Spray characterization measurements of a pendent fire sprinkler

Fire Safety Journal 54 (2012) 36–48

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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

a b s t r a c t

Article history: Received 29 August 2011 Received in revised form 9 February 2012 Accepted 30 July 2012 Available online 30 August 2012

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.

Keywords: Spray measurement Fire sprinkler Shadow-imaging system

1. Introduction Fire sprinkler technology has been the most reliable and effective method for protecting warehouses and factories. A fire sprinkler is designed to deliver water to the burning material to reduce the burning rate, to wet the surrounding combustibles to stop or reduce the flame spread, and to cool the fire products. To achieve the above design objective, the sprinkler spray must have sufficient momentum to penetrate the fire plume in order to reach the burning combustibles, and have sufficient heat absorption capability to lower the temperature of the fire environment. One of the findings that has been quantified by fire sprinkler research is that larger drops are more capable in penetrating the fire plume to reach the burning materials, and smaller drops are more efficient in cooling [1,2]. Effective sprinkler protection requires an optimal drop size distribution for a targeted fire hazard. Numerical modeling of fire protection needs the initial spray characteristics of droplet size, droplet velocity, number density and their spatial distribution as

n

Corresponding author. Tel.: þ1 781 255 4938; fax: þ 1 781 762 9375. E-mail addresses: [email protected], [email protected] (X. Zhou). 0379-7112/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.firesaf.2012.07.007

the starting conditions to calculate the spray transport. However, it is still challenging to predict the spray characteristics because of the complexity and stochastic behavior of the breakup process for actual sprinkler geometrics [3]. Before a complete physicsbased spray formation model is developed and fully validated for fire sprinklers, the initial spray characteristics must be prescribed based on measurements and empirical correlations. Measurements have been performed by Yu [4] to characterize the spray patterns of three upright sprinklers with K-factors ranging from 81 lpm/bar1/2 to 162 lpm/bar1/2 using a laserbased shadowgraph system. Spatial distributions of drop size, velocity and water flux were measured at elevations of 3 m and 6 m below the sprinkler for pressures of 2.7 bar and 3.9 bar. The gross droplet-size distributions of the tested sprinklers were found to be represented by a composite of log-normal and Rosin–Rammler distributions. The same shadowgraph measuring system was also used by Chan [5] to measure the spray patterns of two pendent sprinklers with a K-factor of 205 lpm/bar1/2 at 3.2 m below the ceiling. He also correlated the sprinklers’ gross drop size distributions with the aforementioned composite functions. Using phase doppler interferometry (PDI) and particle image velocimetry (PIV), Widmann [6] measured the droplet size and velocity of residential sprinklers with K-factors ranging from 43 lpm/bar1/2 to 81 lpm/bar1/2. He reaffirmed the previous finding

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

that droplet size varies inversely with 1/3-power of sprinkler operating pressure. Sheppard [7] used the PDI technique to measure the droplet size distribution at a radial distance of 0.38 m from the sprinkler and at a single azimuthal angel almost perpendicular the frame arms. The PIV technique was used to measure the droplet velocities close to the sprinkler. The work showed that the droplet velocity tended to vary more significantly along the elevation angle than along the azimuthal angle. The water flux was calculated by counting droplets in a plane laser sheet and assuming a constant average droplet diameter. The measurements showed that the water flux was strongly dependent on the elevation angle, azimuthal angle, pressure and sprinkler type. Based on the measurements of a uniformlydistributed spray pattern excluding the sprinkler frame’s effect on the spray pattern, Ren et al. [8] developed compact analytical formulations to describe the sprinkler spray. The high order curve-fit polynomials were derived using Fourier series, and the generated spray size distributions agreed reasonably well with the measurements. This paper presents the spray characterization measurements of a pendent warehouse fire sprinkler using a laser-based shadow-imaging system and an array of pressure-transducerequipped water collection tubes and containers, in both the near field and far field of the sprinkler. The shadow-imaging system provided the information on droplet size, velocity and number density in the spray. The water collection tubes and containers provided a separate set of volume flux measurements to compare with the laser-based measurements. The non-uniform spray induced by the sprinkler frame arms and the configuration of tines and slots of the deflector were investigated by performing measurements in a spherical coordinate system at various elevation and azimuthal angles. Empirical correlations were developed for the near-field spray distributions of volume flux, droplet size and droplet velocity under different pressures and spray crosssections. These empirical correlations can be used 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.

2. Experimental setup The laser-based shadow-imaging system was used to visualize droplets from a spray. It is based on the shadowgraph technique with high resolution imaging and pulsed backlight illumination. A collection of droplets occupying a given volume is sampled instantaneously. The measurement volume is defined by the field-of-view area and the depth of field of the imaging system. The light source is a double-cavity-frequency Nd:YAG laser, which provides two light pulses of 532 nm wavelength, each with a pulse energy of about 120 mJ at 15 Hz double-pulse rate. The light source passes through an optical diffuser to provide uniform light intensity at the measuring location. The camera detection system consists of a 14-bit dualframe 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 is possible to ‘‘freeze’’ droplet motions faster than 100 m/s. A doublepulse laser combining with a double-frame camera allows the investigation of size-dependent droplet velocities. This technique is independent of the droplet shape and opacity and allows the measurement of droplet sizes down to 5 mm. The statistical results are calculated from all the detected droplets. By measuring the sizes and velocities of droplets detected in a control volume with sufficient time duration, statistical spray properties can be derived. One of the characteristic droplet diameters describing the statistical spray information is the volume-weighted

