Comparative Analysis of Dynamic Behavior of Liquid Droplet Impacting Flat and Circular Wires

Abstract

The performance of droplets captured by the wire mesh demister in a seawater desalination system seriously affects the quality of water desalination. Therefore, it is of great significance to study the droplet impact in the wire mesh demister to improve the demister’s efficiency. In this paper, a two-dimensional model of the droplet impacting the wire is established. The processes of the droplet impacting a flat wire and a circular wire are simulated by using the VOF model in Fluent, and a comparative analysis is conducted. The results demonstrate that both wires experience spreading and splashing stages, but when the wire is circular, the length of the lifted lamella is longer, the peak force on the wall is larger, the splash’s start time is earlier, and the number of secondary droplets is greater; the variation rule of the force on the wall caused by the change of initial velocity is similar, and the increase in initial velocity will promote the occurrence of splash phenomenon, but the role of the initial velocity on the splash effect is more obvious for the circular wire; and when the droplet impacts the flat wire, the influence of incident angle on the critical splash velocity is non-monotonic, but the critical splash velocity increases with an increase in incident angle when the wire is circular.

1. Introduction

The wire mesh demister plays an important role in many fields, such as seawater desalination. It is made of many wound filaments of metal or other material and the wire shape is generally cylindrical with a diameter of 0.076–0.4 mm or a flat wire of 0.1 × 0.4 mm². When the mesh pad is placed horizontally during the process of the mixture of vapor and liquid droplet flow from the bottom to the top of the mesh demister, the vapor automatically bypasses the mesh wire and passes through the pores, while the droplets carried in the vapor flow will be captured by the mesh wire due to inertial movement. There are many factors that affect the demister efficiency. After the droplet inertia impacts the wire mesh, it may generate secondary droplets, resulting in secondary entrainment, an important factor that affects the demister efficiency. Therefore, it is very important to study the dynamic process of droplet impacting the wire mesh wall and explore the specific factors affecting the splash, so as to reduce the formation of secondary droplets in the wire mesh demister and improve the demister efficiency.

The impact of droplets on solid walls is a common phenomenon. As early as 1876 [1] and 1877 [2], Worthington experimentally studied the process of water and mercury impacting plates smoked and baked by stearic acid candles. After studying the process of milk and mercury droplets impacting the smooth glass plate, he pointed out that the droplet size and the initial distance between the droplet and the wall would affect the generation of secondary droplets [3]. Later, scholars experimentally carried out deeper and more extensive research on the droplet impact phenomenon to discuss the specific factors that affect the splash. Palacios et al. [4] experimentally studied the deposition and coronal splashing mode of droplets impacting the dry glass plane with different viscosities, analyzed the critical Weber number of droplet state transition, and concluded that viscosity had a significant impact on droplet spreading and splashing. Arizona et al. [5] conducted an experimental study on the dynamic behavior of continuous multiple glycol droplets impacting the wall with concentrations of 0%, 5%, and 15%, and found that the smaller the surface tension was, the larger the spreading ratio was. Sikalo et al. [6] investigated water, glycerol, and isopropanol droplets with different Weber numbers’ impact on smooth or rough glass, wax, and PVC surfaces and found that the critical state of splash was related to the Weber number of droplets, and decreasing surface tension or increasing surface roughness would reduce the critical Weber number. Zhang et al. [7] established a droplet impact splash threshold model considering wall wettability based on experimental data, and proposed that surface wettability has a certain influence on droplet splash. Xu et al. [8,9] found that reducing environmental pressure could inhibit or even prevent the occurrence of splash phenomenon. Hao et al. [10] experimentally studied droplets impacting a smooth surface under different inclination angles and environmental gas pressures and concluded that increasing inclination angle and decreasing environmental pressure could completely inhibit droplet splashing. Aksoy et al. [11] experimentally explored the splash phenomenon of nano-droplets with different concentrations impacting the wall, and the results showed that nano-fluid could promote the splash phenomenon at a low Reynolds number. In addition, they established an empirical correlation of splash threshold including nanoparticle concentration for the first time.

