the doorway results. Note also that some mixing of thehot gas with the incoming air has occurred. Ambient air isat 23.5 c yet the "door" flow indicated temperature is 39c and the lower gas deep in the room is 56C. Thesetemperature readings could occur for several reasons ofwhich the more obvious include possible mixing of heatedair from the room with the incoming air or an error of thethermocouple reading due to radiation from the flame, hotupper gas and upper wall and ceiling surfaces. If it isassumed that radiation has raised both these temperatures39 - 23.5 = 15.5 c, then the true deep room temperature,below the hot layer, would be about 40.5 c.The slope of the line drawn through the upper pressurepoints in figure 3 was determined using an average uppergas temperature of219C and the hydrostatic relation,(1)

Alternately if one measures !!.p and T at any height, y, thenthe neutral plane height, N can be determined. The agreement between the line and the upper three points showsclearly the hydrostatic nature of the differential pressureacross the door. Only the upper three points were used sincefurther down the temperature begins to fall dramatically andthe simple two layer temperature expression, i.e., eq (1) willno longer hold. In general, however, as the temperaturedrops the !!.p/H slope will decrease and this is evident on

FIGURE 3. Vertical differential pressure for two-measurement positions.

T(C)00100 I0 0

10..

0~Ie>

.. .. 0~ "[

~ MPERATURES..

DOORWAY T~E LOCATION 0010

_aIRESSURE PCl I-0

FIGURE 4. Vertical temperature distributions, measurements made at thetwo interior pressure tap locations shown infigure 3 and in the doorway fortwo tests.

the pressure plot in the regime between the third and fourthdata points down from the ceiling. The upper three pointsyield a predicted neutral plane, N of 1.3 m or approximately+18 percent higher than the actual, interpolated value of1.1 m.The pressure differential in the lower half of the room forthe model of figure 2 is given by the expression,

(2)

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An average value of Ap for the three sets of lower points(-0.0029 torr, -0.39 N/m2) together with the averageupper gas temperature (219C) will determine the thermaldiscontinuity or N - D = 0.08 m. The vertical line showngoing through the average Ap rises to D = 1.22 m, usingthe predicted N, where it meets the predicted upper hydrostatic line. The horizontal or temperature-break portion offigure 4 showing D is somewhat lower than the actual breakone might choose from the data. If it turns out that theenclosure pressure distribution is representative of the doorway flow then figures 3 and 4 indicate that cold air is beingswept out the door.In reference [1], Rockett states that the thermal discontinuity deep in the room must be below the neutral plan.Comparison of figures 3 and 4 show that this is obviouslynot true. As will be shown below, this "anomaly" arisesfrom the assumption by Rockett [1] that the lower gastemperature is ambient. If the incoming air is heated, thereis no need for the "major" thermal discontinuity to be belowthe neutral plane.The other obvious discrepancy with the simple hydrostaticflow model concerns the nonuniform lower pressure distribution. There is a tendency for IApI to increase as the flooris approached, and this should be evident in the doorwayvelocity profile, with higher flows closer to the floor. In theinterior the cold temperature is also measurably greater thana representative ambient temperature. The fact that the dooris not symmetrically located with respect to the room andburner may be partially responsible for the anomalies. Anadditional swirl due to turning of both the in and out flowssuperimposed on the flow field might lead to an increasedmixing across the supposedly stable thermal discontinuity.How well the data compares with a hydrostatic pressurevariation and an arbitrary temperature distribution can beseen in figure 5 where average pressures Hnd temperatures(interior) from figures 3 and 4 are displayed. The hydrostaticpressure difference, interior minus exterior, referenced tothe neutral plane and assuming an ideal gas is given by