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median droplet diameter, dv50, which denotes that 50% of the cumulated droplet volume is from droplets with diameters smaller than dv50. The dv50 provides a picture of the overall droplets present in a control volume. The volume flux (lpm/m2) of droplets can be calculated as: q_ ¼

3 N X 1 pdi ui 6 A  dofi i¼1

ð1Þ

where N is the number of detected droplets in each image, di is the droplet diameter, ui is the droplet velocity, A is the area of the field view of the camera, and dofi is the depth-of-field that depends on the droplet diameter di. Since the droplet size is small in comparison to the field view area, the A value is assumed to be independent of droplet size. The measuring volume is the product of A and dofi. After calibrating the detection system, the physical size of the camera field view was determined to be 22.488  22.488 mm. The pixel number of each digital image was 2048  2048. The minimum droplet size that could be detected was 0.091 mm. The dof for the expected range of droplet diameters was calibrated using circular opaque objects with known diameters (0.1 mm to 2 mm) printed on a transparent sheet. The sheet was mounted on a translation device with a resolution of 1 mm, and then moved along the line-of-sight into and out of the focal plane. Based on the calibration, the depths of field were correlated with droplet diameters as dof i ¼ 34:18di , where dofi and di are in units of millimeter. The uncertainty of the current shadow-imaging system was determined from the aforementioned calibration. For an object of 2.0-mm in diameter, the measured diameter was from 1.793 mm to 2.052 mm when traversing within the corresponding depth of field. The uncertainty was therefore about 10%. For a 1.0-mm diameter object, the uncertainty was about 8%. As described above, the measurement uncertainty depends on the droplet size and the distance between the droplet and the focal plane. Therefore, the border correction and depth-of-field correction [9] were used in the calculation of the statistical results. The accuracy of the sizing system was also examined by comparing the water flux measurements with those obtained with the water collection containers. This will be discussed in the results section later. A maximum of 80 pairs of images could be captured in each continuous measurement before image data had to be transferred to the hard drive. With the 80 pairs of images, the number of detected droplets ranged from zero to thousands, depending on the water flux density at each measuring location. Generally, all else being equal, a larger droplet sample size leads to a higher confidence level in estimating various statistical properties. However, 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 were captured at each location, but the statistical properties were calculated only when the number of detected droplets exceeded 100. A statistical calculation based on Gaussian distribution showed that the sampling error was 10% with 95% confidence when the sampling size was 100. Fig. 1 shows the overall test setup for the sprinkler spray measurement, which consisted of a movable ceiling, a large-scale traverse, and the laser-based shadow-imaging system. The overall dimensions of the Sprinkler Spray Characterization Lab are about 16.8  10.4  9.1 m high. The ceiling was constructed with a 3  3 m aluminum frame and polycarbonate tiles (transparent). The north edge of the ceiling was supported by two steel columns. The ceiling height could 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

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

with a threaded tee at the ceiling center. The pipe was fastened to the ceiling with pipe hangers. The water supply to the sprinkler pipe was provided at both ends with two 50 mm ID flexible hoses. The sprinkler was installed on the threaded tee and was oriented such that the arms were in alignment with the pipe. A pressure tap was installed on the tee to measure the discharge pressure. The traverse system was composed of three main units: one linear track, one platform on the linear track and four curved tracks. Because the system was operating within a wet environment, all components were made of either aluminum or stainless steel to prevent corrosion. The linear track could sweep azimuthally 1201 across the spray. The pivot of the track was located on the floor directly under the sprinkler. Four curved tracks each with a radius of 1.8 m, 3.6 m, 5.5 m or 7.0 m were integrated with connecting I-beams anchored to the floor. The linear track could be rotated azimuthally on the curved tracks with three pairs of wheels mounted beneath the linear track. The orientation of the curved tracks was such that the two extreme azimuthal positions of the linear track were symmetrical to the plane that was normal to the sprinkler pipe and passed through the pivot point. The platform was put on the linear track with two pairs of wheels mounted beneath the platform. The platform could roll on the linear track in the radial direction for a maximum distance of 7.0 m from the pivot point. The movements of the track and the platform were done manually. A 3D high-precision (1 mm resolution) traversing system was mounted on the platform of the large-scale traverse to position the measuring volume of the shadow-imaging system in the sprinkler spray. The 3D traversing system had a local traverse range of 2  2  1 m high and was remotely controlled by software. The computer, the local 3D traverse controller, the laser power supply and the laser head were all protected in environmental enclosures. To characterize the water volume flux distribution near the sprinkler, seven water collection tubes (ID 41 mm) were installed at seven elevation angles with respect to the sprinkler deflector as shown in Fig. 2. The openings of the individual tubes were aligned along a circle centered with the deflector. The distance from the deflector to the tube openings was 0.76 m. Each tube was connected to a pressure-transducer-equipped container for flow rate measurements. Besides the volume flux measurements obtained with the shadow-imaging system, the far-field water

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.