Researchers have also carried out some numerical simulations to explore phenomena that could not be experimentally investigated. Wu et al. [12] used VOF to simulate droplet splash on a smooth dry solid surface, and determined that the start time of the splash was mainly related to the velocity and radius of the droplet, but not to the viscosity and surface tension. Tan [13] simulated the splashing effect of high-speed micro-droplets impacting the surface of micrographs using a three-dimensional numerical simulation, revealing the important role of impact velocity and wall surface topography on the splash phenomenon. Xia et al. [14] designed a random rough surface, simulated the phenomenon of a paint droplet impacting the wall with COMSOL Multiphysics software, and pointed out that the root mean square roughness (Rr) could more effectively promote droplet splashing than the Wenzel roughness parameter (Wr). Zhang et al. [15] used the SPH method to simulate the effect of a droplet impacting the inclined plane, and concluded that when the impact angle was less than 44°, the droplet impacting the wall would have splash phenomenon. The simulation results of Yokoi [16] showed that increasing the dynamic contact angle could promote the splash phenomenon. Shen et al. [17] used the Boltzmann method to simulate the process of a droplet impacting the tube surface. It was found that the splash occurred on the hydrophilic wall only when the impact velocity was high, while the splash occurred on the hydrophobic wall at a low impact velocity.

In the process of a droplet impacting the wall, the droplet spreads out and forms a liquid film. The shape of the advancing interface (such as the dynamic contact angle or lamellar thickness) and the motion (such as the motion of the vapor–liquid–solid contact line) determine the boundary conditions of the flow. Many scholars have conducted in-depth research on the mechanism of droplet spreading [18,19,20,21,22,23,24,25]. For example, Hoffman [18] studied the shape of the advancing interface, Cox [19] analyzed the dynamic process of the contact line movement, Tanner [20] pointed out that the slope of the advancing interface was related to the velocity at the boundary, and Bazzi et al. [22] concluded that mastering the evolution of film thickness and axial velocity could predict the rupture time. It is necessary to analyze the shape of the forward interface and the three-phase contact line to explore the mechanism of droplet splashing and secondary droplet formation.

Most of the studies have focused on millimeter-scale droplets, and the droplet impact process had no other external force, which is different from the environment in the wire mesh demister. There are two types of wire in the wire mesh demister: flat and cylindrical, whose sections are planar and circular, respectively. The current research has involved the droplet impact phenomenon on the plane, cylindrical surface, and spherical substrate, but there is little comparative analysis. Compared to experiments, simulations are easy, can save labor, and can obtain some parameters that cannot be accurately obtained by experiments. In order to better explore the influencing factors of the droplet impact phenomenon in the wire mesh demister, this paper uses the VOF model in Fluent to simulate the process of droplet impact on a flat wire and a circular wire, and makes a comparative analysis.

2. Model and Method

2.1. Physical Model

The working process of the wire mesh demister is as follows: when a vapor with tiny droplets flows through the wire, the droplets interact with the wire and are finally captured by it. This paper focuses on the inertial capture process. Since the wire shape is mainly composed of flat wire and circular wire, the wall can be simplified into a plane and a circular wall, respectively. The surface of the wire is considered to be absolutely smooth without considering the influence of roughness. In the simulation process, the droplet is simplified into a standard circle, and the process begins from the initial moment when the droplet contacts the wall. The two-dimensional model and the boundary conditions of each side are shown in Figure 1, where point O is the coordinate origin and axis Y is the axis of symmetry. Water and vapor are used as the working fluids for the droplet and surrounding gas respectively.

