plume flow in high rack storages

*Tel.: #46-33-16-50-00; fax: #46-33-13-55-02.E-mail address: [email protected] (H. Ingason).

Fire Safety Journal 36 (2001) 437}457

Plume #ow in high rack storages

Haukur Ingason*Swedish National Testing and Research Institute (SP), Fire Technology, P.O. Box 857,

S-510 15 Bora� s, Sweden

Received 10 July 2000; received in revised form 15 September 2000; accepted 18 January 2001

Abstract

A theoretical and experimental study of rack storage "res is presented. Free-burn testswith multiple-wall corrugated paper cartons were carried out in reduced scale and in largescale. The in-rack #ame height, excess centreline gas temperature and gas velocity wereplotted using axi-symmetric quasi-steady state power law correlations. The correlations includeoverall convective heat release rate, vertical #ue width, height above the #oor and height ofvirtual origin. The correlations obtained can be used to predict activation times of in-racksprinklers and they can be incorporated into engineering models designed to predict #amespread and "re growth in storage geometries. The study shows that it is possible to reproduce#ow conditions and #ame heights in di!erent scales which is of practical importance since alllarge scale testing with high rack storages is very expensive. � 2001 Elsevier Science Ltd.All rights reserved.

1. Introduction

It is not an unusual situation that the "re brigade, even when in attendance withina few minutes, is prevented from entering a warehouse building due to rapid "redevelopment in a high racked storage of goods. Consequently, the "re brigade isforced to "ght the "re from outside with little hope of reaching the seat of the "re. Inorder to avoid this situation, high rack storages are often protected with in-racksprinklers inside and/or on the face of the high rack storage. The e$ciency of thesprinkler system depends on the packaging and storage arrangement as well as the#ammability of the commodity. Other important factors are sprinkler orientation and

0379-7112/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 3 7 9 - 7 1 1 2 ( 0 1 ) 0 0 0 0 7 - 8

Nomenclature

A�

de"ned in Eq. (8)a, b, c de"ned by Eqs (10) and (11) (m/kW��)b�� thermal plume width (m)b��

radius of the "re plume at the mean #ame height (m)c�

speci"c heat (kJ/kgK)C

�,C

�,C

�nondimensional constants

D e!ective diameter (m)E nondimensional constantF function de"ned in reference xFr Froude numberg acceleration of gravity (m/s�)Gr Grashof numberH height of rack storage (m)h height of horizontal #ue (m)�H

�heat of combustion per unit mass of the fuel (J/kg)

¸ characteristic scale length (m)¸�

mean #ame height (m)Q chemical heat release rate (kW)Q

�convective heat release rate (kW)

Re Reynolds number¹ gas temperature (K)¹

�air ambient temperature (K)

T�

centreline gas temperature (K)�¹ temperature rise above ambient (K)�¹

�centreline excess gas temperature (K)

�¹��

centreline excess gas temperature at mean #ame height (K)u gas velocity (m/s)u�

centreline gas velocity (m/s)w width of a vertical #ue (m)z height from #oor level (m)z�

height of virtual origin (m)

Greek letters��

density at ambient temperature (kg/m�)� convective fraction of chemical heat release rate, Q

�/Q

� nondimensional parameter de"ned by Eq. (14)

responsiveness of the heat sensitive element and the type of water supply e.g. a dry orwet pipe sprinkler system. Any possible delay of sprinkler activation is very importantas this may be critical for control of the "re. A signi"cant amount of #ames passinga sprinkler before it activates, may easily ignite combustibles at higher levels, and thus

438 H. Ingason / Fire Safety Journal 36 (2001) 437}457

reduce the possibility for the sprinkler water to reach to the "re seat. In order tocalculate the activation time information on #ow conditions close to the sprinklerhead is necessary. Thus, it is important to investigate how variation in vertical andlateral #ue sizes (gaps created between the stored goods) in#uence the complex #ow"eld near the in-rack sprinkler.

The prediction of sprinkler activation time in simple room con"gurations is doneroutinely using power law correlations of temperature and velocity in plumes andceiling jets [1}5]. Similar correlations for complex con"gurations like high rackstorage are, however, not found in the open literature. Large scale experiments areusually expensive to perform and modelling work with computational #uid dynamics(CFD) often extensive and time consuming. Thus, engineering power laws like thosepresented here are of practical importance. They may reduce the expense of testingand increase our understanding of the important parameters controlling the "regrowth rate. These power law correlations can also facilitate future #ame spreadmodelling and suppression studies in high rack storages. In time it is hoped that afully developed rack storage model (engineering models and/or CFD models) maybe used to predict "re growth rate, #ame spread, activation times of in-rack andceiling sprinklers and suppression e$ciency of rack storage "res.

1.1. Background

Large scale experiments [6}12] have clearly shown that #ame spread and "regrowth rates are very rapid in high racked storage of goods.Modelling of #ame spreadand "re growth rate requires knowledge about #ame heights and heat #ux distribu-tion to the walls of the stored material. In recent years, great e!ort has been focused on#ame spread modelling over vertical surfaces of combustible materials [13}15]. Thephysics and prediction of the "re growth rate is well understood for a single burningvertical wall, whilst the phenomena governing the #ame spread in con"ned con"gura-tions like rack storages has not been thoroughly studied.

Despite the number of all large scale experiments performed throughout the world[6}12], it appears that very little information is available in the open literature on thein-rack temperatures, velocities and #ame heights. This is probably due to the fact thatthe tests were mainly performed to study the behaviour of sprinkler systems incontrolling rack storage "res, rather than to systematically study the in-rack plume#ow and #ame spread. Conclusions on the e!ects of di!erent #ue (gap) sizes on the#ame spread are di$cult to make. Recommendations in NFPA 231C [16] (which arebased on full scale experiments carried out at the Factory Mutual Research TestCenter, West Glocester, Rhode Island ) on the size of #ues (nominal size according toNFPA 231C is 152.4mm) are probably more related to the passage of water in therack storage than e!ects of #ame spread. The Early Suppression Fast Response(ESFR) program conducted by Factory Mutual Research Corporation (FMRC)required numerous large scale tests with ceiling sprinklers as the only rack storageprotection [17]. Previous theoretical and experimental work [7}9,18] on rack storage"res have thus been directed to predict what occurs above the rack storage and underthe ceiling rather than what occurs inside it.