(3)

where z is measured above or below the neutral plane.temperature points on figure 5 were joined by straight liThe integral in eq (3) was evaluated with the "trapozorule" to determine Ap. Due to the sharp temperature disctinuity, the use of higher order polynomial curve fitsgenerally unsatisfactory. The neutral plane was specifrom the actual pressure data.In carrying out the numerical integration the temperatuuncorrected for radiation were used. Had these data bapproximately corrected by substracting 16C for vabelow the (radiating) hot layer, the pressure would hincreased less rapidly with height than the measured valConversely, if the lower three pressures are used to estaba temperature, 47.8 C is obtained. This suggests a radiacorrection closer to 8 C than 16C.Also shown on figure 5 is the two-temperature mobased on a single upper gas temperature and ambient lotemperature. This model yields a slope dependent onperature for the pressure in the upper part of the room avertical line for the differential pressure in the lower pathe room. In the case shown here the upper three po

were used to locate the derived pressure profile forupper portion and the average of the lower pressures tothe vertical line. Their intersection gives the neutral pas opposed to using the measured neutral plane as was dfor the numerical integration plot. By using the derislope for the lower points i.e., T = 59C approximatelyopposed to ambient, an alternate gas model couldsketched onto the figure. This alternate model would apas a line going through the lower pressure points withsame slope as the integrated plot and intersecting the uphydrostatic line somewhere above the neutral plane. D wthen be above N as the data indicates. Obviously mcombinations exist. Temperature data or a two-temperatapproximation can only yield the shape of the presprofile; an additional relation is needed to specifylocation of the profile. This is usually accomplished theoically by coupling the fire plume entrainment flow up tothermal discontinuity with the gas flowing out the door [1Whether one chooses a two-temperature model ornumerical integration of temperature data, figure 5 indicclearly the hydrostatic nature of the vertical pressure di

2.0

-2 -I o toP (N/m"!I 2 3

NUMERICAL INTEGRATION

~ 1.0:r

I01

II III I I ~I , I t01020350005000(TORR) T (OC)

FIGURE 5. Hydrostatic pressure models.

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bution. That aspect of the flow model therefore appearssound. It is left to determine how well the interior pressurereflects the doorway flow.The variation of pressure and temperature due to thelocation of the fire within the enclosure is shown in figure 6.Data for three positions of the burner: the center of theroom, the middle of the rear wall, and a rear corner, arepresented for one size fire, 140 kW. Upper gas temperaturesare significanly hotter for the corner burner configuration ascompared to the center. Additionally, the observed thermaldiscontinuity, as well as a predicted neutral height, will behigher than those corresponding to the center burner configuration.An argument based on plume entrainment could beforwarded to explain these results. The center burner beingcompletely unrestricted is able to entrain more cold air andhence yields cooler upper gas temperatures than the cornerburner which is inhibited on the two sides of the corner.

Also, less entrainment will result in a higher neutral plane.It should be pointed out that the burner was square shapedand was positioned flush with the walls for the corner andwall positions.The effect of fire size on pressure and temperature for agiven burner location, the corner, is shown on figure 7. Inthis figure pressure slopes were derived from the averageupper gas temperature and drawn down through the top mostmeasured pressure. As would be expected, bigger firesproduce higher temperatures and larger differential pressures. Finding the slope of the pressure-height relation,using the data on figure 7 and eq (1), will result in a quitesmall variation in predicted neutral heights for the fourcases, i.e., 1.3 to 1.5 m above the floor with N decreasingwith increasing temperature (straight lines on fig. 7). As wasseen in figure 3, the predicted N also lies well above themeasured values for the cases where data is available.

Having established the hydrostatic nature of the verticalpressure variation within the enclosure it is now left todetermine how well this distribution reflects the doorwayflow field. Figure 8 is a plot of the measured centerlinevelocity in the doorway [4], shown by the lines, as against avelocity calculated from the pressure measurements of figure6, shown by the symbols. Here velocity is defined as (2D.p/p)1/2 where p is calculated using air at the local temperature.It can be seen that the interior pressure measurementsrepresent the doorway character exceedingly well; not onlyis the .magnitude of the static pressure calculation the rightorder, but the position of the interpolated neutral plane isidentical to the position of the measured velocity reversal.