flux distributions were also measured using an array of 15 pressure-transducer-equipped water collection containers. These containers were positioned continuously along a ray on the largescale traverse’s rotating track, starting from directly under the sprinkler, as shown in Fig. 3. The measurements were performed for a pendent fire sprinkler with a K-factor of 205 lpm/bar1/2, for water discharge pressures of 3.5 bar and 5.2 bar. The distance of the ceiling to the sprinkler deflector was 0.4 m. The measurement procedure is described in the following. After the pump started, the water flow control valves were adjusted to reach the desired discharge pressure. After three minutes to allow the water flow to stabilize, the discharge pressure was fine tuned to the desired value. Measurements were conducted in the near field (a spherical surface 0.76 m from the sprinkler deflector), and the far field (two horizontal planes 3.05 m and 4.57 m below the ceiling). In the near field, the laser measuring volume was moved along a spherical coordinate system at various elevation (y) and azimuthal angles (f). The zero-degree azimuthal angle started from one of the sprinkler frame arms. The zero-degree elevation angle was defined at the horizontal level of the deflector. The spherical surface area was divided into 49 cells by seven azimuthal angles and seven elevation angles. Each cell was centered to a location where droplet size, velocity and volume flux measurements were made.

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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 horizontal level. On the spherical surface, the cell area varied with the elevation angle and the minimum was at y ¼901. As mentioned above, the spray in the far field was measured along two horizontal planes. There were 15 measurement locations along the radial direction and seven locations along the azimuthal direction in the 1101 sector. The number of total measurement locations was therefore 105 at each elevation. Each location was also denoted with two indices, i and j. Index i denoted the azimuthal angle and index j denoted the jth radial position from the spray center. For the water volume flux measurements with tubes and containers, water was collected for 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 deflector. The azimuthal angle (f) was designated for each slot from one frame arm where f ¼01. If the sprinkler is symmetrical, the azimuthal distribution in each quadrant is expected to be comparable. Therefore, the azimuthal distribution was measured in the second quadrant in the present investigation. The selected azimuthal locations were 901, 1231 and 1571, corresponding to the deflector tines, and 731, 1071, 1401 and 1801 corresponding to the slots between the tines. In the spray measurement, a dense jet in the spray center and two secondary jets along the direction of each frame arm were observed. These jets were the primary cause for the non-uniform spatial distribution of droplet size and volume flux along the azimuthal angle and elevation angle. It is necessary to choose a proper radial distance from the deflector to conduct measurements in the near field. This is because the spray atomization process currently cannot be directly simulated by numerical modeling. The initial sprinkler spray characteristics must be prescribed based on measurements. Therefore, a proper radial distance should be a location where the spray is fully atomized and the probability of additional breakups would be minimal. To improve the accuracy of the shadowgraph measurement, the droplet number density should be such that the number of overlapped droplet images is sufficiently low as compared to the total number of detected images. Fig. 5(a) illustrates an instantaneous spray image captured at a radial distance of r¼0.15 m from the sprinkler deflector. There are many spray ligaments that have

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

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not been broken into droplets at this distance and some droplets are overlapped in the image. As the radial distance increases, more and more ligaments break into droplets. Fig. 5(b) illustrates an instantaneous spray image captured at r¼0.76 m, where the spray is almost completely atomized. As shown, individual droplet images could be clearly captured. Based on these experimental observations, the radial 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 measured through seven tubes connected to the water containers (see Fig. 2). Fig. 6 presents the water volume flux distribution along the elevation angles in the near field at a sprinkler discharge pressure of 3.5 bar and different azimuthal angles. As shown in the figure, the spray was most dense directly under the sprinkler with elevation angle of y ¼901. Because the spray centerline was not exactly at y ¼901, the water flux obtained from the tube directly under the sprinkler tended to vary as the vertical measuring plane was traversed azimuthally. This is illustrated in Fig. 6 that the measurements at f ¼731 are lower than others. Near the horizontal plane, another higher flux location appeared at the elevation angle of 151 and azimuthal angle of 1801, where a separate water jet from the frame arm was observed during the measurement. As reported previously [3], the discharged water tends to rise up along the frame arms, then broken up into ligaments, and eventually into droplets. Based on the measured volume fluxes, the water discharged in a sub-sector was calculated by integrating the product of the volume flux measured at each location and its corresponding spherical surface area bracketed in the sub-sector. Fig. 7 shows the azimuthal distribution of water flow rate (lpm). It was assumed that the volume flux measured at a location (i, j) represented the average value over the corresponding spherical surface area. At the operating pressures of 3.5 bar and 5.2 bar, Fig. 7 shows that the water flow rate distinctly varied with the deflector tine and slot locations in the near field, i.e., relatively higher rates occurred at the angles corresponding to deflector slots. Furthermore, the water flow rate at the azimuthal angle of 1801 had the highest rate. Therefore, the results indicate that, for the same nozzle design, the spray formation and distribution is strongly affected by the geometries of the sprinkler deflector and sprinkler frame arms. By projecting the water discharge rate calculated in the second quadrant to that of the entire spray, the total water discharge rate at 3.5 bar was estimated to be 424 lpm, which is 10% greater than the nominal flow rate of 384 lpm calculated from K-factor and pressure. The total volume flow 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 Kfactor and pressure. These results illustrate the accuracy of the point measurement with a collection tube (ID 41-mm). 3.1.2. Droplet size After the capture of 80 pairs of images at each measuring location, statistical results were calculated from the sized droplets by considering the border correction and the depth-of-field correction. Fig. 8(a) presents the distributions of volume median droplet size along the elevation angle in the near-field at seven azimuthal angles and a discharge pressure of 3.5 bar. In the sprinkler centerline (y ¼901), the equivalent droplet size was relatively large because the spray jet was not fully atomized. The other area showing relatively larger droplet sizes appeared at the elevation angles from 31 to 151. On the other hand, relatively small droplets appeared at the elevation angles ranging from 301 to 701. At a higher discharge pressure of 5.2 bar, Fig. 8(b) shows

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

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.

