Numerical Simulation and Experimental Study on Flow Field in a Swirl Nozzle

In order to study the internal ﬂow characteristics and external droplet velocity distribution characteristics of the swirl nozzle, the following methods were used: numerical simulations were used to study the internal ﬂow characteristics of a swirl nozzle and phase Doppler particle velocimetry was used to determine the corresponding external droplet velocity distribution under medium and low pressure conditions. The distributions of pressure and water velocity inside the nozzle were obtained. Meanwhile, the velocities of droplets outside the nozzle in diﬀerent sections were discussed. The results show that the ﬂow rate in the swirl nozzle increases with the increase in inlet pressure, and the local pressure in the region decreases because of the excessive velocity at the internal outlet section of the swirl nozzle, resulting in cavitation. The experimental results show that under an external ﬂow ﬁeld, the minimum droplet velocity occurs in the axial direction; starting from the axis, the velocity ﬁrst increases and then decreases along the radial direction. Swirling motion inside the nozzle and velocity variations in the external ﬂow ﬁeld occur under medium and low pressure conditions. The relationship between the inlet pressure and the distributions of water droplets’ velocities was established, which provides a reference for the research and development of the swirl nozzle.


Introduction
Water-mist fire extinguishing technology is playing an increasingly important role in the field of modern fire protection. Water is the main medium employed by this technology, where a pressurized water mist is sprayed to extinguish a fire at the source [1,2]. Pressure nozzles are widely used in fire protection because of their simple structure, large atomization angle, and production of a uniform droplet distribution [3].
Studies on the structural design of a water mist fire extinguishing nozzle have been carried out. Du et al. [4,5] designed a novel nozzle structure to improve atomization. Bhattacharya and Hu investigated the atomization characteristics of the water mist used to extinguish fires; experiments were conducted on the spray characteristics of pressure atomization nozzles, and the intensity of spray was reported to significantly impact fire extinguishing [6,7]. Marchione et al. [8][9][10] studied spray characteristics, such as the spray cone angle and the film breakage length, of the external flow field under different spray pressures. Jedelsky et al. [11,12] studied the formation of a hollow cone spray and the chang law of the spray cone angle. Xia et al. [13] studied spray characteristics and found that the breaking length of the water jet decreases as the gas-liquid ratio in the air increases. Mayer and Branam [14] studied the characteristic parameters of a water-mist fog field under different pressure conditions and found that the intensity distribution of the water mist flow field narrowed as the pressure increased. Wu et al. [15,16] found that the fog cone angle increased with the increase in the discharge coefficient. Wang et al. [17,18] used numerical simulations to investigate the flow mechanism of atomizing nozzles.
However, few studies have been conducted to determine the characteristics of the internal flow in swirl nozzles and the external droplet velocity distribution. erefore, in order to provide more research and corresponding data for reference, the characteristics of the internal flow field and the external droplet velocity distribution of a swirl nozzle are investigated in this study under medium and low pressure conditions; the internal flow profile in the swirl nozzle and the change law of the external droplet velocity are presented.

Geometric Model and Meshing.
e object of this study is a straight-blade swirl nozzle. e two-dimensional nozzle structure is shown in Figure 1. e nozzle inlet diameter D 1 is 14 mm, the outlet diameter D 2 is 6 mm, L 1 is the jet exit section, and L is the total nozzle, in which water flows through. After the two symmetrical straight blades collide with each other to form a swirling flow, water shoots out the nozzle exit section. Figure 2 shows the three-dimensional structure of the nozzle and the three-dimensional water body in the nozzle (which is meshed by ICEM). e total number of grids shown in Figure 3 is 842088.

Parameter Settings.
is study uses Fluent software for double-precision numerical calculation. e inlet pressure of the swirl nozzle is set to 1 MPa, 2 MPa, 3 MPa, 4 MPa, 5 MPa, and 6 MPa, the outlet pressure is one atmosphere, the reference pressure is 0 Pa, and the wall surface is a nonslip boundary. e phase flow model uses the Euler-Euler twofluid model, the turbulence model is the standard k − ε model, and the pressure-velocity coupling uses the SIM-PLEC algorithm.