2.2. Mathematical Model

The VOF model in Fluent for multiphase flow is used to simulate and analyze the phenomenon of droplet impacting the wire. The VOF model uses a volume ratio to describe the proportion of each phase in each control volume, and the sum of the proportion is 1. For the droplet impact model in this paper, there is a gas phase and a liquid phase. α is used to represent the volume ratio of the gas phase in the control volume, that is, the ratio of the volume occupied by the gas phase to the whole control volume. When the control volume is entirely in liquid phase, α = 0; when the control volume is entirely in gas phase, α = 1; if neither, 0 < α < 1.

The volume ratio Equation is:

$$\frac{\partial \alpha }{\partial \tau }+(U\cdot \nabla )\alpha =0$$

(1)

where U is the velocity vector and τ is the time.

Different control volumes have different variables and attributes, which can be obtained by the α value. When only a single phase is contained in the control volume, the fluid in the equation can be calculated according to the physical properties of the phase fluid, otherwise, the density and viscosity of the fluid can be calculated as follows:

$$\{\begin{array}{c}\rho ={\rho }_g\alpha +{\rho }_l\left(1-\alpha \right)\\ \mu ={\mu }_g\alpha +{\mu }_l\left(1-\alpha \right)\end{array}$$

(2)

where ρ and μ are the average density and viscosity of the fluid in the volume, respectively, ρ_g and ρ_l are the density of the gas phase and liquid phase, respectively and μ_g and μ_l are the viscosity of the gas phase and liquid phase, respectively.

The continuity equation and momentum equation are expressed as follows:

$$\nabla \cdot U=0$$

(3)

$$\frac{\partial (\rho U)}{\partial \tau }+\nabla \cdot (\rho UU)=-\nabla p+\nabla \cdot \left[\mu \left(\nabla U+\nabla U^T\right)\right]+\rho g+F_{bf}$$

(4)

where p is the pressure, g is the gravitational acceleration, and F_bf is the surface force per unit volume.

2.3. Grid Independency

A quadrilateral-structured mesh is adopted in the computing domain, and the vicinity of the wall boundary layer is encrypted, as shown in Figure 2. A droplet with a diameter of 30 μm is selected to impact the 0.1 mm × 0.4 mm wire at an initial velocity of 12 m/s to capture the spreading length of the droplet at different times. Five grid sizes are designed according to the ratio of grid size to droplet diameter. Figure 3 shows that when the grid size is 1/20, 1/30, and 1/40 of the droplet diameter, the change of grid size will bring about the change of spreading length, but the spreading process is very similar when the grid size is reduced to 1/50 and 1/60 of the droplet diameter. Considering the accuracy of calculation and reasonable utilization of computer resources, the grid size selected for this paper was 1/50 of the droplet diameter.

2.4. Model Verification

The conditions of a droplet with diameter D = 2.6 mm, impact velocity V = 5 m/s, and wall contact angle 70° are selected to verify the VOF model. The comparison between simulated results and experimental results in reference [7] is shown in Figure 4. It can be seen that the droplet spreads rapidly after impacting the wall, and splashes occur after 100 μs. The spreading and splashing phenomena of the simulated results and the experimental results are highly consistent, indicating that the model in this paper can be used to simulate the splashing phenomenon.

Meanwhile, this paper selects a case from Stow et al. [26], the experimental result of a single droplet impacting a horizontal wall for quantitative comparison, where a droplet with a radius of a = 1.7 mm impacts a dry wall at the velocity of U = 3.8 m/s. In order to better compare to the data in the literature, the simulated data are processed in a dimensionless manner here. The abscissa is dimensionless time, where t is the time after the droplet begins to contact the wall and τ = r/U, where r is the distance from the first spray droplet to the droplet axis and the ordinate is the dimensionless distance. The comparison between the experimental results and the simulated results is shown in Figure 5. It can be seen that the overall trend is the same and the maximum deviation is 7.48%, which proves that the simulation results are in good agreement with the experimental results and quantitatively verifies the accuracy of the model in this paper.

