In the event of a fire in a factory building, there are concerns over the rapid spread of the fire to adjacent buildings in industrial complexes because of a concentration of factories and insufficient separation distances. This leads to the risk of large-scale fires. According to the fire statistics yearbook from the National Fire Agency, factory and warehouse fires have continuously occurred over the last five years (3,804 cases in 2019, 3,722 cases in 2020, 3,717 cases in 2021, 3,768 cases in 2022, and 3,350 cases in 2023), with the average annual damage from these fires representing approximately 53.5% of the total damage from all fire types [1]. The continued occurrence and increased scale of factory fires have required preventive measures, but the current standards [2-4] have no clear criterion for preventing fire spread in factory buildings, which limits the practical application of equipment.

Water curtain systems spray water in front of a target object using nozzles. They can inhibit fire spread by blocking thermal radiation through droplet absorption and scattering [5] and by cooling the surface of the fuel and target object [6]. Studies have been conducted on the prevention of fire spread using water curtain systems [7-11]. Murrell et al. [7] formed water mist curtains between a radiative heat source and heat flux sensor using four types of nozzles, and experimentally analyzed the correlations among the water flow rate, droplet size, droplet velocity, and thermal radiation attenuation rate according to the injection pressure. The thermal radiation attenuation rate ranged from 2.8% to 35.5% depending on the nozzle and pressure conditions. Buchlin [8] evaluated the fire spread prevention performances of water curtains by thermal radiation attenuation using theories and experiments. For vertical curtains, the thermal radiation attenuation rate ranged from 50% to 75%. In the case of impinging water curtains, the rate increased to a maximum of 90% as a result of the liquid film formed on the wall. They mentioned the importance of nozzle installation conditions, such as the distance between the wall and nozzles and overlapping sprays, to achieve such a performance. Choi and Cho [9] presented guidelines for installing water curtain systems to inhibit fire spread by flames and thermal radiation in densely packed environments with limited firefighting activities, such as traditional markets. They reported that the thermal radiation attenuation rate was affected by the droplet size, nozzle installation height, and flow rate, and proposed guidelines for nozzle installation procedures considering the correlations among the number of nozzles, droplet size, and thermal radiation attenuation rate, as well as overlapping sprays. Park et al. [10] experimentally analyzed the correlations among the water flow rate, pressure, and Sauter mean diameter (SMD) by varying the hydraulic diameter of the water curtain nozzle. They found that the SMD tended to decrease as the water supply pressure increased, and proposed a predictive equation for the droplet size. Kwon et al. [11] experimentally evaluated the thermal radiation reduction and core body temperature in sandwich panels according to the nozzle type and nozzle spacing of water curtain systems under factory-fire simulation conditions to verify the effectiveness of the systems. They reported that a water spray nozzle (flat-fan nozzle) exhibited temperature and thermal radiation reduction performances equal to those of a drencher nozzle while consuming only approximately one quarter of the water.

The use of numerical simulation makes it possible to verify the performance of water curtain systems under various nozzle spray patterns, nozzle installation conditions, and fire source conditions at a low cost. Studies on fire spread prevention by water curtains have been conducted using numerical simulations [12-14]. Zhu et al. [12] compared the results from a full-scale experiment and numerical simulation that used the fire dynamics simulator (FDS) to determine the thermal radiation attenuation performance of water curtains under large-scale pool fire conditions. They also developed a water mist curtain nozzle to form more uniform water curtains. They verified a numerical model based on the results of measuring the spray characteristics of a single injector and applied it to full-scale fire analysis. Consequently, they reported that the thermal radiation attenuation rate significantly increased from 59% to 82.7% as the water supply pressure increased from 1.0 to 2.0 MPa, but the rate increased only by approximately 6% as the pressure increased from 2.0 to 3.0 MPa. Ko [13] performed numerical simulation on the thermal radiation attenuation effect of water mist curtains using the FDS, and used the results of a thermal radiation blocking experiment by Murrell et al. [7] to ensure the reliability of the numerical simulation. Based on this, they analyzed the effects of the water flow rate, droplet size, and spray angle (spray spatial distribution) on the thermal radiation attenuation performance through additional numerical simulations. Kang and Lee [14] performed a numerical simulation of a full-scale hazardous material storage tank fire using the FDS. They verified the heat flux prediction accuracy by utilizing the results of an experimental study on a 30 m-diameter kerosene pool fire conducted by Yamaguchi and Wakasa [15], and evaluated the effects of the fire source conditions and water curtain characteristics (spray angle and droplet size) on the heat flux and thermal radiation attenuation rate under conditions in which water curtain systems were applied. The numerical simulation results showed that the thermal radiation attenuation rate achieved by water curtains increased as the injection angle increased and droplet size decreased, with the rate ranging from 33.5% to 83.0%.

