Fire Safety Journal 54 (2012) 36–48

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Fire Safety Journal

0379-71

http://d

n Corr

E-m

xyzhou

journal homepage: www.elsevier.com/locate/firesaf

Spray characterization measurements of a pendent fire sprinkler

Xiangyang Zhou n, Stephen P. D’Aniello, Hong-Zeng Yu

FM Global 1151 Boston-Providence Turnpike Norwood, MA 02062, USA

a r t i c l e i n f o

Article history:

Received 29 August 2011

Received in revised form

9 February 2012

Accepted 30 July 2012Available online 30 August 2012

Keywords:

Spray measurement

Fire sprinkler

Shadow-imaging system

12/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.firesaf.2012.07.007

esponding author. Tel.: þ1 781 255 4938; fax

ail addresses: xiangyang.zhou@fmglobal.com,

_18@yahoo.com (X. Zhou).

a b s t r a c t

The spray patterns of a pendent fire sprinkler were characterized through experimental measurements

in the near and far field of the sprinkler. A laser-based shadow-imaging system was used to measure

the droplet size, velocity and number density in the spray. An array of pressure-transducer-equipped

water collection tubes and containers provided a separate set of water volume flux measurements.

A large-scale traverse was constructed to move the laser optics and water collection tubes and

containers to the designated measurement locations. A pendent fire sprinkler with K-factor of 205 lpm/

bar1/2 (14.2 gpm/psi1/2) was characterized at two discharge pressures 3.5 bar and 5.2 bar (50 and

75 psi). In the near field at 0.76 m from the sprinkler, measurements were performed in a spherical

coordinate at different azimuthal and elevation angles with respect to the sprinkler deflector. In the far

field, the sprays were mapped out in a 1101 circular sector at 3.05 m and 4.57 m below the ceiling. The

shadow-imaging based water flux measurements were verified by the measurements obtained from

water collection containers. The measurements show that the spatial distributions of water volume

flux, droplet size and velocity of sprinkler sprays are strongly influenced by the sprinkler frame arms

and the configuration of sprinkler deflector’s tines and slots. For the purpose of fire protection analysis,

empirical correlations were developed from the near-field measurements to prescribe the spray

starting conditions for the numerical modeling of spray transport through fire plumes. The far-field

measurements can be used to evaluate the spray transport calculations.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Fire sprinkler technology has been the most reliable andeffective method for protecting warehouses and factories. A firesprinkler is designed to deliver water to the burning material toreduce the burning rate, to wet the surrounding combustibles tostop or reduce the flame spread, and to cool the fire products.To achieve the above design objective, the sprinkler spray musthave sufficient momentum to penetrate the fire plume in order toreach the burning combustibles, and have sufficient heat absorp-tion capability to lower the temperature of the fire environment.One of the findings that has been quantified by fire sprinklerresearch is that larger drops are more capable in penetrating thefire plume to reach the burning materials, and smaller drops aremore efficient in cooling [1,2].

Effective sprinkler protection requires an optimal drop sizedistribution for a targeted fire hazard. Numerical modeling of fireprotection needs the initial spray characteristics of droplet size,droplet velocity, number density and their spatial distribution as

ll rights reserved.

: þ1 781 762 9375.

the starting conditions to calculate the spray transport. However,it is still challenging to predict the spray characteristics becauseof the complexity and stochastic behavior of the breakup processfor actual sprinkler geometrics [3]. Before a complete physics-based spray formation model is developed and fully validated forfire sprinklers, the initial spray characteristics must be prescribedbased on measurements and empirical correlations.

Measurements have been performed by Yu [4] to characterizethe spray patterns of three upright sprinklers with K-factorsranging from 81 lpm/bar1/2 to 162 lpm/bar1/2 using a laser-based shadowgraph system. Spatial distributions of drop size,velocity and water flux were measured at elevations of 3 m and6 m below the sprinkler for pressures of 2.7 bar and 3.9 bar. Thegross droplet-size distributions of the tested sprinklers werefound to be represented by a composite of log-normal andRosin–Rammler distributions. The same shadowgraph measuringsystem was also used by Chan [5] to measure the spray patternsof two pendent sprinklers with a K-factor of 205 lpm/bar1/2 at3.2 m below the ceiling. He also correlated the sprinklers’ grossdrop size distributions with the aforementioned composite func-tions. Using phase doppler interferometry (PDI) and particleimage velocimetry (PIV), Widmann [6] measured the droplet sizeand velocity of residential sprinklers with K-factors ranging from43 lpm/bar1/2 to 81 lpm/bar1/2. He reaffirmed the previous finding

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–48 37

that droplet size varies inversely with 1/3-power of sprinkleroperating pressure. Sheppard [7] used the PDI technique tomeasure the droplet size distribution at a radial distance of0.38 m from the sprinkler and at a single azimuthal angel almostperpendicular the frame arms. The PIV technique was used tomeasure the droplet velocities close to the sprinkler. The workshowed that the droplet velocity tended to vary more signifi-cantly along the elevation angle than along the azimuthal angle.The water flux was calculated by counting droplets in a planelaser sheet and assuming a constant average droplet diameter.The measurements showed that the water flux was stronglydependent on the elevation angle, azimuthal angle, pressure andsprinkler type. Based on the measurements of a uniformly-distributed spray pattern excluding the sprinkler frame’s effecton the spray pattern, Ren et al. [8] developed compact analyticalformulations to describe the sprinkler spray. The high ordercurve-fit polynomials were derived using Fourier series, and thegenerated spray size distributions agreed reasonably well withthe measurements.

This paper presents the spray characterization measurementsof a pendent warehouse fire sprinkler using a laser-based sha-dow-imaging system and an array of pressure-transducer-equipped water collection tubes and containers, in both the nearfield and far field of the sprinkler. The shadow-imaging systemprovided the information on droplet size, velocity and numberdensity in the spray. The water collection tubes and containersprovided a separate set of volume flux measurements to comparewith the laser-based measurements. The non-uniform sprayinduced by the sprinkler frame arms and the configuration oftines and slots of the deflector were investigated by performingmeasurements in a spherical coordinate system at various eleva-tion and azimuthal angles. Empirical correlations were developedfor the near-field spray distributions of volume flux, droplet sizeand droplet velocity under different pressures and spray cross-sections. These empirical correlations can be used to prescribe thespray starting conditions for the numerical modeling of spraytransport through fire plumes. The far-field measurements can beused to evaluate the spray transport calculations.

