Distribution Characteristics of Swirling-Straight Sprinklers Inside a Nuclear Power Pressurizer

Abstract

Droplet size and distribution uniformity of sprinklers significantly affect production safety in the processes of steam temperature and pressure reduction within nuclear power, and other high-temperature, high-pressure industries. In industrial sprays with high flow rates and low pressure drops, reducing droplet size poses additional challenges, making improved spray uniformity essential for enhancing heat transfer. This study designed and produced a set of swirling-straight sprinklers, tested their flow characteristics and liquid distribution, and proposed a highly uniform spray mode involving swirl jet interaction mixing. The discharge coefficient (C_d) changes indicated that enlarging the jet channel area diminishes the amplification effect, suggesting a trade-off in industrial high flow sprinkler design. A detailed evaluation and analysis method of the spray process, which is superior to the use of a single uniformity parameter, is proposed based on Gaussian function peak fitting method. It has been observed that the relationship between the Gaussian fitting parameters and the pressure drop of the sprinkler tends to be linear. This discovery provides a new basis for designing nozzles with low pressure drop, high flow rates, and uniform distribution. The findings contribute to the optimization of spray performance and provide valuable data for computational fluid dynamics model verification.

1. Introduction

In recent years, significant advancements in nuclear technology have led to an increase in public acceptance of nuclear energy. According to the International Atomic Energy Agency (IAEA) report for 2022, the global number of nuclear reactors is projected to expand considerably. Currently, there are 442 operational reactors worldwide, with over 120 new reactors in the planning stages. Additionally, 53 new nuclear power plants are under construction, and another 67 reactors are scheduled to commence construction within the coming years [1]. The design and optimization of the key equipment of nuclear power plants has become a very important topic in the field of nuclear power.

In the nuclear power industry, which often involves high-temperature and high-pressure processes, the temperature and pressure reduction in high-temperature steam is crucial to ensure equipment safety and process stability. To achieve this, spray cooling water systems are widely used, where cooling droplets generated by sprinklers help lower the temperature and pressure of the steam. For example, in pressurizers and other important safety equipment in pressurized water reactor nuclear power plants, cooling water sprays control system pressure to enhance operational safety [2]. Malet summarized the successful research and design methods for spray systems in nuclear reactors over the past decade and expressed the importance of research on large-flow sprinklers [3]. In addition to this, large-flow sprinklers are widely used to cool flue gas and remove particles in spray cooling towers [4,5]. In such spray systems, the droplet size and uniform distribution directly affect steam temperature reduction and overall system performance. Previous research on heat exchange spray equipment has primarily focused on droplet size, where a larger pressure drop in the sprinkler results in smaller droplet sizes [6]. However, studies focusing on spray distribution uniformity remain limited [7,8,9].

Past research on spray performance has often centered on the design of small sprays with low flow rates and high-pressure drops [10,11,12,13], while studies on the volume distribution uniformity of spray systems have primarily been found in agricultural spray irrigation research [14,15]. Research focusing on spray distribution uniformity and other performance parameters of large sprays used in important safety equipment, such as pressurizers in pressurized water reactors, is relatively limited. Considering the absence of design data for industrial-scale, large-flow sprinklers, it is worthwhile studying the performance parameters of these sprinklers.

With advancements in spray cooling equipment, computational fluid dynamics (CFD) technology has emerged as a tool to predict and provide detailed flow field information using coupled phase-to-phase heat transfer models, such as Euler–Euler or Euler–Lagrange. However, most CFD results are verified based on temperature or heat transfer, lacking comprehensive verification of the spray process itself [16]. Currently, there exists a notable shortage of experimental data on spray uniformity to verify the accuracy of CFD models [9,17,18,19].