Calculation Model
e water flow inside the water mist nozzle becomes unstable under turbulence. e standard k − ε model [19][20][21][22][23][24] application is currently the most commonly used turbulence model. is model has high calculation accuracy and good stability and is therefore used for numerical calculations in this study. e standard k − ε model equation is given as follows: k transport equation is as follows: ε transport equation is as follows: where G k represents the effect of the velocity gradient on the turbulent kinetic energy k (kg/(m·s 3 )), G b denotes the production of turbulent kinetic energy k caused by buoyancy (kg/(m·s 3 )), Y M represents pulsation expansion in compressible turbulence (kg/ (m·s 3 )), C 1ε , C 2ε , and C 3ε are empirical constants, and S k and S t are user-defined source terms (kg/(m·s 3 )), and C 1ε � 1.44, C 2ε � 1.92, C 3ε � 0.09, σ k � 1.0, and σ ε � 1.3.

Multiphase Flow Model.
e Euler-Euler two-fluid model [25][26][27][28][29][30] established a set of n momentum equations and continuity equations that are solved for each phase. is model has the advantage of fully considering turbulent transport of the particle phase, unlike the Euler-Lagrange method; the Euler-Euler two-fluid model assumes that the discrete droplet phase is a pseudo-fluid, which requires low computation. erefore, the Euler-Euler two-fluid model is used in this study to numerically simulate the internal flow field of the swirl nozzle. e flow is treated as incompressible, and the governing equations are given as follows: Continuity equation of the kth phase is as follows: Momentum conservation equation of the kth phase is as follows: where∇ is the divergence; m pk is the quality of k-phase, kg; v is the gas flow velocity of k-phase, m/s; α k is the volume fraction of the k th phase, %; τ k is the shear stress of the k th phase; p is the pressure, Pa; F L and F Vm are the lift and virtual mass force, respectively, N; and R pq is the interphase force between the phase volumes, where R pq � −R pq and R pq � 0. e volume fraction is defined as the space occupied by each phase, where each phase satisfies the law of conservation of mass and momentum. e volume fraction is denoted by α k . e volume V k of phase k is defined as V k � α k dV, where the sum of the phases of α k is 1.

Pressure Distribution in Swirl Nozzle under Different
Inlet Pressures. Figure 4 shows the numerical simulation results for the swirl nozzle pressure distribution at the center section (Z � 0) of the nozzle under different inlet pressure conditions. e inlet pressure of the swirl nozzle is set to 1 MPa, 2 MPa, 3 MPa, 4 MPa, 5 MPa, and 6 MPa from small to large. Water flows through the straight blades to form a swirling flow in the nozzle chamber and then shoots out the nozzle. Figure 4 shows that for inlet pressures of 1 MPa and 6 MPa, the negative pressure at the center section of the swirl nozzle outlet is 0.29 MPa and 1.59 MPa. As the inlet pressure of the swirl nozzle increases, the local pressure at the outlet section gradually decreases, which causes the velocity of the center point of the jet to be lower than the velocity at other areas after the jet exits from the nozzle.

Velocity Distribution of Swirl Nozzles under Different
Pressures.
e velocity distribution at the center section of the swirl nozzle is shown in Figure 5. e water velocity in the nozzle increases with the inlet pressure.  Figure 6 shows the velocity distribution at the outlet section under different nozzle inlet pressures. e low pressure zone at the center of the nozzle outlet causes the water jet to be ejected from the edge at a high speed. Figure 6 shows that under different inlet pressure conditions, as the radial direction displacement increases, the speed gradually increases from the axis and then decreases rapidly near the edge of the section.

Test System and Measurement Method.
e test system for the external flow field of the swirl nozzle is shown in Figure 7. e system has two main components, an atomization pipe spray system, which is composed of a water supply tank, valve, water pump, nozzle, water collecting tank, and connection pipe, and a test measurement system, which includes pressure sensor, an electromagnetic flowmeter, a phase Doppler velocimeter, particle size analyzer, and a computer. e velocity distribution of the external        Shock and Vibration flow field of droplets is measured under different nozzle inlet pressures during the test. e water tank is filled, and the water is sent to the test nozzle by adjusting valve 1 through the connecting pipe. After the test system is stable, the water pump test is formally started. e pressure sensor displays the water flow pressure; valve 2 is adjusted incrementally to increase the nozzle pressure to 1 MPa, 2 MPa, 3 MPa, 4 MPa, 5 MPa, and 6 MPa; the flow is read from the electromagnetic flowmeter; information from the phase Doppler velocimeter and particle size analyzer are processed using Flowersizer computer software and output as the velocity distribution of the droplets in the fog field. e test site is shown in Figure 8.