2. Experimental setup

The laser-based shadow-imaging system was used to visualizedroplets from a spray. It is based on the shadowgraph techniquewith high resolution imaging and pulsed backlight illumination. Acollection of droplets occupying a given volume is sampled instan-taneously. The measurement volume is defined by the field-of-viewarea and the depth of field of the imaging system. The light source isa double-cavity-frequency Nd:YAG laser, which provides two lightpulses of 532 nm wavelength, each with a pulse energy of about120 mJ at 15 Hz double-pulse rate. The light source passes throughan optical diffuser to provide uniform light intensity at the measur-ing location. The camera detection system consists of a 14-bit dual-frame CCD camera with 4 million pixels resolution, and a 12�zoom system which can achieve a field of view down to 400 mm.Using a short laser pulse (less than 16 ns) as illumination, it ispossible to ‘‘freeze’’ droplet motions faster than 100 m/s. A double-pulse laser combining with a double-frame camera allows theinvestigation of size-dependent droplet velocities. This techniqueis independent of the droplet shape and opacity and allows themeasurement of droplet sizes down to 5 mm.

The statistical results are calculated from all the detecteddroplets. By measuring the sizes and velocities of droplets detectedin a control volume with sufficient time duration, statistical sprayproperties can be derived. One of the characteristic droplet diametersdescribing the statistical spray information is the volume-weighted

median droplet diameter, dv50, which denotes that 50% ofthe cumulated droplet volume is from droplets with diameterssmaller than dv50. The dv50 provides a picture of the overalldroplets present in a control volume. The volume flux (lpm/m2)of droplets can be calculated as:

_q ¼XN

i ¼ 1

1

6

pd3i ui

A� dofi

ð1Þ

where N is the number of detected droplets in each image, di isthe droplet diameter, ui is the droplet velocity, A is the area of thefield view of the camera, and dofi is the depth-of-field thatdepends on the droplet diameter di. Since the droplet size issmall in comparison to the field view area, the A value is assumedto be independent of droplet size. The measuring volume is theproduct of A and dofi.

After calibrating the detection system, the physical size of thecamera field view was determined to be 22.488�22.488 mm. Thepixel number of each digital image was 2048�2048. The mini-mum droplet size that could be detected was 0.091 mm. The dof

for the expected range of droplet diameters was calibrated usingcircular opaque objects with known diameters (0.1 mm to 2 mm)printed on a transparent sheet. The sheet was mounted on atranslation device with a resolution of 1 mm, and then movedalong the line-of-sight into and out of the focal plane. Based onthe calibration, the depths of field were correlated with dropletdiameters as dof i ¼ 34:18di, where dofi and di are in units ofmillimeter.

The uncertainty of the current shadow-imaging system wasdetermined from the aforementioned calibration. For an object of2.0-mm in diameter, the measured diameter was from 1.793 mmto 2.052 mm when traversing within the corresponding depth offield. The uncertainty was therefore about 10%. For a 1.0-mmdiameter object, the uncertainty was about 8%. As describedabove, the measurement uncertainty depends on the droplet sizeand the distance between the droplet and the focal plane. There-fore, the border correction and depth-of-field correction [9] wereused in the calculation of the statistical results. The accuracy ofthe sizing system was also examined by comparing the water fluxmeasurements with those obtained with the water collectioncontainers. This will be discussed in the results section later.

A maximum of 80 pairs of images could be captured in eachcontinuous measurement before image data had to be transferredto the hard drive. With the 80 pairs of images, the number ofdetected droplets ranged from zero to thousands, depending onthe water flux density at each measuring location. Generally, allelse being equal, a larger droplet sample size leads to a higherconfidence level in estimating various statistical properties. How-ever, a larger sample size means more images are needed,especially at the spray edge where the spray is less dense.Therefore, a decision was made such that 80 images werecaptured at each location, but the statistical properties werecalculated only when the number of detected droplets exceeded100. A statistical calculation based on Gaussian distributionshowed that the sampling error was 10% with 95% confidencewhen the sampling size was 100.

Fig. 1 shows the overall test setup for the sprinkler spraymeasurement, which consisted of a movable ceiling, a large-scaletraverse, and the laser-based shadow-imaging system. The overalldimensions of the Sprinkler Spray Characterization Lab are about16.8�10.4�9.1 m high.

The ceiling was constructed with a 3�3 m aluminum frameand polycarbonate tiles (transparent). The north edge of theceiling was supported by two steel columns. The ceiling heightcould be adjusted from 1.8 m to 7.6 m above the floor. A 50 mm(ID) sprinkler pipe was installed 0.3 m below the ceiling and fitted

Fig. 1. Illustration of the overall test setup for ceiling, traverse and shadow-imaging

system.Fig. 2. Illustration of seven tubes at different elevation angles for flux measurements

in the near field.

Fig. 3. Illustration of 15 water collection containers for flux measurements in the

far field.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–4838

with a threaded tee at the ceiling center. The pipe was fastened tothe ceiling with pipe hangers. The water supply to the sprinklerpipe was provided at both ends with two 50 mm ID flexible hoses.The sprinkler was installed on the threaded tee and was orientedsuch that the arms were in alignment with the pipe. A pressuretap was installed on the tee to measure the discharge pressure.

The traverse system was composed of three main units: onelinear track, one platform on the linear track and four curvedtracks. Because the system was operating within a wet environ-ment, all components were made of either aluminum or stainlesssteel to prevent corrosion. The linear track could sweep azimuth-ally 1201 across the spray. The pivot of the track was located onthe floor directly under the sprinkler. Four curved tracks eachwith a radius of 1.8 m, 3.6 m, 5.5 m or 7.0 m were integrated withconnecting I-beams anchored to the floor. The linear track couldbe rotated azimuthally on the curved tracks with three pairs ofwheels mounted beneath the linear track. The orientation of thecurved tracks was such that the two extreme azimuthal positionsof the linear track were symmetrical to the plane that was normalto the sprinkler pipe and passed through the pivot point. Theplatform was put on the linear track with two pairs of wheelsmounted beneath the platform. The platform could roll on thelinear track in the radial direction for a maximum distance of7.0 m from the pivot point. The movements of the track and theplatform were done manually.

A 3D high-precision (1 mm resolution) traversing system wasmounted on the platform of the large-scale traverse to positionthe measuring volume of the shadow-imaging system in thesprinkler spray. The 3D traversing system had a local traverserange of 2�2�1 m high and was remotely controlled by soft-ware. The computer, the local 3D traverse controller, the laserpower supply and the laser head were all protected in environ-mental enclosures.

To characterize the water volume flux distribution near thesprinkler, seven water collection tubes (ID 41 mm) were installedat seven elevation angles with respect to the sprinkler deflector asshown in Fig. 2. The openings of the individual tubes were alignedalong a circle centered with the deflector. The distance from thedeflector to the tube openings was 0.76 m. Each tube wasconnected to a pressure-transducer-equipped container for flowrate measurements. Besides the volume flux measurementsobtained with the shadow-imaging system, the far-field water

flux distributions were also measured using an array of 15pressure-transducer-equipped water collection containers. Thesecontainers were positioned continuously along a ray on the large-scale traverse’s rotating track, starting from directly under thesprinkler, as shown in Fig. 3.

