Study on Spray Characteristics and Breakup Mechanism of an SCR Injector

Abstract

Selective catalytic reduction (SCR) is currently one of the most efficient denitration technologies to reduce nitrogen oxide (NO_x) emissions of diesel engines. AdBlue (urea water solution, UWS) is the carrier of the reducing agent of SCR, and the spray process of UWS is one of the critical factors affecting denitration efficiency. In this paper, a non-air-assisted pressure-driven full process spray (NPFPS) model is proposed to illustrate the breakup mechanism and the spray distribution properties of UWS through computational fluid dynamics (CFD). In the NPFPS model, the mechanism of the primary breakup is described by the volume of fluid (VOF) approach, which realizes the quantitative study of the critical parameters determining spray characteristics such as the breakup length, inclination angle, droplet size of the primary breakup, and primary velocity. The distribution of the spray after the primary breakup is depicted by the discrete phase model (DPM) coupled with the Taylor analogy breakup (TAB) model, through which the degree of secondary breakup can be obtained including quantitative studies of the droplet size distribution and velocity distribution in the different cross-sections. To verify the accuracy and feasibility of the NPFPS model, the experimental data are employed to compare with the simulation data. The results are in good agreement, which indicate the practical value of the model.

1. Introduction

Vehicle exhaust is one of the main culprits of air contamination, which mainly includes carbon monoxide (CO), hydrocarbons (HC), nitrogen oxides (NOx) and particulate matter (PM). Diesel vehicles have been identified as the main contributors to NOx [1]. Selective catalytic reduction (SCR) has been proved by industrial practice to be one of the most effective technologies to eliminate NOx [2]. Ammonia (NH₃) is generally adopted as a reducing agent in the SCR system and is stored in the form of a urea water solution (UWS). UWS is sprayed into the SCR system through an injector, and NH₃ is finally generated through evaporation, pyrolysis, and hydrolysis [3,4]. The spray characteristics of the injector have a significant impact on the decomposition of urea and the formation of a deposit, which eventually affect the denitration efficiency of the SCR system [5,6].

A UWS injector can be divided into two categories: air-assisted injector and non-air-assisted injector [7,8]. The former one is less used in diesel vehicles due to its complex structure, including the air circuit and metering device, whereas the latter one has an extensive application as a result of its simple structure and easy control. Therefore, many studies related to UWS sprays are based on non-air-assisted injectors. Spiteri and Dimopoulos Eggenschwiler [9] provided an indication of the predominant spray distribution properties in exhaust configurations, and the results indicate that the fluid mechanical differences between the spray and gas flow are insufficient to induce substantial secondary breakup. Varna et al. [10] adopted Mie scattering and Phase Doppler Anemometry (PDA) to assess the effects of cross-flow velocity and temperature on the spray structure, droplet size and velocity distributions, which realized a comprehensive characterization of the spray under different exhaust conditions. Liao et al. [11] reported the heat transfer characteristics of the spray/wall interaction in typical diesel exhaust flow conditions and deduced the influence of the gas flow conditions on the heat transfer characteristics. Shahariar et al. [12] carried out a series of investigations including UWS spray, droplet breakup, urea decomposition and deposit formation in a combined experimental and numerical approach. The investigation revealed that the injection pressure influences deposit formation and droplet size; furthermore, the cooling effects of the spray injection prevent urea decomposition. The studies mentioned above focus on the influence of the exhaust on spray distribution, urea decomposition and deposit formation, etc., rather than on the spray characteristics of the injector. However, accurate characterization of the spray is of great importance for the quantitative study of numerical simulations for the SCR system. Therefore, some studies have characterized the spray characteristics by experimental methods such as Mie, PDA, particle image velocimetry (PIV), high resolution laser backlight imaging (HRLBI) and high-speed microscopic imaging (HSMI). The droplet size distribution along the spray axis was measured through PDA, and the spray developing process was investigated through a high-speed photography method in reference [13]. The results indicate that the droplet size distribution of a non-air-assisted injector is wide. Oh and Lee [14] used laser diagnostics and a high-speed camera to analyze the spray characteristics, such as spray angle, injection quantity and Sauter mean diameter (SMD) to clarify the distribution of the sprayed droplets. Kapusta et al. [15] compared the global and local spray parameters of UWS and pure water under the same conditions. The experimental studies have shown differences in almost all considered spray parameters. Bracho et al. [16] compared the reliability of PDA, HRLBI and HSMI for the characterization of spray properties. The droplet size distribution and velocity distribution of the spray can be accurately obtained by these three approaches and applied to the numerical models to optimize exhaust geometries and mixers. The optical methods in the above studies can accurately characterize the macroscopic characteristics of the spray, which are not qualified to study the near-field breakup process because the nozzle size of the injector is small, and the primary breakup occurs in the near-field area of the nozzle exits. For this reason, it is necessary to use computational fluid dynamics (CFD) to study the spray process of a non-air-assisted pressure-driven injector.