In the hydraulics model the velocity (2!1p/ p)1/2 is usedtogether with the area and local density to determine the gasflow rate which is then multiplied by an orifice or dischargecoefficient, thought to be equal to about 0.68. Multiplyingthe pressure calculated values by 0.68 on figure 8 wouldresult in better agreement with the measured velocities forthe incoming flow. However, for the outgoing gases thisprocedure would not improve the agreement. A more detailedevaluation, including off-centerline velocity traverses andtruly steady-state conditions, could yield the accuracy required for evaluation of the discharge coefficient in a realfire situation.Using the pressure and temperature data, the mass flowrate in and out the door can be determined by assuminguniform flow across the door width. Forming (!1p/T)1/2,plotting it versus height, finding the area under the curves,multiplying by an appropriate constant, and arbitrarily cutting off the outflow at the soffit height will yield the flowrates. For the center burner position shown in figure 8 theresulting mass balance is within 12 percent with mout =

0.82 k,g/s and min = 0.72 kg/so (For f~IY involved encloures m = 0.5Ao../Ho = 0.5 X 1.41 X 1.93 = 0.979 kg/

LIP (N/m"J0

I5I T(C) 01.0.000006

0 004

60

} rn.

0

Lt>O

Q=14Ckw BURNERPCSITICNS:60

TEMPERATu:8II PRESSURE 6APS L

6 0

~o

I.01 001.0203L\.P= P-PAMB(TCRR)

FIGURE 6. Vertical pressure arWtemperature distributions/or various fire locations,II

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AP (N/m")-I

03 T( "C)20030000000000I I ffC." 00 AE ~ 1.0I: ,~ ,v CORNER BURNERQ(kw) 0620 1406 34000 459 I.01 00102030405L'l.P P-PAMB (TORR)

FIGURE 7. Vertical pressure and temperature distributions for dijferentfire sizes.

.6002

LI NES: DOORWAY MEASUREMENTSSYMBOLS: CALCULATED FROM ENCLOSURE--- PRESSURE MEASUREMENTS

LLL.LLSOFFIT

PRES~URE ~APS~ JBURNER POSITION-----0 CORNER--0 WALL--.6 CENTER

o o V (rnls) 2 4

FIGURE 8. Comparison of doorwar velocitr measurements with static pressure calculation.

s). Around 10-15 percent is probably as good a balance ascan be expected without going to extraordinary measures.The amount of CH4 required for the size fire used isapproximately 0.0025 kg/s which will not appreciably changethe balance. Since only 0.044 kg/s air is required forcomplete combustion of this amount of methane, about 17times more air is flowing through the enclosure than neededfor combustion.3.2. Small Scale

The pressure drop across the doorway at the ceiling andfloor was measured for a series of fire sizes and differentcombinations of burners in the scale model bum-room.

Specifically, runs were made using three burners,burners and one burner with their normal diffusing coneplace. These allowed the gases to exit 0.055 m abovefloor. Additionally the diffusing cone was removed fromburner and a series of experiments was run with the flaissuing from the floor through a small exit. Different numof burners with different heights and areas should entdifferently and the flow or ~ should be thus effected.Figure 9 represents ~, normalized to doorway openat the ceiling and floor for the above burner combinatplotted against a representative upper gas temperature.shown are the previous full-scale results from figures 67. These are scaled up from 2.13 m, the highest measupoint, to the ceiling via a slope determined from the ac

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FIGURE 9. Ceiling and floor differential pressure versus upper gastemperature .

temperature measurement, through eq (1). Additionally, aleast squares fit of the data of reference [6] is shown by thesolid line.2 This work involved the burning of various sizesheets of polymethylmethacrylate in a small scale enclosure(0.30 X 0.30 X 0.56 m deep) with various size dooropenings. The pressure at the ceiling was recorded duringthe steady burning period and the line shown in figure 9represents 33 experiments extending from low temperature 450C) plume-like burning (small sheets/wide openings)to a condition in which flames occupied nearly the entirevolume, spilling out the door and with temperatures from700 C to noo C (large sheets/small openings).