The measurements were performed for a pendent fire sprink-ler with a K-factor of 205 lpm/bar1/2, for water discharge pres-sures of 3.5 bar and 5.2 bar. The distance of the ceiling to thesprinkler deflector was 0.4 m.

The measurement procedure is described in the following.After the pump started, the water flow control valves wereadjusted to reach the desired discharge pressure. After threeminutes to allow the water flow to stabilize, the dischargepressure was fine tuned to the desired value. Measurements wereconducted in the near field (a spherical surface 0.76 m from thesprinkler deflector), and the far field (two horizontal planes3.05 m and 4.57 m below the ceiling). In the near field, the lasermeasuring volume was moved along a spherical coordinatesystem at various elevation (y) and azimuthal angles (f). Thezero-degree azimuthal angle started from one of the sprinklerframe arms. The zero-degree elevation angle was defined at thehorizontal level of the deflector. The spherical surface area wasdivided into 49 cells by seven azimuthal angles and sevenelevation angles. Each cell was centered to a location wheredroplet size, velocity and volume flux measurements were made.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–48 39

The center of each cell was denoted with two indices, i and j.Index i denoted the ith azimuthal angle from the frame arm,whereas j denoted the jth elevation angle from the horizontallevel. On the spherical surface, the cell area varied with theelevation angle and the minimum was at y¼901.

As mentioned above, the spray in the far field was measuredalong two horizontal planes. There were 15 measurement loca-tions along the radial direction and seven locations along theazimuthal direction in the 1101 sector. The number of totalmeasurement locations was therefore 105 at each elevation. Eachlocation was also denoted with two indices, i and j. Index i

denoted the azimuthal angle and index j denoted the jth radialposition from the spray center. For the water volume fluxmeasurements with tubes and containers, water was collectedfor a maximum duration of 30 min.

3. Results and discussions

3.1. Sprinkler spray in the near field

Fig. 4 shows the geometrical structure of the sprinkler deflec-tor. The azimuthal angle (f) was designated for each slot fromone frame arm where f¼01. If the sprinkler is symmetrical, theazimuthal distribution in each quadrant is expected to be com-parable. Therefore, the azimuthal distribution was measured inthe second quadrant in the present investigation. The selectedazimuthal locations were 901, 1231 and 1571, corresponding tothe deflector tines, and 731, 1071, 1401 and 1801 corresponding tothe slots between the tines. In the spray measurement, a dense jetin the spray center and two secondary jets along the direction ofeach frame arm were observed. These jets were the primary causefor the non-uniform spatial distribution of droplet size andvolume flux along the azimuthal angle and elevation angle.

It is necessary to choose a proper radial distance from thedeflector to conduct measurements in the near field. This is becausethe spray atomization process currently cannot be directly simu-lated by numerical modeling. The initial sprinkler spray character-istics must be prescribed based on measurements. Therefore, aproper radial distance should be a location where the spray is fullyatomized and the probability of additional breakups would beminimal. To improve the accuracy of the shadowgraph measure-ment, the droplet number density should be such that the numberof overlapped droplet images is sufficiently low as compared to thetotal number of detected images. Fig. 5(a) illustrates an instanta-neous spray image captured at a radial distance of r¼0.15 m fromthe sprinkler deflector. There are many spray ligaments that have

Fig. 4. The azimuthal angle designated for each slot of the sprinkler deflector.

not been broken into droplets at this distance and some droplets areoverlapped in the image. As the radial distance increases, more andmore ligaments break into droplets. Fig. 5(b) illustrates an instanta-neous spray image captured at r¼0.76 m, where the spray is almostcompletely atomized. As shown, individual droplet images could beclearly captured. Based on these experimental observations, theradial distance to the sprinkler deflector was chosen to be 0.76 m.This distance was used to characterize the spray in the near field.

3.1.1. Volume flux

The water volume flux (lpm/m2) in the near field was mea-sured through seven tubes connected to the water containers (seeFig. 2). Fig. 6 presents the water volume flux distribution alongthe elevation angles in the near field at a sprinkler dischargepressure of 3.5 bar and different azimuthal angles. As shown inthe figure, the spray was most dense directly under the sprinklerwith elevation angle of y¼901. Because the spray centerline wasnot exactly at y¼901, the water flux obtained from the tubedirectly under the sprinkler tended to vary as the verticalmeasuring plane was traversed azimuthally. This is illustratedin Fig. 6 that the measurements at f¼731 are lower than others.Near the horizontal plane, another higher flux location appearedat the elevation angle of 151 and azimuthal angle of 1801, where aseparate water jet from the frame arm was observed during themeasurement. As reported previously [3], the discharged watertends to rise up along the frame arms, then broken up intoligaments, and eventually into droplets.

Based on the measured volume fluxes, the water discharged ina sub-sector was calculated by integrating the product of thevolume flux measured at each location and its correspondingspherical surface area bracketed in the sub-sector. Fig. 7 showsthe azimuthal distribution of water flow rate (lpm). It wasassumed that the volume flux measured at a location (i, j)represented the average value over the corresponding sphericalsurface area. At the operating pressures of 3.5 bar and 5.2 bar,Fig. 7 shows that the water flow rate distinctly varied with thedeflector tine and slot locations in the near field, i.e., relativelyhigher rates occurred at the angles corresponding to deflectorslots. Furthermore, the water flow rate at the azimuthal angle of1801 had the highest rate. Therefore, the results indicate that, forthe same nozzle design, the spray formation and distribution isstrongly affected by the geometries of the sprinkler deflector andsprinkler frame arms. By projecting the water discharge ratecalculated in the second quadrant to that of the entire spray,the total water discharge rate at 3.5 bar was estimated to be424 lpm, which is 10% greater than the nominal flow rate of384 lpm calculated from K-factor and pressure. The total volumeflow rate at 5.2 bar was estimated to be 492 lpm, which is 5.4%greater than the nominal flow rate of 467 lpm calculated from K-factor and pressure. These results illustrate the accuracy of thepoint measurement with a collection tube (ID 41-mm).

3.1.2. Droplet size

After the capture of 80 pairs of images at each measuringlocation, statistical results were calculated from the sized dropletsby considering the border correction and the depth-of-fieldcorrection. Fig. 8(a) presents the distributions of volume mediandroplet size along the elevation angle in the near-field at sevenazimuthal angles and a discharge pressure of 3.5 bar. In thesprinkler centerline (y¼901), the equivalent droplet size wasrelatively large because the spray jet was not fully atomized.The other area showing relatively larger droplet sizes appeared atthe elevation angles from 31 to 151. On the other hand, relativelysmall droplets appeared at the elevation angles ranging from 301to 701. At a higher discharge pressure of 5.2 bar, Fig. 8(b) shows

Fig. 5. An instantaneous spray image captured at a radial distance of (a) 0.15-m and (b) 0.76-m from the sprinkler with an elevation angle of 301, an azimuthal angle

of 1071 and a pressure of 3.5 bar.