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

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that most of the measured droplet sizes were smaller than those of 3.5 bar at the corresponding elevation angles. Fig. 9 shows the azimuthal droplet size distributions at two elevation angles in the near field of the sprinkler operating at 3.5 bar. At the elevation angle of y ¼151, the spray mainly comes from the tines and the figure shows that the droplet size variation with the azimuthal angle is small, except for the region near the frame arm. At y ¼451, the spray mainly comes from the slots and the figure shows that the azimuthal droplet size distribution varies with the deflector tines and slots.

3.1.3. Droplet velocity The droplet velocities were measured using a double-pulse laser with a double-frame camera. Fig. 10 shows a scatter plot of

near-field droplet velocity magnitude versus diameter for the sprinkler operating at 3.5 bar, where the elevation angle was 301 and the azimuthal angle 1401. The minimum droplet diameter that could be detected was 0.091 mm. The theoretical liquid jet velocity from the nozzle was calculated to be 25 m/s. Fig. 10 shows that all the droplet velocities were smaller than this value because of the momentum loss during the atomization process. There was no direct relationship between droplet size and velocity; however, there was a general trend that larger droplets tended to have a higher velocity magnitude. This is due to the fact that smaller droplets tend to lose momentum faster than the larger droplets. This velocity-size correlation would also change with the droplet transport distance from the deflector because of the air drag force. When the droplet size was smaller than about 0.3 mm, the droplet number density was very high. The small droplet volume and low velocity made only a minor contribution to the total spray flux. In the scatter plot, there were a few droplets that had small diameters ( o0.2 mm) but very high velocities. These velocities might not be correctly measured. Because the number density of small droplets was high and their displacement was small, the image-processing program had trouble distinguishing their movement. As shown in Fig. 10, there were also some droplets with zero velocity. This is because the pairs of corresponding droplets were not identified in the two consecutive shadow images. As a result, the velocity data were not captured. These droplets with zero velocity were ignored in the following calculation of average velocity and volume flux.

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

3 3 N N X X di di hU i ¼ ui = , dof dof i i i¼1 i¼1

ð2Þ

where ui is the velocity magnitude of an individual droplet with diameter di, N is the number of droplets detected at one measuring location (ignoring those droplets with zero velocities), and dofi is a droplet-size-dependent depth-of-field. For each cell on the surface of a virtual sphere centered at the sprinkler deflector, the location of the average velocity vector was assigned at the cell center and the direction was assumed to be normally outward from the sphere surface. Fig. 11 shows the azimuthal distributions of the average droplet velocity magnitude in the near-field of the sprinkler at six elevation angles and for the operating pressure of 3.5 bar. In general, the velocity increased with the elevation angle in the sectors farther away from the sprinkler arms. At elevation angles of y ¼301 and y ¼451, a wavy profile appeared along the azimuthal angle, showing the effect of the deflector tines and slots on the spray pattern. Along the frame arm (f ¼1801), the droplet velocity magnitude at y ¼151 was higher than those at other elevation angles, which was attributed to the spray jet observed along the frame arm mentioned earlier. Similar distribution profiles were observed for droplet velocity measurements under a higher discharge pressure of 5.2 bar.

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Because the droplet velocity was related to its size, to present the droplet velocity at one measuring location, the average velocity magnitude was calculated by weighting the velocity of each droplet by its volume density. Based on Eq. (1) for the volume flux, the average velocity magnitude hU i was calculated as

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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, velocity and number density. For the sprinkler operating at pressure of 3.5 bar, Fig. 12(a) shows a comparison of azimuthal distribution of volume fluxes measured, respectively, by the shadow-imaging system and the water collection tubes in the near field at the elevation angles of 301, whereas Fig. 12(b) shows a similar comparison at y ¼451. In general, the results obtained from the shadowimaging system were in reasonable agreement with those obtained with the water collection tubes. Again, the wavy profile shows the effect of the sprinkler deflector geometry (slot and tine) on the resulting spray pattern. Similar agreements were observed at other elevation angles. Due to the high droplet concentration in the near field, the shadow images of some droplets overlapped. When the shadow images were post-processed, two or more droplets might be identified as one single droplet, or might be filtered out because the droplet image was far from circular and deemed not a valid droplet by the software. Therefore, with the possible image rejection in the

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azimuthal angle (°) from a frame arm 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.

post-processing step, the volume fluxes reported by the shadowimaging system tended to be lower than those obtained with the mechanical collection method. By integrating the volume fluxes measured at different locations with their corresponding spherical surface areas, the total discharge rate obtained from the imaging system was 276 lpm after projecting to the entire spray with the assumption of quadrant symmetry. It was 28% less than the nominal flow rate of 384 lpm calculated from K-factor and discharge pressure. The accuracy in the far field was better as discussed in the next section. 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 radial distributions of water volume flux measured at a discharge pressure of 3.5 bar, 3.05 m below the ceiling and seven azimuthal angles. As shown, along a radius from the spray center, the volume flux generally exhibited a maximum under the sprinkler and decreased from the maximum toward a much smaller value at the spray edge. At the azimuthal angle of 1801, which is in alignment with the frame arm, the flux distribution shows a ‘tail’ around the outer edge of the spray (r43 m), where the water flux was relatively higher than fluxes away from the frame arm. Similar distribution profiles were observed for volume flux measurements under other ceiling heights and discharge pressures. Fig. 14 shows the azimuthal distributions of the integrated flow rate for two pressures and two ceiling heights. The water flow rate discharged in a sub-sector was calculated by integrating the product

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

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Fig. 15. Radial distributions of volume median droplet diameter at 3.05 m below the ceiling for the sprinkler operating at 3.5 bar.