The numerical methods for spray modeling are mainly divided into volume of fluid (VOF) [17,18,19] based on the Eulerian–Eulerian method and discrete phase model (DPM) based on the Eulerian–Lagrangian method [20,21] at present. The VOF approach can be employed to visualize the breakup process of the liquid jet and to obtain a clearer insight into the breakup mechanism [22]. On this basis, it can establish the relationship between the internal flow field of the injector and the external flow field, which is helpful for the optimal design of the injector. However, since the droplet size can be as small as a few microns, the mesh scale of the VOF model also needs to reach this level to capture clear phase interfaces. If the VOF model is adopted to simulate the full process of the spray, the count of computation will be expensive. Therefore, most studies employ the DPM model to characterize the far-field characteristics of the UWS injector. Shahariar et al. [12] discussed the effect of injection pressure on the risk of wall impingement and wall wetting. Kapusta et al. [15] studied the influence of different spray characteristics of water and UWS on wall film formation. Jyothis and Vikaswas [23] developed a model used for spray simulation of UWS droplet evaporation to determine the urea-to-ammonia conversion efficiency. Rogoz et al. [24] proposed a two-zone approach capturing a non-uniform droplet distribution inside the spray cone. The spray models used in these studies can accurately characterize the spray but cannot be used to study the mechanism of the primary breakup and to optimize the injector structure. Moreover, it is known from reference [9] that fluid mechanic differences between the spray and gas flow are insufficient to induce a substantial secondary breakup due to the low working pressure of the non-air-assisted UWS injector. Hence, the primary breakup characteristics of the non-air-assisted UWS injector play a dominant role in the characterization of the spray. To the best of our knowledge, the numerical studies on the primary breakup of a non-air-assisted UWS injector are relatively limited, and thus, this study is necessary. However, it does not mean that the far-field spray model is not important. Parameters such as droplet size distribution, velocity distribution, and inclination angle are of great significance for the quantitative numerical study of the urea-to-ammonia conversion efficiency, ammonia uniformity, and deposit formation, etc. For this reason, it is necessary to establish a numerical model to study the full spray process of the UWS injector. Some studies in other research fields [25,26] have combined the Eulerian–Eulerian and Eulerian–Lagrangian methods to simulate the primary and secondary breakup processes, respectively, and realized the full process simulation of the spray. This method provides a new idea for the study of the spray characteristics of the UWS injector.

In this work, a typical commercial non-air-assisted pressure-driven UWS injector is taken as the research object, and its spray process is modeled and simulated by FLUENT. The simulation based on the VOF approach starts from the pressure chamber of the injector and characterizes the propagation and primary breakup process of a liquid jet in a simplified computational domain. The results of the primary breakup, such as jet inclination angle, droplet size and average droplet velocity, are acquired and applied as initial injection conditions for a subsequent droplet development model based on the DPM approach. The Taylor analogy breakup (TAB) model is coupled with the droplet development model to evaluate the degree of secondary breakup of the droplets. The simulation results are analyzed and validated against experimental data. The primary breakup model is helpful to reveal the primary breakup mechanism and can be applied to optimize the structure of a non-air-assisted UWS injector; in addition, the droplet development model can increase the forecast accuracy in simulations related to the SCR system.