1

10

100

1000

10000

wat

er v

olum

e flu

x (lp

m/m

2 )

elevation angle (°) from horizontal level

73-deg 90-deg123-deg 140-deg157-deg 180-deg107-deg azimuthal angles

1

10

100

1000

10000

0 20 40 60 80 100

0 20 40 60 80 100

wat

er v

olum

e flu

x (L

pm/m

2 )

elevation angle (°) from horizontal level

73-deg 90-deg107-deg 123-deg140-deg 157-deg180-deg azimuthal angles

Fig. 6. Near-field water volume flux distributions along the elevation angle of the sprinkler operating at (a) 3.5 bar and (b) 5.2 bar.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–4840

0

10

20

30

40

50

60

80 100 120 140 160 180

wat

er fl

ow ra

te (l

pm)

azimuthal angle (°°) from a frame arm

3.5 bar 5.2 bar

Fig. 7. Near-field azimuthal distributions of integrated volume flow rate for the

sprinkler operating at 3.5 bar and 5.2 bar.

0.2

2

drop

let d

iam

eter

dv5

0 (m

m)

elevation angle (°) from horizontal level

73-deg 90-deg107-deg 123-deg140-deg 157-deg180-deg azimuthal angles

0.2

2

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100elevation angle (°) from horizontal level

drop

let d

iam

eter

dv5

0 (m

m)

73-deg 90-deg

107-deg 123-deg

140-deg 157-deg

180-deg azimuthal angles

Fig. 8. Near-field volume median droplet diameter distributions along the eleva-

tion angle of the sprinkler operating at (a) 3.5 bar and (b) 5.2 bar.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

70 90 110 130 150 170 190azimuthal angle(°) from a frame arm

drop

let d

iam

eter

d (m

m)

15-deg 45-degelevation angles

Fig. 9. Near-field azimuthal distributions of volume median droplet diameter at

two elevation angles of 151 and 451 for the sprinkler operating at 3.5 bar.

0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8droplet diameter (mm)

velo

city

mag

nitu

de (m

/s)

Fig. 10. Scatter plot of droplet velocity magnitude versus diameter in the near

field at elevation angle 301 and azimuthal angle 1401 for the sprinkler operating at

3.5 bar.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–48 41

that most of the measured droplet sizes were smaller than thoseof 3.5 bar at the corresponding elevation angles.

Fig. 9 shows the azimuthal droplet size distributions at twoelevation angles in the near field of the sprinkler operating at3.5 bar. At the elevation angle of y¼151, the spray mainly comesfrom the tines and the figure shows that the droplet size variationwith the azimuthal angle is small, except for the region near theframe arm. At y¼451, the spray mainly comes from the slots andthe figure shows that the azimuthal droplet size distributionvaries with the deflector tines and slots.

3.1.3. Droplet velocity

The droplet velocities were measured using a double-pulselaser with a double-frame camera. Fig. 10 shows a scatter plot of

near-field droplet velocity magnitude versus diameter for thesprinkler operating at 3.5 bar, where the elevation angle was 301and the azimuthal angle 1401. The minimum droplet diameterthat could be detected was 0.091 mm. The theoretical liquid jetvelocity from the nozzle was calculated to be 25 m/s. Fig. 10shows that all the droplet velocities were smaller than this valuebecause of the momentum loss during the atomization process.

There was no direct relationship between droplet size andvelocity; however, there was a general trend that larger dropletstended to have a higher velocity magnitude. This is due to the factthat smaller droplets tend to lose momentum faster than thelarger droplets. This velocity-size correlation would also changewith the droplet transport distance from the deflector because ofthe air drag force. When the droplet size was smaller than about0.3 mm, the droplet number density was very high. The smalldroplet volume and low velocity made only a minor contributionto the total spray flux. In the scatter plot, there were a fewdroplets that had small diameters (o0.2 mm) but very highvelocities. These velocities might not be correctly measured.Because the number density of small droplets was high and theirdisplacement was small, the image-processing program hadtrouble distinguishing their movement. As shown in Fig. 10, therewere also some droplets with zero velocity. This is because thepairs of corresponding droplets were not identified in the twoconsecutive shadow images. As a result, the velocity data werenot captured. These droplets with zero velocity were ignored inthe following calculation of average velocity and volume flux.

0

20

40

60

80

100

120

80 100 120 140 160 180

80 100 120 140 160 180

wat

er fl

ux (l

pm/m

2 )

azimuthal angle (°) from a frame arm

shadow-imagingwater collection tubes

0

20

40

60

80

100

120

140

160

wat

er fl

ux (l

pm/m

2 )

azimuthal angle (°) from a frame arm

shadow-imagingwater collection tubes

Fig. 12. Comparison of azimuthal distribution of volume fluxes measured with the

shadow-imaging method and the water collection method at (a) elevation angle

301 and (b) elevation angle 451 for the sprinkler in the near-field with pressure

3.5 bar.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–4842

Because the droplet velocity was related to its size, to presentthe droplet velocity at one measuring location, the averagevelocity magnitude was calculated by weighting the velocity ofeach droplet by its volume density. Based on Eq. (1) for thevolume flux, the average velocity magnitude Uh iwas calculated as

Uh i ¼XN

i ¼ 1

d3i

dof i

ui=XN

i ¼ 1

d3i

dofi

, ð2Þ

where ui is the velocity magnitude of an individual droplet withdiameter di, N is the number of droplets detected at one measur-ing location (ignoring those droplets with zero velocities), and dofi

is a droplet-size-dependent depth-of-field. For each cell on thesurface of a virtual sphere centered at the sprinkler deflector, thelocation of the average velocity vector was assigned at the cellcenter and the direction was assumed to be normally outwardfrom the sphere surface. Fig. 11 shows the azimuthal distributionsof the average droplet velocity magnitude in the near-field of thesprinkler at six elevation angles and for the operating pressure of3.5 bar. In general, the velocity increased with the elevation anglein the sectors farther away from the sprinkler arms. At elevationangles of y¼301 and y¼451, a wavy profile appeared along theazimuthal angle, showing the effect of the deflector tines andslots on the spray pattern. Along the frame arm (f¼1801), thedroplet velocity magnitude at y¼151 was higher than those atother elevation angles, which was attributed to the spray jetobserved along the frame arm mentioned earlier. Similar distri-bution profiles were observed for droplet velocity measurementsunder a higher discharge pressure of 5.2 bar.

