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A study of wall and corner fire plumes
Fire Safety Journal 34 (2000) 81}98
A study of wall and corner "re plumes Michael Poreh!,*, Gordon Garrad" !Faculty of Civil Engineering, Technion } Israel Institute of Technology, Haifa 32000, Israel "FRS, Building Research Establishment, Garston, Watford WD2 7JR, UK Received 19 August 1998; received in revised form 1 July 1999; accepted 19 August 1999
Abstract Measurements are presented of #ame heights and mass #uxes of industrial methylated spirits "res burning in di!erent sizes and con"gurations of rectangular trays in the open (away from walls), close to a wall and in a corner. The measurements con"rm previous observations that adjacent walls decrease the mass #ux of plumes and increase the mean and peak #ame heights. They also show that the dimensionless span of the #ame height #uctuations in con"ned "res is larger than that of free "res, so that the increase of the peak values due to walls is larger than the increase of their mean values. On the basis of the experimental data, an approximate, simple model for describing the e!ect of walls on the mass #ux above the #aming region is o!ered. It is shown that the model provides a good description of the present measurements, when used with an assumption by Hansell (1993), that the reduction of the air entrainment into the plume is equal to the ratio of the open to the total perimeters of the trays. Two similar, simple models for predicting the e!ects of walls on the mean #ame height are also presented. These models overestimate the measured values of the mean #ame height above fuel trays close to a wall and in a corner by approximately 15}30%, respectively. ( 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The structure of di!usion #ames produced by "res burning near a wall or a corner of a room is of great practical importance. Fire safety engineers are interested, for example, in the e!ect of walls on the amount of smoke generated by "res, which is determined by the entrainment of ambient air into their plumes. They are also interested in the mean and instantaneous #ame heights of "res burning near walls, which e!ect the spread of the "re. * Corresponding author. E-mail address: [email protected] (M. Poreh) 0379-7112/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 9 9 ) 0 0 0 4 0 - 5
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Nomenclature A C 1 C . D@ D EF g H # I
area of tray, m2 speci"c heat capacity of air, J kg~1 K~1 dimensionless coe$cient in Eq. (12), dimensionless "P/4, m e!ective diameter"(AH4/p)1@2, m entrainment factor, dimensionless acceleration due to gravity, m s~2 heat of combustion per unit mass, J kg~1 intermittency of the #ame height, equals the probability that ¸(t) is greater than a given value, dimensionless IMS industrial methylated spirits, dimensionless k@ a coe$cient in Eqs. (10) and (16), approximately (k@"0.076), dimensionless kA a coe$cient in Eq. (7), dimensionless kH a coe$cient in Eq. (26), approximately (k*"0.132), dimensionless ¸ #ame height in general or the mean #ame height, m ¸ #ame height below which 5% of measurements fall (approximately 0.05 equivalent to height of continuously burning #ames), m ¸ #ame height below which 95% of measurements fall (approximately 0.95 equivalent to peak #ame height), m LFE large "re equation M mass #ow rate in the smoke plume, kg s~1 M@ de"ned in Eq. (18), kg s~1 m~5@2 MA de"ned in Eq. (19), kg s~1k W~1@3 m~5@3 N dimensionless "re parameter de"ned in Eq. (3), dimensionless P perimeter of the fuel source, m P open perimeter of the fuel source, m %& Q total heat release from a "re, measured at the duct with the oxygen consumption method, kW Q convective heat #ux measured at the duct with the oxygen consumption # method, kW h temperature rise in the gas layer ("¹!¹ ), K !." QH dimensionless "re parameter de"ned in Eq. (4), dimensionless r stoichiometric ratio of air to volatile fuel gases, dimensionless o ambient density, kg m~3 !." ¹ ambient temperature, K !." ¹ maximum temperature in gas layer, K .!9 VGR variable geometry rig at Cardington, see Section 3. z height of the elevated layer above the base of the "re, m z distance from base of a "re to the virtual origin of the far-"eld plume, m 0
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The subject has already received some attention [1}5]. However, for various reasons that will be discussed below, the e!ect of walls on typical accidental compartment "res is not fully understood. Along with striving for a better understanding of the structure of such "res, engineers wish to have simple models for "re safety engineering calculations. The mass #ux of the smoke produced by open large "res, for example, is widely calculated in the UK by the Large Fire Equation (LFE) suggested by Thomas et al. [6]: M(z)"0.188Pz3@2,
(1)
where M is the mass #ow rate of smoke, in kg s~1, P is the perimeter of the "re and z is the height above the #oor, in meters. As claimed by Hinkley [7], this empirical equation `gives better "t to the results of experiments2 than some other correlations which are more soundly based theoretically2a. Its validity, according to Hinkley, may extend to heights as large as 10 times the linear dimension of the "re, although it was originally [6] derived for heights below the #ame tip. The LFE is very attractive because of its simplicity and because it o!ers an estimate of the mass #ux produced by a fuel bed of a given size that is independent of the usually unknown heat output of the "re. Naturally, an extension of the LFE to "res near walls would be of great interest. Hansell [4], for example, has described the e!ect of walls on the mass #ux by the equation M(z)"EF(0.188Pz3@2),
(2)
where EF is an Entrainment Factor, which describes the ratio of air entrainment into the con"ned plume relative to the entrainment into an open "re plume. He then suggested that EF is equal to the ratio of the open or ewective perimeter of the fuel source to its total perimeter. Accordingly, the values of EF for square fuel sources in the open, next to a wall and in a corner are 1, 0.75 and 0.5, respectively. However, he has neither substantiated by data his intuitive proposal, which has only been published in his Ph.D. thesis [4], nor has he determined the domain in which it is expected to be valid. Zukoski et al. [2] carried out one set of measurements to determine the e!ect of a vertical wall located close to a square "re source on the entrainment. Their measurements suggest that EF"0.57, which is considerably smaller than the value of 0.75 suggested by Hansell [5] and slightly smaller than the value predicted by the Imaginary Fire Source Model or Mirror Model. The Mirror Model [3,5] assumes the existence of an imaginary xre source on the other side of the wall, which has the same intensity as the original "re source. The temperature and the #ame height of the actual "re are assumed to be equal to those of an uncon"ned &"re' produced by the combined actual and imaginary sources. The mass #ux of the actual "re is assumed to be one-half of that predicted for the uncon"ned "re produced by the combined actual and imaginary sources. Thus, when M in an open "re is proportional to Qn, the value of EF obtained in this model for a wall "re is 0.5]2n. Since the entrainment rate of buoyant plumes in the far "eld is proportional to Q1@3 (see Section 2), the value of EF associated with this odel for wall "res is usually 0.5]21@3"0.63. Similarly, the EF of a corner "re, according to this model, is usually given as 0.25]41@3"0.4. As larger values of n have been suggested for the #aming region, (see Section 2 below) the model implies that the
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blockage by walls of air entrainment closer to the "re base is less e!ective than at larger heights. The general e!ect of walls on the #ame height can also be explained qualitatively, however, their exact quantitative e!ect is not known. Part of the uncertainty stems from the di!erent de"nitions of the mean or peak #ame height by di!erent investigators. McCa!rey [14] used 1-s-exposure photos to determine the #ame height. Hasemi and Tokunaga [3] estimated the mean height of the continuous #ame and the peak height of the #ames by observation during the experiments or by observation of its video recording. The availability of modern data acquisition equipment makes it possible to measure the instantaneous heights of intermittent #ames and to calculate their statistical properties (see for example Cox and Chitty [16] and Zukoski [5]). Hasemi and Tokunaga [3] have conducted an extensive study of "re plumes generated by a 0.5 m square gas burner placed at the height of 0.5 m above the #oor. They have not measured the mass entrainment directly, but their measurements of the #ame heights suggest that placing such a burner #ush with a wall has a very little e!ect on the peak #ame height. On the other hand, the presence of the wall increased the continuous #ame heights by 22%. When the gas burner was placed at the corner of two walls, the peak and continuous #ame heights were 23 and 67% higher than those in free standing burners. They have also measured the excess temperatures in the plume, that are inversely proportional to the entrainment of fresh air into the far-"eld plume, and have concluded that for both wall and corner "res, the actual temperature increase is considerably larger than that predicted by the Mirror Model. It should be noted, in this context, that by adding a mirror image to a square "re base near a wall, one obtains a combined rectangular fuel base. Thus, the use of the Mirror Model in such cases should be based on data of mass #ux in "re plumes above open rectangular and not square fuel bases. It is clear from the above review that although previous studies have depicted the qualitative e!ects of walls on the characteristics of "res, additional systematic investigation of the e!ect of walls on the structure of di!erent types of "res is desired. This paper presents results from the initial phase of such an investigation. Although the number of the experiments in this phase has been rather limited, the experimental results made it possible to develop and evaluate approximate models for estimating the mass #ux and the mean #ame heights in wall and corner "res. 2. Theoretical background When analysing wall e!ects, attention should be given to some basic characteristics of free "re plumes, which will be brie#y reviewed. It has been shown by Heskestad [8] that the relative mean height of "re #ames above their base is determined by a dimensionless number N. Namely, ¸/D"f (N),
(3)
where N"MC ¹ /[go2 (H /r)3]NQ2/D5. !." # 1 !."