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3

radial distance (m) from spray center

azimuthal angle (°) from a frame arm 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.

of the volume flux measured at each radial location and its corresponding annular area bracketed in the sub-sector. The wavy distribution in the far field illustrates that the spray distribution distinctly varied with the deflector tine and slot locations. This result shows the effect of the geometrical configuration of the sprinkler deflector on the water spray pattern. By projecting the volume flux data measured in the quadrant (azimuthal angles from 901 to 1801) to the entire spray area with the assumption of symmetry, the total volume flow rate at 3.5 bar was calculated to be 403 lpm based on the measurements obtained at 3.05 m below the ceiling, which was 5% more than the nominal flow rate of 384 lpm. Based on the water fluxes measured at 4.57 m below the ceiling, the projected sprinkler discharge rate was 349 lpm, which was 9% less than the nominal flow rate. For the discharge pressure of 5.2 bar, the total sprinkler discharge rates were projected to be 452 lpm and 448 lpm at 3.05 m and 4.57 m below the ceiling, respectively, which were about 3% and 4% less than the nominal flow rate of 467 lpm. To check the effect of different sprinkler samples on the spray pattern, the radial distributions of water volume flux at 3.05 m below the ceiling were also measured with a different sprinkler sample (same K-factor) operating at a discharge pressure of 5.2 bar. Similar distribution 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 the radial distributions of volume median droplet diameter at seven azimuthal angles for the sprinkler operating at 3.5 bar. In general,

Fig. 16. Radial distributions of average droplet velocity magnitude at 3.05 m below the ceiling for the sprinkler operating at 3.5 bar.

the droplet size reached a maximum near the sprinkler centerline, decreased to a minimum at around r ¼0.5 m from the center, and then increased gradually with radial distance toward the outer edge of the spray. As shown, the droplet size varied insignificantly with the azimuthal angle. Similar distribution characteristics were observed at other operating conditions. 3.2.3. Droplet velocity Fig. 16 shows the radial distributions of the average droplet velocity magnitude at 3.05 m below the ceiling for the sprinkler operating at 3.5 bar. In general, the droplet velocity reached a maximum near the centerline and then decreased gradually with radial distance toward the outer edge of the spray. However, at the azimuthal angles of 1571 and 1801, the velocity magnitude decreased to a minimum at around r¼0.5 m from the centerline and then increased gradually with radial distance. In the region close to the sprinkler centerline, the droplet velocity varied with the azimuthal angle. When reaching the outer edge of the spray, the droplet 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 of volume fluxes measured, respectively, using the shadowimaging and the water collection methods at an operating pressure of 3.5 bar. The measurements shown in Fig. 17 were conducted at 3.05 m below the ceiling and at two azimuthal angles of 901 and 1401. The droplets could be identified by the shadow-imaging method with a better accuracy because of the relatively lower droplet concentrations at this location, thus

44

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

10

90-deg, shadow

200

90-deg, collection

Droplet Diameter (mm)

140-deg, shadow

150

140-deg, collection

100

1

3.5

4

4.5

radial location (m) from spray center

Cumulative Volume Fraction

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. The gross droplet size distribution, CVFk, for the entire spray was then calculated as

CVF k ¼

Ai,j V€ i,j CVF i,j,k

i¼1j¼1 NJ NI P P

1 Cumulative Volume Fraction

resulting in better agreement between the shadow-imaging and the water collection methods. By integrating the products of the water fluxes measured at different angles and radial locations and their corresponding sub-annular areas, and projecting to the entire spray by assuming quadrant symmetry, the total sprinkler discharge rate obtained from the shadow-imaging method was 390 lpm, about 3.2% less than the rate of 403 lpm obtained from the water collection method, and 1.6% more than the nominal flow rate of 384 lpm calculated from K-factor and operating pressure. The shadow-imaging method used in the present work is different from the PIV and PDI technique employed by Sheppard. In Sheppard’ work, the flux was determined by counting droplets on a plane laser sheet with assumed constant average droplet diameters. On the other hand, both the number of droplets and individual droplet diameters can be measured directly by the shadow-imaging system. Fig. 17 shows that the water fluxes obtained from the shadow-imaging system are reasonably compared to those measured with the containers, especially in the far field.

Fig. 18. Near-field gross droplet size distribution plotted in log-probability coordinates for the sprinkler operating at 3.5 bar.

0.8

0.6

fitting function measurements

0.4

0.2

0 0

1

0.5

1.5

2

2.5 d/dv50

3

3.5

4

4.5

5

1 Cumulative Number Fraction

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.