2. Numerical Models and Methods

2.1. Model Description and Methods of Primary Breakup

2.1.1. Primary Breakup Model of Non-Air-Assisted Injector

Figure 1a shows the diagram of the UWS injector and the fluid domain of the primary breakup. The fluid domain consists of the internal fluid domain (including pressure chamber and nozzle) and external domain of the primary breakup. The liquid phase of the non-air-assisted injector generally exists in the form of a liquid column or liquid sheet in the near-field region. As the diameter of the nozzle is small (Φ 190 μm), and the primary breakup only occurs in the near-field region of the nozzle exits, obtaining a clear interface requires a high-resolution grid. In order to increase the computational efficiency, the geometric model is appropriately simplified into a two-dimensional axisymmetric structure. Figure 1b shows the computational grid and boundary conditions. The yellow boundary represents the symmetric boundary condition, the blue boundary is the pressure inlet, the green boundary corresponds to the wall, and the red boundary is regarded as a pressure outlet, which relates to the atmosphere. The fluid domain of the primary breakup is divided into structured meshes, and the element size is 20 μm. The commercial CFD software FLUENT is adopted to solve the continuity equation, momentum conservation equation and VOF equation to simulate the primary breakup process. LES WNLES S-Omega is employed as the turbulence model to increase the forecast precision. A previous study [9] has demonstrated that water spray and UWS spray behave similarly in terms of bulk spray properties. Therefore, water is selected as the injected fluid in this work to study the spray characteristics. The boundary conditions of the primary breakup process and material properties are shown in

Table 1. Boundary conditions of primary breakup and physical properties of materials.

Boundary Conditions and Material Properties	Value
Injection Pressure/MPa	0.4, 0.5, 0.6
Water Density/kg·m−3	998.2
Dynamic Viscosity of Water/Pa·s	1.4 × 10−3
Surface Tension Coefficient of Water/N·m−1	0.073
Air Density/kg·m−3	1.29
Dynamic Viscosity of Air/Pa·s	1.8 × 10−5

.

2.1.2. Flow Control Equations of Primary Breakup

The spray process is conducted at room temperature; thus, the flow control equations only consist of the continuity equation and momentum conservation equation, which are as follows:

$$\nabla \cdot (\rho u)=0,$$

(1)

$$\frac{\partial }{\partial t}(\rho u)+\nabla \cdot (\rho uu)=-\nabla p+\nabla \cdot (\stackrel{\overline{¯}}{\tau })+\rho g+F,$$

(2)

where ρ is the density, u represents the velocity vector, t is the time, p corresponds to the static pressure, $\stackrel{\overline{¯}}{\tau }$ is the stress tensor, g is the gravitational acceleration, and F is the generalized source term of the momentum equation.

2.1.3. Two-Phase Flow Control Equations of Primary Breakup

The VOF model is employed to track the interface of gas–liquid phases in both internal fluid domain and in the near-field region of the nozzle exit. The volume fraction of the Ith phase in each computing unit is α_i. For this study, α_g and α_l represent the volume fraction of air and water, respectively. For each computing unit, α_g + α_l = 1. The governing equation of the phase interface is as follows:

$$\frac{\partial {\alpha }_i}{\partial t}+u\cdot \nabla {\alpha }_i=0,$$

(3)

The fluid properties in each computing unit are calculated by the linear interpolation of the volume fraction. For example, the density in each computing unit can be expressed as:

$$\rho ={\alpha }_l{\rho }_l+(1-{\alpha }_l){\rho }_g,$$

(4)

where ρ_g and ρ_l are the density of air and water, respectively.

2.1.4. Dynamic Mesh Method

In the field of fluid engineering, there are many objects of study whose fluid domain is varied. Therefore, it is necessary to apply the dynamic mesh method to solve this kind of problem to reduce the simulation error. The dynamic mesh is used to simulate the opening process of the needle valve in this study. For a dynamic mesh, the motion boundary control equation for a general scalar quantity ϕ on an arbitrary control volume V is:

$$\frac{d}{dt}\underset{V}{\int }\rho \varphi dV+\underset{\partial V}{\int }\rho \varphi (u-u_m)\cdot dA=\underset{\partial V}{\int }\Gamma \nabla \varphi \cdot dA+\underset{V}{\int }{S}_{\varphi }dV,$$

(5)

where ρ is the fluid density, u is the fluid velocity, u_m represents the velocity of dynamic mesh, Γ corresponds to the dissipation coefficient, and S_ϕ is the source term of the general scalar quantity ϕ. The time derivative in Equation (5) can be modified through first-order backward difference, which is as follows:

$$\frac{d}{dt}\underset{V}{\int }\rho \varphi dV=\frac{{(\rho \varphi V)}^{n+1}-{(\rho \varphi V)}^n}{\Delta t},$$