(4)
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H is the heat of combustion, r is the mass stoichiometric ratio of air to volatile and # D is the e!ective diameter of the #ame source. (The de"nitions of D and ¸ have been proposed by Heskestad [8] and Zukoski [5], respectively.) It turns out that, for most fuels burning in air, N is proportional to the square of QH, a simpler dimensionless parameter, which is de"ned as QH"Q/[(o C ¹ D2(gD)1@2]. (5) !." 1 !." Thus, it is often suggested [5] that the "re structure is determined by QH and considerable data is presented as a function of QH or Q2@5/D, rather than of N. Although the di!erence between the two formulations may be critical in cases where the oxygen level in the ambient air is reduced [9], the parameter Q2@5/D will be used in this paper to facilitate reference to previous studies. Di!erent empirical equations correlating ¸/D and Q2@5/D (or N) have been proposed in the literature [10,11]. The reviews by Beyler [10] and McCa!rey [11] show, however, that the values proposed by the di!erent equations are quite scattered, particularly for Q2@5/D(14. For example, according to Fig. 2 in Beyler [10], the proposed values of ¸/D at Q2@5/D"10 by six di!erent equations are in the range 0.1(¸/D(2.0. Use will be made in this work of the simple equation suggested by Heskestad [8,12], ¸/D"!1.02#0.23Q2@5/D,
(6)
which describes the general trend of most of the data. The limitations of Eq. (6) are discussed in Ref. [12]. It is noted, however, that a simple linear law ¸/D"kAQ2@5/D,
(7)
has been used with di!erent values of kA to describe data in limited regions of Q2@5/D. The mass #ux across a horizontal plane above the "re at a height z@ also depends on QH and can thus be expressed as a function of Q2@5/D and z@/D. The general form of this function has not been determined. However, various convenient power laws that describe M(z@) in limited regions have been proposed [12}16]. It turns out [9] that, within some restrictions, many of these power laws may be expressed in either the form M/QJ(z@/Q2@5)m
(8)
or the form M/D5@2J(z@/D)m.
(9)
The value of m appears to increase with z@/D. Very close to the "re base, m"1. 2 Higher, below the top of the #aming region, m"3, so that the mass #ux equation 2 becomes M/QJ(z@/Q2@5)3@2
(10)
M/D5@2"k(z@/D)3@2
(11)
or
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as in the LFE. In the far "eld, m"5, so that 3 M/Q"k@(z@/Q2@5)5@3,
(12)
which is often written as M/(Q1@3D5@3)"k@(z@/D)5@3.
(13)
The empirical coe$cients in some of above equations, as well as in some of the forthcoming equations, are not dimensionless. To make them dimensionless, one should replace Q by gQ/(o C ¹ ). Eq. (13), for example, will become in this way !." 1 !." M/[(gQ/(o C ¹ )]1@3D5@3"C (z@/D)5@3, (14) !." 1 !." m where C is a dimensionless constant. m It should be noted that the origin of the vertical axis z@ in the above equations is not uniquely de"ned. In the LFE, z@ is equal to the height z above the base of the fuel source. In the 5 power law, z@"z!z , where z is the height above the fuel base of 3 0 0 a virtual point source that gives at large heights the same mass #ux as the "re plume. The estimates of z are quite scattered and many empirical equations have been 0 proposed [10}12] for describing its dependence on Q2@5. The simple equation z /D"!1.02#0.083Q2@5/D, (15) 0 proposed by Heskestad [11], appears to represent the general trend of the data and will be used in this work. Subtracting Eq. (15) from Eq. (6), one "nds that (¸!z )/D"0.147Q2@5/D, (16) 0 which suggests that (¸!z )/Q2@5 is a constant. 0 Since Eqs. (12) to (14) should be valid at large heights above the #ames, it is appropriate to replace the total heat #ux Q in these equations by the convective heat #ux Q . However, as the convective heat #ux is not easily measurable, its value is # estimated for many fuels to be approximately equal to 0.7Q [12]. Thus, the use of the total heat #ux in this equation is quite common. Following Zukoski et al. [2,5], we shall use Eq. (12) with C "0.21 (which corresponds to k@"0.076 in Eq. (10)). It is clear from m the work of Heskestad [12], however, that this simple power law o!ers only a fair approximation to the vertical variation of the mass #ux above the #ames of real "res. One interesting corollary from Eqs. (12) and (16) is that the mass #ux at the mean #ame height, M 0 , is proportional to Q [11,15]. Namely, L~z M 0 /Q"k@[(¸!z )/Q2@5]5@3"constant. (17) L~z 0 Eq. (17) is consistent with the conclusions of previous investigators [12,17], that the mass #ux at the mean #ame height is approximately proportional to the stoichiometric mass #ux of air required for combustion. It is clear from the above discussion that the pattern of air #ow into "re #ames and, thus, the EF of wall and corner "res, must be functions of both QH (or Q2@5/D) and z/D. This conclusion suggests that a universal EF, that depends on the source/wall con"guration alone, might not exist. Intuitively, one expects that at small values of QH, as in mass "res, the e!ect of walls would be small, whereas at large values of
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QH a nearby wall will more e!ectively reduce entrainment into the #ames and increase the #ame heights, relative to those of similar free "res. Similarly, as suggested in our previous discussion of the Mirror Model, it is expected that the e!ect of walls will slightly decrease as z/D decreases. 3. Apparatus and experimental procedure The experiments were performed in the Variable Geometry Rig of BRE at Cardington (VGR), which provides a 6 m]6 m]4 m high space for large "re experiments, quite similar to the hood apparatus used by Zukoski [2]. A detailed description of the rig and its operation is available in Williams [18]. The sides and ceiling of the rig are constructed from sheets of 20 mm thick proprietary calcium silicate heat resistant boards. The bottom 2.5 m of the VGR was open on two sides to provide air inlet to the "re. One side provided a wall against which some of the "res were burned. Two mobile 2.4 m high]1.2 m wide frames supporting heat resistant boards were used to provide the other wall for corner "res. During tests, the hot smoke creates an elevated layer in the VGR. At one side of the roof of the VGR there is an open vent into a 3.0 m long duct, through which the hot gases rise and leave. A manual shutter is installed at the top of the duct, allowing control of the height of the elevated layer in the VGR. The duct is instrumented with an oxygen analyser, thermocouples, and a calibrated bidirectional velocity probe, located at the centre of the duct and connected to a sensitive, electronic di!erential pressure gauge. A calibration factor relating the reading of the probe and the average velocity in the duct was determined from measurements of velocity pro"les in the duct. The mass #ux was determined using the reading of the probe and the density of the smoke, which was calculated from the measured values of the temperatures. Gas was sampled across the duct through a perforated stainless-steel tube and its oxygen level was determined by the oxygen analyzer. The digital outputs of the instruments that monitored the sensors in the duct were recorded every 5 s and mean values of the recorded values over periods of 30}120 s were calculated. From these mean values, the values for the steady-state periods of the mass #ux at the height z of the lower interface of the elevated layer (which is equal to the mass #ux in the duct) and the total heat output from the "re, Q, which was determined by the consumption of oxygen by the "res, were calculated. The measuring system has been checked using a calibrated propane burner and its accuracy is estimated to be $6% of the readings. Four columns of thermocouples were suspended from the ceiling of the rig and measured the vertical temperature pro"le in the rig. Each column consisted of 16 bare junctions of Type K (Chromel/Alumel) thermocouples. From the temperature pro"le the height to the base of the elevated layer is de"ned as
P
H h dz@, 0 where H is the ceiling height, was determined. z"H!(1/(h ) .!9
(18)
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The "res were produced by burning industrial methylated spirits (IMS) in square steel trays, ranging in size from 0.25 to 1.0 m2, giving heat outputs between 20 and 800 kW. (The caloric value of IMS is 26.58 MJ/kg.) Some of the trays were placed directly on the #oor, whereas some of them were placed in a larger tray "lled with water. The water-cooled trays maintained a more steady burning. Cooling the trays also reduced the heat output for a given "re size, which gave a slightly wider range of heat outputs with the limited range of "re trays available. Each tray was "lled with IMS to a depth of between 10 and 30 mm, to give "res of 5}20 min duration. That allowed the "re, in most tests, to reach a quasi-steady-state burning for at least 1 min, at which the required data was acquired. During some of the tests, the position of the shutter at the top of the duct was changed, to alter the area of the vent. That changed the mass #ux through the duct, resulting in changes in the height z of the elevated layer. The development of a typical "re, as depicted in the time variation of its total heat output, is shown in Fig. 1. One sees that it took about 200 s for this particular "re to reach a quasi-steady burning rate. The period from 260 to 360 s was considered as a representative period of quasi-steady combustion for this "re, and statistical properties of the "re and #ame were taken from measurements during that period. At 360 s the vent was partially closed. That change led to a storage of energy in the hot gas layer, so that the heat output of the "re was not equal to the heat #ux through the duct for about 2 min. At 600 s a quasi-steady state was re-established. At 750 s the vent was slightly opened and a new transition in the calculated heat output was again observed. The #ame heights during the various tests were video recorded at 25 frame s~1. The video records have also depicted a vertical scale showing the height above the #oor.
Fig. 1. A typical variation with time of the measured heat #ux in a test.