NJ NI P P

0.999

3

0.99

2.5

0.9

2

0.8

1.5

0.7

1

0.4 0.5 0.6

0.5

0.3

0

0.2

0.1

0

0.1

50

0.01

water volume flux (lpm/m2)

250

0.8

0.6

fitting function measurements

0.4

0.2

0 0

,

1

0.5

ð3Þ

Ai,j V€ i,j

i¼1j¼1

where NI and NJ are the number of measurement locations in the azimuthal and radial (or elevation) directions, respectively. It was assumed that the droplet size distribution and volume flux measured at position (i, j) represented the average values over the entire area of each cell. The volume flux V€ i,j was obtained from the water collection method. For the near-field measurements at a discharge pressure of 3.5 bar, Fig. 18 shows the gross droplet size distribution in logprobability coordinates. As shown, the distribution roughly follows a straight line, implying a log-normal distribution. Therefore, the log-normal distribution function was used to express the

1.5

2

2.5 d/dv50

3

3.5

4

4.5

5

Fig. 19. (a) CVF distributions fitted with the log-normal function and measurements, and (b) CNF distributions calculated from the CVF function in the near field of the sprinkler operating at 3.5 bar.

gross droplet size distribution as 1 FðdÞ ¼ pffiffiffiffiffiffi 2p

Z

d

d0

  0 2 ! ln d =dv50 1 0 exp  dd , 2s2 sd0

ð4Þ

where F(d) is the CVF of droplets with a diameter less than d, and s is an empirical parameter. Because the minimum droplet size detected 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

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

dv50 C ¼ , Dor We1=3

ð5Þ

where Dor is the orifice diameter of the sprinkler, and C is an empirical parameter, which may vary from one type of sprinkler spray to another. The Weber number, the ratio of inertial force to surface tension force, is given by We ¼

rw U 2 Dor , sw

ð6Þ

where rw is the water density, U is the water discharge velocity, and sw is the water surface tension (sw ¼72.8  10  3 N/m at 20 1C for clean water). The discharge velocity can be computed from the water flow rate, depending on the sprinkler’s operating pressure, K-Factor and orifice diameter. For the sprinkler spray measured at different operating pressures and locations, Table 1 presents the values of dv50 and s (Eq. (4)) obtained from the least-square regression analysis, and the values of the C coefficient (Eq. (5)). The values of the C coefficient were calculated with an orifice diameter of Dor ¼ 18 mm for the current sprinkler and the median droplet diameters presented in the same table. Table 1 shows that the median droplet sizes at 3.5 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 relative variance was 4.3% for dv50, 4.7% for s, and 2% for C. However, at 5.2 bar, the value of dv50 in the near field is 19% smaller than those measured in the far field. The reason is not clear and it might be the measuring error induced by a denser spray in the near field, where the images taken by the shadowgraph contained some large droplets far from circular in shape due to the overlapping of droplets (see Fig. 5). During post-processing of the image data, these irregular images tended to be excluded by the shadowimaging system. In the far field, values of s and C are comparable for the two operating pressures. The average values are s ¼0.7570.02 and C¼1.98 70.04. Only in the near field at the discharge pressure of 5.2 bar was the C value lower because of the smaller dv50 value. Table 1 The 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) 3.5 3.5 3.5 5.2 5.2 5.2

Measuring location

dv50 (mm)

s

C

3.4. General empirical correlations The spray distributions of droplet size, volume flux and velocity measured in the near field of the sprinkler can be used to prescribe the spray starting condition for the numerical modeling of spray transport through the fire plume. Along the elevation and azimuthal angles, the measurements show that the spray distributions were non-uniform and were strongly influenced by the geometrical composition of the sprinkler structures (i.e., tine, slot, boss and frame arm). At a discharge pressure of 3.5 bar and the azimuthal angle of 1401, the CVFs of droplets versus the non-dimensional diameter are displayed for different elevation angles in Fig. 20. The plot shows that a single function could not closely represent the distributions at different elevation angles. Each elevation angle will, therefore, need to be represented by its own function. Fig. 21 shows the volume flux distributions along the elevation angle for two operating pressures and four azimuthal angles. The flux distributions along the elevation angle at different azimuthal angles were different because of the presence of the frame arm. The pressure’s impact on the flux distribution at each azimuthal angle was also different. Fig. 21(a) shows that the flux at f ¼1571 increased almost linearly with the elevation angle. At f ¼1401, there was a relatively high flux region near the deflector plane and this region moved from y ¼151 to y ¼301 as the discharge pressure increased from 3.5 bar to 5.2 bar. This indicates that the spray angle was reduced. Aligned with the frame arm (f ¼1801), Fig. 21(b) shows that the high flux region remained at y ¼151 as the pressure increased. However, at f ¼901, the high flux region is enlarged from y ¼151 to y ¼301 for higher pressure. At the elevation angle of y ¼151, the flux increased with pressure for f ¼1801; however, the flux decreased with pressure for f ¼901. For these complex spray patterns shown in Figs. 20 and 21, a regression method was used to develop empirical correlations for the pertinent near-field spray measurements in order to prescribe the starting conditions of the sprinkler spray. The volume flux distribution along the elevation angle at a discharge pressure and an azimuthal angle can be expressed with the following multiple-term function: "  "   #  # y15 2 y35 2 V€ ðyÞ ¼ a0 þ a1 exp  þ a2 exp  7 15 "  "   #  # y55 2 y90 2 þ a3 exp  þ a4 exp  , 15 10