Traditional pressure-swirl atomizers have been widely used for their advantages, such as large spray angles, wide coverage areas, and small droplet sizes. However, owing to the influence of the rotating vortex within the atomizer cavity, an air core can easily form at the center of the sprinkler, resulting in flow loss in the center and poor spray distribution. This problem becomes more prominent when the structure of the pressure-swirl atomizer is scaled up for industrial spray equipment, amplifying the uneven spray distribution. To address this, an axial flow channel was added to the rotational core structure of a traditional pressure-swirl sprinkler to avoid air core formation and compensate for flow loss in the central area [20]. Moreover, a flow-blocking structure was placed at the base of the rotational core, enhancing the mixing of fluids with different velocity properties within the chamber. This interaction and neutralization of the two fluids promoted a uniform tangential velocity gradient, improving overall spray distribution uniformity. Lan et al. measured the liquid distribution of swirling-straight sprinklers, which is consistent with the liquid distribution law in this paper [21].

Various performance indicators, such as sprinkler flow uniformity, distribution uniformity coefficient, and Christiansen’s coefficient of uniformity, have been commonly used to evaluate spray distribution uniformity [15,22,23,24]. However, a single uniformity coefficient parameter does not adequately represent the liquid volume distribution within the spray range or comprehensively evaluate spray distribution performance. In this study, a swirling-straight sprinkler was designed and manufactured, and its flow rate and spray volume distribution were measured under different pressure drops. A Gaussian peak fitting method was introduced, treating the radial flow distribution curve as the superposition of three Gaussian functions. This approach provided a more comprehensive assessment and analysis method for spray distribution uniformity. The study aimed to explore the relationship between spray pressure drop and the constants of the Gaussian function to inform the design of sprays with low-pressure drops, high flow rates, and uniform distribution. Additionally, radial flow distribution data and peak fitting results were provided to support future CFD verification.

2. Experimental Setup

2.1. Experimental Process

The experimental system included a centrifugal pump, water tank, mass flowmeter, pressure gauge, sprinkler, and a series of closely arranged square cylinders. The centrifugal pump provided the required system pressure. A square cylinder array, uniformly distributed, was positioned 900 mm below the spray. Each cylinder had a capacity of 750 mL (5 × 5 × 30 cm), with a total of 33 cylinders. The schematic of experimental system is shown in Figure 1.

Before conducting the experiment, a diaphragm was placed over the inlet of each measuring cylinder. The centrifugal pump was then started, and its speed, along with the opening of the pipeline’s regulating ball valve, was adjusted to achieve the desired pressure drop (20 kPa, 50 kPa, 70 kPa, 90 kPa, 120 kPa, and 150 kPa). Once the spray stabilized, the diaphragm was removed, and timing commenced. The diaphragm was replaced after 120 s (with slight adjustments according to flow rate), and the timing stopped. The centrifugal pump was then shut off to stop the spray. The liquid level in each measuring cylinder was recorded, and a liquid volume distribution curve was plotted. The process was repeated for each working condition, and then the sprinkler was rotated horizontally by 90° to measure the liquid volume distribution in a direction perpendicular to the initial measurement.

2.2. Structural Design of Sprinkler

A traditional sprinkler only features a swirl channel, in which the liquid-phase flow is primarily driven by rotary motion. This results in a high tangential velocity at the spray outlet, often creating negative pressure at the center of the sprinkler that draws in air. This phenomenon forms an air core, resulting in a hollow central spray area and poor distribution uniformity [11]. The swirling-straight sprinkler used in this study was an improved version of the traditional pressure-swirl sprinkler, featuring an added axial flow passage at the center of the swirling core to increase the axial velocity of the liquid flow at the outlet. The specific internal structure of the sprinkler divides the liquid flow through the core into axial flow and rotary vortex. These two flows, with distinct motion characteristics, were thoroughly mixed in the mixing chamber. During spraying, the axial and tangential velocities were distributed evenly along the radial direction with a certain gradient, achieving high spray distribution uniformity. The structure of the swirling-straight sprinkler is shown in Figure 2.

