Influence law of structural parameters of pressure-swirl nozzle on atomization effect based on multiscale model

The dust pollution at the fully mechanized heading face has seriously threatened the health of the miners. As the main technical means, the outer spray of a roadheader has the problems of small coverage of the fog field and low dust removal efficiency. Based on the multiscale swirl atomization model of LES-VOF, this study simulated and analyzed the atomization process of the nozzle. The influence law of the diameter, the length and the circulation area ratio of the swirl chamber, and the swirl core angle on the swirl number and atomization effect were determined, and the nonlinear function relationship between variables was obtained. With the help of the BP neural network model, a new type of swirl nozzle is developed which is suitable for the outside spray system at the fully mechanized heading face. The experimental results show that the error between the predicted results of the new swirl nozzle and BP network model is less than 15%, the atomization angle θc is 24.2°, the average particle size D32 is 64.43 µm, and the effective range Reff is about 2.1 m. At the same time, the total dust removal efficiency and respirable dust removal efficiency of the new swirl nozzle at the driver’s place are 61.10% and 63.85%, respectively, which are 21.69% and 20.92% higher than the original nozzle.


Introduction
At present, coal is the main energy source for economic and social development. From 2001 to 2019, Chinese coal consumption increased from 1060 million tons of standard coal to 2810 million tons of standard coal (Liu 2020). However, with the accelerated mining of coal mines, disasters have become increasingly prominent, especially the high concentration of dust pollution, which seriously threatens the lives and health of coal miners (National Academies of Sciences and Medicine 2018; Fan and Liu 2021). Pneumoconiosis is a systemic disease mainly characterized by diffuse fibrosis of lung tissue, which is mainly caused by workers inhaling large amounts of productive dust in their occupational activities. Under the current medical level, this disease is extremely difficult to completely cure Shekarian et al. 2021). In addition, the progressive mass fibrosis, lung function loss, and emphysema caused by this disease are slow, and the harm to the human body increases year by year. It is not as severe as coal dust explosions and other accidents, so it is often ignored by coal mine practitioners (Zhang et al. 2021;Trechera et al. 2022). According to the report released by the National Health Commission, a total of 17,064 new cases of occupational diseases were reported nationwide in 2020, including 14,367 cases of occupational pneumoconiosis (2021), accounting for more than 84% of the total number of occupational diseases, and more than 50% of the patients were engaged in the mining industry. Dust has become one of the biggest health threats to coal miners Niu et al. 2021).
In coal mine operations, the most commonly used means to reduce dust concentration is nozzle atomization dust Responsible Editor: Shimin Liu 1 3 removal (Wang et al. 2019b;Li and Li 2021). Atomization dust removal by nozzle mainly captures dust flying in the air through various effects such as fog droplet inertial collision, interception, and gravity settlement and condenses it into large enough dust-containing droplets to settle. Nozzles have indispensable applications in fuel, cooling, spraying, fire prevention, irrigation, anti-virus, and other fields (Cui et al. 2018;Patil et al. 2020;Shi et al. 2020). Their types include direct injection, pressure swirl, ultrasonic atomization, air-assisted atomization, electrostatic atomization, and other forms, among which swirl pressure nozzles have been widely used in coal mine working faces. The swirl nozzle's geometry, the differential between spray pressure and environmental gas leeward pressure, the nature of the gas medium, and the physical properties of the liquid have a significant impact on jet atomization angle, effective range, droplet size, and speed of droplets (Yang et al. 2019;Wang et al. 2019a;Xu et al. 2019), especially when the influences of the nozzle structure parameters on the effect of dust removal are still vague; all these problems make it difficult to improve the nozzle dust removal.
Scholars usually use experimental and simulation methods to study the atomization law of a nozzle; the experimental methods include laser holography, high-speed photography, and the laser phase Doppler interferometer. For example, Li and Li (Li and Li 2021) used a high-speed camera and a Malvern Spraytec diffractometer to study the liquid breaking intensity and droplet size changes in an internal mixed dual-fluid atomizer approaching the nozzle area. Santangelo (Santangelo 2010) used Malvern Spraytec and the particle image velocimetry (PIV) technique to measure the fog droplet size, fog droplet speed, and atomization angle and realized the quantitative description of the fog field based on this. Wang et al. (Wang et al. 2019b) used the Malvern droplet size analyzer and orthogonal test design method to carry out the determination and analysis of particle size of an X-type pressure-swirl atomizer with an exit orifice diameter of 1.0 ~ 2.0 mm and obtained the prediction mathematical model of the Sauter mean diameter in the fog field. However, the above experimental methods still have obvious defects, such as insufficient laser transmission efficiency and a too-short orbit length, which make it difficult to measure the fog field information of high-density fog field and fog field with a length of more than 1.0 m. Because of the pulse effect of the booster pump, it is difficult to keep the atomization pressure constant. However, with the continuous improvement of the performance of computer hardware, the