As is clearly indicated in figure 9 there is considerabledisagreement between the full-scale results and both smallscale results. In the previous section it was determined thatthe measured pressure overestimates the neutral plane heightby 18 percent. If N is reduced by 18 percent the pressurewill increase somewhat but the disagreement will still besubstantial. Note that in general as the number of burners isreduced in the small scale and the position of the burner isset to the floor incorporating a smaller exit (due to removingthe diffuser cap to lower the burner), the neutral planeheight will increase and l1p decrease thus the results willtend toward those of full-scale. In any event, it is clear thatthe l1p is smaller in the full-scale than in the model and,with our instrumentation, this difference cannot be attributed

MODELNUMBER OF BURNERSo 3 2o I6 I (AT FLOOR)

0.1

o

0.2

800

MODELNUMBER OF BURNERSo ,o 1t J. I (AT FLOOR)

100

o

FULL SCALEBURNER POS IT ION CORNER REAR WALL CENTER

o

0.5

0.5

0.1

0.4

0.2

0.3~'o 0.2

o OA:I:'-Z 0.3

FIGURE 10. Calculated values of neutral plane and thermal discontinuityheight normalized to door height.

0.6

to experimental error. The reason for this is not known; wecan speculate, however, about possible reasons. Since botheffects reduce entrainment to a first approximation it can betentatively concluded that small scale fires tend to entrainmore than the corresponding full-scale fire, or at least someeffect causing larger l1p's is present in small scale.Different netural heights for the different burner configurations is explicitly shown in figure 10 together with thecalculated thermal discontinuities both normalized to theopening height and both displayed as a function of temperature. N /H 0 is calculated solely from eq (1) using the measuredceiling l1p and T. D /H 0 requires both the floor and ceilingmeasurement of l1p and utilizes both equation 2 for D andeq (1) for N. Here it is being assumed that the twotemperature model is sufficiently representative. Also displayed are the least squares results from reference [6] andthe previous large scale results reduced by 18 percent inorder to produce a more realistic picture of the actualneutral plane location. Note that the discrepancy betweenlarge and small scale is now less dramatic and in fact thelarge scale center burner (darkened triangle; most entrainment of large scale) neutral plane is practically coincidentwith that of the small scale one burner at the floor case(opened triangle; least entrainment of small scale).

9

800

6

5~z 14?0..~3 2

8REF. 6-'7

700

FULL SCALEBURNER POSITION CORNER REAR WALL.. CENTER

00CO

CEILING 8a Ao ArFAcPOA

00 o:>O

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FIGURE II. Massflow rates versus upper gas temperature.o 100 200 300 400 500 600 700T(OC)

temperature hydrostatic model. All that is required is Nand the upper gas temperature, T. From reference [2]outflow is:

J2g(l- ;)(i -:J~ + 2~J

.6 f-

o !'f*M H~tj~l BURNERSN o 3on o I'E 6. I (ATFlOOR)~: FULL SCALE.y~f POSITION: CORNERR EAR WAL L CENTER~ 'E .2

and the inflow

Also shown are full-scale results (darkened symbwhich again fall below those of small scale and exhgreater inflow than outflow (high N). In comparing largesmall scale there is nothing new in this plot. Small scalyielding higher J).p's and therefore lower Nand D andmore flow. The full-scale center burner result (large trianis once again approaching that of the small scale, sin