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The statistical properties of the #ame height during the period of quasi-steady-state burning were analysed from the video recordings using a model VP116 Video Imaging System supplied by HVS Image of Twickenham, England. The system tracked the height of the tip of the #ame from frame to frame of the video records, and the data was stored on a personal computer. Before analysing a given recorded video, the Video Imaging System was calibrated and adjusted to track the tip of the #ame. The readings of the #ame heights were corrected for the parallax produced by the distance between the centre of the #ame and the scale in the open "res tests. Around 40 runs were made with di!erent size trays and con"gurations: Single square trays in the open away from walls (single/open), double adjacent square trays in the open (double/open), single and double trays close to a vertical wall (single/wall and double/wall) and single trays in a corner (single/corner). (The abbreviated notation in the parentheses is used in the legends of the "gures.) A careful examination of the data suggested, however, that only 26 experiments yielded reliable data. The main reason for discarding the other data was a lack of a clear, steady-state burning phase. We have also observed that "res in apparently similar tray con"gurations did not always develop in a similar manner and did not have the same characteristics during what appeared to be steady-state phases. These di!erences might have been caused by uncontrolled ambient air movements, but we suspect that another factor that might have contributed to this variability was the level of fuel in the tray. We controlled neither its initial value nor its rate of change. Observation of the "res indicated that in some cases the base area of the #ame rising from the trays was smaller than the tray, and that near the walls of the trays either a strip of laminar burning or a small vortex with an axis parallel to the wall existed, particularly when the di!erence between the level of the alcohol and the height of the walls of the tray was large. In addition, since neither the heights of the walls of the trays nor the level of the alcohol were proportional to the diameter of the trays, the expected similarity of the results at di!erent dimensionless parameters that include D, such as QH, might have been slightly a!ected by these uncontrolled parameters. Table 1 summarises the measurements from the successful runs. Included in the table are the mass #uxes for the four corner runs. Unfortunately, the heights of elevated layers in these runs were higher than the height of one wall of the mobile frame that formed the corner (2.4 m). Thus, we have not plotted the mass #ux measurements of these runs in the forthcoming "gures.
4. Analysis of the results 4.1. Mass entrainment We have plotted in Fig. 2 the measurements of M/(PHEF) versus z and compared them with the modi"ed LFE (Eq. (2)), using the EF values suggested by Hansell [4]. The "gure shows that, in spite of the large number of the experimental con"gurations, the data are well grouped. However, most of the measured values are larger than those predicted by the modi"ed LFE. This form of the LFE makes it di$cult to understand
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Table 1 Summary of "re and plume properties for test "res Run Tray number width (m)
Fire Fire perimeter position (m)
Tray Total heat Mass #ow Height of cooled release (kg s~1) elevated rate (kW) layer (m)
¸ ¸ 0.05 &(m) (m)
¸ 0.95 (m)
33 6 7 8 36 37 24 32 22 23 11 13 16 12 25 38a 26 31 39a 39b 15 20 17** 27** 29** 30**
1.0 1.2 1.2 2.0 2.0 2.0 2.0 3.0 3.2 4.0 4.0 3.0 3.0 3.0 1.5 1.5 1.5 2.25 1.0 1.0 2.0 2.0 1.0 1.0 1.5 2.0
Yes No Yes No Yes Yes Yes Yes No No Yes No No Yes No Yes Yes Yes Yes Yes No Yes No Yes Yes Yes
0.25 0.48 0.61 0.58 0.68 } 0.57 0.86 0.77 1.30 1.02 } 0.75 0.74 0.71 0.76 0.70 0.92 0.51 } 1.21 0.59 0.91 0.76 1.01 1.42
0.53 0.85 0.94 0.94 1.15 } 1.15 1.64 1.26 2.08 1.75 } 1.33 1.30 1.27* 1.66 1.18 1.79 1.24 } 2.57 1.62 2.16 1.72 2.29 2.56*
0.25 0.3 0.3 0.5 0.5 0.5 0.5 0.75 0.8 1.0 1.0 2]0.5 2]0.5 2]0.5 0.5 0.5 0.5 0.75 2]0.25 2]0.25 2]0.5 2]0.5 0.5 0.5 0.75 1.0
In open In open In open In open In open In open In open In open In open In open In open In open In open In open Near wall Near wall Near wall Near wall Near wall Near wall Near wall Near wall In corner In corner In corner In corner
19$1.4 38$1.8 30$2.2 108$3.2 107$8 113$6 113$9 309$20 280$10 563$24 430$21 208$4 218$11 196$7 154$10 110$6 124$5 343$16 53$3 50$3 360$22 246$10 157$9 138$5 327$16 664$27
1.17$0.06 1.57$0.05 1.43$0.07 2.12$0.14 1.43$0.06 2.22$0.09 2.26$0.13 2.92$0.17 2.82$0.09 3.39$0.11 3.11$0.13 2.63$0.07 2.78$0.13 2.55$0.16 2.36$0.10 2.00$0.13 2.28$0.09 3.06$0.12 1.33$0.05 1.64$0.08 2.81$0.13 2.60$0.09 2.09$0.11 1.93$0.07 2.81$0.10 3.41$0.10
2.77$0.14 2.91$0.06 2.91$0.05 2.73$0.06 2.43$0.09 2.64$0.08 2.84$0.04 2.64$0.04 2.51$0.06 2.61$0.03 2.54$0.06 2.43$0.09 2.44$0.13 2.45$0.04 3.51$0.11 3.16$0.05 3.35$0.14 3.17$0.13 3.37$0.05 3.49$0.05 3.34$0.09 3.32$0.08 3.35$0.18 3.62$0.10 3.45$0.19 3.29$0.19
0.38 0.64 0.78 0.73 0.89 } 0.85 1.24 0.98 1.70 1.32 } 1.00 1.05 1.01 1.07 0.90 1.32 0.78 } 1.80 0.96 1.38 1.08 1.52 2.06
} Not measured. *Peak #ame height extended above the video "eld of view, the table shows the maximum measured value. **See remark at the end of Section 3.
why. A better insight is gained by expressing the modi"ed LFE in the form of Eq. (11): M@"0.752(z/D@)3@2,
(19)
where M@"(M/EF)/D@5@2
(20)
and D@"P/4. Fig. 3 compares the measurements of M@ with Eq. (19). Also plotted in this "gure are the open "re data of Hinkley [7]. It is clear from this "gure that Hinkley's data and the present measurements are quite consistent. One also observes in the "gure that the deviations of the measurements from the modi"ed LFE exist only at z/D@'3, where
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Fig. 2. The measured variation of M/P with z in the present tests. %&
Fig. 3. The measured and predicted variation of M@ with z/D@.
most of the present measurements were made, and that they increase as z/D@ does. It is, thus, plausible to conclude that these deviations are due to the fact that the present data fall beyond the range where the LFE is valid. As noted earlier, this range has not been accurately determined. The LFE had been originally [6] developed for the
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Fig. 4. The measured and predicted variation of MA with (z!z )/D. 0
#aming region. Hinkley [7] suggested that it is valid to z/D@"10. The present data suggest that it is valid only to approximately z/D@"3. In view of the above conclusion, it was decided to examine whether the e!ect of the walls on the entrainment for large values of z/D@ could be evaluated using a modi"ed form of the far-"eld equations (12) and (13) in which the mass #ux is replaced by M/EF, where EF"Pef/P, as suggested by Hansell [4]. In other words, we assume that in the far "eld, MA"(M/EF)/(Q1@3D5@3)]"k@[(z!z )/D]5@3, 0 which may also be written as
(21)
M/Q"EF k@[(z!z )/Q2@5]5@3. (22) 0 Plotted in Fig. 4 are the measured values of MA versus (z!z )/D and Eq. (21) with 0 k@"0.076, (C "0.21) [5]. As seen from the "gure, the modi"ed far-"eld equation . provides a very good description of all the measured mass #uxes at (z!z )/D'5. 0 4.2. Flame heights Fig. 5 shows the time variation of the instantaneous #ame height ¸(t) for a period of 21 s (525 video frames) in a typical test (Test 39). Using these data we have calculated for all but three runs the cumulative probability distribution P(¸), which is equal to the probability that the instantaneous #ame height is larger than a given value ¸. Following Zukoski [5], we have then calculated the mean #ame height, ¸, the continuous #ame height, ¸ and the peak #ame height, ¸ . The calculated values 0.05 0.95 appear in the 3 last columns of Table 1. Table 2 summarises our data for the 0.5 m trays.
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Fig. 5. A typical variation with time of the instantaneous #ame height.
Table 2 Average #ame heights and relative #ame span for "res above 0.5 m trays Tray location
Test nos.
¸ (m)
¸ 0.95 (m)
¸ 0.05 (m)
(¸ !¸ )/¸ 0.95 0.05 }
In the open Near a wall In a corner
8, 24, 36 25, 26, 38a 17, 27
0.82 0.99 1.23
1.08 1.37 1.94
0.61 0.72 0.84
0.57 0.65 0.90
As seen from Table 2, the continuous, mean, and peak #ame heights of "res burning near walls and corners are considerably larger than those from a similar "re source burning in the open. These observations are fairly similar to those of Hasemi and Tokunaga [3]. In addition, the table shows that adjacent walls increase the dimensionless span of the #uctuations of the #ame heights, as demonstrated in Fig. 6. As a result, the peak #ame heights of wall and corner "res in these experiments were larger than the peak heights of the free "res from the same sources by 26 and 80%, respectively, although the mean #ame height of the wall and corner "res increased by only 21 and 50%. It should be realised, however, that part of the increase in the values of the #ame heights of the con"ned "res depicted in Table 2 is due to the increased values of the heat #ux in the wall and corner "res. To get a quantitative explanation for the increase of the mean #ame height in con"ned "res, the following model was developed. It was assumed that the ratio M 0 /Q, see Eq. (17), is a universal constant for all the "res. Using Eqs. (22) and (12), L~z the mass #ux at the mean #ame height can be written as M
L~z0
/Q"k@EF[(¸!z )/Q2@5]5@3"k@ ) 1.0[(0.147]5@3. 0
(23)
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Fig. 6. The measured intermittency of the #ame height #uctuations.