H. Ingason / Fire Safety Journal 36 (2001) 437}457 439

There are a few investigations found in the literature which can be related to thework presented here. Ingason [44] presented a simple theoretical model to predictplume #ow in a two dimensional rack storage "res. Karlsson [21] introduced anengineering approximation method combining a thermal theory of concurrent #amespread [13] with empirical #ame height correlations [22] and test data obtained fromthe cone calorimeter [23]. Grant and Drysdale [19] modi"ed Karlsson's technique forthe speci"c problem of modelling the upward spread of #ame over cellulosic packag-ing materials commonly found in warehouses. The work by Foley and Drysdale [20]is important for studies of heat #uxes from the #ames in a rack storage geometry. Theyshowed that, for a given heat release rate (line burner at their base) the heat #ux isincreased when the separation of two parallel walls is decreased. Blocking the ingressof air at the base of the walls is shown to increase the heat #uxes dramatically.Hamer and Beyler [24], demonstrated the possibilities of using CFD for the calcu-lation of the #ow conditions within a rack storage in order to predict the activation ofin-rack sprinklers. The simulation by Hamer and Beyler [24] was not compared toany experiments but it clearly shows the potential of using CFD for this type ofcomplex con"guration. Yan and Holmstedt [25] developed a CFD submodel topredict #ame spread over vertical fuel surfaces. The CFD code includes a simple ande$cient pyrolysis model which can be used to predict the #ame spread in a rackstorage.

Ingason [26] presented a quasi-steady state "re plume law for in-rack centrelinegas temperature and gas velocity derived from a simple physical model. The air wasassumed to be entrained through the vertical #ues. This exploratory theoretical modelsuggested that the in-rack centreline gas temperature and velocity should have thesame functional form as a convective plume #ow above a linear "re source [27].However, a plot of the measured temperature and velocity in the two di!erent scalesused (1 : 1 and 1 : 3) showed a substantial scatter [26]. In order to obtain similarcorrespondence for the velocity in the two scales it was necessary to use Froudenumber scaling with storage height as length scale. This does not comply with theresults of the linear plume model derived [26] which indicates constant velocityindependent of height z. Ingason and de Ris [45] concluded that their #ame heightdata from experiments with four steel towers (no horizontal #ues) and a gas burner inthe centre were better represented with the aid of the of axi-symmetric power laws[4, 28}30]. The authors had expected the #ame heights to correlate with Q�� sugges-tive of linear plume because the #ue widths did not change with height. Instead the#ame height data correlated better with Q�� suggestive of axi-symmetric plumes.Hence, it is of interest to investigate whether the axi-symmetric "re plume laws willcorrelate better with the experimental data presented by Ingason [26].

2. Fire tests

A series of model scale tests was carried out followed by one large scale test [26].The fuel array consisted of four equally separated cartons at each tier. The commoditywas piled up to four levels, or tiers, with equal heights of the horizontal #ues between


Fig. 1. A model scale test (1 : 3) with wall corrugated paper cartons under a hood to measure heat releaserate.

every consecutive tiers. Geometrically, the commodity used in the model scale wasapproximately one-third of the large scale commodity. Both commodities were madeof combined corrugated paper cartons and paper sheets and di!ered only in type andsize.

2.1. Model scale test

The experiments were carried out under a calorimeter consisting of an exhaust ductand a hood which is located above the "re [31], see Fig. 1. The calorimeter had thecapacity to measure up to about 2MW. The hood size was 3m�3m with the lowestpoint 2.5m from #oor. Both the convective and chemical heat release rates weremeasured. The convective heat release rate was obtained by measuring the temper-ature and mass #ow rate in the exhaust duct and the chemical heat release rate bymeasuring the oxygen depletion at the same location. The commodity consisted of3.7mm thick single wall corrugated paper cartons folded inside with four layers of6.5mm thick single wall corrugated paper sheets on each side of the carton. The totalthickness of each side was thus 29.7mm. The sheets and the paper carton weremounted on a supporting rectangular box made of 9mm thick rigid Navilite N insula-tion boards. The outer dimensions of each carton were 0.39m�0.39m with a heightof 0.305m and the moisture content was 9% by weight. A total of 16 cartons were usedin each test. Four separated vertical steel rods were used to support the cartons.On each steel rod four cartons were centrally mounted and secured in position. InTable 1 summary of test conditions is given.


Table 1Summary of test conditions

Test no. w (mm) h (mm) H (m) Comment

1 50 50 1.42 Model scale2 50 75 1.52 Model scale3 50 100 1.62 Model scale4 75 50 1.42 Model scale5 100 50 1.42 Model scale6 150 300 5.52 Large scale

At the lowest tier, four ignition sources were mounted at the bottom of each cartonas close as possible to centre #ue space of the fuel array, see Fig. 3. The ignition sourceconsisted of a 12mm thick insulating "bre board measuring 17mm�17mm, soakedwith 2.8ml heptane and wrapped in a polyethylene bag. The mean #ame height of theignition source was about 0.25m measured from the bottom of the carton. This heightcorresponds to 83% of the carton height. One test was carried out with a 24mm thickignition source measuring 25mm�30mm, soaked with 12ml heptane (w"50mmand h"50mm).