The results of previous studies showed that the fire spread prevention performance of water curtain systems depends on the spray characteristics (e.g., the water flow rate and supply pressure, droplet size and velocity, and spray angle), and that water curtain systems are also effective in wall cooling and thermal radiation attenuation under factory-fire simulation conditions [11]. However, only a small number of studies have dealt with the effects of overlapping water curtains produced by two or more nozzles on the water curtain characteristics, wall cooling, and thermal radiation attenuation performance [8-11,14]. Quantitative comparisons of the wall temperature and heat flux reductions in the nozzle-center areas and areas between nozzles have not been sufficiently presented. Furthermore, the effects of the different spatial distributions of water curtain characteristics caused by the different spray patterns available in the field, such as the flat-fan, full-cone, and hollow-cone patterns, on the wall temperature and heat flux reductions under the same water flow rate conditions have not been sufficiently examined. Therefore, the optimization of water curtain systems for fire spread prevention requires quantitative examinations that consider the nozzle spray patterns and overlapping water curtains, in addition to the main factors examined previously.

Thus, this study performed numerical simulations on fire spread prevention using water curtain systems in a fire adjacent to factory buildings using the FDS. In addition to the water flow rate and water curtain characteristics examined in previous studies, the effects of the nozzle spray patterns and overlapping water curtains on the wall temperature and heat flux reductions provided by water curtains were examined. The water curtain characteristics of the flat-fan nozzle used in a previous experimental study [11] were measured, and the results were utilized as nozzle-input conditions (droplet size distribution, droplet velocity, and spray angle) for the numerical simulations. In addition, full-cone and hollow-cone spray patterns were implemented by modifying the spray angle from the input conditions of the flat-fan nozzle to evaluate the effects of different spray patterns. Under the scenario of a fire adjacent to a factory sandwich panel, six numerical simulation conditions (Cases 1-6) were considered by combining two water supply pressures (0.12 and 0.2 MPa) and three spray patterns (flat-fan, full-cone, and hollow-cone). The spatial distributions of the water curtain characteristics in relation to the water flow rate, spray pattern, and overlapping water curtains, as well as the wall temperature and gauge heat flux at the nozzle installation positions and positions between nozzles, were compared and analyzed.

Figure 1 shows a schematic of the numerical simulations of the water curtain systems while Figure 2 shows the nozzle orientations and spray angles. Table 1 summarizes the common conditions used for the numerical simulations, which were conducted using the FDS, Version 6.10.1 [16]. The total simulation time was 180 s, grid size was 0.1 m, and number of grid cells was 672,000. The ambient temperature, sandwich panel size and construction, type and position of the fire source, and nozzle installation positions in the numerical simulation were set by referring to the experimental conditions used by Kwon et al. [11]. The ambient temperature was set to 31 °C, and the sandwich panel had a width of 7 m (x), height of 5 m (z), and thickness of 10 mm (thickness of the steel sheet on both sides of the panel: 0.5 mm, thickness of the polyurethane foam: 9 mm). The fuel was gasoline. The properties of steel [17], polyurethane foam [18], and gasoline [19] are shown in Table 1. The fire source (fuel pan) was 1 m away from the target panel wall, and the heat release rate, Q˙, was 1,212 kW. The characteristic fire diameter, D*, was 1.025 m according to Eq. (1). When grid size △x = 0.1 m was applied, D* / △x (plume resolution index) was 10.25, which fell within the recommended range of 4-16 [20].

Here, ρ_∞ is the density of the atmosphere, c_p is the specific heat of the atmosphere, T_∞ is the atmospheric temperature, and g is the gravitational acceleration. Nozzles were installed at three points at a height of 5 m from the ground and 0.25 m away from the wall. The distance between the nozzle installation positions was 2 m. There were two nozzle outlets at each nozzle installation position. Based on the -z direction, water was sprayed at 45° angles on each side (+x and -x). The total number of nozzle outlets was six. Water curtains were sprayed from 90 s to 180 s, at which point the calculation ended. In this instance, the representative nozzle installation position at a height of 1 m from the ground at the center of the panel wall was defined as the centerline (CL) point, and the measurement point at the center between the nozzle installation positions at a distance of 1 m from the CL in the +x direction was defined as the between-nozzles (BN) point. The wall temperature and gauge heat flux were measured at these two points. In addition, the droplet mass density on the sandwich panel wall, wall temperature distribution, and gauge heat flux distribution were measured. In this study, the gauge heat flux ( q˙"_gauge) was calculated using Eq. (2).