3. Results and Discussion

3.1. Dynamic Evolution Analysis

After the impact of a droplet on a solid wall, several dynamic behaviors such as spreading, deposition, splashing, retraction, and rebound will occur due to the difference of droplet physical properties and wall state. For the wire mesh demister, the spreading and splashing behavior of droplets impacting the single wire will directly affect the demister efficiency. Therefore, this paper focuses on the dynamic evolution of the droplet spreading and splashing process. Figure 6 shows the dynamic evolution process when a droplet with a diameter of 30 μm impacts a flat wire and a circular wire with a diameter of 0.15 mm at an initial velocity of 10 m/s.

It can be seen from Figure 6 that the droplet splashes after spreading for a period of time when they impact different shapes of wire, forming secondary droplets. When the droplet impacts the flat wire, the splashing time is between 4 μs and 6 μs, and two secondary droplets are generated in total. However, the splashing time is between 2 μs and 4 μs when the droplet impacts the circular wire, and a total of six secondary droplets are generated. Therefore, when the droplet impacts the circular wire, splash occurs earlier and more secondary droplets are generated. Furthermore, the length of the lifted lamella generated during the droplet spreading is longer. Figure 7 shows the velocity distribution and pressure distribution inside the droplet at 0.2 μs. When the droplet impacts the wall, the liquid in the contact area is rapidly compressed. The closer the liquid to the wall, the higher the pressure, and a sharp pressure gradient is formed near the gas–liquid–solid three-phase contact line. When the moving velocity of compression wave exceeds that of the contact line, the pressurized liquid escapes from the liquid surface to the air surface in the form of a high-speed jet [27]. From the velocity vector diagram, it can be seen that the fluid in the droplet moves vertically upward first. When the fluid contacts the wall, the vertical velocity will change to the horizontal direction, so that the impacted part of the droplet will spread out to form a liquid film. The velocity stagnation zone appears at the center of the droplet, and the velocity at the edge of the liquid film is the highest. When the jet is generated, the fluid with the highest velocity leaves the wall first and then moves along the horizontal direction. Therefore, due to the different shapes of the wire, when the droplet impacts the flat wire, the movement direction of the end of the lifted lamella is roughly the same as that of the contact line and the velocity difference is small, which is not conducive to the growth of the lifted lamella; however, when the droplet impacts the circular wire, the end of the lifted lamella moves along the horizontal direction while the three-phase contact line continues to move along the circumferential tangent direction and there is a certain angle between the two, which makes the end of the lifted lamella farther and farther from the contact line and the lamella becomes longer and narrower. When the kinetic energy of the droplet at the lamella end is large enough, the surface tension cannot balance with the inertia force and the vapor flow force, so the lamella end disconnects and generates secondary droplets.

The force on the wall from the droplet over time is depicted in Figure 8. It can be seen that the force on the wall increases rapidly and then decreases during the droplet’s impact with the wire. This is because the movement of the initial stage is dominated by inertial force and the movement of the droplet is blocked after vertical upward impact on the wall. Then, the fluid movement changes from a vertical direction to a horizontal direction and the impact kinetic energy of the droplet is also transformed into spreading kinetic energy. Compared to the flat wire, when the droplet impacts circular wire, the peak force on the wall appears later, and the peak force on the wall is larger than that of the flat wire because of the contact area between droplet and wall is larger, which also promotes the formation and development of jet to a certain extent. After 4 μs, the force on the wall tends to be gentle when the droplet impacts the flat wire. This is because the fluid movement direction is parallel to the wall in the droplet spreading stage, there is almost no pressure on the wall, and the fluctuation is very small. However, in the later stage of droplet impact with a circular wire, the wall force is larger than that of a flat wire, and there is fluctuation. This is because the length of the lifted lamella formed in the droplet spreading process is longer and the number of secondary droplets is greater. With the separation of the secondary droplets, a reaction force is formed to make the remaining lifted lamella press towards the wall, so the force on the wall fluctuates.