Centreline in-rack temperatures and velocities were measured at four elevations: forh"50mm measurements were made at z"0.25, 0.61, 0.96 and 1.32m; for h"75m:z"0.28m, 0.66, 1.04 and 1.42m; and for h"100mm: z"0.3, 0.71, 1.11 and 1.52m,see Fig. 3. Each of these positions corresponds to two-third of the height of the carton.The velocity probes were mounted in a staggered form (at the centreline and $45mmfrom the centreline) to avoid interference in these measurements. The ambient temper-ature varied between 13 and 153C during the test series.

2.2. The large scale test

One large scale experiment was carried out under the Industry Calorimeter [32,33]in SP's Fire Hall, see Fig. 2. The calorimeter, which is of same type as the FMRC FireProducts Collector [34], can measure up to 10MW. Both the convective and thechemical heat release rates were measured. A standard class II commodity was usedwhich consists of double triwall corrugated paper cartons (each 12mm thick). Thedouble cartons were folded onto a sheet-metal liner and then placed onto a woodpallet. The outer dimensions of each carton were 1.08m�1.08m�1.08m and themoisture content was 11% by weight.

A double-row steel rack was used to hold the commodity. The width of the vertical#ues was 150mm and the height of the horizontal #ues was 300mm. The total heightof the rack storage was 5.52m. Four ignition sources were placed as close as possibleto the centre #ue space of the fuel array, at the bottom of each carton at the lowest tier.The ignition source consisted of insulating "bre board (similar to cellucotton rolls),75mm in diameter and 75mm long, each soaked with 120ml heptane and wrapped ina polyethylene bag. The mean #ame height of the ignition source was about 0.9mmeasured from the bottom of the carton. This height corresponded to 83% of the


Fig. 2. A test-setup for the fullscale test using wall corrugated paper cartons.

Fig. 3. De"nition of parameters and location of ignition source and measuring points in both model andlarge scale test.

carton height. Centreline in-rack temperatures and velocities were measured at fourelevations: z"1.02, 2.40, 3.78 and 5.16m (the experimental data at z"1.02m is notused in this study as it did not "t very well to the correlations used). Each of thesepositions corresponds to two-third of the height of the carton, see Fig. 3. The ambienttemperature was 113C during the test.


2.3. Instruments

The in-rack temperatures were measured with welded thermocouples of typeK (Chromel}Alumel) with a wire of diameter 0.25mm. The in-rack velocity wasmeasured with bidirectional probes (D"16mm and ¸"32mm) [35] locatedat same elevation as the thermocouples, see Fig. 3. The thermocouples wereattached to each bidirectional probes close to the sensor head. No correctiondue to radiation e!ects on the temperature measurements was carried out in thisstudy. The velocity was corrected for variation in the Reynolds number accordingto calibration curves reported in [35]. The data were recorded by a dataacquisition system every second in the full scale test and every 1.7 s in the small scaletests.

In this study, only the initial "re growth period is considered. This period isde"ned here as the time from ignition until the #ames starts to spread upwards onthe face of the rack storage. Following the procedure of Yu and Kung [7] forgrowing rack storage "res, a rolling time-averaging process was applied to alltemperature, velocity and heat release rate measurements in order to smooth out#uctuations due to turbulence. The averaging period was 10 s. Thus each measure-ment was averaged using di!erent numbers of data points before and after the point ofinterest. The time averaged results followed the trends of the unprocessed data verywell.

All data points measured prior to the incipient time of "re growth, t�, were

disregarded in the data analysis and in plot of the data. The time t�was de"ned here as

the time when the convective heat release rate started to increase notably in size. Thistime was obtained by investigating the measured convective heat release rates and byobserving the initial #ame heights from video recordings. The time t

�agreed well with

the time when the mean #ame height of the ignition source just started to increase insize.

3. In-rack 5re plume

The exploratory theoretical model obtained by Ingason [26] suggested that theexcess in-rack centreline gas temperature should be proportional to the instantaneousconvective heat release rate, Q��

�and be inversely proportional to height, z. The

in-rack gas velocity should be proportional to Q��

and be independent of z. A plot ofthe measured temperature in the two di!erent scales, appeared to give a reasonablegood correlation but the scatter was, however, substantial. In order to obtain similarcorrespondence for the velocity in the two scales it was necessary to use Froudenumber scaling with storage height as length scale. This does not comply with theresults of a linear plume model which indicates constant velocity independent ofheight z. Hence, in order to investigate whether other sets of correlations wouldimprove the results, the experimental data are plotted here using axi-symmetric "replume laws [4,28}30].


3.1. Modelling

First we consider the scaling laws. The number of dimensionless groups that shouldbe preserved is quite large as the forces relating to buoyancy, inertia and viscosity areall involved. Dimensionless groups such as the Froude number (Fr), the Reynoldsnumber (Re) and the Grashof number (Gr) should be preserved from scale to scale.For geometrically similar enclosure "res, it is possible to maintain all these groupsconstant if the gas temperature is kept constant and the pressure, p, is increased andthe characteristic scale length, ¸, reduced such that the product p�¸� is conserved [36]from scale to scale. In the study presented here both the large scale test and the modelscale tests were performed at atmospheric pressure, i.e. p�¸� was not preserved. Iftemperature and pressure are constant from scale to scale, constancy of both Froudenumber and Reynolds number, as required for strict modelling, cannot be satis"edsimultaneously [36]. Hence, Froude modelling is only possible for situations in whichviscous forces are relatively unimportant [36}38]. Froude number modelling requiresthat velocities are scaled relative to the square root of the characteristic length, i.e.u/¸�� must be maintained constant. If the geometric similarity is conserved the heatrelease rate, Q, must be scaled relative to the �

�power of the characteristic length

[36}38], i.e. Q/¸�� must be a constant from scale to scale. The question is what shouldbe the characteristic length of the rack con"guration for which thedimensionless groups are de"ned? One could expect the #ue space, w, the horizontal #ueheight h as well as the rack height H to in#uence on the #ow "eld of in-rack "re plumes.