Here, ∈_gauge and T_gauge are the emissivity and cooling temperature of the water-cooled gauge heat flux sensor, respectively; q˙"_inc is the incident heat flux; σ is the Stefan-Boltzmann constant; h_c is the convective heat transfer coefficient; and T_g is the temperature of the adjacent gas. In addition, the droplet size, droplet velocity (component in the -z direction), and droplet mass flux (component in the -z direction) were measured at 59 points with a spacing of 0.2 m, which were 0.25 m away from the sandwich panel wall and at a height of 1 m from the ground. The droplet mass flux distribution (component in the -z direction) was measured at 590 points with a spacing of 0.2 m, which were 0.1-1.9 m away from the panel wall at a height of 1 m from the ground.

The nozzle conditions used in the numerical simulations of the water curtain system were based on the water curtain characteristics of the flat-fan nozzle used in a study by Kwon et al. [11]. Water curtain characteristics were measured at a vertical distance of 100 mm from the outlet of the flat-fan nozzle using a phase Doppler particle analyzer (PDPA) and used as input values in the numerical simulations. Based on this, OFFSET = 0.1 m (100 mm) was applied in the numerical simulation, as shown in Figure 2(b). Considering the spray range of the flat-fan nozzle, measurements were performed at a total of 147 points within a rectangular area with respect to the nozzle CL, which combined 21 points at 20 mm intervals across a width of 400 mm and seven points at 10 mm intervals across a height of 60 mm. Two water supply pressures of 0.12 and 0.2 MPa were considered. The volume median diameter (VMD) was derived for all the droplets measured over a period of 10 s at each measurement point, and the CL droplet velocity was measured. The spray angle was then derived based on the range in which droplets were measured. The measurement results showed that droplets were sprayed in an elliptical area. At a water supply pressure of 0.12 MPa, the water flow rate was found to be 7.58 L/min, VMD was 487 µm, the CL droplet velocity was 13.1 m/s, and the spray angles were 53° (wide) and 6° (narrow). At a water supply pressure of 0.2 MPa, the water flow rate was 10.4 L/min, VMD was 396 µm, CL droplet velocity was 17.5 m/s, and spray angles were 57° (wide) and 8° (narrow). The numerical simulation conditions were based on these measurement results.

Table 2 lists the numerical simulation conditions used for Cases 1-6, which examined the different water flow rates and nozzle spray patterns. Cases 1-3 had a water supply pressure of 0.12 MPa. At a water flow rate of 7.58 L/min from a nozzle outlet, the total water flow rate was 45.5 L/min, while VMD was set to 487 µm and the initial droplet velocity was 13.1 m/s. In Cases 4-6, at a water flow rate of 10.4 L/min from a nozzle outlet, the total water flow rate was 62.4 L/min, while VMD was set to 396 µm and the initial droplet velocity was 17.5 m/s. Under the same water supply pressure conditions, the three spray patterns were implemented by setting different spray angle ranges. For the flat-fan nozzle in Cases 1 and 4, the wide spray angles were set to 53° and 57° and the narrow spray angles were set to 6° and 8°, respectively, based on the measurements of the water curtain characteristics. In this instance, the wide spray angle was defined in the xz-plane containing the nozzle CL, while the narrow spray angle was defined in a plane that contained the nozzle CL and was perpendicular to the xz-plane. For the full-cone nozzle in Cases 2 and 5, droplets were sprayed within ranges of 0°-53° and 0°-57°, respectively. In the case of the hollow-cone nozzle used in Cases 3 and 6, droplets were sprayed within ranges of 26.5°-53° and 28.5°-57°, respectively. Figure 3 shows the experimental results for the cumulative number fraction (CNF) and cumulative volume fraction (CVF) of the droplet size, along with the results applied in the numerical simulations based on the experiment results. Figures 3(a) and 3(b) show the results for Cases 1-3 and 4-6 under water supply pressures of 0.12 and 0.2 MPa, respectively.