numerical simulation of the fluid domain by computer has made rapid progress, which makes it feasible to get the solution of the liquid atomizing process and discrete fog droplet movement model by computer. In recent years, numerical simulation has become a means that cannot be ignored in the study of mine dust removal (Ren et al. 2014), especially the empirical spray model developed by some CFD software for different types of nozzles, such as the pressure-swirl atomizer model by ANSYS Fluent. Muddapur et al. (Muddapur et al. 2020) used Fluent to study the influence of droplet collision on the nozzle atomization field. In the case of high ambient pressure, the fog field was narrower and the penetration was smaller. Han et al. (Han et al. 2020) simulated the internal and external fluid fields of the nozzle under different water supply pressures and studied the atomization characteristics of the nozzle in the self-developed atomizing dust removal system. The results showed that the dust removal efficiency increased first and then decreased with the increase in water supply pressure. Xu et al. (Xu et al. 2019) analyzed the atomization results of swirl nozzles with different spray pressures and aperture pressures based on the model. The pressure-swirl atomizer model can predict atomization particle size by adopting some empirical formulas and providing atomizer dispersion angle, ligament, and sheet constant parameters. Initial empirical values are often impossible to obtain through experimental methods.
Generally, the atomization process of a swirl pressure nozzle is divided into three cross-scale stages: atomizer inner flow, primary atomization, and secondary atomization (Yu et al. 2021). In the fluid field inside the nozzle, the liquid presents a swirl flow characteristic under the influence of the internal flow passage, which is a typical turbulent flow with a high Reynolds number. Since direct numerical simulation (DNS) of turbulence based on the NS equation requires too much for the computer hardware, it is too low in feasibility, the Reynolds average method (RANS) is usually used to perform the Reynolds average of the fluid dynamic equation and obtain the turbulence model equation after time average. Commonly used turbulence models can be divided into the Raylow stress model and the swirl viscosity model. The swirl viscosity model is widely used in the engineering field. The swirl viscosity model is divided into a zero equation model, a one-equation model, and a dual-equation model. The dual-equation model can be divided into the standard k-ε model, the RNG k-ε model, the realizable k-ε model, and the k-ω model. Compared with the standard k-ε model, the RNG k-ε model is obtained by renormalization group theory, and the dissipation rate equation is modified, which can better deal with the accuracy of high-speed fluid and swirl flow.
In the primary atomization process, there are various swirl clusters of different sizes, so when simulating, the calculation cost of directly simulating the whole fluid field is too high, making it difficult to be widely used. However, the Reynolds average method will lose a lot of fluid field information. Therefore, large eddy simulation (LES) is usually used in the primary atomization stage. The LES model divides the swirl clusters in the fluid field into solvable scales, namely, large eddies, and unsolvable scales, namely, small eddies. Since the large eddies play a dominant role in the fluid field, they are directly solved to obtain the real structure state. The influence of small eddies on large eddies is represented by introducing additional stress terms, namely, a sub-lattice scale model. As second-order implicit was selected in the simulation process, Jasak et al. (Jasak et al. 1999) proposed the implicit LES (ILES) method. The ILES method has been successfully applied in various fluid working conditions, including uniform turbulence (Aspden et al. 2008), free shear flow (Xia and Tucker 2012), wall boundary flow , and spray processes involving reactions .
In the secondary atomization process, the droplets of large particles are broken into droplets of smaller particle sizes. In 1982, Reitz (Reitz 1982) created the KH model of jet fragmentation, and the KH model was only applicable to the process of jet surface fragmentation but could not be applied to droplets directly exposed to air. Later, O'Rourke and Amsden (O'Rourke andAmsden 1996, 2000) proposed the Rayleigh-Taylor (R-T) wave atomization model to describe the droplet-crushing process in the gas-liquid mixing zone. The R-T surface wave instability theory is used to describe the process in which droplets moving at high speed in the air are decelerated by air resistance, resulting in unstable waves on the leeward side of droplets and forming the small droplets as split. The Weber number of droplets in the secondary atomization stage of the swirl pressure nozzle is more than 10,000. Therefore, the aerodynamic driven KH model is adopted to solve secondary crushing by combining the RT method driven by droplet acceleration spewed out in free flow.
In this study, aiming at the problem that the influence law of the structural parameters of the swirl pressure nozzle on the atomization effect is not clear, the swirl nozzle is simulated and analyzed based on the multiscale swirl atomization model. Through the comparative analysis of the structural parameters of different nozzles, the nonlinear function relationship between the nozzle structural parameters and the atomization effect is obtained. The influence law of nozzle structure parameters on the atomization effect is clarified, and a new series of swirl nozzles suitable for the spray system outside the fully mechanized heading face were developed with the help of the BP neural network algorithm, which provided theoretical guidance for the design and development of the mine nozzle.