Here, the geometrical similarity can be maintained if the non-dimensional height,H/w, is constant from scale to scale, where H is the total height of the rack storage andw is the vertical #ue width. The nondimensional height, H/w, for w"50mm (modelscale), varies from 28.4 to 32.4 (H"1.42m for h"50mm, H"1.52m for h"75mmand H"1.62m for h"100mm), for w"75m H/w is equal to 18.9, for w"100mmH/w is equal to 14.2. H/w is equal to 36.8 for the large scale test (H"5.52m,w"50mm, h"300mm). Another geometrical similarity parameter is the nondimen-sional height, H/h. For the model scale H/h varies between 28.4 and 32.4 forw"50mm while H/h is equal to 18.4 for the large scale test. Thus, the requirementof geometrical similarity is not fully satis"ed here and the results can only be regardedas approximate. However, it is of interest to compare the results between thesetwo scales. Therefore, a comparison was made between the measured values ofthe chemical heat release rate, Q, the excess centreline gas temperature, �¹

�, and the

centreline gas velocity, u, for model scale tests with w"50mm and the values for thelarge scale test at the highest measuring point, i.e. one-third of the box height belowthe top of the rack storage at the time when the #ame height reached the top of therack storage (H"¸

�). In Table 2, calculated values according to the scaling laws

discussed are given. This means that the heat release rate, Q, should be preservedon the linear scale, H, to the �

�power, the excess temperature, �¹

�, should be the

same in both scales and the velocity should be preserved on the linear scale, H, to the��power.The overall correspondence between the model scale and the large scale tests is

reasonably good with one exception, i.e. where Q/Q

"33.5 and (H

/H

)��"21.4.


Table 2Froude number scaling of the measured values at the time when ¸

�"H. The index F refer to the large scale

test and index M to the model scale tests

Q

Q

�H

H

�

�� u��

u��

�H

H

�

��

��¹

�� ¹

��

w"50mm, h"50mm 33.2 29.8 1.98 1.97 1.20w"50mm, h"75mm 26.7 25.1 1.61 1.90 0.98w"50mm, h"100mm 33.5 21.4 1.68 1.84 1.03

The reason for this discrepancy is not known the discrepancy could be attributed tothe uncertainties in the characteristic lengths. Heskestad [37] discusses the need thatthe thermal properties of the walls must be modelled for proper response. This was notconsidered here but since the excess temperature appears to scale reasonably well thisis probably not important here. The results obtained in the model scale tests shouldgive reasonable answers concerning the "re behaviour in large scale tests.

In the following the in-rack #ame height, centreline excess gas temperatureand centreline gas velocity are plotted using the concept of a virtual origin andassuming that the data can be plotted according to axi-symmetric power law correla-tions.

3.2. In-rack yame height

In Fig. 4, the #ame height data are plotted for the experiments with paper cartons intwo di!erent scales. The #ame height data was obtained from video recordings bycomparing the &average' #uctuation of the #ame tip to a ruler painted on the boxes.This method, although subjective, was found to be reasonably accurate ($50mm byestimation) as the #uctuations of the #ames were substantially less than thoseobserved in free axi-symmetric plumes. A more objective method would be to de"nethe #ame height as a mean temperature but that would require either signi"cantlymore instrumentation or more comprehensive analysis. For the purpose of the presentstudy the method used here is, however, considered satisfactory. A least square "t tothe #ame height data (model and large scale tests) shown in Fig. 4 yields the followingequation:

¸�"!3.73w#0.343Q��. (1)

The linear correlation coe$cient, R, is equal to 0.993. Eq. (1) is valid for ¸�(H.

Eq. (1) does not include data for w"50mm, h"75mm and w"50mm, h"100mm.The reason is that the #ame height data for the model scale experiments withw"50mm, h"75mm and w"50mm, h"100mm clearly diverged from the other#ame height data. The excluded data are plotted instead in Fig. 5 where it can beobserved that as the height h is increased the #ame height tends to increase forcorrespondingQ and w. A plot of the experimental in-rack #ow data (see Figs. 6 and 9)


Fig. 4. The nondimensional #ame height (¸�/w) plotted as a function ofQ��/w for the model scale tests and

the large scale test. The #ame height for axi-symmetric "re plumes according to Heskestad [1] is plotted forcomparison assuming w"D"0.15m.

show, however, that h does not have any distinct e!ect on the in-rack centrelinetemperature and velocity. The e!ects of h on the in-rack #ow data may, however, behidden in the scattering of the experimental data. A more thorough systematicexperimental analysis is required in order to better understand the importance ofh on the #ow conditions within the rack. Why the large scale #ame height data(w"150mm, h"300mm) agreed well with the model scale data at h"50mm andvarying w and not h"100mm as expected is not known.

Any conclusion about the in#uence of #ue spaces narrower than 50mm in themodel scale or 150mm in the large scale is not possible to make now. One mightexpect that the air entrainment into the rack will behave di!erently as the #ue spaces(w and h) become smaller and smaller. On the other hand as w and h become largerand larger one might expect the #ame height to become more similar to open "replumes.

The #ame height for open axi-symmetric "re plumes according to Heskestad [1] isalso plotted in Fig. 4 for comparison:

¸�"!1.02D#0.23Q��, (2)

where D is the e!ective diameter of the "re source in meters. In order to compareHeskestad's #ame height correlation with the in-rack #ame height correlation wereplaced D with w in Eq. (2) and put w equal to 0.15m. The in-rack #ame heightdiverges from the axi-symmetric #ame height as Q increases. The increase is small for


Fig. 5. The nondimensional #ame height plotted as a function of Q��/w for tests diverging from Eq. (1).

Fig. 6. The excess centreline temperature versus (z!z�)/Q��

�for model scale tests and large scale test.

low Q, and increases asymptotically to ��

"1.49, i.e. nearly one and a half times theaxi-symmetric #ame height for high Q. The e!ective diameter of the "re source, D, isassumed to be equal to w in all cases. If D increases as Q increases the #ame height will


become lower and hence, the ratio ¸��

/¸��

may easily exceed 1.5. The index r relatesto rack storage and index a to axi-symmetric.