Fig. 7. The measured and predicted variation of EF3@5[(¸!z )/D] with Q2@5/D. 0
Eq. (23) suggests that the general form of Eq. (16) is EF3@5[(¸!z )/D]"0.147Q2@5/D. 0
(24)
Fig. 7 compares Eq. (24) with the values calculated from the experimental data. One sees that most of the experimental values of EF3@5[(¸!z )/D] are below the 0
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Fig. 8. The variation of EF2@3(¸/D) with Q2@5/D.
corresponding values of 0.147Q2@5/D. The average deviation of all the data from this model is 15%, but the standard deviation from their average value is only 10%. One notices, however, that the deviation of the open "re data is only 3%, the deviation of the wall "res is 21% and the deviation of the corner "res is 29%. Eqs. (23) and (24) are based on the assumption that the far-"eld equation can be used to estimate the mass #ux at the mean #ame height. If one assumes, instead, that the mass #ux at that region, for the limited range of values of Q2@5/D in the present experiments, can be expressed by the LFE, which may also be expressed by Eq. (10), one may write that M(¸)/Q"k@EF[¸/Q2@5]3@2.
(25)
Eq. (25) and the present data suggest that EF2@3[¸/D]"kHQ2@5/D.
(26)
where kH"0.132. This value of kH has been determined by the open "re data, which are described by this equation with an accuracy of 4%, see Fig. 8. The average measured values of the #ame heights for the wall and corner "res are smaller than the values predicted by this equation by 15 and 24%, respectively. Also shown in the "gure is the variation of ¸/D for open "res, EF"1, according to Heskestad [8,12] (Eq. (6)). It is noted that the di!erence between Eqs. (6) and (26), within the limited range of values of Q2@5/D at the present experiments, is not large.
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5. Discussion and conclusions The qualitative e!ect of walls on "res appears to be simple. Walls block the #ow of ambient air into the "re plume. As a result, the entrainment of air and oxygen into the fuel laden "re #ames is reduced and the burning of the fuel is completed at higher heights. Since the mass #ux of smoke at a given height, M(z), is approximately equal to the entrainment rate of air into the "re plume up to that height, the presence of walls close to a "re reduces its value. This qualitatively simple picture of the e!ect of walls had raised hopes that it could be described by very simple quantitative models such as the Mirror Model or a simple modi"cation of the LFE [4], which is being used to predict the mass #ux in the #aming region of "re plumes. It turns out that the Mirror Model was not successful in consistently describing the properties of the small number of wall and corner "res that had been previously investigated. The predictions of the modi"ed LFE, on the other hand, have never been compared with experimental results. Our initial comparison between its predictions and the data collected in the present investigation gave the impression that this simple model overestimates the e!ect of walls on entrainment. However, when expressing the mass #ux variation according to this equation as a function of z/D@, it became apparent that most of the present data, which include open "re data, fall beyond the #aming region and that the deviation of the data from the modi"ed LFE increases as the relative height z/D@ increases beyond 3.0. This observation suggests that the region of validity of the LFE is bounded by this relative distance. However, it does not rule out at all the possibility that this simple model could predict M(z) in wall and corner "re plumes when z/D@(3. Encouraged by this result, the intuitive assumption of Hensell, that EF is approximately proportional to the length of the free perimeter of the "re, was used to develop a model that extends the approximate classical far-"eld equation for the mass #ux to wall and corner plumes. The model also assumes that the location of the virtual source z for such plumes can be predicted by the equation that has been developed for free 0 "re plumes. The mass #ux in the far "eld of wall and corner "re plumes predicted by this model was found to be in good agreement with the present measurements. Similarly, a simple model for predicting the mean #ame height for di!erent con"gurations of wall and corner "res was developed. This model assumes that the ratio of the mass #ux at the mean #ame height to the stoichiometric mass #ux of air required for combustion is the same for free and con"ned plumes. It also assumes that the mass #ux at that height is given by the modi"ed far-"eld equation derived earlier. Based on these assumptions, the model extends Heskestad's classical equation for the height of the mean #ame tip, ¸!z , to wall and corner "res and suggests that ¸!z is 0 0 inversely proportional to EF3@5. The present open "re measurements were found to be very close to the classical equation for ¸!z , on which this model was based. 0 However, when the values of EF were assumed to be equal to the ratio of the e!ective perimeter to the total perimeter of the fuel source, the measured values of the mean #ame height for the present wall and corner "res tests were found to smaller by 21 and 29%, respectively, from the predictions of this model. The model itself, should be noted, as being independent of this assumption.
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A di!erent model for the mean #ame height, based on the 3 power law (Eq. (10)) for 2 the mass #ux at the mean #ame height, has also been derived. The proportionality coe$cient in this model has been determined by the present open "re data. This model predicts, see Eq. (26), that ¸ is inversely proportional to EF2@3. This model, too, overestimates the mean #ame height of the wall and corner "res, but by slightly smaller relative values; approximately 15 and 24%, respectively. One may attribute the deviation of the data from the predictions of these two models to the assumption that the ratio M 0 /Q is the same for open and con"ned L~z "res as, in addition to their blocking e!ect, walls decrease the size of the large eddies in con"ned plumes and change the entire turbulent structure of such "res. Another possible explanation is that the e!ect of the walls near the base of the "re is not as large as proposed by Hansell [4]. This explanation is supported by the slightly lower deviations of the wall and corner #ame height data from the second model. It is also consistent with the predictions of the Mirror Model, that the rate of entrainment close to the "re base is relatively lower than in the far "eld, as explained in the Introduction. In addition to the above physical explanations, one should remember that the original classical power laws for uncon"ned "res, on which the presented models are based, are not very accurate either, particularly in predicting the mean #ame height. Thus, it is a priori clear that a simple universal model for open and con"ned "res cannot be very accurate. For this reason, the good agreement between the proposed mass #ux model and the present limited data is not a su$cient proof for its universal validity. Users of these equations in Fire Protection Engineering practice should take these limitations into consideration. An answer to the questions, which of the above explanations is correct and how reliable and universal are the models and equations that have been derived in this work, can be given only by comparing them with a much larger set of data, which are the backbone of any semi-empirical model. Acknowledgements The authors extend their thanks to a number of their colleagues for their help during the course of the work, and especially for help in conducting the experiments. We are grateful to B.K. Ghosh, R. Harrison and P. Samme for their help in conducting the experiments. Thanks are due to D. Hayward and R. Mallows, for their help in video recording of the experiments, and to L. Ferrier, for providing technical support in the analysis of the recordings. Finally, we thank H.P. Morgan and G. Cox for their continued support and encouragement during the entire work, for reviewing this paper and for their constructive and valuable advice. The work of the "rst author was partially supported by The Fund for Promotion of Research at the Technion, Israel Institute of Technology. References [1] Grella JJ, Faeth GM. Measurements in a two-dimensional thermal plume along a vertical adiabatic wall. J Fluid Mech 1975;71(Part 4):701}10.
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[2] Zukoski EE, Kubota T, Cetegen B. Entrainment in "re plumes. Fire Safety J 1981;3:107}21. [3] Hasemi Y, Tokunaga T. Some experimental aspects of turbulent di!usion #ames and buoyant plumes from "re sources against a wall out in a corner of walls. Combustion Sci Technol 1984;40:1}17. [4] Hansell GO. Heat and mass transfer processes a!ecting smoke control in atrium buildings. Ph.D. thesis. South Bank University, London, 1993. [5] Zukoski EE. Properties of "re plumes. In: Cox G, editor. Combustion fundamentals of "re. London: Academic Press, 1995. p. 101}220. [6] Thomas PH, Hinkley PL, Theobald CR, Simms DL. Investigations into the #ow of hot gases in roof venting. Fire Research Tech Paper 7. London: HMSO, 1963. [7] Hinkley PL. Rates of production of hot gases in roof venting experiments. Fire Safety J 1986;10:57}65. [8] Heskestad G. Luminous heights of turbulent di!usion #ames. Fire Safety J 1983;5:103}8. [9] Poreh M, Morgan HP. On power laws for describing the mass #ux in the near "eld of "res. Fire Safety J 1996;27:159}78. [10] Beyler CL. Fire plumes and ceiling jets. Fire Safety J 1986;11:53}74. [11] McCa!rey BJ. Flame height, In: The SFPE Handbook of Fire Protection Engineering, 2nd Ed., NFPA, Quincy, MA, 1995. p. 2-1}2-8. [12] Heskestad G. Plume theory. In: The SFPE Handbook of Fire Protection Engineering. 2nd Ed., NFPA, Quincy, MA, 1995. p. 2-9}2-19. [13] McCa!rey BJ. Purely buoyant di!usion #ames: some experimental results. NBSIR 79-1910, National Bureau of Standards, Washington, DC, 1979. [14] McCa!rey BJ, Cox G. NBSIR 82-2473, National Bureau of Standards, Washington, DC, USA, 1982. [15] Cox G, Chitty R. A study of the deterministic properties of unbounded "re plumes. Combust Flame 1980;39:191}202. [16] Cox G, Chitty R. Some stochastic properties of "re plumes. Fire Mater 1982;6(3&4):127}34. [17] Delichatsios MA. Air entrainment into buoyant jet #ames and pool "res. In: The Handbook of Fire Protection Engineering, 2nd Ed., NFPA, Quincy, MA, 1995. p. 2-20}2-31. [18] Williams C. The downward movement of smoke due to a sprinkler spray. Ph.D. thesis. South BankUniversity, London, 1993.