3.1.4. Validation of the shadow-imaging system

The volume flux at each measuring location was calculated (Eq.(1)) with the obtained shadow-imaging data on droplet size, velocityand number density. For the sprinkler operating at pressure of3.5 bar, Fig. 12(a) shows a comparison of azimuthal distribution ofvolume fluxes measured, respectively, by the shadow-imagingsystem and the water collection tubes in the near field at theelevation angles of 301, whereas Fig. 12(b) shows a similar compar-ison at y¼451. In general, the results obtained from the shadow-imaging system were in reasonable agreement with those obtainedwith the water collection tubes. Again, the wavy profile shows theeffect of the sprinkler deflector geometry (slot and tine) on theresulting spray pattern. Similar agreements were observed at otherelevation angles. Due to the high droplet concentration in the nearfield, the shadow images of some droplets overlapped. When theshadow images were post-processed, two or more droplets might beidentified as one single droplet, or might be filtered out because thedroplet image was far from circular and deemed not a valid dropletby the software. Therefore, with the possible image rejection in the

0

1

2

3

4

5

6

7

8

9

10

70 80 90 100 110 120 130 140 150 160 170 180azimuthal angle(°) from a frame arm

aver

age

velo

city

mag

nitu

de (m

/s)

3-deg 15-deg 30-deg 45-deg

60-deg 75-deg elevation angles

Fig. 11. Near-field azimuthal distributions of the average droplet velocity magnitude

at six elevation angles for the sprinkler operating at 3.5 bar.

post-processing step, the volume fluxes reported by the shadow-imaging system tended to be lower than those obtained with themechanical collection method. By integrating the volume fluxesmeasured at different locations with their corresponding sphericalsurface areas, the total discharge rate obtained from the imagingsystem was 276 lpm after projecting to the entire spray with theassumption of quadrant symmetry. It was 28% less than the nominalflow rate of 384 lpm calculated from K-factor and discharge pres-sure. The accuracy in the far field was better as discussed in the nextsection.

3.2. Sprinkler spray in the far field

3.2.1. Volume flux

The spray in the far field was measured at two horizontal planes:3.05 m and 4.57 m below the ceiling. Fig. 13 shows the radialdistributions of water volume flux measured at a discharge pressureof 3.5 bar, 3.05 m below the ceiling and seven azimuthal angles. Asshown, along a radius from the spray center, the volume fluxgenerally exhibited a maximum under the sprinkler and decreasedfrom the maximum toward a much smaller value at the spray edge.At the azimuthal angle of 1801, which is in alignment with the framearm, the flux distribution shows a ‘tail’ around the outer edge of thespray (r43 m), where the water flux was relatively higher thanfluxes away from the frame arm. Similar distribution profiles wereobserved for volume flux measurements under other ceiling heightsand discharge pressures.

Fig. 14 shows the azimuthal distributions of the integrated flowrate for two pressures and two ceiling heights. The water flow ratedischarged in a sub-sector was calculated by integrating the product

0

5

10

15

20

25

30

35

40

80 100 120 140 160 180

wat

er fl

ow ra

te (l

pm)

azimuthal angle (°) from a frame arm

3.5 bar, 3.05 m

3.5 bar, 4.57 m

5.2 bar, 3.05 m

5.2 bar, 4.57 m

Fig. 14. Azimuthal distributions of the integrated water flow rate in the far field

(3.05 m and 4.57 m below the ceiling) for the sprinkler operating at 3.5 bar and

5.2 bar.

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

drop

let d

iam

eter

dv5

0 (m

m)

radial location (m) from spray center

73-deg 90-deg 107-deg

123-deg 140-deg 157-deg

180-deg azimuthal angles

Fig. 15. Radial distributions of volume median droplet diameter at 3.05 m below

the ceiling for the sprinkler operating at 3.5 bar.

0

1

2

3

4

5

6

7

8

9

0 0.5 1 1.5 2 2.5 3

aver

age

velo

city

mag

nitu

de (m

/s)

radial distance (m) from spray center

73-deg 90-deg 107-deg

123-deg 140-deg 157-deg

180-deg azimuthal angles

Fig. 16. Radial distributions of average droplet velocity magnitude at 3.05 m

below the ceiling for the sprinkler operating at 3.5 bar.

0.001

0.01

0.1

1

10

100

1000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

wat

er v

olum

e flu

x (lp

m/m

2 )

radial location (m) from spray center

73-deg 90-deg107-deg 123-deg140-deg 157-deg180-deg

Fig. 13. Radial distributions of water volume flux measured at seven azimuthal

angles and 3.05 m below the ceiling for the sprinkler operating at 3.5 bar.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–48 43

of the volume flux measured at each radial location and itscorresponding annular area bracketed in the sub-sector. The wavydistribution in the far field illustrates that the spray distributiondistinctly varied with the deflector tine and slot locations. This resultshows the effect of the geometrical configuration of the sprinklerdeflector on the water spray pattern. By projecting the volume fluxdata measured in the quadrant (azimuthal angles from 901 to 1801)to the entire spray area with the assumption of symmetry, the totalvolume flow rate at 3.5 bar was calculated to be 403 lpm based onthe measurements obtained at 3.05 m below the ceiling, which was5% more than the nominal flow rate of 384 lpm. Based on the waterfluxes measured at 4.57 m below the ceiling, the projected sprinklerdischarge rate was 349 lpm, which was 9% less than the nominalflow rate. For the discharge pressure of 5.2 bar, the total sprinklerdischarge rates were projected to be 452 lpm and 448 lpm at 3.05 mand 4.57 m below the ceiling, respectively, which were about 3% and4% less than the nominal flow rate of 467 lpm.

To check the effect of different sprinkler samples on the spraypattern, the radial distributions of water volume flux at 3.05 m belowthe ceiling were also measured with a different sprinkler sample(same K-factor) operating at a discharge pressure of 5.2 bar. Similardistribution profiles were observed for these two sprinkler samples.

3.2.2. Droplet size

For a 3.05 m location below the ceiling, Fig. 15 shows theradial distributions of volume median droplet diameter at sevenazimuthal angles for the sprinkler operating at 3.5 bar. In general,

the droplet size reached a maximum near the sprinkler centerline,decreased to a minimum at around r¼0.5 m from the center, andthen increased gradually with radial distance toward the outeredge of the spray. As shown, the droplet size varied insignificantlywith the azimuthal angle. Similar distribution characteristicswere observed at other operating conditions.

3.2.3. Droplet velocity

Fig. 16 shows the radial distributions of the average dropletvelocity magnitude at 3.05 m below the ceiling for the sprinkleroperating at 3.5 bar. In general, the droplet velocity reached amaximum near the centerline and then decreased gradually withradial distance toward the outer edge of the spray. However, at theazimuthal angles of 1571 and 1801, the velocity magnitudedecreased to a minimum at around r¼0.5 m from the centerlineand then increased gradually with radial distance. In the region closeto the sprinkler centerline, the droplet velocity varied with theazimuthal angle. When reaching the outer edge of the spray, thedroplet velocity varied insignificantly with the azimuthal angle.