To demonstrate the e!ects of the presence of rack storage on the #ame height wecan use Eqs. (1) and (2). A 500kW "re within a rack storage with a #ue width w equalto 0.15m yield a #ame height of 3.56m, whilst from a free burning "re source witha diameter of 0.15m the #ame height will be 2.61m. This corresponds to an increase inheight by 36%. If we double Q corresponding #ame heights will be 4.88 and 3.49m,respectively, i.e. 40% increase. The reason for the higher #ame heights in the rackstorage is that less air is entrained into the "re plume per unit height. The visible #amevolume contains the combustion zone and if less air is entrained the #ame tip is&raised' up to a height where enough air is entrained to complete the combustion of thefuel pyrolysed at lower levels.

3.3. In-rack temperature and velocity

Turbulent buoyant axi-symmetric "re plumes with a large density defect or temper-ature rise relative to the surrounding are known as strong plumes, while plumes witha small density defect or temperature rise are known as weak plumes. Numerousstudies can be found in the literature on weak plumes and strong plumes[4,28}30,39,40,43]. Weak plume theories have been extended to accommodate forlarge density de"ciencies (strong plumes) and, to account for area sources a virtualorigin, z

�, is introduced. The virtual origin is most conveniently determined from

temperature data above the #ames along the plume axis. This method is, however,quite sensitive and the task is di$cult in practice [41]. Slight inaccuracies in thedetermination of centreline temperatures have large e!ects on the value obtained forthe virtual origin.

Above axi-symmetric buoyant turbulent di!usion #ames, the plume radius andcentreline values of excess temperature and velocity obey the following relationships:

b��"C��

¹�

¹��

��(z!z

�), (3)

�¹�

¹�

"C��

1

gc��

¹��

�� Q��

(z!z�)��

, (4)

u�"C

��g

c��

¹��

�� Q��

(z!z�)��

, (5)

where b�� is the plume radius to the point where the temperature rise has declined to��¹

�and ¹

�is the centreline temperature. These relations are known as strong plume

relationships [1,28]. The values of the nondimensional constants C�, C

�and C

�are

according to Heskestad [1]: 0.12, 9.1 and 3.4, respectively.Heskestad [41] has presented a theoretical method to determine the virtual origin

of "re plumes. The method is based on the assumption that the distance of the virtualorigin below the level of the mean #ame height will scale proportionally with the localwidth of the #ow "eld at the elevation of the mean #ame height, or expressed


mathematically:

z�"¸

�!Eb

��, (6)

where z�is the elevation of the virtual origin above the top of the combustible, ¸

�is

the mean #ame height, b��

is the radius of the "re plume at the mean #ame height,speci"cally the radius where the mean velocity is equal to �

�the centreline value and

E is a nondimensional constant. Combining the equations for the mean #ame height[42] and plume width, one can obtain for z

�:

z�"!1.02D#FQ��, (7)

where F includes variables of environment at ambient conditions, fuel and nondimen-sional constants. Heskestad [41] plotted virtual origins from a number of investiga-tions using a rearranged form of Eq. (7), i.e. z

�/D versusQ��/D. Eq. (7) was found to be

well represented for common fuels and normal atmospheric conditions with thecoe$cient F, i.e. the slope of the curve, equal to 0.083m/kW�� and z

�/D intercept at

!1.02. Data points deviating from this representation appeared not to be correlat-able with the fuel type [41]. Eq. (7) is valid for porous fuel arrays, provided anyin-depth combustion is not substantial, i.e., provided most of the volatiles releasedundergo combustion above the array of the crib [41,42]. In a recent study Heskestad[18] showed that this relation is also valid for #ame heights above rack storages, i.e.fuels with considerably in-depth combustion.

Another method to determine z�is to apply the measured centreline temperature

data. You and Kung [7] used a technique based on Eq. (4) for strong "re plumesabove a burning rack storage and Kung and Stavrianidis [40] used it for strong "replumes above pool "res. Eq. (4) can be rearranged into a form as follows:

z"A��

�¹M�

Q��

��#z

�, (8)

where A�"C

�[1/gc�

��

¹��]�� and �¹M

�"�¹

�/¹

�. Thus, the plume height, z,

varies with the variable, [�¹M�/Q��

�]��, linearly with a slope of A��

�.

You and Kung [7] did as follows: For each test, the centreline temperatures at threeselected levels were used to determine the slope, A��

�, before #ames persistently

touched the lowest selected level (4m above the rack storage). For each test, anaveraged value of A��

�was obtained from the determined values of A��

�at about "ve

time instants (a growing "re). The average value of A��

for all tests was obtained(A��

�"0.256m/kW�� and C

�"11) and used in Eq. (8) to "nally determine the

virtual origin. The virtual origin was then plotted against Q��

and a best representa-tion of the data was found to be

z�"!2.4#0.095Q��

�, (9)

for three, four and "ve-tier storage heights. Slightly di!erent representation was givenfor two-tier storage height.