The case and swirling core of the swirling-straight sprinkler used in the experiment were 3D printed from 316L stainless steel and subsequently welded into their final shape. Four sprinklers with different structural parameters were tested for radial distribution uniformity, flow rate, and pressure drop. The structural parameters of these four sprinklers are presented in Figure 3 and

Table 1. Structure parameters of swirling-straight sprinkler.

Parameter	D1	D2	H	b	h	t	dc	dt	hsc	S
Sprinkler A	40	17	30	12	5.4	2	10	22	20	9.67
Sprinkler B	48	20.4	36	14.4	6.48	2.4	12	26.4	24	11.6
Sprinkler C	40	17	30	12	5.4	2	11.6	22	20	9.67
Sprinkler D	48	20.4	36	14.4	6.48	2.4	13.92	26.4	24	11.6

. Among them, sprinklers A and C are characterized by identical parameters, with the sole exception being the variable dc. Sprinklers B and D, on the other hand, are derived from sprinklers A and C by applying a uniform scaling factor of 1.2 to their respective dimensions. All length measurements are in millimeters, with each swirling core featuring six spiral slots and an acceleration chamber contraction angle of 35°. On the whole, the structural differences in the four sprinklers are mainly reflected in the value of d_c and the amplification ratio.

3. Results and Discussion

3.1. Relationship Between Flow Rate and Pressure Drop

The discharge coefficient, C_d, is a crucial parameter in the design of atomizers and their control systems. Specifically, C_d is defined as the ratio of the actual mass flow rate through the atomizer orifice outlet to the theoretical maximum mass flow rate. The C_d was calculated using the Formula (1) [25]:

$$Q={\displaystyle \frac{\pi }{4}}{d_2^{2}C}_d\sqrt{{\displaystyle \frac{2∆P}{\rho }}}\times 3600\times {10}^{-3}$$

(1)

where Q denotes the flow rate of the sprinkler in m³/h, C_d is the discharge coefficient, d₂ denotes the sprinkler outlet diameter in mm, ∆P denotes the water supply pressure in MPa, and $\rho$ symbolizes the liquid density in kg/m³. For this study, $\rho$ = 1000 kg/m³.

The relationship between fluid flow rate Q and discharge coefficient C_d with pressure drop is depicted in Figure 4 and Figure 5. The flow–pressure drop characteristics revealed that the flow–pressure drop curves for sprinklers A and C, as well as for sprinklers B and D, nearly overlapped. However, at the same flow rate, sprinklers B and D exhibited lower pressure drops compared to A and C, indicating that scaling up the sprinklers effectively reduced the resistance coefficient. Hence, from a structural design standpoint, the impact of altering the through-hole size of the rotary core in the sprinkler on its flow characteristics is significantly less critical, provided that the overall specifications and dimensions remain unchanged. This underscores the fact that scaling up the sprinkler structure to industrial dimensions may reveal issues that are not apparent in the study of smaller-scale sprinklers. Consequently, research into the industrial scale-up of sprinkler structures is of paramount importance.

Analysis of the discharge coefficient C_d versus pressure drop showed that scaling up sprinkler A increased C_d, whereas scaling up sprinkler C did not significantly affect C_d. While sprinklers B and D represent structures that are scaled up by a factor of 1.2 from sprinklers A and C, respectively, the primary difference between the two enlargements lies in the ratio of the jet channel area to the swirl channel area. Consequently, when this ratio is low, equal magnification results in a pronounced shift in the discharge coefficient C_d curve with respect to pressure drop, demonstrating a significant amplification effect. Conversely, when the ratio of jet channel area to swirl channel area is high, the proportional scaling has a minimal impact on the variation pattern of the discharge coefficient C_d, thereby diminishing the amplification effect. As depicted in the figure, the discharge coefficient C_d for sprinklers C and D is lower than that for sprinklers A and B, suggesting that increasing the diameter of the central through hole in sprinklers on this scale leads to greater energy loss, primarily utilized to enhance the mixing and turbulence between the jet and swirl. In this study, the ratio of the jet flow channel to the swirl flow channel area for sprinklers A and B is 0.202, whereas for sprinklers C and D, it is 0.272.