Numerical approach
The internal swirl field (Δx ~ O(10 −4 ) m) of the swirl pressure nozzle has a complex fluid passage. The k-ε model is used to solve the turbulence characteristics, and then transfer the velocity, turbulent kinetic energy, and turbulent dissipation rate to the initial atomization stage. In the primary atomization stage (Δx ~ O(10 −5 ) m), the liquid core is broken mainly due to aerodynamics. The LES model and the volume of fluid (VOF) model can be used to describe the turbulence characteristics and capture the gas-liquid interface, respectively, to obtain the initial liquid film characteristics, and then transfer the initial liquid film velocity field value, velocity direction, position distribution, and volume fraction to the secondary atomization stage. In the secondary atomization stage (Δx ~ O(10 −5 ) m), the continuous phase is separated into fog droplets. At last, the k-ε model and the discrete phase model (DPM) are used to calculate the further fragmentation of fog droplets. A unidirectional coupling module is built with the help of the C + + language, as shown in Fig. 1.

Internal flow field model
Both water and air are regarded as incompressible fluids in the multiscale simulation model (Zhang et al. 2015). The internal flow field is a turbulent flow with a high Reynolds number. The basic idea is to represent Fig. 1 Schematic of the simulation method the instantaneous pulsating quantity of the fluid in the time-averaged equation via RNG k-ε two-equation models. The RNG k-ε model is employed due to its improved accuracy for capturing the effect of swirl on turbulence and flows with strong streamline curvatures, vortices, and rotation (Prabkeao and Aoki 2005;Amini et al. 2015;Gabor et al. 2017).

Primary atomization model
The primary atomization is mainly driven by the change in gas-liquid interface topology. Hirt and Nichols (Hirt and Nichols 1981a) proposed a VOF model for solving the gas-liquid free surface. Both the gas and liquid phases were considered as incompressible and immiscible, and the incompressible Navier-Stokes equations were solved for the conservation of mass and momentum. The momentum equation is dependent on the volume fractions of all phases through density and viscosity.
This research adopts the continuum surface force (CSF) model, where the surface curvature was computed from local gradients in the surface normal at the interface. Let ⃗ n be the surface normal and the surface curvature is =∇ ⋅ ⃗ n (ANSYS, Inc 2015). To describe the interface motion precisely, handle pressure jump conditions at the interface without artificial smoothing, and respect mass conservation, the level set (LS) algorithms are incorporated into the VOF model (Hirt and Nichols 1981b;Ménard et al. 2007;). In addition, the second-order implicit method was selected. The implicit LES (ILES) approach (Boris 2013;Doisneau et al. 2017;Laurila et al. 2019) by discretizing the convection term in the momentum equation with the nonlinear flux limiting scheme. The ILES approach has been successfully applied in a wide range of flow scenarios including homogeneous turbulence (de Wiart et al. 2015), free shear flows (Karaca et al. 2012), wall-bounded flows , and in multiphysics applications such as reacting sprays (Wehrfritz et al. 2016).

Injection method of droplets
The pressure-swirl nozzle has an X-swirl core structure, which makes the liquid column of the nozzle have swirl characteristics. Considering the velocity difference between the central core and the peripheral film, the characteristics of the first liquid film entering the secondary atomization inlet are stored as the droplet injection parameters.

KH-RT model for secondary breakup
In the secondary crushing process, large droplets are broken into small droplets, which are mainly driven by aerodynamics (Tavangar et al. 2015). According to Liu and Reitz (Liu and Reitz 1993), with the increase in crushing behavior, the crushing mechanism of secondary atomization is generally divided into bag crushing, stripping (shear) crushing, and catastrophic crushing. The KH-RT model is used to deal with the rupture (Wang et al. 2019c) (ANSYS, Inc 2015) under high Weber numbers. The aerodynamic KH model is combined with the RT method driven by droplet acceleration. The KH-RT model assumes that there is a liquid core near the nozzle, and the sub-droplets split from the liquid core, accelerate, and are affected by RT instability.

Single droplet forces
The forces on a single droplet include drag, weight, buoyancy, and forces due to pressure gradient and added mass. Some of these forces are negligibly small due to the highdensity ratio between droplets and air (Schiller 1935). The total force acting on dust particles can be expressed as follows: where P is the static pressure; μ denotes the laminar viscosity; ⃗ u is the air velocity vector; ⃗ u p is the particle velocity vector; d P is particle diameter; V P is particle volume; C D represents the drag coefficient, a frequently used correlation in spray modelling, which is defined as when Re is less than 0.1, C D = 24/Re; when Re is greater than 0.1 and less than 1000, C D = 24 × (1 + 1 6 Re 2 3 )∕Re ; when Re is greater than 1000, C D = 0.44.where Re is the Reynolds number, 1981). In addition, the algorithm of O'Rourke uses the concept of a collision volume to calculate the probability of collision (Peng et al. 2019).