A study of wall and corner "re plumes Michael Poreh!,*, Gordon Garrad" !Faculty of Civil Engineering, Technion } Israel Institute of Technology, Haifa 32000, Israel "FRS, Building Research Establishment, Garston, Watford WD2 7JR, UK Received 19 August 1998; received in revised form 1 July 1999; accepted 19 August 1999
Abstract Measurements are presented of #ame heights and mass #uxes of industrial methylated spirits "res burning in di!erent sizes and con"gurations of rectangular trays in the open (away from walls), close to a wall and in a corner. The measurements con"rm previous observations that adjacent walls decrease the mass #ux of plumes and increase the mean and peak #ame heights. They also show that the dimensionless span of the #ame height #uctuations in con"ned "res is larger than that of free "res, so that the increase of the peak values due to walls is larger than the increase of their mean values. On the basis of the experimental data, an approximate, simple model for describing the e!ect of walls on the mass #ux above the #aming region is o!ered. It is shown that the model provides a good description of the present measurements, when used with an assumption by Hansell (1993), that the reduction of the air entrainment into the plume is equal to the ratio of the open to the total perimeters of the trays. Two similar, simple models for predicting the e!ects of walls on the mean #ame height are also presented. These models overestimate the measured values of the mean #ame height above fuel trays close to a wall and in a corner by approximately 15}30%, respectively. ( 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The structure of di!usion #ames produced by "res burning near a wall or a corner of a room is of great practical importance. Fire safety engineers are interested, for example, in the e!ect of walls on the amount of smoke generated by "res, which is determined by the entrainment of ambient air into their plumes. They are also interested in the mean and instantaneous #ame heights of "res burning near walls, which e!ect the spread of the "re. * Corresponding author. E-mail address: [email protected] (M. Poreh) 0379-7112/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 9 9 ) 0 0 0 4 0 - 5
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Nomenclature A C 1 C . D@ D EF g H # I
area of tray, m2 speci"c heat capacity of air, J kg~1 K~1 dimensionless coe$cient in Eq. (12), dimensionless "P/4, m e!ective diameter"(AH4/p)1@2, m entrainment factor, dimensionless acceleration due to gravity, m s~2 heat of combustion per unit mass, J kg~1 intermittency of the #ame height, equals the probability that ¸(t) is greater than a given value, dimensionless IMS industrial methylated spirits, dimensionless k@ a coe$cient in Eqs. (10) and (16), approximately (k@"0.076), dimensionless kA a coe$cient in Eq. (7), dimensionless kH a coe$cient in Eq. (26), approximately (k*"0.132), dimensionless ¸ #ame height in general or the mean #ame height, m ¸ #ame height below which 5% of measurements fall (approximately 0.05 equivalent to height of continuously burning #ames), m ¸ #ame height below which 95% of measurements fall (approximately 0.95 equivalent to peak #ame height), m LFE large "re equation M mass #ow rate in the smoke plume, kg s~1 M@ de"ned in Eq. (18), kg s~1 m~5@2 MA de"ned in Eq. (19), kg s~1k W~1@3 m~5@3 N dimensionless "re parameter de"ned in Eq. (3), dimensionless P perimeter of the fuel source, m P open perimeter of the fuel source, m %& Q total heat release from a "re, measured at the duct with the oxygen consumption method, kW Q convective heat #ux measured at the duct with the oxygen consumption # method, kW h temperature rise in the gas layer ("¹!¹ ), K !." QH dimensionless "re parameter de"ned in Eq. (4), dimensionless r stoichiometric ratio of air to volatile fuel gases, dimensionless o ambient density, kg m~3 !." ¹ ambient temperature, K !." ¹ maximum temperature in gas layer, K .!9 VGR variable geometry rig at Cardington, see Section 3. z height of the elevated layer above the base of the "re, m z distance from base of a "re to the virtual origin of the far-"eld plume, m 0
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The subject has already received some attention [1}5]. However, for various reasons that will be discussed below, the e!ect of walls on typical accidental compartment "res is not fully understood. Along with striving for a better understanding of the structure of such "res, engineers wish to have simple models for "re safety engineering calculations. The mass #ux of the smoke produced by open large "res, for example, is widely calculated in the UK by the Large Fire Equation (LFE) suggested by Thomas et al. [6]: M(z)"0.188Pz3@2,
(1)
where M is the mass #ow rate of smoke, in kg s~1, P is the perimeter of the "re and z is the height above the #oor, in meters. As claimed by Hinkley [7], this empirical equation `gives better "t to the results of experiments2 than some other correlations which are more soundly based theoretically2a. Its validity, according to Hinkley, may extend to heights as large as 10 times the linear dimension of the "re, although it was originally [6] derived for heights below the #ame tip. The LFE is very attractive because of its simplicity and because it o!ers an estimate of the mass #ux produced by a fuel bed of a given size that is independent of the usually unknown heat output of the "re. Naturally, an extension of the LFE to "res near walls would be of great interest. Hansell [4], for example, has described the e!ect of walls on the mass #ux by the equation M(z)"EF(0.188Pz3@2),
(2)
where EF is an Entrainment Factor, which describes the ratio of air entrainment into the con"ned plume relative to the entrainment into an open "re plume. He then suggested that EF is equal to the ratio of the open or ewective perimeter of the fuel source to its total perimeter. Accordingly, the values of EF for square fuel sources in the open, next to a wall and in a corner are 1, 0.75 and 0.5, respectively. However, he has neither substantiated by data his intuitive proposal, which has only been published in his Ph.D. thesis [4], nor has he determined the domain in which it is expected to be valid. Zukoski et al. [2] carried out one set of measurements to determine the e!ect of a vertical wall located close to a square "re source on the entrainment. Their measurements suggest that EF"0.57, which is considerably smaller than the value of 0.75 suggested by Hansell [5] and slightly smaller than the value predicted by the Imaginary Fire Source Model or Mirror Model. The Mirror Model [3,5] assumes the existence of an imaginary xre source on the other side of the wall, which has the same intensity as the original "re source. The temperature and the #ame height of the actual "re are assumed to be equal to those of an uncon"ned &"re' produced by the combined actual and imaginary sources. The mass #ux of the actual "re is assumed to be one-half of that predicted for the uncon"ned "re produced by the combined actual and imaginary sources. Thus, when M in an open "re is proportional to Qn, the value of EF obtained in this model for a wall "re is 0.5]2n. Since the entrainment rate of buoyant plumes in the far "eld is proportional to Q1@3 (see Section 2), the value of EF associated with this odel for wall "res is usually 0.5]21@3"0.63. Similarly, the EF of a corner "re, according to this model, is usually given as 0.25]41@3"0.4. As larger values of n have been suggested for the #aming region, (see Section 2 below) the model implies that the
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blockage by walls of air entrainment closer to the "re base is less e!ective than at larger heights. The general e!ect of walls on the #ame height can also be explained qualitatively, however, their exact quantitative e!ect is not known. Part of the uncertainty stems from the di!erent de"nitions of the mean or peak #ame height by di!erent investigators. McCa!rey [14] used 1-s-exposure photos to determine the #ame height. Hasemi and Tokunaga [3] estimated the mean height of the continuous #ame and the peak height of the #ames by observation during the experiments or by observation of its video recording. The availability of modern data acquisition equipment makes it possible to measure the instantaneous heights of intermittent #ames and to calculate their statistical properties (see for example Cox and Chitty [16] and Zukoski [5]). Hasemi and Tokunaga [3] have conducted an extensive study of "re plumes generated by a 0.5 m square gas burner placed at the height of 0.5 m above the #oor. They have not measured the mass entrainment directly, but their measurements of the #ame heights suggest that placing such a burner #ush with a wall has a very little e!ect on the peak #ame height. On the other hand, the presence of the wall increased the continuous #ame heights by 22%. When the gas burner was placed at the corner of two walls, the peak and continuous #ame heights were 23 and 67% higher than those in free standing burners. They have also measured the excess temperatures in the plume, that are inversely proportional to the entrainment of fresh air into the far-"eld plume, and have concluded that for both wall and corner "res, the actual temperature increase is considerably larger than that predicted by the Mirror Model. It should be noted, in this context, that by adding a mirror image to a square "re base near a wall, one obtains a combined rectangular fuel base. Thus, the use of the Mirror Model in such cases should be based on data of mass #ux in "re plumes above open rectangular and not square fuel bases. It is clear from the above review that although previous studies have depicted the qualitative e!ects of walls on the characteristics of "res, additional systematic investigation of the e!ect of walls on the structure of di!erent types of "res is desired. This paper presents results from the initial phase of such an investigation. Although the number of the experiments in this phase has been rather limited, the experimental results made it possible to develop and evaluate approximate models for estimating the mass #ux and the mean #ame heights in wall and corner "res. 2. Theoretical background When analysing wall e!ects, attention should be given to some basic characteristics of free "re plumes, which will be brie#y reviewed. It has been shown by Heskestad [8] that the relative mean height of "re #ames above their base is determined by a dimensionless number N. Namely, ¸/D"f (N),
(3)
where N"MC ¹ /[go2 (H /r)3]NQ2/D5. !." # 1 !."