Figures 4-6 show the measurement results for the droplet size, droplet velocity, and droplet mass flux distribution at a height of 1 m from the ground and a distance of 0.25 m from the sandwich panel wall, respectively. The values for each measurement point are averages over the 160-180 s period. Figure 4(a) shows the droplet size (SMD) measurement results for Cases 1-3 (water supply pressure: 0.12 MPa), while Figure 4(b) shows the measurement results for Cases 4-6 (water supply pressure: 0.2 MPa). Overall, the hollow-cone pattern produced the smallest droplet size, followed by the full-cone and flat-fan patterns. Figures 5(a) and 5(b) show the droplet velocity measurement results for Cases 1-3 and 4-6, respectively. Considering the scattering of the data, there was no significant difference in droplet velocity depending on the spray pattern. Figures 6(a) and 6(b) show the droplet mass flux measurement results for Cases 1-3 and 4-6, respectively. The flat-fan pattern produced the largest droplet mass flux, while there was no significant difference between the full-cone and hollow-cone patterns considering the scattering of the data.

Figures 7(a)-7(f) show the droplet mass flux distributions measured at a height of 1 m from the ground and distance of 1.8 m from the sandwich panel for Cases 1-6, respectively. The presented values are averages over the 160-180 s period. For the flat-fan pattern results shown in Figures 7(a) and 7(d), the droplet mass flux was the largest beneath the nozzle installation position, and it was concentrated in the region close to the sandwich panel. In the cases of the full-cone pattern results shown in Figures 7(b) and 7(e) and hollow-cone pattern results shown in Figures 7(c) and 7(f), the spray of droplets extended farther from the sandwich panel compared to the spray produced using the flat-fan pattern.

Figures 8(a)-8(f) show the measurement results for the droplet mass per unit area on the sandwich-panel wall at 170 s during the spray of water curtains for Cases 1-6, respectively. In this instance, droplets that collided with the sandwich-panel wall descended under the influence of gravity, and the droplet mass per unit area was derived based on the total mass of droplets within a cell [16]. As seen in Figures 8(a) and 8(d), the flat-fan pattern produced the lowest droplet mass per unit area among the three spray patterns. This appears to be because the droplet mass flux was concentrated beneath the nozzle rather than on the wall, as shown in Figures 7(a) and 7(d). For the full-cone pattern results shown in Figures 8(b) and 8(e), the droplet mass per unit area was higher at positions between the nozzles compared to the values at the nozzle installation positions. As seen in Figures 8(c) and 8(f), the hollow-cone pattern had the highest droplet mass per unit area among the three spray patterns. The droplet mass per unit area was higher at positions below the nozzles compared to the values at positions between the nozzles. In addition, the droplet mass per unit area values were higher in Cases 4-6 (total water flow rate: 62.4 L/min) compared to Cases 1-3 (total water flow rate: 45.5 L/min).

The temperature changes over time measured at the CL and BN points (as shown in Figure 1) for Cases 1-3 are shown in Figures 9(a) and 9(b), respectively, with the results for Cases 4-6 shown in Figures 10(a) and 10(b), respectively. In addition, visualizations of the wall temperature distributions for Cases 1-6 are shown in Figures 11(a)-11(f), respectively. The FDS modeled heat transfer by assuming the droplets were a thin film when they reached the vertical wall [16]. As the droplet mass per unit area increased, a larger wall cooling effect by droplets occurred. The wall temperatures measured at the CL (Figures 9(a) and 10(a)) were the lowest for the hollow-cone pattern, followed by those for the flat-fan and full-cone patterns. The wall temperatures at the BN point (Figure 9(b) and 10(b)) were the lowest for the full-cone pattern, followed by those for the flat-fan and hollow-cone patterns. This appears to be because the droplet mass per unit area was high at the CL for the hollow-cone pattern (Figures 8(c) and 8(f)) and at the BN point for the full-cone pattern (Figures 8(b) and 8(e)), as confirmed in Figure 8. In addition, the wall temperatures were lower in Cases 4-6 (Figure 10) compared to those in Cases 1-3 (Figure 9) during the spraying of the water curtains. This appears to be because the numbers of droplets that reached the wall were greater in Cases 4-6 (Figures 8(d)-8(f), respectively), with higher water flow rates and larger spray angles, compared to those for Cases 1-3 (Figures 8(a)-8(c), respectively). As seen in the wall temperature distributions during the spraying of the water curtains, the flat-fan pattern (Figures 11(a) and 11(d)) had higher temperatures than the other spray patterns. In addition, the wall temperatures were relatively lower during the spraying of the water curtains in the areas between the nozzles for the full-cone pattern (Figures 11(b) and 11(e)) and in areas near the nozzle CL for the hollow-cone pattern (Figures 11(c) and 11(f)).