3.2. Splash Effect Comparison

The dynamic evolution characteristics of droplet impact on different shapes of wire shows that the droplet impacting circular wire is more likely to splash. This section focuses on the investigation of the effects of initial impact velocity on splash.

Table 1. Droplet splashing at different initial velocities (flat wire)/μs.

V (m/s)	7	8	9	10	11	12
Splash Time	/	/	/	5.1	4.4	3.5
Number of Secondary Droplets	0	0	0	2	2	2

and

Table 2. Droplet splashing at different initial velocities (circular wire)/μs.

V (m/s)	7	8	9	10	11	12
Splash Time	/	8.0	5.3	3.3	2.2	1.9
Number of Secondary Droplets	0	2	4	6	8	8

show the splash start time and the number of secondary droplets generated when the droplet with a diameter of 30 μm impacts the flat wire and the circular wire with a diameter of 0.15 mm at different initial velocities, respectively, where “/” represents no splashing.

It can be seen from the data in Table 1 and Table 2 that after the droplet impacts the wire of different shapes, the impact process will change from no splash to splash with an increase in initial velocity, and in case of splash, the larger the initial velocity, the earlier the splash appears. This is because the larger the initial velocity, the greater the kinetic energy, and the greater the fluid inertia at the end of the lamella, the easier secondary droplets form. The difference is that if the wire is flat, the critical velocity at which the droplet starts to splash is between 9 m/s–10 m/s, and the number of secondary droplets does not change for 10 m/s–12 m/s initial velocity. If the wire is circular, the critical velocity is between 7 m/s–8 m/s and when the initial velocity is 8 m/s–12 m/s, the number of secondary droplets gradually increases with the increase in velocity. It can be seen that the initial velocity has a more obvious influence on the splash effect when the droplet impacts the circular wire under the same other conditions, this is mainly reflected in the following aspects: the critical splash velocity is smaller; at the same velocity, the splash starts earlier; and the change of velocity has a greater impact on the total number of secondary droplets.

Figure 9 shows the time-dependent change of the force on the wall from the droplet at different initial velocities. It can be seen that the force on the wall increases rapidly and then decreases during the droplet impacting the wire, and the larger the initial velocity, the greater the peak force, which makes the reverse thrust of the droplet after impacting the wire larger, so the droplet generates jet and splash more easily. Therefore, for different shapes of the wire, the variation in wall force caused by the change of droplet initial velocity is similar.

Figure 10 shows the maximum spreading length of droplets impacting flat and circular wires at different initial velocities. When the droplet impacts the flat wire, the variation trend of the maximum spreading length with the increase in the initial velocity is increase-decrease-increase and the initial velocity improves the impact kinetic energy of the droplet and converts it into a higher spreading kinetic energy so the maximum spreading length increases, while the formation of the secondary droplets takes away part of the droplet and its kinetic energy, resulting in a decrease. When the droplet impacts the circular wire, the maximum spreading length first decreases and then increases, the reason for this is the same as that in the case of flat wire. The difference between the two trends is due to the different critical splash velocities. The maximum spreading length of the circular wire is smaller in the case of splash, which reflects that more liquid film remains when the droplet impacts the flat wire under the same conditions.

When the droplet impacts the wire at an initial velocity of 10 m/s, the velocity distribution inside the droplet before the secondary droplet being generated is illustrated in Figure 11. For the flat wire, the maximum velocity before the splash forming is 15.18 m/s, whereas the same measurement is 22.02 m/s if the wire is circular. This velocity is reached at the position where the secondary droplet is to be generated and connected with the splash. Combined with the data in Table 1 and Table 2, it can be seen that, although the splash occurs earlier when the wire is circular, the lifted lamella velocity is higher and the proportion of high-speed fluid (taking 10 m/s or more as an example) is larger, which also makes an increasing amount of fluid enter the lifted lamella after the droplet impacts the circular wire and causes the lifted lamella to become increasingly long. According to the statistics of post-processing data, the larger the initial velocity, the larger the maximum velocity difference between the droplet impacting the circular wire and the flat wire before splashing. Therefore, the impact of velocity change on splashing is more obvious if the wire is circular.