3.2.4. Validation of the shadow-imaging system

Fig. 17 shows a comparison of the radial distributions ofvolume fluxes measured, respectively, using the shadow-imaging and the water collection methods at an operatingpressure of 3.5 bar. The measurements shown in Fig. 17 wereconducted at 3.05 m below the ceiling and at two azimuthalangles of 901 and 1401. The droplets could be identified by theshadow-imaging method with a better accuracy because of therelatively lower droplet concentrations at this location, thus

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

wat

er v

olum

e flu

x (lp

m/m

2 )

radial location (m) from spray center

90-deg, shadow

90-deg, collection

140-deg, shadow

140-deg, collection

Fig. 17. Comparison of volume fluxes measured with the shadow-imaging

method and the water collection method at a pressure of 3.5 bar, 3.05 m below

the ceiling and azimuthal angles of 901 and 1401.

0.99

0.99

9

0.01 0.

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.1

1

10

Cumulative Volume Fraction

Dro

plet

Dia

met

er (m

m)

Fig. 18. Near-field gross droplet size distribution plotted in log-probability

coordinates for the sprinkler operating at 3.5 bar.

0

0.2

0.4

0.6

0.8

1

d/dv50

Cum

ulat

ive

Volu

me

Frac

tion

fitting functionmeasurements

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–4844

resulting in better agreement between the shadow-imaging andthe water collection methods. By integrating the products of thewater fluxes measured at different angles and radial locations andtheir corresponding sub-annular areas, and projecting to theentire spray by assuming quadrant symmetry, the total sprinklerdischarge rate obtained from the shadow-imaging method was390 lpm, about 3.2% less than the rate of 403 lpm obtained fromthe water collection method, and 1.6% more than the nominalflow rate of 384 lpm calculated from K-factor and operatingpressure.

The shadow-imaging method used in the present work isdifferent from the PIV and PDI technique employed by Sheppard.In Sheppard’ work, the flux was determined by counting dropletson a plane laser sheet with assumed constant average dropletdiameters. On the other hand, both the number of droplets andindividual droplet diameters can be measured directly by theshadow-imaging system. Fig. 17 shows that the water fluxesobtained from the shadow-imaging system are reasonably com-pared to those measured with the containers, especially in thefar field.

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5d/dv50

Cum

ulat

ive

Num

ber F

ract

ion

fitting functionmeasurements

Fig. 19. (a) CVF distributions fitted with the log-normal function and measure-

ments, and (b) CNF distributions calculated from the CVF function in the near field

of the sprinkler operating at 3.5 bar.

3.3. Gross droplet size distributions

At the ith azimuthal and jth radial (or jth elevation) position,the cumulative volume fraction (CVF), CVFi,j,k below a droplet size,dk, was obtained with the shadow-imaging measurements. Thegross droplet size distribution, CVFk, for the entire spray was thencalculated as

CVFk ¼

PNI

i ¼ 1

PNJ

j ¼ 1

Ai,j€V i,jCVFi,j,k

PNI

i ¼ 1

PNJ

j ¼ 1

Ai,j€V i,j

, ð3Þ

where NI and NJ are the number of measurement locations in theazimuthal and radial (or elevation) directions, respectively. It wasassumed that the droplet size distribution and volume fluxmeasured at position (i, j) represented the average values overthe entire area of each cell. The volume flux €V i,j was obtainedfrom the water collection method.

For the near-field measurements at a discharge pressure of3.5 bar, Fig. 18 shows the gross droplet size distribution in log-probability coordinates. As shown, the distribution roughly fol-lows a straight line, implying a log-normal distribution. Therefore,the log-normal distribution function was used to express the

gross droplet size distribution as

FðdÞ ¼1ffiffiffiffiffiffi2pp

Z d

d0

1

sd0exp �

ln d0=dv50

� �� �22s2

!dd0, ð4Þ

where F(d) is the CVF of droplets with a diameter less than d, and sis an empirical parameter. Because the minimum droplet sizedetected by the current shadow-imaging system was of 0.091 mm,the low side of the integral, d0, is set to be 0.091 mm. The value of s

0.6

0.8

1

ume

Frac

tion

gross fitting

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–48 45

was determined by iteration to achieve the least sum of the squaresof the errors.

Fig. 19(a) shows the regression of the CVF versus the dropletdiameter normalized by dv50, where the value of s was found tobe 0.784 and the discharge pressure was 3.5 bar. The distributionis reasonably represented by the log-normal function. If theLagrangian approach is used to simulate the droplet transport,the cumulative number fraction (CNF) is needed to describe thedroplet size distribution. This can be determined by differentiat-ing the CVF curve, dividing the derivatives by the cube of thecorresponding droplet diameter, and integrating the results toobtain the CNF. Fig. 19(b) shows the CNF curve calculated fromthe CVF fitting function and results from the measurements. Theagreement is good.

The median drop diameter of a sprinkler spray can beexpressed as a function of the sprinkler orifice diameter andoperating pressure as follows [3]

dv50

Dor¼

C

We1=3, ð5Þ

where Dor is the orifice diameter of the sprinkler, and C is anempirical parameter, which may vary from one type of sprinklerspray to another. The Weber number, the ratio of inertial force tosurface tension force, is given by

We¼rwU2Dor

sw, ð6Þ

where rw is the water density, U is the water discharge velocity,and sw is the water surface tension (sw¼72.8�10�3 N/m at20 1C for clean water). The discharge velocity can be computedfrom the water flow rate, depending on the sprinkler’s operatingpressure, K-Factor and orifice diameter.

For the sprinkler spray measured at different operating pres-sures and locations, Table 1 presents the values of dv50 and s (Eq.(4)) obtained from the least-square regression analysis, and thevalues of the C coefficient (Eq. (5)). The values of the C coefficientwere calculated with an orifice diameter of Dor¼18 mm for thecurrent sprinkler and the median droplet diameters presented inthe same table. Table 1 shows that the median droplet sizes at3.5 bar are larger than those at 5.2 bar. The values of dv50, s and C

at 3.5 bar are comparable in the near and far fields. The relativevariance was 4.3% for dv50, 4.7% for s, and 2% for C. However, at5.2 bar, the value of dv50 in the near field is 19% smaller than thosemeasured in the far field. The reason is not clear and it might bethe measuring error induced by a denser spray in the near field,where the images taken by the shadowgraph contained somelarge droplets far from circular in shape due to the overlapping ofdroplets (see Fig. 5). During post-processing of the image data,these irregular images tended to be excluded by the shadow-imaging system. In the far field, values of s and C are comparablefor the two operating pressures. The average values ares¼0.7570.02 and C¼1.9870.04. Only in the near field at thedischarge pressure of 5.2 bar was the C value lower because of thesmaller dv50 value.

Table 1The gross volume median diameters (dv50), the values of s of the log-normal

function and the values of C for the sprinkler.