The spray distribution uniformity coefficient was calculated using Christiansen’s 1942 method for liquid volume distribution uniformity, and the radial distribution uniformity was determined from the liquid level data measured using the cylinders [22]. It remains the most commonly used method for calculating spray distribution uniformity. The uniformity of the distribution for the four sprinklers under different pressure-drop conditions is shown in Figure 6, and the corresponding spray-state diagram is shown in Figure 7. The spray distribution uniformity coefficient is calculated using Formula (2).

$$C_u=\left(1-{\displaystyle \frac{{\sum }_{i=1}^n\mid q_i-\overline{q}\mid }{n\overline{q}}}\right)\times 100\%$$

(2)

where $q_i$ denotes liquid level of the ith measuring cylinder in cm, $\overline{q}$ is the average level of all measuring cylinders, n denotes number of cylinders receiving liquid.

3.2. Peak Fitting Mechanism of Spray Volume Distribution Curve

In this study, the primary focus was on the spray liquid quantity distribution curve of the spray equipment, which reflects the vertical apparent liquid velocity distribution. The shape of this curve is closely related to the internal flow dynamics of the spray. Within the spray, the jet and swirl passing through the swirling core were thoroughly mixed in the mixing chamber. At the sprinkler, the axial vertical velocity decreased gradually from the center to the side wall, while the tangential swirl velocity increased gradually from the center to the side wall. A significant reduction in central liquid volume was observed when the traditional swirl sprinkler was scaled up, resulting in a discontinuous distribution curve with two symmetrical peaks. By contrast, the liquid volume distribution curve of an ordinary flat-hole sprinkler exhibited a single peak centered in the middle region. By considering the spray flow field of the coaxial swirl spray as the superposition of the flow fields from an ordinary flat-hole sprinkler and a pressure-swirl sprinkler, the spray liquid quantity distribution curve can be viewed as the superposition of three peaks at any section below the spray sprinkler. As depicted in Figure 8, we divided the flow field of the coaxial swirl spray into jet- and swirl-influence zones, where their interaction formed an overlapping zone.

Upon measuring the spray liquid quantity distribution curve, it was observed that under a pressure drop range of 20–150 kPa, sprinklers A and B exhibited a “double-peak pattern”, as shown in Figure 9, while sprinklers C and D showed a “triple peak pattern”, as shown in Figure 10. These liquid volume distribution curves for both patterns could be represented by the superposition of three Gaussian distribution curves, confirming our analysis of the jet–swirl interaction flow field. Therefore, the three Gaussian curves obtained from the fitting corresponded to the jet-influence and swirl-influence regions.

Gaussian peak-splitting fitting methods have been discussed in several studies [26,27,28,29]. The Gaussian function is expressed as follows:

$$y=y_0+{\displaystyle \frac{A{e}^{\frac{-4\mathit{ln}(2\left)\right(x-x_c{)}^2}{w^2}}}{w\sqrt{\frac{\pi }{4\mathit{ln}(2)}}}}$$

(3)

where y denotes fitting liquid level height in cm, A, w and x_c are fitting parameters. In this fitting, y₀ is equal to 0.