(4)
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H is the heat of combustion, r is the mass stoichiometric ratio of air to volatile and # D is the e!ective diameter of the #ame source. (The de"nitions of D and ¸ have been proposed by Heskestad [8] and Zukoski [5], respectively.) It turns out that, for most fuels burning in air, N is proportional to the square of QH, a simpler dimensionless parameter, which is de"ned as QH"Q/[(o C ¹ D2(gD)1@2]. (5) !." 1 !." Thus, it is often suggested [5] that the "re structure is determined by QH and considerable data is presented as a function of QH or Q2@5/D, rather than of N. Although the di!erence between the two formulations may be critical in cases where the oxygen level in the ambient air is reduced [9], the parameter Q2@5/D will be used in this paper to facilitate reference to previous studies. Di!erent empirical equations correlating ¸/D and Q2@5/D (or N) have been proposed in the literature [10,11]. The reviews by Beyler [10] and McCa!rey [11] show, however, that the values proposed by the di!erent equations are quite scattered, particularly for Q2@5/D(14. For example, according to Fig. 2 in Beyler [10], the proposed values of ¸/D at Q2@5/D"10 by six di!erent equations are in the range 0.1(¸/D(2.0. Use will be made in this work of the simple equation suggested by Heskestad [8,12], ¸/D"!1.02#0.23Q2@5/D,
(6)
which describes the general trend of most of the data. The limitations of Eq. (6) are discussed in Ref. [12]. It is noted, however, that a simple linear law ¸/D"kAQ2@5/D,
(7)
has been used with di!erent values of kA to describe data in limited regions of Q2@5/D. The mass #ux across a horizontal plane above the "re at a height z@ also depends on QH and can thus be expressed as a function of Q2@5/D and z@/D. The general form of this function has not been determined. However, various convenient power laws that describe M(z@) in limited regions have been proposed [12}16]. It turns out [9] that, within some restrictions, many of these power laws may be expressed in either the form M/QJ(z@/Q2@5)m
(8)
or the form M/D5@2J(z@/D)m.
(9)
The value of m appears to increase with z@/D. Very close to the "re base, m"1. 2 Higher, below the top of the #aming region, m"3, so that the mass #ux equation 2 becomes M/QJ(z@/Q2@5)3@2
(10)
M/D5@2"k(z@/D)3@2
(11)
or
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as in the LFE. In the far "eld, m"5, so that 3 M/Q"k@(z@/Q2@5)5@3,
(12)
which is often written as M/(Q1@3D5@3)"k@(z@/D)5@3.
(13)
The empirical coe$cients in some of above equations, as well as in some of the forthcoming equations, are not dimensionless. To make them dimensionless, one should replace Q by gQ/(o C ¹ ). Eq. (13), for example, will become in this way !." 1 !." M/[(gQ/(o C ¹ )]1@3D5@3"C (z@/D)5@3, (14) !." 1 !." m where C is a dimensionless constant. m It should be noted that the origin of the vertical axis z@ in the above equations is not uniquely de"ned. In the LFE, z@ is equal to the height z above the base of the fuel source. In the 5 power law, z@"z!z , where z is the height above the fuel base of 3 0 0 a virtual point source that gives at large heights the same mass #ux as the "re plume. The estimates of z are quite scattered and many empirical equations have been 0 proposed [10}12] for describing its dependence on Q2@5. The simple equation z /D"!1.02#0.083Q2@5/D, (15) 0 proposed by Heskestad [11], appears to represent the general trend of the data and will be used in this work. Subtracting Eq. (15) from Eq. (6), one "nds that (¸!z )/D"0.147Q2@5/D, (16) 0 which suggests that (¸!z )/Q2@5 is a constant. 0 Since Eqs. (12) to (14) should be valid at large heights above the #ames, it is appropriate to replace the total heat #ux Q in these equations by the convective heat #ux Q . However, as the convective heat #ux is not easily measurable, its value is # estimated for many fuels to be approximately equal to 0.7Q [12]. Thus, the use of the total heat #ux in this equation is quite common. Following Zukoski et al. [2,5], we shall use Eq. (12) with C "0.21 (which corresponds to k@"0.076 in Eq. (10)). It is clear from m the work of Heskestad [12], however, that this simple power law o!ers only a fair approximation to the vertical variation of the mass #ux above the #ames of real "res. One interesting corollary from Eqs. (12) and (16) is that the mass #ux at the mean #ame height, M 0 , is proportional to Q [11,15]. Namely, L~z M 0 /Q"k@[(¸!z )/Q2@5]5@3"constant. (17) L~z 0 Eq. (17) is consistent with the conclusions of previous investigators [12,17], that the mass #ux at the mean #ame height is approximately proportional to the stoichiometric mass #ux of air required for combustion. It is clear from the above discussion that the pattern of air #ow into "re #ames and, thus, the EF of wall and corner "res, must be functions of both QH (or Q2@5/D) and z/D. This conclusion suggests that a universal EF, that depends on the source/wall con"guration alone, might not exist. Intuitively, one expects that at small values of QH, as in mass "res, the e!ect of walls would be small, whereas at large values of
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QH a nearby wall will more e!ectively reduce entrainment into the #ames and increase the #ame heights, relative to those of similar free "res. Similarly, as suggested in our previous discussion of the Mirror Model, it is expected that the e!ect of walls will slightly decrease as z/D decreases. 3. Apparatus and experimental procedure The experiments were performed in the Variable Geometry Rig of BRE at Cardington (VGR), which provides a 6 m]6 m]4 m high space for large "re experiments, quite similar to the hood apparatus used by Zukoski [2]. A detailed description of the rig and its operation is available in Williams [18]. The sides and ceiling of the rig are constructed from sheets of 20 mm thick proprietary calcium silicate heat resistant boards. The bottom 2.5 m of the VGR was open on two sides to provide air inlet to the "re. One side provided a wall against which some of the "res were burned. Two mobile 2.4 m high]1.2 m wide frames supporting heat resistant boards were used to provide the other wall for corner "res. During tests, the hot smoke creates an elevated layer in the VGR. At one side of the roof of the VGR there is an open vent into a 3.0 m long duct, through which the hot gases rise and leave. A manual shutter is installed at the top of the duct, allowing control of the height of the elevated layer in the VGR. The duct is instrumented with an oxygen analyser, thermocouples, and a calibrated bidirectional velocity probe, located at the centre of the duct and connected to a sensitive, electronic di!erential pressure gauge. A calibration factor relating the reading of the probe and the average velocity in the duct was determined from measurements of velocity pro"les in the duct. The mass #ux was determined using the reading of the probe and the density of the smoke, which was calculated from the measured values of the temperatures. Gas was sampled across the duct through a perforated stainless-steel tube and its oxygen level was determined by the oxygen analyzer. The digital outputs of the instruments that monitored the sensors in the duct were recorded every 5 s and mean values of the recorded values over periods of 30}120 s were calculated. From these mean values, the values for the steady-state periods of the mass #ux at the height z of the lower interface of the elevated layer (which is equal to the mass #ux in the duct) and the total heat output from the "re, Q, which was determined by the consumption of oxygen by the "res, were calculated. The measuring system has been checked using a calibrated propane burner and its accuracy is estimated to be $6% of the readings. Four columns of thermocouples were suspended from the ceiling of the rig and measured the vertical temperature pro"le in the rig. Each column consisted of 16 bare junctions of Type K (Chromel/Alumel) thermocouples. From the temperature pro"le the height to the base of the elevated layer is de"ned as
P
H h dz@, 0 where H is the ceiling height, was determined. z"H!(1/(h ) .!9
(18)
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The "res were produced by burning industrial methylated spirits (IMS) in square steel trays, ranging in size from 0.25 to 1.0 m2, giving heat outputs between 20 and 800 kW. (The caloric value of IMS is 26.58 MJ/kg.) Some of the trays were placed directly on the #oor, whereas some of them were placed in a larger tray "lled with water. The water-cooled trays maintained a more steady burning. Cooling the trays also reduced the heat output for a given "re size, which gave a slightly wider range of heat outputs with the limited range of "re trays available. Each tray was "lled with IMS to a depth of between 10 and 30 mm, to give "res of 5}20 min duration. That allowed the "re, in most tests, to reach a quasi-steady-state burning for at least 1 min, at which the required data was acquired. During some of the tests, the position of the shutter at the top of the duct was changed, to alter the area of the vent. That changed the mass #ux through the duct, resulting in changes in the height z of the elevated layer. The development of a typical "re, as depicted in the time variation of its total heat output, is shown in Fig. 1. One sees that it took about 200 s for this particular "re to reach a quasi-steady burning rate. The period from 260 to 360 s was considered as a representative period of quasi-steady combustion for this "re, and statistical properties of the "re and #ame were taken from measurements during that period. At 360 s the vent was partially closed. That change led to a storage of energy in the hot gas layer, so that the heat output of the "re was not equal to the heat #ux through the duct for about 2 min. At 600 s a quasi-steady state was re-established. At 750 s the vent was slightly opened and a new transition in the calculated heat output was again observed. The #ame heights during the various tests were video recorded at 25 frame s~1. The video records have also depicted a vertical scale showing the height above the #oor.
Fig. 1. A typical variation with time of the measured heat #ux in a test.