Nozzle structure parameters
The fully mechanized heading face of a coal mine is selected as the research object in this study. The fully mechanized heading face is an arc arch section with a width of 5.74 m, a height of 4.12 m, and a section area of 21.19 m 2 . The total thickness of the rock layer is 20 m and the dip angle of the rock layer is 82 ~ 86°. Pressure ventilation is adopted, and the ventilation volume is 620 m 3 /min. The EBZ-260 type roadheader is used for tunneling in the way of full sections once formed. The distance between the end of the cutting arm and the headface area is 1.84 m.
Considering the influence of other factors comprehensively, the effective range of the nozzle needs to reach 2.0 m. The EBZ-260 roadheader is equipped with 8 swirl nozzles with a diameter of 2.2 mm, but the average particle size of the droplet in the fog field sprayed out by the nozzles is more than 120 µm, the effective range is only 1.5 m, the atomization angle is only 19°, and the dust removal efficiency is too low when spraying. In this study, the typical swirl pressure nozzle is studied, the influence law of swirl nozzle structure parameters on dust removal efficiency is analyzed, and then the swirl nozzle suitable for fully mechanized heading face is optimized (Fig. 2). The structure parameters of the swirl nozzle determine the velocity distribution and turbulence intensity of the liquid core at the nozzle outlet. Under the condition of constant spray pressure, the structure parameters of the nozzle indirectly affect the atomization angle, average particle size, and effective range of the fog field. This article selected the swirl nozzle with a built-in X-type swirl core. As there are too many structural parameters affecting the atomization effect, such as swirl chamber aperture diameter D s , swirl chamber length L s , swirl chamber circulation area ratio SCR, spiral core angle α, tapered angle β, contraction section type and length L g , exit section length L e , nozzle aperture diameter d 0 , and nozzle flaring type and angle, among which the types of nozzle flaring can be divided into a rectangular cutting angle, trapezoidal cutting angle, smooth curve cutting angle, etc. (Ménard et al. 2007), as shown in Fig. 3.
In order to analyze the influence law of an X-type swirl core on the atomization effect of a swirl nozzle, four structural parameters, namely swirl chamber aperture D s , swirl chamber length L s , swirl chamber circulation area ratio SCR, and swirl core angle α, were selected for comparative analysis, and 20 different nozzle structural design schemes were formed based on these parameters, as shown in Table 1.
The diameter of the water inlet is 6.7 mm, the length of the inlet section is 7.5 mm, and the length of the swirl core is 5.7 mm. Other parameters are shown in Fig. 3. The length of the primary atomization stage L 2nd is 12 mm, and the length of the secondary atomization stage is 3000 mm. Considering that the static pressure of the working face water supply is higher than 3.0 MPa, the inlet water pressure of 3.0 MPa is selected to carry out the study.

Boundary conditions
According to the atomization simulation process of a swirl nozzle, this study is divided into the following three aspects to set the conditions: (1) The water inlet boundary type of the fluid field in the nozzle is the pressure-inlet, the pressure is 3.0 MPa, and the velocity is perpendicular to the inlet surface of the nozzle. The outlet boundary type of the nozzle is pressure-outlet, and the pressure is 0 Pa. An X-shaped swirl core and the inner wall of the nozzle are all nonslip wall boundary types. (2) In the primary atomization stage, the inlet surface boundary type is velocityinlet, and a user-defined function is added to ensure that the velocity and turbulence intensity is the same as the fluid field outlet in the nozzle. The other surface boundary type is pressure-outlet as 0 Pa, and the surface tension coefficient is 0.071 N/m. (3) All surface boundary types at the secondary atomization stage are all pressure-outlet Due to the influence of different nozzle structure parameters, the fluid velocity varies differently in the internal flow field, the primary atomization, and the secondary atomization, leading to different simulation times required in each spray stage. In the simulation, it is mainly to judge whether the flow field in each stage reaches a stable state and then stop the simulation. Other parameters are shown in Table 2. I represents the fluid field in the nozzle, II represents the primary atomization stage, and II represents the secondary atomization stage.

Validation of model
The fully mechanized heading working face is often accompanied by high-speed airflow to ensure the breathing quality of coal miners and the safety of coal production. High-speed airflow will seriously affect the fog field morphology and significantly reduce the dust removal effect of the nozzle. Therefore, this study selected three water inlet pressures and designed fog droplet size and fog field morphology measurement to verify the accuracy of the multiscale model, as shown in Fig. 4. A BPZ75/12 booster pump was used to provide different pressures in the range of 0 ~ 7 MPa. After the booster pump, water was sprayed  (1) Fog field morphological image collection experiment: a K45-6 exhaust fan with a rated speed of 980 rpm and a maximum flow of 28.5 m 3 /s is used to provide a steady airflow at 0.5 m/s in a ventilation box with the size of 9.5 m × 2.1 m × 2.1 m. The morphological image of the fog field is captured by a high-speed camera perpendicular to the direction of the airflow.
(2) Droplet size measurement experiment: the Malvern Spraytec particle size analyzer of the phase Doppler anemometer (PDA) was used to measure the droplet size across a wide size range (0.1 ~ 2000 µm) without requiring constant optic changes. The particle size analyzer is equipped with an air compressor to avoid droplets falling on the lens of the transmitter and receiver. According to the transmission efficiency of the laser, the droplet diameter was determined by transmitting and receiving the pulsed laser within Considering the influence degree of lateral wind on the fog field, a 1.5-m spray field was intercepted for comparative analysis, and the results are shown in Fig. 5. With the increase of the jetting distance, the kinetic energy of the droplet gradually decreased under the action of air resistance. Figure 5 shows that the initial position (area I) was significantly deviated from the cone of the droplet field, and the initial position was similar in both the experimental and simulation results. Under the action of lateral wind flow, the lateral offset of the droplets gradually increased (area II), and the coverage of the droplet field has changed. The values δ s and δ e were used to indicate the coverage of the simulated and experimental droplet field at 1.5 m, respectively. The relative error between δ s and δ e was about 7.0% ~ 17.0%. Considering that there were some uncontrollable factors in wind experiments, the multiscale simulation can be considered accurate.
Due to the complexity of the spray atomization process, it is often difficult to obtain the droplet size distribution with good consistency. The Sauter mean diameter (D 32 ) and the De Brouckere mean diameter (D 43 ) are the most widely used indices in coal mines. The results are shown in Table 3. With the increase of the spray pressure, the D 32 and D 43 values in both the simulation and the experimental results were gradually reduced, and the trends in both the simulation and the experiment were similar. Compared with the experimental results, the relative error of D 32 was 18.06% ~ 21.04%, and the relative error of D 43 was 11.18% ~ 17.11%. The relative