The changes in the gauge heat flux over time measured at the CL and BN positions (as shown in Figure 1) for Cases 1-3 are shown in Figures 12(a) and 12(b), respectively, and those for Cases 4-6 are shown in Figures 13(a) and 13(b), respectively. In addition, visualizations of the gauge heat flux distributions on the wall for Cases 1-6 are shown in Figures 14(a)-14(f), respectively. The gauge heat flux measured at the CL (Figures 12(a) and 13(a)) was the lowest for the hollow-cone pattern, followed by those for the flat-fan and full-cone patterns. One of the reasons for this tendency was that the hollow-cone pattern (Figures 7(c) and 7(f)) formed a water curtain farther away from the sandwich panel, which extended the thermal radiation attenuation path, as seen in Figure 7. The gauge heat flux measured at the BN point (Figures 12(b) and 13(b)) did not differ significantly with the spray pattern. In addition, the gauge heat flux values were lower in Cases 4-6 (Figure 13) compared to Cases 1-3 (Figure 12) during the spraying of the water curtains. One of the reasons for this tendency was that the thermal radiation attenuation effects in Cases 4-6 were larger than those in Cases 1-3 as a result of the higher total water flow rates, smaller droplet sizes, and larger spray angles. As seen in the gauge heat flux distributions during the spraying of the water curtains, the flat-fan pattern (Figures 14(a) and 14(d)) produced a higher gauge heat flux than the other spray patterns. In addition, the gauge heat flux was relatively lower during the spraying of water curtains in areas between the nozzles for the full-cone pattern (Figures 14(b) and 14(e)) and in areas near the nozzle CL for the hollow-cone pattern (Figures 14(c) and 14(f)).

Table 3 summarizes the wall temperature and gauge heat flux reductions at the CL and BN positions for Cases 1-6. For the temperature and gauge heat flux reductions, the mean values and standard deviations are expressed for the differences between the values at 90 s (start of spray) and those in the 160-180 s period. The temperatures at the CL and BN positions at 90 s were 236 and 223 °C, respectively, while the gauge heat flux values were 16.90 and 13.66 kW/m², respectively. Overall, the temperature reductions ranged from 98 to 207 °C, and the gauge heat flux reductions ranged from 5.35 to 15.58 kW/m².

This study performed numerical simulations of the wall temperature and heat flux reductions produced by water curtain systems. The FDS was used to quantitatively evaluate the fire spread prevention performance achieved by the systems in a fire adjacent to factory buildings. The characteristics of the water curtain produced using the flat-fan spray pattern investigated in a previous experimental study [11] were measured, and the results were utilized as nozzle input conditions for the numerical simulations. The water curtain characteristics, wall temperature, and gauge heat flux values were compared when using flat-fan (Case 1), full-cone (Case 2), and hollow-cone (Case 3) spray patterns under a water supply pressure of 0.12 MPa, and flat-fan (Case 4), full-cone (Case 5), and hollow-cone (Case 6) spray patterns under a water supply pressure of 0.2 MPa.

The results for the characteristics of the water curtain established between the fire source and a sandwich panel showed that the hollow-cone (Cases 3 and 6) pattern produced the smallest droplet size, followed by the full-cone (Cases 2 and 5) and flat-fan patterns (Cases 1 and 4). Considering the scattering of the data, there was no significant difference in droplet velocity associated with the spray pattern. The flat-fan pattern produced the highest droplet mass flux distribution, while water curtains were formed farther from the wall when using the full-cone and hollow-cone patterns. The full-cone and hollow-cone patterns also produced larger droplet masses on the wall than the flat-fan pattern.

The hollow-cone pattern produced the lowest wall temperature and gauge heat flux at the nozzle CL, followed by the flat-fan and full-cone patterns. At the BN position, the full-cone pattern produced the lowest wall temperature, followed by the flat-fan and hollow-cone patterns, while there was no significant difference in the gauge heat flux values associated with the spray pattern. These results confirmed that wall temperature and heat flux reductions at the CL and BN positions were closely related to the droplet mass and spray range on the wall, which depended on the spray pattern. In addition, the wall temperature and gauge heat flux were lower under a water supply pressure of 0.2 MPa (Cases 4-6) compared to their values under 0.12 MPa (Cases 1-3). This appeared to be due to the higher total water flow rate, smaller droplet size, and larger number of droplets reaching the wall. Under the numerical simulation conditions of this study, water curtains decreased the wall temperature by 98-207 °C and the gauge heat flux by 5.35-15.58 kW/m².

In this study, the numerical simulations were performed under the assumption that conditions other than the spray pattern (e.g., droplet size and velocity) were identical to evaluate the effects of different spray patterns (flat-fan, full-cone, and hollow-cone). In the future, experiments to measure droplet characteristics, experiments on wall temperature and heat flux reduction, and numerical simulation studies will be required for various conditions of each spray pattern.