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The statistical properties of the #ame height during the period of quasi-steady-state burning were analysed from the video recordings using a model VP116 Video Imaging System supplied by HVS Image of Twickenham, England. The system tracked the height of the tip of the #ame from frame to frame of the video records, and the data was stored on a personal computer. Before analysing a given recorded video, the Video Imaging System was calibrated and adjusted to track the tip of the #ame. The readings of the #ame heights were corrected for the parallax produced by the distance between the centre of the #ame and the scale in the open "res tests. Around 40 runs were made with di!erent size trays and con"gurations: Single square trays in the open away from walls (single/open), double adjacent square trays in the open (double/open), single and double trays close to a vertical wall (single/wall and double/wall) and single trays in a corner (single/corner). (The abbreviated notation in the parentheses is used in the legends of the "gures.) A careful examination of the data suggested, however, that only 26 experiments yielded reliable data. The main reason for discarding the other data was a lack of a clear, steady-state burning phase. We have also observed that "res in apparently similar tray con"gurations did not always develop in a similar manner and did not have the same characteristics during what appeared to be steady-state phases. These di!erences might have been caused by uncontrolled ambient air movements, but we suspect that another factor that might have contributed to this variability was the level of fuel in the tray. We controlled neither its initial value nor its rate of change. Observation of the "res indicated that in some cases the base area of the #ame rising from the trays was smaller than the tray, and that near the walls of the trays either a strip of laminar burning or a small vortex with an axis parallel to the wall existed, particularly when the di!erence between the level of the alcohol and the height of the walls of the tray was large. In addition, since neither the heights of the walls of the trays nor the level of the alcohol were proportional to the diameter of the trays, the expected similarity of the results at di!erent dimensionless parameters that include D, such as QH, might have been slightly a!ected by these uncontrolled parameters. Table 1 summarises the measurements from the successful runs. Included in the table are the mass #uxes for the four corner runs. Unfortunately, the heights of elevated layers in these runs were higher than the height of one wall of the mobile frame that formed the corner (2.4 m). Thus, we have not plotted the mass #ux measurements of these runs in the forthcoming "gures.
4. Analysis of the results 4.1. Mass entrainment We have plotted in Fig. 2 the measurements of M/(PHEF) versus z and compared them with the modi"ed LFE (Eq. (2)), using the EF values suggested by Hansell [4]. The "gure shows that, in spite of the large number of the experimental con"gurations, the data are well grouped. However, most of the measured values are larger than those predicted by the modi"ed LFE. This form of the LFE makes it di$cult to understand
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Table 1 Summary of "re and plume properties for test "res Run Tray number width (m)
Fire Fire perimeter position (m)
Tray Total heat Mass #ow Height of cooled release (kg s~1) elevated rate (kW) layer (m)
¸ ¸ 0.05 &(m) (m)
¸ 0.95 (m)
33 6 7 8 36 37 24 32 22 23 11 13 16 12 25 38a 26 31 39a 39b 15 20 17** 27** 29** 30**
1.0 1.2 1.2 2.0 2.0 2.0 2.0 3.0 3.2 4.0 4.0 3.0 3.0 3.0 1.5 1.5 1.5 2.25 1.0 1.0 2.0 2.0 1.0 1.0 1.5 2.0
Yes No Yes No Yes Yes Yes Yes No No Yes No No Yes No Yes Yes Yes Yes Yes No Yes No Yes Yes Yes
0.25 0.48 0.61 0.58 0.68 } 0.57 0.86 0.77 1.30 1.02 } 0.75 0.74 0.71 0.76 0.70 0.92 0.51 } 1.21 0.59 0.91 0.76 1.01 1.42
0.53 0.85 0.94 0.94 1.15 } 1.15 1.64 1.26 2.08 1.75 } 1.33 1.30 1.27* 1.66 1.18 1.79 1.24 } 2.57 1.62 2.16 1.72 2.29 2.56*
0.25 0.3 0.3 0.5 0.5 0.5 0.5 0.75 0.8 1.0 1.0 2]0.5 2]0.5 2]0.5 0.5 0.5 0.5 0.75 2]0.25 2]0.25 2]0.5 2]0.5 0.5 0.5 0.75 1.0
In open In open In open In open In open In open In open In open In open In open In open In open In open In open Near wall Near wall Near wall Near wall Near wall Near wall Near wall Near wall In corner In corner In corner In corner
19$1.4 38$1.8 30$2.2 108$3.2 107$8 113$6 113$9 309$20 280$10 563$24 430$21 208$4 218$11 196$7 154$10 110$6 124$5 343$16 53$3 50$3 360$22 246$10 157$9 138$5 327$16 664$27
1.17$0.06 1.57$0.05 1.43$0.07 2.12$0.14 1.43$0.06 2.22$0.09 2.26$0.13 2.92$0.17 2.82$0.09 3.39$0.11 3.11$0.13 2.63$0.07 2.78$0.13 2.55$0.16 2.36$0.10 2.00$0.13 2.28$0.09 3.06$0.12 1.33$0.05 1.64$0.08 2.81$0.13 2.60$0.09 2.09$0.11 1.93$0.07 2.81$0.10 3.41$0.10
2.77$0.14 2.91$0.06 2.91$0.05 2.73$0.06 2.43$0.09 2.64$0.08 2.84$0.04 2.64$0.04 2.51$0.06 2.61$0.03 2.54$0.06 2.43$0.09 2.44$0.13 2.45$0.04 3.51$0.11 3.16$0.05 3.35$0.14 3.17$0.13 3.37$0.05 3.49$0.05 3.34$0.09 3.32$0.08 3.35$0.18 3.62$0.10 3.45$0.19 3.29$0.19
0.38 0.64 0.78 0.73 0.89 } 0.85 1.24 0.98 1.70 1.32 } 1.00 1.05 1.01 1.07 0.90 1.32 0.78 } 1.80 0.96 1.38 1.08 1.52 2.06
} Not measured. *Peak #ame height extended above the video "eld of view, the table shows the maximum measured value. **See remark at the end of Section 3.
why. A better insight is gained by expressing the modi"ed LFE in the form of Eq. (11): M@"0.752(z/D@)3@2,
(19)
where M@"(M/EF)/D@5@2
(20)
and D@"P/4. Fig. 3 compares the measurements of M@ with Eq. (19). Also plotted in this "gure are the open "re data of Hinkley [7]. It is clear from this "gure that Hinkley's data and the present measurements are quite consistent. One also observes in the "gure that the deviations of the measurements from the modi"ed LFE exist only at z/D@'3, where
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Fig. 2. The measured variation of M/P with z in the present tests. %&
Fig. 3. The measured and predicted variation of M@ with z/D@.
most of the present measurements were made, and that they increase as z/D@ does. It is, thus, plausible to conclude that these deviations are due to the fact that the present data fall beyond the range where the LFE is valid. As noted earlier, this range has not been accurately determined. The LFE had been originally [6] developed for the
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Fig. 4. The measured and predicted variation of MA with (z!z )/D. 0
#aming region. Hinkley [7] suggested that it is valid to z/D@"10. The present data suggest that it is valid only to approximately z/D@"3. In view of the above conclusion, it was decided to examine whether the e!ect of the walls on the entrainment for large values of z/D@ could be evaluated using a modi"ed form of the far-"eld equations (12) and (13) in which the mass #ux is replaced by M/EF, where EF"Pef/P, as suggested by Hansell [4]. In other words, we assume that in the far "eld, MA"(M/EF)/(Q1@3D5@3)]"k@[(z!z )/D]5@3, 0 which may also be written as
(21)
M/Q"EF k@[(z!z )/Q2@5]5@3. (22) 0 Plotted in Fig. 4 are the measured values of MA versus (z!z )/D and Eq. (21) with 0 k@"0.076, (C "0.21) [5]. As seen from the "gure, the modi"ed far-"eld equation . provides a very good description of all the measured mass #uxes at (z!z )/D'5. 0 4.2. Flame heights Fig. 5 shows the time variation of the instantaneous #ame height ¸(t) for a period of 21 s (525 video frames) in a typical test (Test 39). Using these data we have calculated for all but three runs the cumulative probability distribution P(¸), which is equal to the probability that the instantaneous #ame height is larger than a given value ¸. Following Zukoski [5], we have then calculated the mean #ame height, ¸, the continuous #ame height, ¸ and the peak #ame height, ¸ . The calculated values 0.05 0.95 appear in the 3 last columns of Table 1. Table 2 summarises our data for the 0.5 m trays.
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Fig. 5. A typical variation with time of the instantaneous #ame height.
Table 2 Average #ame heights and relative #ame span for "res above 0.5 m trays Tray location
Test nos.
¸ (m)
¸ 0.95 (m)
¸ 0.05 (m)
(¸ !¸ )/¸ 0.95 0.05 }
In the open Near a wall In a corner
8, 24, 36 25, 26, 38a 17, 27
0.82 0.99 1.23
1.08 1.37 1.94
0.61 0.72 0.84
0.57 0.65 0.90
As seen from Table 2, the continuous, mean, and peak #ame heights of "res burning near walls and corners are considerably larger than those from a similar "re source burning in the open. These observations are fairly similar to those of Hasemi and Tokunaga [3]. In addition, the table shows that adjacent walls increase the dimensionless span of the #uctuations of the #ame heights, as demonstrated in Fig. 6. As a result, the peak #ame heights of wall and corner "res in these experiments were larger than the peak heights of the free "res from the same sources by 26 and 80%, respectively, although the mean #ame height of the wall and corner "res increased by only 21 and 50%. It should be realised, however, that part of the increase in the values of the #ame heights of the con"ned "res depicted in Table 2 is due to the increased values of the heat #ux in the wall and corner "res. To get a quantitative explanation for the increase of the mean #ame height in con"ned "res, the following model was developed. It was assumed that the ratio M 0 /Q, see Eq. (17), is a universal constant for all the "res. Using Eqs. (22) and (12), L~z the mass #ux at the mean #ame height can be written as M
L~z0
/Q"k@EF[(¸!z )/Q2@5]5@3"k@ ) 1.0[(0.147]5@3. 0
(23)
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Fig. 6. The measured intermittency of the #ame height #uctuations.