Figure 12 presents the dynamic evolution process of droplet impacting the flat wire and the circular wire at different initial velocities. At 2 μs, the droplet spreading increases with the increase in the initial velocity, but the change of the initial velocity has little influence on the jet development for the flat wire. When the droplet impacts the circular wire, the larger the initial velocity, the larger the spreading degree of the droplet. It can be clearly seen that an increase in the initial velocity has an important impact on the shape of the lifted lamella, that is, the larger the initial velocity, the narrower the lifted lamella. From the previous velocity analysis, it can be known that the larger the initial velocity, the larger the jet velocity formed after the droplet impact. When the initial velocity reaches 12 m/s, the surface tension at the small neck position is difficult to balance with the inertia force and vapor flow disturbance force, thus generating secondary droplets. At 6 μs, there is little difference in the position of the three-phase contact line when the droplet impacts the flat wire at different initial velocities, that is, after the formation of secondary droplets, the lifted lamella shrinks with similar morphology; however, for the circular wire, the lifted lamella continues to grow after the formation of secondary droplets. It can be seen from the velocity vector direction in Figure 10 that when the droplet impacts the circular wire, the velocity direction of the fluid near the three-phase contact line deviates greatly from that at the end of the lifted lamella, making the three-phase contact line move slowly and the fluid in the droplet more easily enter the lifted lamella, and the larger the initial velocity is, the faster the liquid film spreads, and the larger the velocity direction deviation is. When the droplet impacts the flat wire, the velocity direction near the three-phase contact line is roughly along the horizontal direction, although the velocity direction in the end of the lifted lamella above the jet is also at a certain angle with the wall, the deviation is small. Therefore, the three-phase contact line moves faster and there will not be a large amount of fluid entering the lifted lamella. At 10 μs, the three-phase contact line of the droplet impacting the flat wire at the initial velocity of 8 m/s has exceeded that at the initial velocity of 10 m/s. This is because when the initial velocity is 10 m/s, secondary droplets are generated, taking away part of the kinetic energy and the three-phase contact line velocity becomes slower. However, when the initial velocity is 8 m/s, no secondary droplets are generated and the three-phase contact line still moves at a faster velocity. For the circular wire, this situation does not occur because the droplet splashes at three initial velocities.

3.3. The Effect of Incident Angle

The incident angle is defined as the angle between the incident direction and the horizontal direction. The impact of the 30 μm droplet on the flat wire and the circular wire with a diameter of 0.1 mm are analyzed and discussed.

Table 3. Splash timetable for droplets with different incident angles (flat wire)/μs.

	V (m/s)	6	7	8	9	10
Incident Angle (°)
15		/	17.6	16.8	15.1	13.3
30		/	/	20.3	15.8	13.3
45		/	21.9	/	12.7	9.2
60		/	/	10.0	7.9	7.2
75		/	/	/	6.4	5.6
90		/	/	/	/	5.1

is the splash situation of droplet impacting flat wire at different incident angles.

When the incident angle is 15°, the critical splashing velocity is 6 m/s–7 m/s and the critical splashing velocity is between 7 m/s–8 m/s when the incident angle is 30°. With an increase in incident angle, the critical splash velocity increases, and the time of splash emerging increases at the same initial velocity. For an incident angle of 45°, splash occurs when the initial velocity is 7 m/s, but does not occur when the initial velocity is 8 m/s. When the incident angle is 60°, the critical splash velocity appears again between 7 m/s–8 m/s. Therefore, when the incident angle increases from 30° to 60°, the critical splash velocity does not have a uniform variation rule. When the incident angle is 75°, the critical splashing velocity is 8 m/s–9 m/s and the critical splashing velocity is between 9 m/s–10 m/s when the incident angle is 90°. Therefore, when the incident angle increases from 60° to 90°, with an increase in the incident angle, the critical splash velocity increases and the splash emerging time decreases for a definite velocity.