(6)

where n stands for the time step. The control volume at the n + 1th time step is:

$$V^{n+1}=V^n+\frac{dV}{dt}\Delta t,$$

(7)

where dV/dt can be calculated by:

$$\frac{dV}{dt}=\underset{\partial V}{\int }{u}_m\cdot dA={\displaystyle \sum _j^{n_f}{u}_{m,j}}\cdot A_j,$$

(8)

where n_f is the number of motion surfaces of the control body, A_j is the motion surface vector, and u_m,j·A_j is defined as follows:

$$u_{m,j}\cdot A_j=\frac{\delta V_j}{\Delta t},$$

(9)

where δV_j is the volume swept by the motion surface of the control volume in the time step ∆t.

2.2. Model Description and Methods of Droplet Development Process

The liquid jet is transformed into a group of droplets after the primary breakup. Although the VOF model has high precision for multiphase flow simulation, it often takes several weeks to solve a case, which is computationally expensive [27]. Thus, a DPM model is used to characterize the droplet development process group after the primary breakup.

2.2.1. Droplet Development Model

Figure 2 shows the fluid domain of the droplet development process. Figure 2a compares the size relationship of the fluid domain between the droplet development and the primary breakup, and Figure 2b shows the computational grid and boundary conditions of the model. The diameter and the height of the cylindrical computational domain are 60 and 120 mm, respectively. The computational domain is adopted to O-shaped subdivision, and local refinement is performed in the central region. The minimum element size is 1 mm. Realizable k-ε is selected as the turbulence model for the droplet development process, since the LES model cannot be applied to two-way coupling interaction. The degree of secondary breakup of the droplets was evaluated by the Taylor analogy breakup (TAB) model. The droplets generated by the primary breakup are processed into groups of droplets, and the droplet groups are loaded at the position where the primary breakup takes place, as shown in Figure 2a. The results of the primary breakup (droplet size, inclination angle, and average velocity, etc.) are used as the initial conditions for the droplet development process.

Table 2. Parameters and boundary conditions of the droplet development process.

Boundary Conditions and Parameters		Value
Initial velocity of droplet group/(m·s−1)		21.39, 22.50, 23.52
Inclination angle α/°		9.9
Spray cone angle β/°		5.4
Rosin–Rammler distribution	Minimum diameter/μm	10
	Maximum diameter/μm	400
	Mean diameter/μm	11.24
	Spread parameter	2.26

shows the parameters of the droplet development process.

2.2.2. Control Equations of the Droplet Development Process

The droplet development process is solved by the DPM method, that is to say, the trajectory of the droplet can be solved according to the force balance of the droplet. The force balance equation is as follows:

$$m_l\frac{d{u}_l}{dt}=f+m_l\frac{g({\rho }_l-{\rho }_g)}{{\rho }_l}+F_{\mathrm{d}},$$

(10)

where m_l is the droplet mass, u_l corresponds to the droplet velocity, F_d represents the additional force, f is the drag force and can be expressed as:

$$f=m_l\frac{18{\mu }_g}{{\rho }_l{d}_l^2}\frac{C_{D}Re}{24}(u_g-u_l),$$

(11)

where u_g is gas velocity, d_l represents the droplet diameter, μ_g is the dynamic viscosity of air, C_D stands for drag coefficient, Re is the Reynolds number, and the expression is as follows:

$$Re=\frac{{\rho }_g{d}_l\left|u_l-u_g\right|}{{\mu }_g},$$

(12)

2.2.3. Secondary Breakup Model

With the movement of the droplet, the droplet may deform or even breakup under the action of drag force, gravity and additional force, and the fragment of the droplet is resisted by surface tension and viscosity. For inviscid fluids, the gas Weber number (We_g) is employed as a criterion for secondary breakup.