Analysis of the swirl degree of the fluid field in the nozzle
In order to quantify the swirl motion in the internal flow field, the dimensionless swirl number S n was adopted to characterize the swirl degree of water flow. S n is the ratio of the axial moment of momentum of tangential force to the axial moment of momentum of axial force. The calculation formula defined by Chigier and Beer was generally adopted (Sun et al. 2019): where G m and G t are the axial flux of angular momentum and axial momentum, respectively; u and w are the axial velocity and tangential velocity, respectively; r is the distance from the grid position to the center of the section; and R indicates the radius of the reference section. The static pressure term can be ignored when calculating the swirl number according to the velocity distribution of a section.
The swirl number Ω was computed by Eqs.
(2)-(4), as shown in Fig. 6. The influence law of different structural parameters on swirl number was as follows: under the influence of the contraction segment, the variation of swirl number along the journey of different swirl chamber apertures all showed the trend of decreasing first and then increasing. The curve fitting of the Ω value on the outlet surface showed that the Ω value decreased with the increase of swirl chamber aperture, obeying the quadratic function relationship: Ω = 1.38 − 0.3D s + 0.02D s 2 , and the fitting variance was 0.9858. Because the swirl chamber length varied greatly, the variation trend of the swirl number along the different swirl chamber lengths was not consistent. The curve fitting of the Ω value at the outlet surface showed that the swirl number increased with the increase of swirl chamber length. Under the influence of the contraction section, the variation of swirl number along the journey with different swirl chamber circulation area ratios showed a trend of decreasing first, then increasing, and then decreasing. The curve fitting of the Ω value at the outlet surface showed that the Ω value decreased with the increase of the swirl chamber circulation area ratio. Under the influence of the contraction segment, the variation of swirl number along the journey at different swirl core angles basically showed a trend of decreasing first, then increasing, and then decreasing. The curve fitting of the swirl number at the outlet surface showed that the value of Ω decreased with the increase of the swirl angle.

Comparative analysis of atomization angle
Water flow leaves the nozzle to atomize and form an approximately hollow cone fog field. Because the internal velocity of the fog field is higher than the surface, negative pressure is formed in the center of the fog field, and the fog field shrinks along the journey due to the effect of the internal and external pressure difference. Compared with the atomization angle at the outlet, the conditional atomization angle can better reflect the dust coverage of the spray field. The conditional atomization angle under different structural parameters is shown in Fig. 7. As the fog field is basically circumferentially symmetric, only the left part of the fog field is shown in the figure.
Combined with the contrast diagram of the atomization angle of different swirl chamber apertures, it can be seen that the swirl chamber aperture has the most significant influence on the swirl degree of the nozzle. As the swirl chamber aperture increases from 4.0 to 8.0 mm, the swirl number at the nozzle outlet decreases from 0.49 to 0.17, which is 65.31% lower, and the atomization angle gradually decreases from 28.0 to 16.0°, which is 42.86% lower. The function relationship is obtained by nonlinear curve fitting: θ c = 52.14 − 7.39D s + 0.357D s 2 , and the fitting variance is 0.9868.
It can be seen from Fig. 6 that the variation trend of the swirl number along the journey of different swirl chamber lengths was very different, increasing from 0.28 to 0.80 with an increase of 185.71%. However, it can be seen from Fig. 7 that the swirl chamber length had no significant influence on the atomization angle. As swirl chamber length increased from 7.0 to 16.0 mm, the atomization angle variation degree is less than 4.0%, indicating that the atomization angle of different swirl chamber lengths is close to a constant 25.0° when other nozzle parameters are fixed. The circulation area ratio of the swirl chamber has a significant influence on the swirl degree of the nozzle. With the increase of the swirl chamber circulation area ratio, the swirl number at the nozzle outlet gradually decreases to 0.31, and the atomization angle also decreases to 23.0°, decreasing by 32.35%. However, with the increase of the swirl chamber circulation area ratio, the decreasing speed of the atomization angle gradually slows down. As the swirl angle increases from 30 to 50°, the swirl angle has a significant influence on the swirl number along the journey, and the swirl number at the nozzle outlet gradually decreases to 0.19, and the atomization angle also decreases to 20.0°, with a decrease of 28.57% (Fig. 8).