ð7Þ

1 Cumulative Volume Fraction

was determined by iteration to achieve the least sum of the squares of the errors. Fig. 19(a) shows the regression of the CVF versus the droplet diameter normalized by dv50, where the value of s was found to be 0.784 and the discharge pressure was 3.5 bar. The distribution is reasonably represented by the log-normal function. If the Lagrangian approach is used to simulate the droplet transport, the cumulative number fraction (CNF) is needed to describe the droplet size distribution. This can be determined by differentiating the CVF curve, dividing the derivatives by the cube of the corresponding droplet diameter, and integrating the results to obtain the CNF. Fig. 19(b) shows the CNF curve calculated from the CVF fitting function and results from the measurements. The agreement is good. The median drop diameter of a sprinkler spray can be expressed as a function of the sprinkler orifice diameter and operating pressure as follows [3]

45

0.8

0.6

gross fitting 15-deg 30-deg

0.4

45-deg 60-deg

0.2

75-deg 90-deg

Near field (0.76 m radius) 3.05 m below ceiling 4.57 m below ceiling Near field (0.76 m radius) 3.05 m below ceiling 4.57 m below ceiling

0.617 0.645 0.630 0.464 0.580 0.568

0.784 0.756 0.747 0.760 0.765 0.710

1.89 1.98 1.93 1.62 2.03 1.99

0

0

0.5

1

1.5

2

2.5 d/dv50

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.

46

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

Table 2 Empirical coefficients of the volume flux (lpm/m2) distribution along the elevation angle for the sprinkler operating at 3.5 bar.

350 3.5 bar, 157-deg

volume flux (lpm/m2)

300

5.2 bar, 157-deg

250

Azimuthal angle

3.5 bar, 140-deg

200

901

1071

1231

1401

1571

1801

0.0 241.7 47.3 220.6 2326

0.0 177.4  1.7 59.8 2326

0.0 115.5 51.7 211.9 2326

0.0 20.7 35.9 51.9 2326

0.0 449.3 18.8 39.9 2326

5.2 bar, 140-deg 0.0 179.4 54.9 124.5 2326

a0 a1 a2 a3 a4

150 100 50 0 0

10

20

30

40

50

60

70

80

2500

elevation angle (°)

measurements 3.5 bar, 90-deg

700 volume flux (lpm/m2)

volume flux (lpm/m2)

800

5.2 bar, 90-deg

600

3.5 bar, 180-deg

500

5.2 bar, 180-deg

400 300

2000

correlation curve

1500

1000

500

200

0

100

0

0 0

10

20

30

40

50

60

70

20

elevation angle (°) 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) f ¼1571 and f ¼1401, and (b) f ¼ 1801 and f ¼901.

40

60

80

100

elevation angle (°)

80

Fig. 22. The correlation curve and water fluxes measured at the azimuthal angle of f ¼901 for the sprinkler operating at 3.5 bar.

0.35

where the coefficients ai can be obtained through regression analysis with the least-squares method. It is emphasized that this function form (Eq. (7)) is not a physics-based function. For the volume fluxes measured at a discharge pressure of 3.5 bar, Table 2 shows the empirical coefficients for different azimuthal angles. Fig. 22 shows the regression curve and the volume fluxes measured at the azimuthal angle of 901. The measurements are well represented by the empirical correlation. For any azimuthal angle other than the angles given in Table 2, the coefficients can be obtained through interpolation. Eq. (7) was also used to correlate with the elevation angle for the volume median droplet size (dv50), and the parameter s in the log-normal function for the droplet size distribution. All empirical coefficients can be obtained through regression analysis with the least-squares method. By assuming a symmetrical distribution in adjacent quadrants, the empirical coefficients obtained in the second quadrant (azimuthal angles from 901 to 1801) can be applied to other quadrants. For all the droplets detected at a measuring location, the velocity scatter plot of Fig. 10 showed that larger droplets had higher velocities. The weighted average velocity of all the droplets at the same location was calculated by weighting the velocity of each droplet with its volume density. However, in order to prescribe the spray starting condition based on the near-field measurements, correlations need to be developed to relate each droplet velocity to its size. Fig. 10 shows that for each droplet size the velocity varies in a range with respect to its mean value, where the mean value is simply the arithmetic mean of the velocities of all the droplets for a particular droplet size. For instance, for a sample of droplets collected in a size interval from

droplet number fraction

0.3 0.25 0.2 0.15 0.1 0.05 0 0

2

4

6 8 10 12 droplet velocity magnitude (m/s)

14

16

18

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.

0.1 mm to 0.2 mm, Fig. 23 shows the number fraction of droplets versus their velocity magnitudes, where the droplets were measured in the near-field with an elevation angle of 301 and azimuthal angle of 1401 at a discharge pressure of 3.5 bar. The figure shows that the velocity for a particular droplet size was approximately normally-distributed. As mentioned above, for each size interval of Dd, the mean value of the velocity magnitude P was calculated as UðdÞ ¼ N i ¼ 1 ui ðdÞ=N, where UðdÞ is a sizedependent mean velocity, N is the number of droplets collected in the size interval of Dd, and ui is the velocity of an individual droplet within the size interval. The standard deviation of the droplet velocity magnitude in each size interval was calculated as

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

ZðdÞ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i ¼ 1 ðui UÞ =ðN1Þ. From the data shown in Fig. 23, the

calculated value was U ¼ 4:4 m=s and Z ¼ 1:8 m=s. Based on the calculations in each size interval with Dd¼ 0.1 mm, Fig. 24 shows the distributions of the mean velocity magnitude and standard deviation versus droplet diameter at the same measuring condition as that of Fig. 23. The correlation curve was derived for the mean value and is expressed by the following function. UðdÞ ¼ U m ½10:8 expðd=dc Þ2 ,