$$W{e}_g=\frac{{\rho }_g{(u_l-u_g)}^2{d}_l}{{\sigma }_l},$$

(13)

where σ_l is the surface tension of the droplet, and We_g is the ratio of the aerodynamic force to the surface tension of the droplet. With the increase in We_g, the droplet tends to breakup. At present, there are mainly three secondary breakup models, namely the TAB model [28], WAVE model [21] and KH-RT model [29]. According to the research of Zeoli et al. [20], the TAB model is applicable to the condition of We_g < 80, while the WAVE model and KH-RT are available for the condition of We_g > 80. The TAB model is used to study the secondary breakup of a droplet cluster, considering the We_g of the primary breakup droplet in this study. The TAB model takes the spring-mass system as an analogy to a deformed droplet and takes the critical deformation as the criterion of breakup. Breakup occurs when the displacement x of the droplet equator from the undisturbed position exceeds a critical value C_br_l. Let y = x/(C_br_l), then the governing equation of the droplet deformation is:

$$\frac{d^{2}y}{d{t}^2}=\frac{C_f}{C_b}\frac{{\rho }_g}{{\rho }_l}\frac{{\left|u_g-u_l\right|}^2}{{r_l}^2}-\frac{C_k{\sigma }_l}{{\rho }_l{r}_l^3}y-\frac{C_d{\mu }_l}{{\rho }_l{r}_l^2}\frac{dy}{dt},$$

(14)

where r_l is the initial diameter of the droplet. C_b, C_d, C_f and C_k are dimensionless constants. Droplet fragments only for y > 1. When secondary breakup occurs, the droplet will be transformed into a set of small droplets with a definite Sauter mean radius (r32) expressed as:

$$r_{32}=\frac{r_l}{1+\frac{4y^2}{3}+\frac{{\rho }_l{r}_l^3{(dy/dt)}^2}{8{\sigma }_l}},$$

(15)

3. Results and Discussion

3.1. Analysis of the Primary Breakup Process

3.1.1. Primary Breakup Mode of Liquid Jet

Initially, the primary breakup process of the injector with the needle valve movement is studied. The motion of the needle valve is simplified as a uniform motion. Figure 3 exhibits the displacement curve of the needle valve.

Figure 4 shows the development and breakup of the liquid jet at different times when the inlet pressure is 0.6 MPa, where the volume fraction of the phase interface is 0.5. With the opening of the needle valve, the liquid flows obliquely from the pressure chamber into the nozzle and finally sprays into the static air. The jet is subjected to the interaction of aerodynamic force, viscous force, and surface tension, resulting in an impact of the jet front, and then, surface waves are generated and transmitted to the upstream of the liquid jet. The length of the liquid column gradually develops until the aerodynamic force overcomes the resistance of the liquid surface tension and viscous force, and then, the liquid column becomes unstable and fragments, forming ligaments and small droplets. The breakup process of the liquid jet can be divided into two stages. In the first stage, the liquid column shows a periodic fluctuation with an intense amplitude, as shown in Figure 4a–c. The periodic fluctuation of the liquid jet tends to be gentle, and the breakup process tends to be stable in the second stage, as shown in Figure 4d–f.

Figure 5 explains the cause of the difference in the primary breakup. The pressure field inside the nozzle is constantly changing, due to the movement of the needle valve. The variation of the pressure field leads to a periodic fluctuation of the initial radial velocity of the jet (the radial velocity at the nozzle exit), and then causes the periodic radial disturbance of the liquid jet in the first stage. When the needle is stationary (at top dead center), the pressure field in the injector as well as the liquid distribution in the nozzle tend to be relatively stable, the radial velocity fluctuation weakens and tends to fluctuate in a small range, and the primary breakup is dominated by asymmetric surface waves.

There are two basic types of surface waves: dilational wave and sinuous wave. At low jet velocities (usually corresponding to low Re numbers), the jet periodically exhibits a wave pattern of increasing and decreasing diameter, which is dominated by a dilational wave. With the increase in the Re number, the jet axis mainly presents asymmetric disturbance, which is the sinuous wave [30,31].

In the study of primary breakup of the liquid jet, three important dimensionless numbers, Reynolds number (Re), Weber number (We) and Ohnesorge number (Oh), are often used to classify the breakup mode of the jet. They are defined as:

$$Re=\frac{{\rho }_l{u}_0{d}_0}{{\sigma }_l}$$

(16)

$$We=\frac{{\rho }_l{u}_0^2{d}_l}{{\sigma }_l}$$

(17)

$$Oh=\frac{{\mu }_l}{\sqrt{{\rho }_l{\sigma }_l{d}_0}}$$

(18)

where d₀ and u₀ denote the diameter and average axial velocity of the jet at the nozzle exit, respectively. As shown in Figure 6, Reitz et al. [32] divided the breakup modes of the liquid jets into four categories based on the Re number and Oh number, which are Rayleigh breakup, first wind-induced breakup, second wind-induced breakup and atomization. When a criterion of the Re and Oh is considered, the cases of primary breakup in this study should be in the first wind-induced breakup regime.