Pressure-Flow Analysis.
A photograph of the nozzle used in this study is shown in Figure 9. e nozzle is placed 1.5 m above ground. e measured nozzle inlet pressure and the flow rate through the nozzle are used to produce the pressure-flow curve, shown in Figure 10. e initial pressure of the atomizing nozzle is 1 MPa. e flow rate increases approximately linearly with the inlet pressure, showing that indicates that increasing the inlet pressure increases the swirling motion of the water flow in the nozzle.

Velocity Distribution of Particles in Fog Field.
A field test is conducted to determine the external flow field of the nozzle, a straight-blade swirl nozzle is fixed on the bracket, and the pressure is adjusted to 2 MPa, 3 MPa, and 4 MPa for the test. Phase Doppler velocimetry measurement technology is used to determine the velocity at four cross-sections. Figure 11 shows the axial test sections of the nozzle at 20 mm, 30 mm, 40 mm, and 50 mm. Figure 12 shows the variation in the radial velocity or Section 1 at a distance of 20 mm from the nozzle axial outlet. In the swirling nozzle, water flow through the swirling chamber produces a jet that is ejected from the nozzle in a rotating form and breaks into droplets in the surrounding air. For nozzle inlet pressures of 2 MPa and 3 MPa, the minimum speed is 28 m/s and 31.9 m/s, respectively. For an inlet pressure of 4 MPa, the minimum speed is 35.6 m/s. e droplet velocity gradually increases with the radial distance and reaches a maximum at 10 mm from the axial center. e maximum velocity is 43.2 m/s, 45.9 m/s, and 51.2 m/s for inlet pressures of 2 MPa, 3 MPa, and 4 MPa, respectively. Figure 12 shows that the smallest droplet velocity occurs along the axis of the swirl nozzle. At the same cross-section, as the radial distance increases, the velocity first increases   from the axis and then decreases. is behavior is caused by cavitation from the low local pressure in the outlet section of the nozzle. Figure 13 shows the variation in the radial velocity or Section 2 at a distance of 30 mm from the nozzle axial outlet. For an inlet pressure of 3 MPa, the maximum speed of 52.8 m/s occurs at 15 mm along the radial direction for Section 2. For an inlet pressure of 4 MPa, the maximum speed of 59 m/s occurs at 17 mm along the radial direction for Section 2. Figure 13 shows that the radial speed curve is approximately "M-shaped." e variation in the radial velocity or Section 3 at 40 mm from the nozzle outlet is shown in Figure 14. At the axis, the minimum speed for the swirl nozzle is 24.1 m/s, 29.7 m/s, and 35.4 m/s for inlet pressures of 2 MPa, 3 MPa, and 4 MPa, respectively. In Section 3, the droplet velocity of the external flow field gradually increases along the radial direction and reaches a maximum at 15 mm. e maximum velocity is 44.3 m/s and 53.1 m/s for inlet pressures of 2 MPa and 3 MPa, respectively. For an inlet pressure of 4 MPa, the maximum speed is 60.7 m/s. Figure 15 shows the variation in the radial velocity or Section 4 at a distance of 50 mm from the nozzle axial outlet. At the axis, the minimum speed in the nozzle is 25.0 m/s, 33.2 m/s, and 39.5 m/s for inlet pressures of 2 MPa, 3 MPa, and 4 MPa, respectively. e speed along the radial direction    e speed of displacement increases rapidly to a maximum and decreases rapidly near the edge of the jet; under different nozzle inlet pressures, the speed reaches a maximum between 10 mm and approximately 15 mm and then rapidly decreases. ese results are consistent with the conclusion of numerical simulation.

Conclusion
In this paper, numerical simulation and experimental study on the swirl nozzle are carried out. e results show that the speed and flow rate of water in a swirling nozzle increase gradually with the increase in pressure, which conforms to the general law of motion or a nozzle jet. As the inlet pressure of the swirl nozzle is gradually increased, an excessive velocity at the outlet section inside the nozzle causes a gradual decrease in the pressure at the outlet center. e results of experiments and numerical simulations show that the variation in the velocity in the swirl nozzle is caused by cavitation at the outlet center induced by low pressure. e smallest velocity for the external flow field occurs along the axial direction, and as the displacement in the radial direction of the external flow field increases, the velocity gradually increases starting from the axis and then decreases rapidly near the radial edge.

Data Availability
e data used to support the findings of this study are available from the #2 author (Yufan Fu) upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.