To derive z�for the experiments presented in this study, a combination of these two

methods was applied. This was done by rearranging Eq. (4) and applying the excess


centreline temperature, �¹��, i.e. the centreline #ame temperature at the measured

mean #ame height, ¸�. The #ame height data for the combustible rack storage

experiments (model scale tests with h"50mm and one large scale) was found to bebest represented by Eq. (1), which can be written in more general form as

¸�"a#bQ��, (10)

where a"!3.73wm and b"0.343m/kW��. If we assume that the mean #ameheight, ¸

�, has a corresponding excess gas temperature we can with aid of Eq. (4)

express the #ame height using z"¸�and �¹

�(¸

�)"�¹

��as

¸�"z

�#cQ��, (11)

where c"(A�¹

�/�¹

��)��, �"Q

�/Q and A

�"C

�[1/gc�

��

¹��]��. The ratio

� is usually in the range of 0.6}0.7 for free burning #ames, whilst it is in the range of0.4}0.7 for rack storage "res. It is possible to combine Eqs. (10) and (11) such that

z�"a#(b!c)Q��. (12)

Thus, (b!c) equals the coe$cient F given by Heskestad [41]. The coe$cients b andc can be obtained from the experiments and thus it should be possible to obtain anexpression for z

�, which is consistent with the gas temperature and the #ame height

data, and with an intercept, a. We have already determined that b"0.343m/kW��,and c will be determined from the excess centreline temperature data. But "rst we needto con"rm that this method yields reasonable results. Heskestad [41] predictedtheoretically that c/��"0.15m/kW�� for strong "re plumes by using variables ofcommon fuels and environment at ambient conditions. This is in accordance withdata from Kung and Stavrianidis [40] which showed that c/�� is in the range of0.10}0.16m/kW�� for strong "re plumes. Using variables of fuels and environment atatmospheric conditions and, C

�"9.1 as in Eq. (4) we can, with aid of Eq. (11),

calculate c/��. Thus, using �"0.7, c�"1.01 kJ/kgK, ¹

�"293K, �¹

��"500K

(Ref. [1,41]), ��

"1.2 kg/m� and g"9.81m/s� we obtain A�"0.085 and conse-

quently c/��"0.165m/kW��, which should be compared to 0.15m/kW��. We also"nd that c"0.143m/kW��. If b"0.23m/kW��, see Eq. (2), then b!c"

0.087m/kW�� which should be compared to F"0.083m/kW�� in Eq. (7). Similarexercise as shown above has been made by Heskestad [42].

The constants A�

and �¹��

were determined in the following way for eachexperiment carried out in this study. An average value of �¹

��was determined

through a curve "t (method of least squares) of a plot of �¹�versus z/¸

�. The value of

�¹��

was then determined at z/¸�"1. The value of A��

�for each test was then

determined with aid of Eq. (8). The values of [�¹M�/Q��

�]�� were calculated for the

time period when the mean #ame reached the base of the second tier until the #amesreached up to the top of the rack storage. The results are shown in Table 3. The valuesare average values during the time period considered. There is a great variation in theresults. The variation in (b!c) values as presented in Table 3 will lead to qualitativediscrepancies in Eq. (12). A possible explanation of this variation in the results is thatthe method to determine A��

�is very sensitive and highly dependent on the quality of

the experimental data. It probably requires more well de"ned experiments than were


Table 3Determination of (b!c) in Eq. (12)�

A��

(m/kW��)�¹

��

(K) �"

Q�

Qc"�

A�¹

��¹

��

��

(m/kW��)

b!c(m/kW��)

Model w"50mm, h"50mm 0.405 469 0.533 0.234 0.109Model w"75mm, h"50mm 0.683 593 0.576 0.354 !0.011Model w"100mm, h"50mm 0.189 210 0.595 0.186 0.157Large scale w"150mm,h"300mm

0.453 518 0.500 0.240 0.104

�¹�

"287K for model scale tests and ¹�

"284K for large scale test.

performed in this study and there is a great need for more large scale testing in orderto establish more reliable values of (b!c). Meantime, we use a value which appears togive a reasonably good representation of the model scale and the large scale tests usedin the study. The value obtained by Heskestad [41], i.e. F"(b!c)"0.083m/kW��

for axi-symmetric turbulent "re plumes could be used since it appears to be reason-ably close to many of the values obtained in Table 3.

Now we will plot the temperature data and velocity data using the power lawcorrelations given by Eqs. (4) and (5) and with aid of Eq. (12) where a"!3.73wmand (b!c)"0.083m/kW��. In Fig. 6, a plot of the excess centreline temperature,�¹

�, versus the ratio (z!z

�)/Q��

�is shown. The e!ects of the #ue width, w, on the

results is accounted by the virtual source, z�. It was found necessary to adjust z

�for

the test with w"100mm and h"50mm, in order to obtain a correspondence withthe other data. The data for this test is plotted with b!c"0.083m/kW�� anda"!0.8m. Overall, there is reasonable correspondence, except in the model scaletests at high values of (z!z

�)/Q��

�where the gas temperature diverge from the

large-scale data. These low temperatures are related to data at high elevations withlow heat release rates. There is still considerable scatter in the model scale data but thedata for the large scale tests fall nicely into a single curve. The scatter may be partlycontributed to the fact that the e!ects of h is not considered in the analysis. Further,experimental inaccuracymay play some role as well. To obtain a better representationof the data in Fig. 6 it is plotted such that every third data point is shown for the modelscale tests and every fourth data point for the large scale test. For comparison thecentreline temperature for the large scale test is plotted with every second data pointin Fig. 7.

For (z!z�)/Q��

�'0.20, the excess centreline temperature is inversely proportional

to ((z!z�)/Q��

�)��. A curve "t of the large scale test using the least square method for

(z!z�)/Q��

�'0.20 yields the following relation of the gas temperature (R"0.975):

�¹�"28[¹

�/gc�

��]��

Q��

(z!z�)��

, (13)


Fig. 7. The excess centreline temperature versus (z!z�)/Q��

�for the large scale test. Eq. (21) is a curve "t of

the data for (z!z�)/Q��

�'0.20. (every second data point plotted).

where c�"1.01 kJ/kgK, ¹

�"284K, �

�"1.238 kg/m� and g"9.81m/s� were

used to determine the nondimensional constant, C�

"28. Thus, the coe$cient C�is

increased by nearly a factor 3 compared to axi-symmetric free burning "res. Thisequation is valid for z(H. Eq. (13) correlates better to the large scale experimentaldata than the simple linear plume correlation presented by Ingason [26]. This can beshown by plotting the large scale experimental temperature data (Fig. 8) using thelinear plume correlation and compare the results against the axi-symmetric plumecorrelation (Fig. 7). The temperature data fall nicely into a single line in Fig. 7(R"0.975) whereas there is more scatter in the data in Fig. 8 (R"0.958).