3.1.2. Breakup Length of Liquid Jet

The average breakup length (L_c) of a liquid jet is one of its important characteristic parameters. Sallam et al. [33] summarized the empirical equation for the average breakup length of common liquid jets (such as water and ethanol) based on previous studies:

$$\frac{L_c}{d_0}=5W{e}^{1/2}, \mathrm{for} We<400$$

(19)

Figure 7 compares the correlation between the average breakup length of the simulations and the empirical curve. The average breakup length is the average of the transient breakup lengths over a given period. It can be seen from Figure 7 that the three cases are basically consistent with the empirical curve. Therefore, the empirical equation is also applicable to the average breakup length of the liquid jet in this study when We < 510.

For the injector in this study, the jet velocity increases gradually with the increase in injection pressure, while the characteristic diameter of the liquid jet hardly changes. Thus, the Reynolds number increases monotonously with the increase in pressure, and the breakup length of the liquid jet also increases.

3.1.3. Inclination Angle of Liquid Jet

The inclination angle of the liquid jet refers to the angle between the liquid jet and the axis of the nozzle. Figure 8 shows the comparison between the numerical simulation result and the experimental result of Kapusta et al. [15] for the inclination angle at an inlet pressure of 0.5 MPa. The comparison shows that both are well consistent. In addition, the inclination angles were also measured at inlet pressures of 0.4 and 0.6 MPa. The results show that the inclination angle is insensitive to the inlet pressure, which is about 9.9° under all operating pressures. The inclination angle is related to the deviation of the connected domain from the axis of the nozzle, as shown in Figure 8c.

There are some differences between the experimental and simulated results of the breakup modes in Figure 8. The simulation failed to realize the phenomenon of liquid filament peeling in the experiment. The main reason is that the accuracy of the grid cannot be further improved due to the computing power. However, the simulation results have certain accuracy in comparison with the fragmentation form and key parameters of the liquid jet.

3.1.4. Droplet Diameter and Velocity of the Primary Breakup

The area of the first breakup droplet was measured by Image-J software after gray-scale processing of the primary breakup result in Figure 4f. The droplets are approximated to circles with the same area, and the range of droplet diameter is 6–187 μm. In addition, the initial velocities of the primary droplets are also counted, and the initial velocities range from 6.42 to 30.68 m/s, with an average velocity of 23.52 m/s.

3.2. Analysis of the Droplet Development Process

The Eulerian–Lagrangian method combined with the Realizable k-ε model is used to simulate the droplet development process because the LES model cannot be used for gas–liquid two-way coupling interaction. The primary breakup parameters such as the inclination angle, the average velocity, and the position of the primary breakup are taken as the boundary conditions of the droplet development process. The Rosin–Rammler distribution function is adopted to fit the droplet diameter distribution of the primary breakup, and the droplet size distribution is corrected by the experimental results of Kapusta et al. [15]. The Taylor analogy breakup (TAB) model is used to evaluate the degree of the secondary breakup.

3.2.1. Distribution Characteristics of Droplet Development Process

Figure 9 shows the droplet diameter distribution, aerodynamic Weber number distribution and velocity distribution at an inlet pressure of 0.6 MPa. In the simulation of the droplet development process, about 2.7 million parcels are introduced in the computational domain, and only 3‰ of parcels are illustrated for a clear representation. According to the study by Li et al. [25], for a droplet to fragment, its aerodynamic Weber number should exceed a critical value (We_g,crit = 12). However, it can be seen from Figure 9b that the maximum aerodynamic Weber number of the droplet is 2.69, which is much smaller than the critical value of the secondary breakup. Thus, the droplet hardly undergoes secondary breakup. It can be concluded from Equation (13) that the aerodynamic Weber number is affected by two variables: the droplet diameter and the gas–liquid relative velocity. Since the droplet diameter of the primary breakup is very small (6–300 μm), only when the relative velocity is large enough, can the aerodynamic force overcome the surface tension of the droplet. However, the object of this study is a low-pressure injector; thus, the relative velocity cannot meet the condition of a secondary breakup. That is to say, the droplet size distribution of the primary breakup determines the droplet size distribution characteristics of the spray. In addition, it can also be observed from Figure 9 that the velocity of the droplet with a larger diameter is relatively high, that is, the deceleration effect of the aerodynamic force on small droplets is more obvious.