The serial number of each measuring cylinder from left to right was used as the horizontal coordinate, while the liquid level height over 120 s for each measuring cylinder served as the vertical coordinate. Three groups of Gaussian curves were superimposed. During the fitting process, the y₀ value of each Gaussian curve function was set to zero. The three curves were labeled as curves 1, 2, and 3 from left to right. The fitting curve of the liquid distribution diagram matched the experimental data closely, demonstrating high consistency.

$$y={\displaystyle \frac{A_1{e}^{\frac{-4\mathit{ln}(2\left)\right(x-x_{c1}{)}^2}{{w_1}^2}}}{w_1\sqrt{\frac{\pi }{4\mathit{ln}(2)}}}}+{\displaystyle \frac{A_2{e}^{\frac{-4\mathit{ln}(2\left)\right(x-x_{c2}{)}^2}{{w_2}^2}}}{w_2\sqrt{\frac{\pi }{4\mathit{ln}(2)}}}}+{\displaystyle \frac{A_3{e}^{\frac{-4\mathit{ln}(2\left)\right(x-x_{c3}{)}^2}{{w_3}^2}}}{w_3\sqrt{\frac{\pi }{4\mathit{ln}(2)}}}}$$

(4)

In the function expression, the liquid distribution curve was obtained by superimposing three Gaussian curves, with the shape of each curve determined by three parameters: A_i, w_i, and x_ci. The distribution areas of curves 1 and 3 corresponded to the swirl-influence zones, while the distribution area of curve 2 represented the jet-influence zone. The overall shape of the liquid volume distribution curve depended on the mixing ratio and the intensity of two fluids with different motion characteristics. During the experiment, we measured the liquid volume distribution for the four sprinkler samples under different pressure-drop conditions and fitted the distribution curves. In the 24 groups of fitting involved in this paper, the resulting R-squared values exceeded 0.99, indicating a high degree of fit.

At present, there are relatively few works of literature about the optimization of sprinkler distribution uniformity. In the only experimental study and numerical simulation of the distribution uniformity of rotary jet composite nozzle, there is no further mathematical analysis of the liquid distribution curve or the promotion mechanism of nozzle distribution uniformity [20,21]. Therefore, the peak fitting method of Gaussian function for liquid distribution curve of sprinkler proposed in this study further strengthens the in-depth understanding of liquid distribution and uniformity.

For the “double-peak” condition, the jet-influence zone had a lower peak value, wider width, and a significant peak deviation in the actual liquid volume distribution curve from the fitted swirl-influence zone. In the “three-peak” condition, the jet-influence zone showed a higher peak value and narrower width, with the three peaks of the actual liquid volume distribution curve aligning closely with the fitted peaks for both the jet and swirl-influence zones. The “double-peak” state arose from a smaller axial flow channel size and weaker spray intensity. The liquid that passes through the axial flow channel of the swirling core was entrained by the swirl flow, resulting in a higher tangential velocity and deviation from the central region. However, in the “three-peak” morphology, the larger axial flow channel size and stronger jet intensity resulted in a relatively weak interaction effect among the three fitted peaks.

Compared to traditional parameters, such as the uniformity coefficient, curve fitting provides a more detailed and convincing representation of the spray volume distribution shape. For instance, under similar uniformity coefficient conditions, the spray volume distribution curve in this study could exhibit either two or three peaks (as shown in Figure 6 for Sprinkler B at 150 kPa and Sprinkler D at 50 kPa), which could not be discerned using a single uniformity parameter.

3.3. Effect of Pressure Drop on Peaking Fitting Parameters

The shape of the Gaussian function in the liquid volume distribution curve is determined by its mathematical characteristics, with each of the three Gaussian constants having distinct influences on the curve. Specifically, X_ci determines the positions of the Gaussian peaks, w_i sets the width of each peak, and the ratio of A_i to w_i determines the peak height. By obtaining the liquid distribution curve equation, analyzing the liquid distribution under different pressure-drop conditions was transformed into studying the behavior of the three Gaussian constants under different pressure drops.

It was observed that changes in pressure drop had minimal impact on x_ci and w_i. This indicates that the position and width of each Gaussian peak remained largely consistent despite variations in the pressure drop (flow). The predominant factors that affected x_ci and w_i were the structural parameters of the sprinkler. Therefore, the relationship between pressure drop and the liquid volume distribution curve was reduced to examining the relationship between pressure drop and the heights of the three Gaussian peaks, expressed as the A_i/w_i value. The average values and standard deviations of x_ci and w_i for the Gaussian curves of each sprinkler are presented in

Table 2. Mean and standard deviation of x_ci and w.