Discharge

pressure (bar)

Measuring location dv50 (mm) s C

3.5 Near field (0.76 m radius) 0.617 0.784 1.89

3.5 3.05 m below ceiling 0.645 0.756 1.98

3.5 4.57 m below ceiling 0.630 0.747 1.93

5.2 Near field (0.76 m radius) 0.464 0.760 1.62

5.2 3.05 m below ceiling 0.580 0.765 2.03

5.2 4.57 m below ceiling 0.568 0.710 1.99

3.4. General empirical correlations

The spray distributions of droplet size, volume flux andvelocity measured in the near field of the sprinkler can be usedto prescribe the spray starting condition for the numericalmodeling of spray transport through the fire plume. Along theelevation and azimuthal angles, the measurements show that thespray distributions were non-uniform and were strongly influ-enced by the geometrical composition of the sprinkler structures(i.e., tine, slot, boss and frame arm). At a discharge pressure of3.5 bar and the azimuthal angle of 1401, the CVFs of dropletsversus the non-dimensional diameter are displayed for differentelevation angles in Fig. 20. The plot shows that a single functioncould not closely represent the distributions at different elevationangles. Each elevation angle will, therefore, need to be repre-sented by its own function.

Fig. 21 shows the volume flux distributions along the elevationangle for two operating pressures and four azimuthal angles. Theflux distributions along the elevation angle at different azimuthalangles were different because of the presence of the frame arm.The pressure’s impact on the flux distribution at each azimuthalangle was also different. Fig. 21(a) shows that the flux at f¼1571increased almost linearly with the elevation angle. At f¼1401,there was a relatively high flux region near the deflector planeand this region moved from y¼151 to y¼301 as the dischargepressure increased from 3.5 bar to 5.2 bar. This indicates that thespray angle was reduced. Aligned with the frame arm (f¼1801),Fig. 21(b) shows that the high flux region remained at y¼151 asthe pressure increased. However, at f¼901, the high flux region isenlarged from y¼151 to y¼301 for higher pressure. At theelevation angle of y¼151, the flux increased with pressure forf¼1801; however, the flux decreased with pressure for f¼901.For these complex spray patterns shown in Figs. 20 and 21, aregression method was used to develop empirical correlations forthe pertinent near-field spray measurements in order to prescribethe starting conditions of the sprinkler spray.

The volume flux distribution along the elevation angle at adischarge pressure and an azimuthal angle can be expressed withthe following multiple-term function:

€V ðyÞ ¼ a0þa1exp �y�15

7

� �2" #

þa2exp �y�35

15

� �2" #

þa3exp �y�55

15

� �2" #

þa4exp �y�90

10

� �2" #

, ð7Þ

0

0.2

0.4

0d/dv50

Cum

ulat

ive

Vol

15-deg

30-deg45-deg60-deg75-deg

90-deg

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Fig. 20. A log-normal fitting curve and near-field droplet size distributions at

different elevation angles for the sprinkler operating at 3.5 bar. The distributions

were measured at the azimuthal angle of 1401.

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

volu

me

flux

(lpm

/m2 )

elevation angle (°)

3.5 bar, 157-deg

5.2 bar, 157-deg

3.5 bar, 140-deg

5.2 bar, 140-deg

0

100

200

300

400

500

600

700

800

volu

me

flux

(lpm

/m2 )

elevation angle (°)

3.5 bar, 90-deg

5.2 bar, 90-deg

3.5 bar, 180-deg

5.2 bar, 180-deg

Fig. 21. Near-field water volume flux distributions along the elevation angle for

the sprinkler operating at 3.5 bar and 5.2 bar. The measurements were made at

the azimuthal angles of (a) f¼1571 and f¼1401, and (b) f¼1801 and f¼901.

Table 2Empirical coefficients of the volume flux (lpm/m2) distribution along the elevation

angle for the sprinkler operating at 3.5 bar.

Azimuthal angle

901 1071 1231 1401 1571 1801

a0 0.0 0.0 0.0 0.0 0.0 0.0

a1 179.4 241.7 177.4 115.5 20.7 449.3

a2 54.9 47.3 �1.7 51.7 35.9 18.8

a3 124.5 220.6 59.8 211.9 51.9 39.9

a4 2326 2326 2326 2326 2326 2326

0

500

1000

1500

2000

2500

0 20 40 60 80 100

volu

me

flux

(lpm

/m2 )

elevation angle (°)

measurements

correlation curve

Fig. 22. The correlation curve and water fluxes measured at the azimuthal angle

of f¼901 for the sprinkler operating at 3.5 bar.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 2 4 6 8 10 12 14 16 18droplet velocity magnitude (m/s)

drop

let n

umbe

r fra

ctio

n

Fig. 23. The distribution of the number fraction of droplets within a size interval

(0.1 mm) versus the velocity magnitude measured in the near field with elevation

angle of 301 and azimuthal angle of 1401 for the sprinkler operating at 3.5 bar.

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–4846

where the coefficients ai can be obtained through regressionanalysis with the least-squares method. It is emphasized thatthis function form (Eq. (7)) is not a physics-based function. For thevolume fluxes measured at a discharge pressure of 3.5 bar, Table 2shows the empirical coefficients for different azimuthal angles.

Fig. 22 shows the regression curve and the volume fluxesmeasured at the azimuthal angle of 901. The measurements arewell represented by the empirical correlation. For any azimuthalangle other than the angles given in Table 2, the coefficients canbe obtained through interpolation.

Eq. (7) was also used to correlate with the elevation angle forthe volume median droplet size (dv50), and the parameter s in thelog-normal function for the droplet size distribution. All empiricalcoefficients can be obtained through regression analysis with theleast-squares method. By assuming a symmetrical distribution inadjacent quadrants, the empirical coefficients obtained in thesecond quadrant (azimuthal angles from 901 to 1801) can beapplied to other quadrants.

For all the droplets detected at a measuring location, thevelocity scatter plot of Fig. 10 showed that larger droplets hadhigher velocities. The weighted average velocity of all the dropletsat the same location was calculated by weighting the velocity ofeach droplet with its volume density. However, in order toprescribe the spray starting condition based on the near-fieldmeasurements, correlations need to be developed to relate eachdroplet velocity to its size. Fig. 10 shows that for each droplet sizethe velocity varies in a range with respect to its mean value,where the mean value is simply the arithmetic mean of thevelocities of all the droplets for a particular droplet size. Forinstance, for a sample of droplets collected in a size interval from

0.1 mm to 0.2 mm, Fig. 23 shows the number fraction of dropletsversus their velocity magnitudes, where the droplets were mea-sured in the near-field with an elevation angle of 301 andazimuthal angle of 1401 at a discharge pressure of 3.5 bar. Thefigure shows that the velocity for a particular droplet size wasapproximately normally-distributed. As mentioned above, foreach size interval of Dd, the mean value of the velocity magnitudewas calculated as UðdÞ ¼

PNi ¼ 1 uiðdÞ=N, where UðdÞ is a size-

dependent mean velocity, N is the number of droplets collectedin the size interval of Dd, and ui is the velocity of an individualdroplet within the size interval. The standard deviation of thedroplet velocity magnitude in each size interval was calculated as

X. Zhou et al. / Fire Safety Journal 54 (2012) 36–48 47

ZðdÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN

i ¼ 1 ðui�UÞ2= N�1ð Þ

q. From the data shown in Fig. 23, the

calculated value was U ¼ 4:4 m=s and Z¼ 1:8 m=s.Based on the calculations in each size interval with Dd¼0.1 mm,

Fig. 24 shows the distributions of the mean velocity magnitude andstandard deviation versus droplet diameter at the same measuringcondition as that of Fig. 23. The correlation curve was derived for themean value and is expressed by the following function.