The droplet size distribution at 20 mm from the nozzle exits is measured at an inlet pressure of 0.5 MPa and is compared with the experimental result by Kapusta et al. [15], as shown in Figure 10. The droplet size distribution of the simulation is in good agreement with the experimental result. The Sauter Mean Diameter (D32) measured by the simulation and experiment is 103.2 and 106.6 μm, respectively. The accuracy of the simulation of the droplet development process is verified by comparing with the experimental results. In addition, the droplet size distribution at 30, 60 and 90 mm from the nozzle exits is also measured by the simulation. As shown in Figure 11, the droplet size distribution at 20, 30, and 60 mm from the nozzle exits remains almost unchanged, confirming that there is almost no secondary breakup of droplets. In other words, the droplet size distribution is mainly determined by the primary breakup. With the increase in axial distance (90 mm from the nozzle exits), it is hardly meant to count droplets less than 55 μm. This is because the inertia of small droplets is small, and they are more likely to be decelerated by aerodynamic force than large droplets.

3.2.2. Velocity Distribution Characteristics of the Droplet Development Process

Figure 12 and Figure 13 show the probability density curves for the droplet velocity in the radial and axial components, respectively, which are compared with the experimental data of Bracho et al. [16]. The results show that the simulated radial velocity distribution is consistent with the experimental data. For the axial velocity, the simulation underestimates its distribution range compared with the experiment. This is because the average velocity of the primary breakup is used as the initial condition of the droplet development process, such that a small number of droplets with higher initial velocity are ignored in the simulation of the droplet development process. However, the characteristic of axial velocity distribution is consistent between the simulation and the experiment.

4. Conclusions

In this study, a NPFPS numerical model is proposed to simulate the spray process of a commercial non-air-assisted pressure-driven UWS injector. The coupled simulation includes the primary breakup process of the liquid jet by the VOF approach and the subsequent droplet development process by the DPM approach.

The primary breakup simulation can capture relevant details of liquid jet propagation and disintegration, which reveals the primary breakup mechanism. The primary breakup simulation obtains a reasonable prediction on the parameters such as jet inclination angle, location of primary droplet formation, primary droplet size and primary droplet velocity. Furthermore, the influence of injection pressure on the parameters including jet breakup length and jet inclination angle are also discussed. The results obtained by the primary breakup simulation are as follows.

The primary breakup of the injector spray has the relevant characteristics of the first wind-induced breakup regime according to the liquid phase volume distribution, We number and Oh number. It was also found from the primary breakup simulation that the characteristic diameter of the liquid jet is related to the connected domain between the pressure chamber and the nozzle, which can be used for optimal design of the injector structure to improve the droplet size distribution. The results show that the jet breakup length increases with the increase in the injection pressure, and the jet inclination angle of the liquid is insensitive to the injection pressure.

Furthermore, a droplet development simulation based on the DPM approach is performed and the primary breakup parameters such as jet inclination angle, location of primary droplet formation, primary droplet size and primary droplet velocity are taken as the initial injection conditions. A TAB model is coupled with a droplet development simulation to determine whether a secondary breakup occurs. The main results of the droplet development simulation are:

It is proven that the droplet development model can well characterize the far-field spray by comparing the droplet size distribution and droplet velocity distribution obtained by the simulation and experiment separately. It can be concluded that the relative velocity between the spray and still gas is insufficient to induce a substantial secondary breakup according to the aerodynamic Weber number and the particle size distribution data of different cross-sections. In other words, for the low-pressure non-air-assisted injector, the primary breakup characteristics determine the distribution characteristics of the spray. We also found that small droplets are more susceptible to aerodynamic forces to change their state of motion.

Overall, the NPFPS numerical model presented in this study is a valuable alternative to study low pressure non-air-assisted injector sprays. The primary breakup model can be used to study the breakup mechanism and to optimize the injector structure. The droplet development model is conducive to improve the prediction accuracy of the numerical studies related to the SCR system.