Parameter	Sprinkler A	Sprinkler B	Sprinkler C	Sprinkler D
xc1	8.02 ± 0.25	8.01 ± 0.78	9.93 ± 0.44	10.30 ± 0.24
xc2	116.95 ± 0.98	16.89 ± 0.57	16.67 ± 0.28	17.09 ± 0.11
xc3	26.59 ± 0.54	26.48 ± 0.44	23.78 ± 0.25	24.23 ± 0.24
w1	4.26 ± 0.34	4.46 ± 0.30	5.25 ± 0.47	4.81 ± 0.34
w2	16.77 ± 2.40	15.66 ± 1.41	5.30 ± 0.29	5.73 ± 0.25
w3	4.37 ± 0.53	4.79 ± 0.39	5.67 ± 0.48	5.41 ± 0.52

.

As shown in Figure 11, while the x_ci values for the three Gaussian functions of sprinklers A and C remained nearly constant across different pressure drops, the small difference between x_c3 and x_c1 for sprinkler C suggests that increasing the diameter of the through-hole at the center of the core weakened the swirl intensity, thereby reducing the spray angle and spray diameter. As shown in Figure 12, sprinklers B and D also present the same phenomenon.

The change pattern of the Gaussian peak ratio (A_i/w_i) for sprinklers C and D is similar to that of sprinklers A and B, with a key difference: the second Gaussian peak shifted from being the lowest peak in sprinklers A and B to the highest in sprinklers C and D. This shift was primarily influenced by increasing the diameter of the central through-hole. The liquid volume distribution curve of the atomizer after proportional scaling remained similar to that before scaling, but the peak value increased with the rate of pressure drop change. The peak value change curves for atomizers C and D indicates that the height difference between the primary peak and the other two peaks grew with the pressure drop. This finding suggests that when the central hole diameter is larger, increased pressure can reduce spray distribution uniformity.

Since the first and third Gaussian peaks for sprinklers A and B, which exhibit two-peak liquid volume distributions, are smaller than the actual experimentally measured values (as shown in Figure 9), while the first and third Gaussian peaks for sprinklers C and D, which exhibit three-peak liquid volume distributions, closely match the experimental values (as shown in Figure 10), it is necessary to differentiate the analysis and comparison of A_i/w_i based on the types of liquid volume distributions of the sprinklers.

The growth rate of the A₂/w₂ value for sprinkler A with a pressure drop was slower than that for sprinkler C. Similarly, the growth rate of A₂/w₂ for sprinkler B was slower than that for sprinkler D. This indicates that the growth rate of A₂ increased with a higher ratio of the diameter of the central through-hole to the total flow channel area of the rotating core. As shown in Figure 13 and Figure 14, the relationship curves of the three Gaussian peaks of sprinklers A and B with pressure drop are almost parallel, and the second Gaussian peak of sprinklers C and D increases at a higher rate as the pressure drop increases. This finding suggests that a smaller central through-hole diameter resulted in a smaller height difference among the three peaks at high-pressure drops, promoting a better uniformity coefficient. Therefore, a smaller central through-hole diameter should be used to achieve high spray distribution uniformity under high pressure. Conversely, a sprinkler with a larger central through-hole diameter is better suited for low-pressure applications. In practical terms, this is reflected in the flow field dynamics. The enhancement effect of the swirling-straight sprinkler on the flow in the axial flow channel increased with a larger central through-hole diameter. When the central through-hole diameter was smaller, the enhancement effect on the flow field in the rotating channel could surpass that of the axial flow field as pressure increased.