Fig. 7. The measured and predicted variation of EF3@5[(¸!z )/D] with Q2@5/D. 0
Eq. (23) suggests that the general form of Eq. (16) is EF3@5[(¸!z )/D]"0.147Q2@5/D. 0
(24)
Fig. 7 compares Eq. (24) with the values calculated from the experimental data. One sees that most of the experimental values of EF3@5[(¸!z )/D] are below the 0
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Fig. 8. The variation of EF2@3(¸/D) with Q2@5/D.
corresponding values of 0.147Q2@5/D. The average deviation of all the data from this model is 15%, but the standard deviation from their average value is only 10%. One notices, however, that the deviation of the open "re data is only 3%, the deviation of the wall "res is 21% and the deviation of the corner "res is 29%. Eqs. (23) and (24) are based on the assumption that the far-"eld equation can be used to estimate the mass #ux at the mean #ame height. If one assumes, instead, that the mass #ux at that region, for the limited range of values of Q2@5/D in the present experiments, can be expressed by the LFE, which may also be expressed by Eq. (10), one may write that M(¸)/Q"k@EF[¸/Q2@5]3@2.
(25)
Eq. (25) and the present data suggest that EF2@3[¸/D]"kHQ2@5/D.
(26)
where kH"0.132. This value of kH has been determined by the open "re data, which are described by this equation with an accuracy of 4%, see Fig. 8. The average measured values of the #ame heights for the wall and corner "res are smaller than the values predicted by this equation by 15 and 24%, respectively. Also shown in the "gure is the variation of ¸/D for open "res, EF"1, according to Heskestad [8,12] (Eq. (6)). It is noted that the di!erence between Eqs. (6) and (26), within the limited range of values of Q2@5/D at the present experiments, is not large.
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5. Discussion and conclusions The qualitative e!ect of walls on "res appears to be simple. Walls block the #ow of ambient air into the "re plume. As a result, the entrainment of air and oxygen into the fuel laden "re #ames is reduced and the burning of the fuel is completed at higher heights. Since the mass #ux of smoke at a given height, M(z), is approximately equal to the entrainment rate of air into the "re plume up to that height, the presence of walls close to a "re reduces its value. This qualitatively simple picture of the e!ect of walls had raised hopes that it could be described by very simple quantitative models such as the Mirror Model or a simple modi"cation of the LFE [4], which is being used to predict the mass #ux in the #aming region of "re plumes. It turns out that the Mirror Model was not successful in consistently describing the properties of the small number of wall and corner "res that had been previously investigated. The predictions of the modi"ed LFE, on the other hand, have never been compared with experimental results. Our initial comparison between its predictions and the data collected in the present investigation gave the impression that this simple model overestimates the e!ect of walls on entrainment. However, when expressing the mass #ux variation according to this equation as a function of z/D@, it became apparent that most of the present data, which include open "re data, fall beyond the #aming region and that the deviation of the data from the modi"ed LFE increases as the relative height z/D@ increases beyond 3.0. This observation suggests that the region of validity of the LFE is bounded by this relative distance. However, it does not rule out at all the possibility that this simple model could predict M(z) in wall and corner "re plumes when z/D@(3. Encouraged by this result, the intuitive assumption of Hensell, that EF is approximately proportional to the length of the free perimeter of the "re, was used to develop a model that extends the approximate classical far-"eld equation for the mass #ux to wall and corner plumes. The model also assumes that the location of the virtual source z for such plumes can be predicted by the equation that has been developed for free 0 "re plumes. The mass #ux in the far "eld of wall and corner "re plumes predicted by this model was found to be in good agreement with the present measurements. Similarly, a simple model for predicting the mean #ame height for di!erent con"gurations of wall and corner "res was developed. This model assumes that the ratio of the mass #ux at the mean #ame height to the stoichiometric mass #ux of air required for combustion is the same for free and con"ned plumes. It also assumes that the mass #ux at that height is given by the modi"ed far-"eld equation derived earlier. Based on these assumptions, the model extends Heskestad's classical equation for the height of the mean #ame tip, ¸!z , to wall and corner "res and suggests that ¸!z is 0 0 inversely proportional to EF3@5. The present open "re measurements were found to be very close to the classical equation for ¸!z , on which this model was based. 0 However, when the values of EF were assumed to be equal to the ratio of the e!ective perimeter to the total perimeter of the fuel source, the measured values of the mean #ame height for the present wall and corner "res tests were found to smaller by 21 and 29%, respectively, from the predictions of this model. The model itself, should be noted, as being independent of this assumption.
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A di!erent model for the mean #ame height, based on the 3 power law (Eq. (10)) for 2 the mass #ux at the mean #ame height, has also been derived. The proportionality coe$cient in this model has been determined by the present open "re data. This model predicts, see Eq. (26), that ¸ is inversely proportional to EF2@3. This model, too, overestimates the mean #ame height of the wall and corner "res, but by slightly smaller relative values; approximately 15 and 24%, respectively. One may attribute the deviation of the data from the predictions of these two models to the assumption that the ratio M 0 /Q is the same for open and con"ned L~z "res as, in addition to their blocking e!ect, walls decrease the size of the large eddies in con"ned plumes and change the entire turbulent structure of such "res. Another possible explanation is that the e!ect of the walls near the base of the "re is not as large as proposed by Hansell [4]. This explanation is supported by the slightly lower deviations of the wall and corner #ame height data from the second model. It is also consistent with the predictions of the Mirror Model, that the rate of entrainment close to the "re base is relatively lower than in the far "eld, as explained in the Introduction. In addition to the above physical explanations, one should remember that the original classical power laws for uncon"ned "res, on which the presented models are based, are not very accurate either, particularly in predicting the mean #ame height. Thus, it is a priori clear that a simple universal model for open and con"ned "res cannot be very accurate. For this reason, the good agreement between the proposed mass #ux model and the present limited data is not a su$cient proof for its universal validity. Users of these equations in Fire Protection Engineering practice should take these limitations into consideration. An answer to the questions, which of the above explanations is correct and how reliable and universal are the models and equations that have been derived in this work, can be given only by comparing them with a much larger set of data, which are the backbone of any semi-empirical model. Acknowledgements The authors extend their thanks to a number of their colleagues for their help during the course of the work, and especially for help in conducting the experiments. We are grateful to B.K. Ghosh, R. Harrison and P. Samme for their help in conducting the experiments. Thanks are due to D. Hayward and R. Mallows, for their help in video recording of the experiments, and to L. Ferrier, for providing technical support in the analysis of the recordings. Finally, we thank H.P. Morgan and G. Cox for their continued support and encouragement during the entire work, for reviewing this paper and for their constructive and valuable advice. The work of the "rst author was partially supported by The Fund for Promotion of Research at the Technion, Israel Institute of Technology. References [1] Grella JJ, Faeth GM. Measurements in a two-dimensional thermal plume along a vertical adiabatic wall. J Fluid Mech 1975;71(Part 4):701}10.
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[2] Zukoski EE, Kubota T, Cetegen B. Entrainment in "re plumes. Fire Safety J 1981;3:107}21. [3] Hasemi Y, Tokunaga T. Some experimental aspects of turbulent di!usion #ames and buoyant plumes from "re sources against a wall out in a corner of walls. Combustion Sci Technol 1984;40:1}17. [4] Hansell GO. Heat and mass transfer processes a!ecting smoke control in atrium buildings. Ph.D. thesis. South Bank University, London, 1993. [5] Zukoski EE. Properties of "re plumes. In: Cox G, editor. Combustion fundamentals of "re. London: Academic Press, 1995. p. 101}220. [6] Thomas PH, Hinkley PL, Theobald CR, Simms DL. Investigations into the #ow of hot gases in roof venting. Fire Research Tech Paper 7. London: HMSO, 1963. [7] Hinkley PL. Rates of production of hot gases in roof venting experiments. Fire Safety J 1986;10:57}65. [8] Heskestad G. Luminous heights of turbulent di!usion #ames. Fire Safety J 1983;5:103}8. [9] Poreh M, Morgan HP. On power laws for describing the mass #ux in the near "eld of "res. Fire Safety J 1996;27:159}78. [10] Beyler CL. Fire plumes and ceiling jets. Fire Safety J 1986;11:53}74. [11] McCa!rey BJ. Flame height, In: The SFPE Handbook of Fire Protection Engineering, 2nd Ed., NFPA, Quincy, MA, 1995. p. 2-1}2-8. [12] Heskestad G. Plume theory. In: The SFPE Handbook of Fire Protection Engineering. 2nd Ed., NFPA, Quincy, MA, 1995. p. 2-9}2-19. [13] McCa!rey BJ. Purely buoyant di!usion #ames: some experimental results. NBSIR 79-1910, National Bureau of Standards, Washington, DC, 1979. [14] McCa!rey BJ, Cox G. NBSIR 82-2473, National Bureau of Standards, Washington, DC, USA, 1982. [15] Cox G, Chitty R. A study of the deterministic properties of unbounded "re plumes. Combust Flame 1980;39:191}202. [16] Cox G, Chitty R. Some stochastic properties of "re plumes. Fire Mater 1982;6(3&4):127}34. [17] Delichatsios MA. Air entrainment into buoyant jet #ames and pool "res. In: The Handbook of Fire Protection Engineering, 2nd Ed., NFPA, Quincy, MA, 1995. p. 2-20}2-31. [18] Williams C. The downward movement of smoke due to a sprinkler spray. Ph.D. thesis. South BankUniversity, London, 1993.