where CD is the orifice coefficient, here taken as 0.Figure 11 is a plot of the mass flows in and out normaliby the ventilation parameter, WoHfP. The simple modeprediction [1] for mlAo../Ho is about 0.4 to 0.6 kg s-lm-for D = O. The symbols give the average of the flow inout and the error bars indicate the extremities of theflows. For both sets of data where the burners were raiabove the floor, computed outflow exceeds inflow anddoes so significantly, especially at higher temperaturHigher outflow versus inflow results from a low value oirrespective of D. The excess mass is generally greaterthe three burner case, which is consistent with figureFor the case where the burner is located at the floor,inferred inflow is greater than outflow. Here the oppocondition is true, N is larger. This lack of mass balanceweakness of the present model. Note the behavior ofthree burner case as T approaches 550 e - the avermass flow rate ceases to increase even through the outfappears to be consistently increasing with T and the infconsistently decreasing.

flows were measured and experimental neutral heights areavailable for 4 of the 6 (solid) points plotted on figure 10.These 4 values of N, if plotted, would all lie below thereference [6] result and above the 1 burner (open squares)result. The lines shown are linear least squares fit of thedata and the slope for the small scale results decreases ingoing from the three burner (opened circles) most entrainment case to the one burner at the floor (opened triangles)least entrainment case. Based on the above, a representativeneutral plane versus upper gas temperature relation for atypical room, i.e., one with a "normal" door, would fallsomewhere around the lines representing the data of reference [6] and those of the open triangles. In general doorwidth is another important parameter which must also beconsidered [5].The effect of entrainment is even more evident in thethermal discontinuity relation. On figure 10 the lines on theD IH 0 portion are fair representations of the data with someextrapolation. The implication of this figure is significant. ltis well established experimentally that the air flowing in andout of the compartment for fully involved fires will tendtoward a maximum. This is the so called "flashed over"room or ventilation controlled fire. In modeling, this maximum flow condition is obtained by allowing the thermaldiscontinuity, D, to approach zero. By inspection of eq (2)the pressure drop in the lower part of the room (or inflow)maximizes asD approaches zero for fixed T and N. Therefore,how D drops with increasing temperature will be importantin predicting flashover. The significant differences noted inthe figure are postulated to be due to different entrainment,and hence the importance of the character of the fire orplume cannot be overstressed. Using the extrapolated linesa difference of 150 e from about 550 e to 700 e resultsfor the two small scale cases previously discussed. It isinteresting to note that in reference [6], where the fuelconsisted of a single sheet of PMMA burning near the floor,the fully involved fires were all grouped at temperatures of700 e and beyond. The data grouped into two regimes,points below 450 e and those above 700 e with none inbetween. From the standpoint of figure 10 a room fireconsisting of more than one discreet plume would appear tobe more dangerous than a single plume of the same totalheat release rate. Obviously, however, radiation consideration and possible ceiling impingement from a single largerplume may well invalidate this conclusion .Also shown on the D IH 0 portion of figure 10 are full-scaleresults using the pressure measurement at 0.305 m abovethe floor as was done for figure 9. Since the pressuredifference appears to be getting larger as one approaches thefloor these results probably indicate a higher thermal discontinuity than one which would result if the pressure wasmeasured at the floor. Note the center burner point is nottoo different from the small scale single burner at the floorresults, but obviously more full-scale data is required beforedefinite conclusions can be drawn. Here again, the fullscale data were treated consistently with the model data. Ifthe additional experimental data available for 4 of the 6 thefull-scale tests were used, all four full scale points wouldfall lower in the plot, most noticeable the point at 320 e.They would scatter around the open triangles.Having derived both neutral plane and thermal discontinuity heights from independent measurements of the ceilingand floor differential pressure it would be interesting tocompare the derived inflow and outflow using the two

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FIGURE 12. Upper gas temperature as afuru:tion of.fire and compartmentsize.