Comparative analysis of average particle size in fog field
In the fog droplet group, the proportion of droplets in different particle size ranges is called fog droplet size distribution. In order to analyze the average particle size of the fog field under different spray parameters, D 32 is uniformly selected as the evaluation index of fog field particle size distribution, and the results are shown in Fig. 9. It can be seen from Fig. 9 that the average particle size D 32 of different swirl chamber aperture D s , swirl chamber length L s , swirl chamber circulation area ratio SCR, and swirl core angle α all tend to be stable in the region where SL is greater than 0.8 m, so the average particle size is selected for analysis when SL = 0.8 m. The average particle size change along the journey of different chamber apertures has a similar trend, showing a trend of significantly decreasing at first, then increasing in a fluctuating manner, and then gradually stabilizing. When SL = 0.8 m, the Different swirl chamber lengths, swirl chamber circulation area ratios, and the swirl core angles affect the mean  The results of droplet mean diameter D 32 with different nozzle parameters along the axial direction, (a) Swirl chamber aperture, (b) Swirl chamber length, (c) Swirl chamber circulation area ratio, (d) Swirl core angle particle size change trend along the journey is similar to swirl chamber aperture, all showing the trend of significantly decreasing first, then increasing in the type of fluctuations, and then gradually being stable. With the increase of swirl chamber length, average particle size shows the trend of decreasing first and then increasing. When the swirl chamber length is 7.0 mm, the average particle size is 89.2 μm. When the length of the swirl chamber is 13.2 mm, the average particle size decreases to 78.9 μm, a decrease of 11.55%, and when the length of the swirl chamber was 19.0 mm, the average particle size increases to 83.7 μm, an increase of 6.08%. When the swirl chamber circulation area ratio is 0.056 and 0.080, the variation range of the average particle size change along the journey is larger than the other three groups. When the swirl chamber circulation area ratio is 0.106, 0.136, and 0.170, the variation range of the average particle size change along the journey is close. With the increase of the swirl chamber circulation area ratio, the average particle size shows a trend of decreasing first and then stabilizing. The average particle size decreases from 101.0 to 79.3 μm, which decreases by 21.49% when the swirl chamber circulation area ratio increases from 0.056 to 0.136. When the swirl chamber circulation area ratio of the swirl chamber increases to 0.170, the average particle size increases to 81.2 μm, increasing by 2.40%. With the increase of swirl core angle, the change curve of an average particle along the journey size shows a general decreasing trend, except α = 45°. With the swirl core angle increasing to 50°, the average particle size generally shows a gradually decreasing trend, decreasing from 93.7 to 71.2 μm, decreasing by 24.01%.

Comparative analysis of speed along the journey
Through the analysis of droplet velocity fitting results along the central axis of the fog field, it is found that the influence of the swirl chamber length of swirl chamber on droplet velocity can be basically ignored, but other nozzle structural parameters mainly have a great influence on the injection distance within 1.0 m, and the influence is not significant when the injection distance exceeds 1.0 m. The droplet velocity at SL = 2.0 m and SL = 3.0 m is extracted for analysis and calculation, and the fluctuation rate of droplet velocity variation caused by the change of each structural parameter of the nozzle is obtained.
With the increase of the swirl chamber aperture, circulation area ratio, and swirl core angle, the droplet velocity tends to increase, and the droplet velocity fluctuates within 1.5 m/s under different parameters. At SL = 2.0 m and SL = 3.0 m, the fluctuations of different swirl core angles are the lowest, only 12.0% and 13.1%, followed by the fluctuations of different swirl chamber apertures are 12.2% and 13.7%, and the fluctuations of different swirl chamber circulation area ratio are the highest, which are 18.0% and 24.1%. With the increase in injection distance, the final droplet velocity of different swirl chamber apertures approaches 4.6 m/s, the final droplet velocity of different swirl chamber lengths and different swirl core angles approaches 3.8 m/s, and the final droplet velocity of different swirl chamber lengths approaches 3.5 m/s (Fig. 10).