At (z!z�)/Q��

�(0.20 the average excess temperature is equal to 836K

(std"46K). If we replace z with ¸�and put �¹

�"518K (from Table 3) into Eq. (13)

and use the values of c�,¹

�, �

�and g given above and �"0.50 we obtain that c in

Eq. (11) is equal to 0.24m/kW��, which is the same value as in Table 3 for the largescale test.

A parameter, �, relating the plume centreline temperature with the plume centrelinevelocity was postulated by Heskestad [39] to be a constant and con"rmed bya number of "re tests:

�"

¹��

(c��)��

g��u

(�¹�Q

�)��

. (14)

A plot of u/(�¹�Q

�)�� as a function of Q

�for 48(Q

�(738 kW (¸

�(H) yield

a reasonably constant value of �"2.71 (std"0.37). Here we used the ambient condi-tions given earlier for the parameter ¹��

�(c

��)��/g��. The value of � obtained here


Fig. 8. The excess centreline temperature versus (z!z�)��/Q

�for the large scale test (every second data

point plotted).

should be compared to �"2.628 given by You and Kung [7], �"2.4 given by Kungand Stavrianidis [40] and �"2.2 given by Heskestad [39].

Now we can use the Froude scaling laws discussed earlier to plot the velocity data.In Fig. 9, the normalised centreline velocity is plotted against Q��

�/(z!z

�)��/H��. In

Fig. 9, every third data point is plotted for model scale tests and every fourth for thelarge scale test.

Fitting a curve (least squares) to the large scale test for Q��

/(z!z�)��(3.4 gives

the following equation, see Fig. 9,

u"3.54�g

c��

¹��

��

�Q

�(z!z

�)�

��. (15)

This equation is valid for z(H. It is interesting to observe that the coe$cientC

�"3.54 is nearly the same as for axi-symmetric plumes (C

�"3.4) although the

power dependence has been changed from ��to 0.45. Any e!ects of h on the results

have not been considered in the analysis.

4. Conclusions

Free-burn tests were carried out in reduced scale and in large scale. In-rack #ameheights, centreline excess temperatures and velocities were plotted using axi-symmet-ric quasi-steady power law correlations. The correlations include chemical andconvective heat release rate, vertical #ue width, height above the #oor and height of


Fig. 9. The normalised velocity as a function of Q��

(z!z�)��/H�� for the model scale tests and the large

scale test.

virtual "re source. The study provide a sound basis for future studies of #ame spreadand "re growthmodelling of high rack storages. Other "elds of application include theprediction of activation times of in-rack sprinklers and the results may increase ourunderstanding of parameters governing "re growth rates in di!erent types of storagecon"gurations. The study shows that it is possible to reproduce #ow conditions and#ame heights in di!erent scales which is of practical importance since all large scaletesting is very expensive. Another "eld where this work is useful is in future sup-pression studies of rack storage "res.

It appears that using ordinary axi-symmetric power law correlations to plotthe experimental data yields a better representation of the mechanisms governing thein-rack plume #ow than using linear power law correlations as suggested bythe simple in-rack plume model derived by Ingason [26]. The results presented hereare very encouraging but there is still a need for further large scale testing in order toestablish more reliable correlations for predictions of the in-rack #ow. The equationspresented here are only based on limited number of experiments and should thereforebe regarded as approximative. The in#uences of the horizontal #ue space, h, on thein-rack #ow and #ame height were not considered in the theoretical analysis. A morethorough systematic experimental analysis is required in order to understandthe importance of h on the #ow conditions within the rack.

In the study the "re was ignited at the centre of the #ue where the air is able toentrain from four sides (symmetric). In a double-row rack storage there is usually


a certain blockage of the entrained air due to the neighbouring stored boxes(i.e. perpendicular to the direction of loading). It is also important to investigate howthis might a!ect the results. Such a study could presumably be made in an intermedi-ate scale (1 : 2) or model scale (1 : 3) with veri"cation in large scale.

Acknowledgements

Special thanks to Dr. Bror Persson at the Swedish National Testing and ResearchInstitute (SP) for his encouragement, comments and valuable discussions. I would alsolike to express my appreciation to FactoryMutual Research Corporation (FMRC) fortheir co-operation especially Drs. G. Heskestad and J. de Ris for their advice andhelpful discussions concerning topics both theoretical and experimental. The projectwas sponsored by the Swedish Fire Research Board (BRANDFORSK) which isgratefully acknowledged.

References

[1] Heskestad G. Engineering relations for "re plumes. Fire Safety J 1984;7:25}32.[2] Alpert R. Turbulent ceiling*jet induced by large scale "res, C3. Combustion Science and Technology

II, 1975, p. 197}213.[3] Beyler CL. Fire plumes and ceiling jets. Fire Safety J 1988;11:53}75.[4] Morton BR, Taylor G, Turner JS. Turbulent gravitational convection from maintained and instan-

taneous sources. Proc R Soc (London) A234, 1956, p. 1}23.[5] Heskestad G, Delichatsios MA. The initial convective #ow in "re. 17th International Symposium on

Combustion, Combustion Institute, Pittsburgh, 1978, p. 1113}23.[6] Thomas PH. Some comments on "re spread in high racked storage of goods. Department of Fire

Safety Engineering, Lund University, 1993.[7] YuH-Z, Kung H-C. Strong buoyant plumes of growing rack storage "res. The Twentieth Symposium

(International) on Combustion, The Combustion Institute, Pittsburgh, 1984, p. 1567.[8] Kung H-C, Yu H-Z, Spaulding RD. Ceiling #ows of growing rack storage "res. Twenty-First