00~

000R 8c

0C

6g ALL H- 2 .29mC C , ..ENTEROt! o 0 03 BURNERS}6. C. H-O.4Im6 I (atfkKtr)burner at the floor results (small triangles). Had the experimental N's been used rather than calculated N's the calculated full-scale flows would be larger. The value of m/Ao.JH 0is 0.373 kg s-lm-5/2 for both inflow and outflow or m =0.73 kg/s which compares favorably to the values measureddirectly from the vertical pressure distribution on fig. 8,i.e., mo = 0.82, mi = 0.72 kg/so Recall however that thesevalues were not multiplied by a discharge coefficient.Since most of the previous parameters are expressed asfunctions of upper gas temperature it would be convenient tobe able to relate temperature with the burning rate of thefuel and the size ofthe compartment. A completely analyticalexpression incorporating type, size and position of the fuelarray, type of wall material, ventilation, etc. is beyond thescope of the present work. There is available however,sufficient data to obtain some phenomenological relationsbetween the various variables.From plume theory, correlations exist relating fire size,temperatures and height above the plume source. For anisolated ceiling (no walls), the temperature rise is given as [7]

700

600

500_ 400U.!.-I-4 300

200

100

o 2 4 6 8 ~ ~ ~02131-15/3 (kw2l3rii5/3)

16

(6)

3.3. Plume Entrainment

Choosing a D results in a fixed N for a given T, and Nresults in a unique flow rate from eq (4). The agreementbetween theory and experiment is good and figure 13demonstrates both the consistency between the separatefloor and ceiling pressure measurements as well as theadequacy of the simple enclosure flow model.

enclosure flow model is illustrated in figure 13. The pointsrepresent the average flow into and out of the enclosureusing equations 4 and 5 where Nand D were determineddirectly from the ceiling and floor measurement of t!.ptogether with upper gas temperature. The abcissa is simplythe thermal discontinuity normalized to opening height. Thedownward curving lines on figure 13 are the theoreticalcalculation for three absolute temperature ratios. They arederived from equation 4 plus another relation, that ofcontinuity, mo = mi, which gives N in terms ofD for varioustemperature ratios. For completeness it is presented herefrom reference [1]:

The remaining piece of the enclosure fire picture concernsthe fire plume. Cold air is swept through the door and isimagined to be heated in the plume and carried up from thelower to the upper portion of the room by entrainment intothe plume from the base of the burner up to the thermaldiscontinui ty, D. This amount of flow is equal to what iscoming into the enclosure as well as what is leaving.Entraining of hot gases above D does not contribute to themass balance but rather it accounts for the recirculating flowresponsible for the well stirred temperatures found in theupper portion of the room. The problem reduces to finding arelation involving the amount of entrainment and the heightof the thermal discontinuity for a given fire such that itslocus will intersect the enclosure flow at the appropriateflow and height, i.e., the points on figure 13.

(7)(I-NIH)3 ( D)2T0 = (l - DIN) 1+ - -.Ho 2N To

where r is the radial distance away from the axis of theplume. It might be expected that for an enclosure the stirredupper gas temperature might also scale with the productQ2/3H-5/3 where H is the enclosure height. Figure 12 showsthe present data as well as additional full-scale burnersimulation results from reference [8]. In general the smallscale results are at a slightly higher temperature than thoseof full-scale. Note that these results are for the preflashoverregime i.e. temperatures below about 500C. The one fullscale point at 700C is not expected to fall with the lowertemperature points based on the results of reference [6]. Inthat work no correlation appeared to exist for the hightemperature, complete flame- over, runs while all the lowtemperature results correlated very nicely with the empiricalrelation mass loss rate to the two-thirds power multiplied bya ventilation parameter or width factor to the minus onethird power. Ventilation was not included as a parameter forthe results on figure 12 since geometrically the door widthswere approximately all scaled similiarly.A straight line through the data of figure 12 yields theconstant for the right-hand side of equation 6 equal to 13with most of the scatter within 15 percent. Note that aslope of a line through the full-scale data is dT/Q2/3H-5/3 =:'34 5 K/kW2/3 m-5/3. Since (c;,p'f,gITo)I/3 = 0.380, for Qin kW and H in meters, this implies an f of 13. Thiscompares to a value of about 6.6 [7] for the isolated ceilingdirectly above the plume source (r = 0) beyond which thetemperature drops due to entrainment of cold air into theceiling jet. These findings together with figure 10 indicatethat for a H = 2.3 m high room between 500 and 700 kW(depending on the plume character, i.e., whether the thermaldiscontinuity approaches the floor at 550C or 700 0c) arerequired for a fully involved fire. However, flashover willoccur at much smaller fire sizes not requiring D to gocompletely to the floor. As an example, for flashover Lee [4]finds only about 475 kWare required for a fire in the centerof a room of this size, with 400 and 340 kW for the wall andcomer, respectively.The adequacy of the two temperature hydraulics-orificeus