The evolution of droplet morphology when the droplet impacts the flat wire with initial velocity 8 m/s at incident angles of 15°, 60°, and 90°, respectively is shown in Figure 13. When the incident angle is 90°, the droplets will spread symmetrically after impacting the wire, and no secondary droplets are generated. However, if the incident angle is not 90°, the deformation of the droplet after impacting the wire is asymmetric, the lifted lamella on the right side is longer, and secondary droplets emerge. Furthermore, the smaller the incident angle, the larger the volume of the secondary droplet. When the droplet impacts the wire at a certain angle of incidence, the inertial force can be decomposed into the impact force perpendicular to the wall and the force driving the droplet spreading along the wall to right, so the spreading kinetic energy of the droplet to the right is larger than that to the left. At the same time, when the droplet is in the central position, the action of vapor flow pushes the droplet spreading. However, when the droplet deviates from the Y axis, the effect of vapor flow on the droplet spreading to the left is weakened. Under the combined action of the inertia force of the droplet and the vapor flow, the right spreading length of the droplet is gradually larger than the left spreading length, resulting in an asymmetric development of the spreading. At the same initial velocity, the horizontal component of the force increases with the decrease in the incident angle, and will accelerate the droplet spreading to the right and cause more fluid to enter into the lifted lamella, so it is more likely to break and form secondary droplets. However, the component force in the vertical direction will decrease, which is the key factor in the generation of jet and splash. Therefore, a decrease in the incident angle will inhibit the generation of splash. The effects of the two phenomena are reversed: vapor flow pushes the droplet to the right; therefore, with an increase in incident angle, the splash situation does not show a single change rule, but is balanced by the force of each direction. In Table 3, when the incident angle is 15°–30°, the horizontal component plays an important role on the splash start time, so the smaller the incident angle, the greater the horizontal component, and the earlier the splash. When the incident angle is between 30°–90°, the vertical component is more important. Therefore, for the situation where splashing can occur, the larger the incident angle, the larger the vertical component, and the earlier the splashing.

Figure 14 and Figure 15 demonstrate the dynamic evolution process and the change of maximum velocity along the X (-Y) axis over time when the droplet impacts the flat wire at the initial velocity of 7 m/s and 8 m/s and the incident angle is 45°. It can be seen from Figure 14 that when the initial velocity is 8 m/s, the droplet spreads rapidly after impacting the wall, but the lifted lamella formed by the jet is small, the angle between the lifted lamella, and the wall is small as well. When the initial velocity is 7 m/s, the droplet spread is slow, but the angle between the lifted lamella generated by the jet and the wall surface is large, and the amount of fluid in the lifted lamella is greater. Finally, the end of the lifted lamella breaks and forms secondary droplet. Combined with Figure 15, we can determine that due to the difference in initial droplet velocities and the different driving effects of vapor flow at different velocities on droplet spreading, the maximum velocity in the X axis direction after the droplet impacts the wall at the initial velocity of 8 m/s is greater than that at the initial velocity of 7 m/s, while the velocity in the (-Y)axis direction is larger at the initial velocity of 8 m/s before 5 μs, but continues to be larger at the initial velocity of 7 m/s after 5 μs. Therefore, when the initial velocity is 8 m/s, the droplet spreads rapidly along the horizontal direction in the initial stage, the three-phase contact line moves faster, and the velocity direction is more inclined to the X axis, resulting in less fluid flowing into the lifted lamella, despite the presence of jet. When the initial velocity is 7 m/s, the droplet spreads slowly in the initial stage, the three-phase contact line also moves slowly, and the direction of the resultant velocity is more deviated from the X axis after 5 μs. Therefore, the angle between the lifted lamella and the wall is large and the fluid in the droplet continues to enter the lifted lamella. When the momentum at the end of the lifted lamella is large enough, a secondary droplet is generated. Due to the above differences, the splash occurs at the initial velocity of 7 m/s but does not occur at the initial velocity of 8 m/s.