Symposium (International) on Combustion, The Combustion Institute, 1986, p. 121}8.[9] Yu H-Z, Stavrianidis P. The transient ceiling #ows of growing rack storage "res. Fire Safety

Science*Proceedings of the Third International Symposium, p. 281}90.[10] Field P. E!ective sprinkler protection for high racked storage. Fire Surveyor, October 1985, p. 9}24.[11] Fire Tests on High-Piled Storage Protected by Automatic Sprinklers, Comite Europeen des Assuran-

ces, TE 30153, April 1990.[12] Person H. Evaluation of the RDD-measuring Technique. RDD-tests of the CEA and FMRC

standard plastic commodities. Swedish National Testing and Research Institute, SP-Report 1991 : 04.[13] Saito K, Quintiere JG, Williams FA. Upward turbulent #ame spread. Proceedings of the First

International Symposium on Fire Safety Science, Gaithersburg, MD, 1985, p. 75}86.[14] Hasemi Y, Yoshida M, Nohara A, Nakabayashi T, Unsteady-state upward #ame spreading velocity

along vertical combustible solid and in#uence of external radiation on the #ame spread. Fire SafetyScience*Proceedings of the Third International Symposium, p. 197}206.

[15] Delichatsios MM, Mathews MK, Delichatsios MA. An upward "re spread and growth simulation.Fire Safety Science*Proceedings of the Third International Symposium, p. 207}16.

[16] NFPA 231C, vol. 6. National Fire Protection Association, Batterymarch Park, Quincy.[17] Yao C. The development of the ESFR sprinkler system. Fire Safety J 1988;14:65}73.


[18] Heskestad G. Flame heights of fuel arrays with combustion in depth. The Fifth InternationalSymposium on Fire Safety Science, Melbourne, Australia, 1997, p. 427}38.

[19] Grant G, Drysdale DD. Numerical modelling of early #ame spread in warehouse "res. Fire SafetyJ 1995;24:247}78.

[20] Foley M, Drysdale DD. Heat transfer from #ames between vertical parallel walls. Fire SafetyJ 1995;24:53}73.

[21] Karlsson B. A mathematical model for calculating heat release rate in the room corner test. FireSafety J 1993;20:93}113.

[22] Tu K-M, Quintiere JG. Wall #ame heights with external radiation. Fire Technol 1991;27:195}203.[23] ISO 5660, Fire Tests-Reaction to Fire-Rate of Heat Release from Building Products. International

Standards Organisation, Geneva, Switzerland, 1991.[24] Hamer A, Beyler C. Modeling the activation of dry pipe sprinklers in high rack storage. Proceedings

International Conference on Fire Research and Engineering, 10}15 September, Orlando, Florida,1995, p. 65}70.

[25] Yan Z, Holmstedt G. CFD simulation of upward spread over fuel surface. The Fifth InternationalSymposium on Fire Safety Science, Melbourne, Australia, 1997.

[26] Ingason H. In-rack "re plumes. The Fifth International Symposium on Fire Safety Science, Mel-bourne, Australia, 1997.

[27] Lee S-L, Emmons HW. A study of natural convection above a line "re. J Fluid Mech 1961;3(11):353}69.

[28] Morton BR. Modeling "re plumes. Tenth Symposium (Int) on Combustion, The CombustionInstitute, 1965, p. 973}982.

[29] Rouse H, Yih CS, Humphreys HW. Gravitational convection from a Boundary Source. Tellus1952;4:201}10.

[30] Morton BR. Forced plumes. J Fluid Mech 1959;5:151}63.[31] Babrauskas V, Grayson S. Heat release in "res. Amsterdam: Elsevier Applied Science, 1992.[32] Dahlberg M. The SP industry calorimeter, for rate of heat release rate measurements up to 10MW.

SP Report 1992 : 43, The Swedish National Testing and Research Institute (SP), Bora� s, Sweden.[33] Dahlberg M. Error analysis for heat release rate measurement with the SP industry calorimeter. SP

Report 1994 : 29, The Swedish National Testing and Research Institute (SP), Bora� s, Sweden.[34] Heskestad G. A "re products collector for calorimetry into the MW Range. Report FMRC J.I.

OC2E1.RA, Factory Mutual Research Corporation, Norwood.[35] McCa!rey BJ, Heskestad G. A robust bi-directional low-velocity probe for #ame and "re application.

Combust Flame, 1976;26:125}7.[36] Heskestad G. Physical modeling of "re. J. Fire Flammability, 1975;6:253}73.[37] Heskestad G. Modeling of enclosure "res. 14th International Symposium on Combustion, The

Combustion Institute, Pittsburgh, PA, USA, 1973, p. 1021}30.[38] Orlo! L, de Ris, J. Froude modeling of pool "res. 19th International Symposium on Combustion, The

Combustion Institute, Pittsburgh, PA, USA, 1982, p. 885}95.[39] HeskestadG. Peak gas velocities and #ame heights of buoyancy-controlled turbulent di!usion #ames.

Eighteenth Symposium (International) on Combustion, The Combustion Institute, 1981, p. 951}60.[40] Kung H-C, Stavrianidis P. Buoyant plumes of large-scale pool "res. Nineteenth Symposium (Interna-

tional) on Combustion, The Combustion Institute, Pittsburgh, PA, USA, 1982, p. 905}12.[41] Heskestad G. Virtual origins of "re plumes. Fire Safety J 1983;5:109}14.[42] Heskestad G. Luminous heights of turbulent di!usion #ames. Fire Safety J 1983;5:103.[43] Heskestad G. Fire plume air entrainment according to two competing assumptions. 21st Symposium

(Int) on Combustion/The combustion Institute, 1986, p. 111}20.[44] Ingason H. Modelling of a two-dimensional rack storage "re. Fire Safety J 1998;30:47}69.[45] Ingason H, de Ris J. Flame heat transfer in storage geometries. Fire Safety J 1998;31:39}60.


plume flow in high rack storages

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