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.7

.6N~E .50",co.. .40~ 0 .3E .2

ENCLOSURE

Wf . 08Q/s

,FULL SCALEBURNER POSITION CORNER REAR WALLA CENTER

PLUME

MODELNUMBER OFBURNERSo 3o I6 I (AT FLOOR)

--- THEORYCORRELATIONFROM FIG.14

o .4D/H.

.5 .6 .7

FIGURE 13. Enclosure mass flow rate as a function of thermal discontinuity height.

Several fire plume models exist; the one chosen here fromreference [1] is an adaptation of work by Fang [9] andStewart [10]. The total flow in the plume, Wp, is given as afunction of the fuel injection rate, Wf; a fuel property, w;density ratio, ambient to fuel, PO/Pf; plume entrainmentcoefficient, ke, and finally, the height above the burner, D.Rockett 's [1] eq (6) is

W = W w Po ( {~k4/5 [ ~ (_1_-_W_)_7T2gp2 T/5f Pf 5 e 12 w3 f

characteristics will not span a wide enough range to cthe extremities of the data on figure 13 unless the plvaries with Wf to a greater degree than given by the moFigure 14 contains the plume flow versus injectionboth normalized to D5/2 for the theoretical model, i.e.,(8), for three entrainment coefficients: 0.1, 0.25, andshown by the solid lines. The data is obtained by takingaverage mass flow rate through the enclosure and divid

//~//, 0o //0.' CENTER/RAISE

o .....0..60 .,6 0/ CORNER/FLOOR9'''' ./ /.............

.'"q,........ ~ .......... 6

~ jy tr'

(D5/2 Y/5 }5/2 )- + 1 - 1 + WfWf .and

(9)where MOif/ Mo is the ratio of the molecular weight of theflame gas to that of air; All is the heat of combustion; r isthe air-fuel weight ratio and Cp the specific heat. Formethane w = 0.091. Note that the entrained portion of theplume flow is a function of the entrainment constant to thesecond power, the thermal discontinuity to the two-and-onehalf power, and is practically independent of the initital fuelinjection rate, Wf' This latter result, typical of most plumeanalysis by their very nature will render the model incapableof reproducing all the data on figure 13. For a given set ofsymbols on figure 13 the only parameter varied was theinjection or burner gas flow rate, Wf' If a single entrainmentcoefficient is used for a given burner geometry the plume

2

I[

X 10-2

Wf/D512 (kc;js'm-5/2)2

3 1. Quin tiere (o f the C enter for Fire Research , NBS) has recently verified t he applicab ility oft hi s app roxima te exp re ss ion by sol vi ng t he f ul l e quat ions o fS tewa rt 's " -l odel . For a sou rc e w it h sma llmomen tum the r esul ts wer e v ir tu al l) " i dent ic al b etween eq (8) and t he exact exp re ss ion g iven byStewart but not actually used in his calcula tions. FIGURE 14. Plume entrainedflow versus burner injection rate.

116

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