Table 4. Splash timetable for droplets with different incident angles (circular wire)/μs.

	V (m/s)	4	5	6	7	8	9	10
Incident Angle (°)
15		/	21.2	12.6	10.6	7.4	6.1	5.6
30		/	25.3	18.6	16.2	12.4	10.3	8.9
45		/	/	/	13.3	12.1	11.8	10.2
60		/	/	/	14.8	13.8	13.6	9.3
75		/	/	/	13.2	11.2	7.9	4.5
90		/	/	/	/	9.6	6.7	4.8

shows the splash of a 30 μm diameter droplet impacting a 0.1 mm diameter circular wire at different incident angles. When the incident angle is between 15°–30°, 45°–75°, and 90°, the critical splash velocity is between 4 m/s–5 m/s, 6 m/s–7 m/s, and 7 m/s–8 m/s, respectively. Therefore, unlike the droplet impacting the flat wire, the critical splash velocity shows the same rule when the wire is circular, that is, the critical splash velocity increases with the increase in incident angle. In addition, the splash start time first increases and then decreases with the incident angles increase for a definite initial velocity. This phenomenon is related to the dominant position of tangential and radial components of inertia force, which is similar to the analysis of droplet impacting flat wire, and will not be repeated.

Figure 16 extracts the spreading and splashing of the droplet with initial velocity of 7 m/s impacting the circular wire at different incident angles. When the incident angle is 90°, the droplet impacts the wall and spreads symmetrically, forming the lifted lamella but no secondary droplets. When the incident angle is 60° and 30°, the process of droplet impacting the wire changes asymmetrically, and because the droplet at the right end is excessively large, separation occurs. When the incident angle is 30°, the secondary droplet volume will be larger, this is due to the same reason as when the droplet impacts the flat wire. Due to the smooth wall without friction and the effect of the vapor flow below, the droplet completely shifts to the right side of the Y axis when the incident angle is 30°. Different from the flat wire, due to the existence of the curvature of the circular wire, the spreading asymmetry at a non-90° incident angle is more obvious, which makes the droplet at the right end larger in volume and kinetic energy and more likely to produce secondary droplets.

4. Conclusions

The VOF model is used to simulate the process of a droplet impacting a single flat wire and a circular wire under the action of vapor flow in the wire mesh demister, and comparative analysis is carried out. The following conclusions are drawn:

(1)

When a droplet with a diameter of 30 μm impacts flat wire and circular wire with diameters of 0.15 mm at an initial velocity of 10 m/s, the dynamic behaviors are similar for the two types of wire, both of which have experienced the stages of spreading and splashing, and the internal velocity and pressure distribution of the droplet are similar at the initial moment of impact. However, when the droplet impacts the circular wire, the lifted lamella is longer, the peck force on the wall is larger, the splash start time is earlier, and the number of secondary droplets is greater.

(2)

When the droplet impacts the flat wire or the circular wire, the change rule of the force on the wall caused by the change of the initial velocity of the droplet is similar, and the increase in the initial velocity will promote the occurrence of splash. However, when the droplet impacts the circular wire, the initial velocity has a more obvious impact on the splash effect: the critical velocity of droplet splashing is smaller, the change of velocity has a greater effect on the total number of secondary droplets, at the same velocity, splash starts earlier, and droplet morphology changes after impact are greatly affected by velocity.

(3)

Due to the difference in the wire shape, the incident angle has different effects on droplet splashing. When the droplet impacts the flat wire, the influence of incident angle on the critical splash velocity is non-monotonic, while the critical splash velocity increases with the increase in incident angle if the wire is circular.