Maz used particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) to measure and analyze the flow field within the swirl chamber of a large single-cylinder atomizer. The results showed that the flow field in the swirl chamber was highly symmetrical [30]. Based on these experimental results, it can be concluded that the liquid volume distribution curve of the coaxial cyclone distributor also demonstrates high symmetry. The parameters of the first and third Gaussian curves are correlated, which means that the liquid volume distribution curve can be characterized using six parameters. When X_c2 is defined as zero, the curve shape is determined by five parameters, and the curve function expression is as follows:

$$y={\displaystyle \frac{A_1{(e}^{\frac{-4\mathit{ln}(2\left)\right(x-x_{c1}{)}^2}{{w_1}^2}}+e^{\frac{-4\mathit{ln}(2\left)\right(x-2x_{c2}+x_{c1}{)}^2}{{w_3}^2}})}{w_1\sqrt{\frac{\pi }{4\mathit{ln}(2)}}}}+{\displaystyle \frac{A_2{e}^{\frac{-4\mathit{ln}(2\left)\right(x-x_{c2}{)}^2}{{w_2}^2}}}{w_2\sqrt{\frac{\pi }{4\mathit{ln}(2)}}}}$$

(5)

4. Conclusions

In this study, four straight swirling sprinklers (A, B, C, and D) were designed and manufactured. The d_c value of central through-holes diameters were 10, 12, 11.6, and 13.92 mm, respectively. Sprinkler C had an increased jet flow channel compared to sprinkler A, while Sprayers B and D are structures obtained by enlarging the equal ratio of sprayers A and C by 1.2 times, respectively. These variations were used to compare and analyze the amplification effects of the sprinklers and study the peak fitting of the liquid distribution. The change in the discharge coefficient C_d indicated that increasing the jet channel area weakened the amplification effect.

The results showed that the d_c value of central through-holes diameters of the sprinkler significantly affected the spray distribution. Increasing the central channel diameter weakened the swirl intensity and improved the spray distribution uniformity. This finding was important for optimizing sprinkler design to achieve broader coverage and more uniform spray distribution.

The Gaussian fitting parameter analysis method introduced in this study offered a new perspective for evaluating the spray distribution performance of sprinkler. This method described the spray volume distribution more accurately, and the relationship between spray volume distribution, key parameters, and pressure drop was found to be linear. This provided a valuable tool for performance evaluation and design optimization of sprinklers. The experimental data revealed that the influence of pressure on the spray distribution was mainly concentrated on the value of the Gaussian peak A_i/w_i, which represented the peak height of the spray distribution curve. The Gaussian fitting parameters w and X_C of the same sprinkler remained almost unchanged with changes in pressure drop, indicating that the structural parameters of the sprinkler were the main factors affecting these parameters.

When comparing the spray patterns of various sprinklers across different pressure drops, it was observed that the spray volume distribution curves might present with either double or triple peaks, despite having similar uniformity coefficients. This complexity cannot be captured by a single uniformity parameter. This highlighted the advantage of the Gaussian peak fitting method for evaluating spray distribution performance. Overall, evaluating the spray distribution performance of sprinklers based on the fitting parameters after peak-splitting fitting was demonstrated to be feasible. Our proposed method provided a better description of the spray volume distribution, and the relationship between key parameters and pressure drop was linear. Further experimental data allow for the exploration of the functional relationship between sprinkler structural parameters and Gaussian fitting parameters. This research can lead to the development of formulas predicting spray distribution performance. Such formulas can guide the design of large-flow sprinklers and help reduce the investment costs associated with industrial tests.

In this research, we have focused on the study of industrial-grade sprinklers with particular structural configurations, from which we have derived certain conclusions. Given the limited number of test samples and operating conditions, our findings may not be directly applicable to the design of sprinklers with different structures or scales. Moving forward, we intend to expand upon this work by conducting further research on industrial-grade, high-flow sprinklers. The objective is to develop precise, standardized design guidelines and performance prediction methodologies tailored to the needs of industrial-grade sprinklers.