Comparative analysis of an effective range
After the droplets are emitted from the nozzle mouth, the place where is near the nozzle is the conical effective action area. The droplets in this area have a higher speed and smaller particle sizes, and the droplets can effectively capture dust in this area. The length of this area is called the effective range of the nozzle. In order to compare the effective ranges of different fog fields, a horizontal line is drawn along the nozzle outlet, and the intersection point of the horizontal line and the contour of the fog droplet concentrated area is taken as the effective range. The results are shown in Figs. 11,12,13,14,and 15. It can be found in comparative Fig. 11, which shows the effective ranges of different swirl chamber apertures, that when the swirl chamber aperture is small enough, the fog field formed by the swirl atomizing nozzle will become a hollow fog field. With the increase of the swirl chamber aperture, the atomization angle decreases by 42.86%, resulting in a gradual decrease in resistance along the journey, and the effective range increases from 1.55 to 2.61 m, an increase of 68.39%. The function relationship is obtained through curve fitting, for example, R eff = 0.819 + 0.1623D s + 0.007D s 2 , and the fitting variance is 0.9813. According to Fig. 12, the atomization angle varies less than 4.0% with different swirl chamber lengths, the average particle size of the fog field is different, and the resistance along the path has different effects on the fog field. As a result, with the increase of swirl chamber lengths, the effective range tends to decrease generally, decreasing from 2.17 to 1.88 m, a decrease of 13.36%. As can be seen from Fig. 13, the swirl chamber circulation area ratio has a significant impact on the effective range. With the increase of the swirl chamber circulation area ratio, the effective range gradually increases from 1.70 to 2.15 m, an increase of 26.47%. According to the analysis of Fig. 14, different swirl core angles have a significant influence on both the atomization angle and the effective range. With the increase in core angle, the effective range gradually increases from 1.80 to 2.35 m, increasing by 30.56%.

Neural network prediction and optimization
The internal structure parameters of the swirl nozzle significantly affect the atomization effect of the nozzle, but it is difficult to obtain the quantitative calculation model of the 1 3 atomization effect of the multi-parameters so as to realize the inverse derivation from the atomization effect to nozzle structure. Therefore, a BP neural network model is proposed in this study. BP neural network, through the establishment of a multi-layer perceptron model, using the learning mechanism of signal forward propagation and error reverse adjustment, through multiple learning to build a network model to deal with nonlinear information, and then, aiming at the swirl nozzle, carries out the atomization effect prediction based on the network model and optimizes the nozzle structure suitable for fully mechanized heading face.

Construction of BP neural network model
BP neural network is a kind of multilayer feedforward neural network trained according to an error backward propagation algorithm, which needs a large number of input and output data as samples. Therefore, this study will combine the nonlinear relationship equation between the nozzle structure and the atomization effect to realize the expansion of data samples. The optimization process of the nozzle parameter scheme is as follows: Firstly, the number of samples is calculated and expanded according to the nonlinear relation equation. The BP algorithm is constructed by MATLAB program. The input layer variables are selected as swirl chamber aperture D s , swirl chamber length L s , swirl chamber circulation area ratio SCR, and swirl core angle α. The value range is 4.0 ~ 8.0 mm, 7.0 ~ 19.0 mm, 0.056 ~ 0.170, and 30° ~ 40°, respectively. In order to obtain the optimal nozzle structure and divide the value range of D s , L s , SCR, and α into 20 equal parts, and a total of 160,000 groups of nozzle parameter schemes are prepared. The 160,000 groups of data would be read into the model successively. The net model completed by training would be used to predict the atomization effect and determine whether the screening conditions are met. According to the screening principle, structural parameters with large atomization angle and small average particle  (Table 4).
In order to prevent the over-fitting of the BP neural network model, MATLAB adopts the following method, which divides the data into three groups: training samples (150 groups), verification samples (78 groups

Analysis of optimization results of BP neural network model
The verified BP neural network is used to optimize the swirl nozzle, and the new swirl nozzle parameter design scheme is obtained. The nozzle swirl chamber aperture D s is 4.0 mm, the swirl chamber length L s is 13.0 mm, the swirl chamber circulation area ratio SCR is 0.0959, and the swirl core angle α is 37°. In the simulation results, the atomization angle θ c is 28.528°, the average particle size D 32 is 75.3237 μm, and the effective range R eff is 2.255 m. In order to verify the atomization effect of the new swirl nozzle, physical processing of the new swirl nozzle is carried out, and laser cutting is carried out on the nozzle. After processing, the parameters and sizes of the nozzle are measured. The measured effective water-passed area of the nozzle is 0.599 mm 2 , and the area of the contraction section is 12.5 mm 2 . The new swirl nozzle is shown in Fig. 17   experimental platform of the swirl nozzle fog field characteristics described in Fig. 4, the atomization angle, droplet size distribution, and effective range of the new swirl nozzle are experimentally determined, and the measurement results are shown in Fig. 17. At 3.0 MPa inlet pressure, the atomization angle of the new swirl nozzle is 24.2°, 13.82% lower than the simulated value of 28.0794°. However, the average particle size of the new swirl nozzle at 0.8 m D 32 is 64.43 μm, 13.31% lower than the simulated value of D 32 74.3237 μm. The measured effective range is about 2.1 m, which is 6.85% lower than the simulated effective range of 2.2545 m. Therefore, it can be inferred that the prediction and optimization method of the swirl nozzle based on the BP neural network of a nonlinear equation is relatively accurate and feasible. In conclusion, the new swirl nozzle meets the requirements of the spray range outside the surface of the fully mechanized heading face, and the average particle size is lower than the simulated value, which makes up for the disadvantage of small atomization particle size at low inlet pressure.