ð8Þ

where Um ¼15 m/s corresponds to the velocity of large droplets, and dc ¼0.5 mm is a droplet diameter selected to fit the curve. The empirical coefficient Um is a variable that changes with the sprinkler at different operating pressures, elevation angles and azimuthal angles. The value of dc ¼0.5 mm was assumed for the current sprinkler and is assumed to be independent of pressure and angle. Fig. 24 shows that the measurements of the mean velocity were well represented by the empirical function. Fig. 24 shows that the standard deviation varies slightly with the droplet size. To simplify the empirical correlation, the average value of Z ¼ 1.7 m/s was assumed for all droplet sizes. This value was also found to be applicable to different elevation and azimuthal angles for the sprinkler operating at 3.5 bar. A higher value of Z ¼2.3 m/s was determined for the operating pressure of 5.2 bar. At any operating pressures and any azimuthal angles, the empirical coefficient Um in Eq. (8) was expressed as a function of the elevation angle as "  "   #  # y15 2 y60 2 U m ðyÞ ¼ a0 þ a1 exp  þ a2 exp  , ð9Þ 10 40 where the coefficients ai can be obtained through regression analysis with the least-squares method. At a discharge pressure of 3.5 bar, Table 3 presents the fitted coefficients in Eq. (9) for the parameter Um.

18

velocity magnitude (m/s)

16 14 12 10

mean velocity correlation curve

8

standard deviation

6 4 2 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

droplet diameter (mm) 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 3 Empirical coefficients of the parameter Um (m/s) distribution along the elevation angle for the sprinkler operating at 3.5 bar. Azimuthal angle 901 a0 a1 a2

8.152  0.251 8.348

1071 9.026  0.896 7.546

47

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

4. Summary and conclusions A laser-based shadow-imaging system and pressure-transducerequipped water collection tubes and containers were used to measure the near-field and far-field spray patterns of a pendent fire sprinkler with K-factor of 205 lpm/bar1/2. The volume fluxes reported by the shadow-imaging system were calculated based on the measurements of droplet size, number density and velocity and compared with the water collection method. Reasonable agreement between the shadow-imaging and water collection methods was observed, which improved in the far field where the spray was less dense and had been fully atomized, and distinct droplet prevailed in the shadow images. In the near field, the spray patterns were strongly influenced by the sprinkler frame arms and the configuration of tines and slots of the deflector. The volume flux measurements showed the spray was most dense directly under the sprinkler (i.e., y ¼901). Near the horizontal plane, another higher flux location appeared at the elevation angle of 151 and azimuthal angle of 1801 where a separate water jet from the frame arm was observed. The wave distribution profiles along the azimuthal angle showed that the water flow rate varied distinctly with the deflector tine and slot locations, where relatively higher rates occurred at the angles corresponding to deflector slots. In the spray center (y ¼901), because the spray jet was not fully atomized, the equivalent droplet size was relatively large. Other larger droplet sizes appeared at elevation angles from 31 to 151. The azimuthal droplet size distributions showed that the size variation was small at an elevation angle of 151, but varied with the deflector tines and slots at an elevation angle of 451. The droplet velocities measured from the shadow-imaging showed a general trend that a larger droplet tends to have a higher velocity. In the far field, the wavy profiles of the flow rates denoted the effect of the deflector’s structure on the spray pattern. The droplet size reached a maximum near the spray center, decreased to a minimum at around 0.5 m from the center, and then increased gradually with radial distance toward the outer edge of the spray. The droplet size in the far field was approximately constant with the azimuthal angle. The radial distributions of the droplet velocity showed that the droplet velocity reached the maximum near the center and then decreased gradually with the radial distance toward the outer edge of the spray. The near-field distributions of the droplet size, water flux and droplet velocity were correlated with respective multiple-term functions. These functions can be used to prescribe the starting spray conditions for numerical simulations of spray transport in the fire plume. The far-field measurements are useful in evaluating the spray transport calculations. References

1231 9.344 0.532 5.619

1401 9.468  0.162 6.315

1571 9.741  1.063 4.102

1801 8.011 2.802 5.717

[1] C. Yao, Extinguishing role of water sprinklers, Proceedings of Engineering Applications of Fire Technology Workshop, April 16–18, 1980, National Bureau of Standards, Gaithersburg, MD, pp. 51–88. [2] J.A. Schwille, R.M. Lueptow, The reaction of a fire plume to a droplet spray, Fire Saf. J. 41 (2006) 390–398.

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[3] X. Zhou, H.Z. Yu, Experimental investigation of spray formation as affected by sprinkler geometry, Fire Saf. J. 46 (2011) 140–150. [4] H.Z. Yu, Investigation of spray patterns of selected sprinklers with the FMRC drop size measuring system, Proceedings of the First International Symposium on Fire Safety Science, Hemisphere Publishing Corp., 1986, pp. 1165–1176. [5] T.S. Chan, Measurements of water density and droplet size distributions of selected ESFR sprinklers, J. Fire. Prot. Eng. 6 (2) (1994) 79–87.

[6] J.F. Widmann, Phase doppler interferometry measurements in water spray produced 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 characterizing 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.