UðdÞ ¼Um½1�0:8 expð�d=dcÞ2�, ð8Þ

where Um¼15 m/s corresponds to the velocity of large droplets, anddc¼0.5 mm is a droplet diameter selected to fit the curve. Theempirical coefficient Um is a variable that changes with the sprinklerat different operating pressures, elevation angles and azimuthalangles. The value of dc¼0.5 mm was assumed for the currentsprinkler and is assumed to be independent of pressure and angle.Fig. 24 shows that the measurements of the mean velocity were wellrepresented by the empirical function.

Fig. 24 shows that the standard deviation varies slightly with thedroplet size. To simplify the empirical correlation, the average valueof Z¼1.7 m/s was assumed for all droplet sizes. This value was alsofound to be applicable to different elevation and azimuthal anglesfor the sprinkler operating at 3.5 bar. A higher value of Z¼2.3 m/swas determined for the operating pressure of 5.2 bar.

At any operating pressures and any azimuthal angles, theempirical coefficient Um in Eq. (8) was expressed as a functionof the elevation angle as

UmðyÞ ¼ a0þa1exp �y�15

10

� �2" #

þa2exp �y�60

40

� �2" #

, ð9Þ

where the coefficients ai can be obtained through regressionanalysis with the least-squares method. At a discharge pressureof 3.5 bar, Table 3 presents the fitted coefficients in Eq. (9) for theparameter Um.

0

2

4

6

8

10

12

14

16

18

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

velo

city

mag

nitu

de (m

/s)

droplet diameter (mm)

mean velocitycorrelation curvestandard deviation

Fig. 24. The mean velocity magnitude and derived correlation curve, and the

standard deviation versus droplet diameter in the near field for the sprinkler

operating at 3.5 bar for an elevation angle of 301 and azimuthal angle of 1401.

Table 3Empirical coefficients of the parameter Um (m/s) distribution along the elevation

angle for the sprinkler operating at 3.5 bar.

Azimuthal angle

901 1071 1231 1401 1571 1801

a0 8.152 9.026 9.344 9.468 9.741 8.011

a1 �0.251 �0.896 0.532 �0.162 �1.063 2.802

a2 8.348 7.546 5.619 6.315 4.102 5.717

All empirical coefficients in the general empirical functions(Eqs. (7)–(9)) were derived for two operating pressures. Theempirical coefficients of each spray parameter for a selectedoperating pressure (p) can be calculated through interpolation.For the droplet size and its distribution parameters, the empiricalcoefficients are linearly interpolated as a function of p�1/3. For thevolume flux and droplet velocity magnitude, the empirical coeffi-cients are linearly interpolated through p1/2. The value of thestandard deviation for the velocity-size correlation is also linearlyinterpolated through p1/2 for a selected pressure.

4. Summary and conclusions

A laser-based shadow-imaging system and pressure-transducer-equipped water collection tubes and containers were used tomeasure the near-field and far-field spray patterns of a pendentfire sprinkler with K-factor of 205 lpm/bar1/2. The volume fluxesreported by the shadow-imaging system were calculated based onthe measurements of droplet size, number density and velocity andcompared with the water collection method. Reasonable agreementbetween the shadow-imaging and water collection methods wasobserved, which improved in the far field where the spray was lessdense and had been fully atomized, and distinct droplet prevailed inthe shadow images.

In the near field, the spray patterns were strongly influenced bythe sprinkler frame arms and the configuration of tines and slots ofthe deflector. The volume flux measurements showed the spray wasmost dense directly under the sprinkler (i.e., y¼901). Near thehorizontal plane, another higher flux location appeared at theelevation angle of 151 and azimuthal angle of 1801 where a separatewater jet from the frame arm was observed. The wave distributionprofiles along the azimuthal angle showed that the water flow ratevaried distinctly with the deflector tine and slot locations, whererelatively higher rates occurred at the angles corresponding todeflector slots. In the spray center (y¼901), because the spray jetwas not fully atomized, the equivalent droplet size was relativelylarge. Other larger droplet sizes appeared at elevation angles from 31to 151. The azimuthal droplet size distributions showed that the sizevariation was small at an elevation angle of 151, but varied with thedeflector tines and slots at an elevation angle of 451. The dropletvelocities measured from the shadow-imaging showed a generaltrend that a larger droplet tends to have a higher velocity.

In the far field, the wavy profiles of the flow rates denoted theeffect of the deflector’s structure on the spray pattern. The dropletsize reached a maximum near the spray center, decreased to aminimum at around 0.5 m from the center, and then increasedgradually with radial distance toward the outer edge of the spray.The droplet size in the far field was approximately constant withthe azimuthal angle. The radial distributions of the dropletvelocity showed that the droplet velocity reached the maximumnear the center and then decreased gradually with the radialdistance toward the outer edge of the spray.

The near-field distributions of the droplet size, water flux anddroplet velocity were correlated with respective multiple-termfunctions. These functions can be used to prescribe the startingspray conditions for numerical simulations of spray transport inthe fire plume. The far-field measurements are useful in evaluat-ing the spray transport calculations.

References

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[2] J.A. Schwille, R.M. Lueptow, The reaction of a fire plume to a droplet spray, FireSaf. J. 41 (2006) 390–398.

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[3] X. Zhou, H.Z. Yu, Experimental investigation of spray formation as affected bysprinkler geometry, Fire Saf. J. 46 (2011) 140–150.

[4] H.Z. Yu, Investigation of spray patterns of selected sprinklers with theFMRC drop size measuring system, Proceedings of the First InternationalSymposium on Fire Safety Science, Hemisphere Publishing Corp., 1986,pp. 1165–1176.

[5] T.S. Chan, Measurements of water density and droplet size distributions ofselected ESFR sprinklers, J. Fire. Prot. Eng. 6 (2) (1994) 79–87.

[6] J.F. Widmann, Phase doppler interferometry measurements in water sprayproduced by residential fire sprinklers, Fire Saf. J. 36 (2001) 545–567.

[7] D.T. Sheppard, Spray Characteristics of Fire Sprinklers, NISTGCR 02-838,National Institute of Standards and Technology, Gaithersburg, MD, 2002.

[8] N. Ren, A.W. Marshall, H. Baum, A comprehensive methodology for character-izing sprinkler sprays, Proc. Combust. Inst. 33 (2) (2011) 2547–2554.

[9] K.S. Kim, S.S. Kim, Drop sizing and depth-of-field correction in TV imaging,Atomization Sprays 4 (1) (1994) 65–78.