Field measurement
In order to obtain the improvement effect of the new swirl nozzle on dust removal efficiency, the new swirl nozzle was installed on the spraying system of the roadheader at a fully mechanized heading face, and dust sampling was carried out using the filter film sampling method, CCZ20 mine dust sampler, and organic filter film. The dust reduction efficiency η is calculated by the formula (5), where C 1 is the dust concentration when the nozzle is not used, and C 2 is the dust concentration after the nozzle is used.
During the experiment, a total of five sampling points were set up: the roadheader driver's place, 20 m, 40 m, 60 m, and 80 m away from the heading face, and the sampling height was 1.5 m respirable height. A total of three groups of comparative experiments were conducted: no nozzle was used, the original nozzle was used, and the new nozzle was used. The results are shown in Fig. 18. Respiratory dust is a kind of dust particle that can be inhaled by the human body, and dust smaller than 7.07 μm is generally referred to as respirable dust; these dust particles will directly enter the human lungs, causing lung lesions. Therefore, the concentration of respirable dust is particularly important. The results show that the dust removal efficiency of total dust and respirable dust using the original nozzle is 39.41% and 42.92% at the driver's place of the roadheader. While the dust removal efficiency of total dust and respirable dust using the new swirl nozzle is 61.10% and 63.85%, the dust removal efficiency increases by 21.69% and 20.92%, respectively. It can be found that the dust reduction efficiency of respirable dust is slightly better than that of large-particle dust in the preferred spray technology scheme. It can be inferred that when spray technology is not used, large-particle dust can quickly settle to the floor under the action of gravity, while respirable dust can only settle after combining with the droplets. Therefore, after adding spray, the dust reduction effect of small particle dust is more significant and slightly better than that of large particle dust (Fig. 19).
With the increasing distance between the sampling point and the heading face, the proportion of respirable dust at each point shows an increasing trend. At 80 m away from the heading face, the dust removal efficiency of respirable dust using the original nozzle is 39.77%, and that using the new nozzle is 55.89%. Compared with the original nozzle, the dust removal efficiency of the new swirl nozzle is still improved by 16.12%. Therefore, the new swirl nozzle plays a significant role in improving the dust removal efficiency of the spray at the fully mechanized heading face.  80m from heading face

Conclusions
The multiscale method was used to perform the atomization process of the pressure-swirl nozzle. The relative error of mean droplet diameters between simulation and experimental results was obtained to be 18.06% ~ 21.04%. The simulation results of the droplet field morphology were basically consistent with the experimental results. Based on the analysis, the following conclusions were obtained: (1) Under the influence of the contraction section, the change of swirl number Ω along the journey of different swirl chamber apertures D s shows the trend of decreasing first and then increasing. The change of Ω along the journey of different swirl chamber circulation area ratios SCR, and different swirl core angles α shows the trend of decreasing first, then increasing, and then decreasing. As the change of swirl chamber length L s parameters is large, the change trend of Ω along the journey of different swirl chamber lengths is not consistent. The swirl number Ω at the outlet surface decreases with the increase of the swirl chamber aperture D s , the swirl chamber circulation area ratio SCR, and the swirl core angle α, decreasing by 65.31%, 16.22%, and 47.22%, respectively, and increases with the increase of the swirl chamber length L s , increasing by 185.71%. (2) The atomization angle θ c decreases with the increase of the swirl chamber aperture D s , the swirl chamber circulation area ratio SCR, and the swirl core angle α. The atomization angle of SCR has the largest variation, with a decrease of 32.35%. L s has no significant effect on θ c . With the increase of D s , L s , SCR, and α, D 32 shows a trend of significantly decreasing at first, then increasing in a type of fluctuation, and then gradually being stable. The average particle size decreases with the increase of D s and α. With the increase of L s , the average particle size shows a trend of decreasing first and then increasing.
With the increase of SCR, the average particle size shows a trend of decreasing first and then stabilizing, which decreases by 21.49%. With the increase of D s , SCR, and α, U shows an increasing trend. The drop velocity fluctuation under different parameters is within 1.5 m/s, and the fluctuation rate of SCR is the highest. The effective range R eff increases by 68.39%, 26.47%, and 30.56% with the increases of D s , SCR, and α, respectively, and decreases by 13.36% with the increase of L s . (3) After the BP neural network passes the verification, the BP neural network is used to optimize the design scheme of a new swirl nozzle with an inlet pressure of 3.0 MPa. The new swirl nozzle has an effective range of 2.1 m, an atomization angle of 24.2°, and an average particle size of 64.43 μm. After the new nozzle is applied to the fully mechanized heading face, the total dust removal efficiency and respirable dust removal efficiency at the driver's site are 61.10% and 63.85%, respectively, which are 21.69% and 20.92% higher than that of the original nozzle. The respirable dust removal efficiency in the area 80 m away from the heading face is also 16.12% higher than that of the original nozzle.