1 Introduction

The effervescent atomizer has many advantages, such as low operating pressure, simple structure, less gas consumption, and low cost [1,2,3,4]. The effervescent atomization technology has been widely studied and applied in various fields such as liquid fuel combustion [5], spray drying [6], medical treatment [7], fire extinguishing [8], and surface spraying [9]. Effervescent atomization is an efficient and cost-effective technology derived from traditional atomization. It involves injecting gas and liquid into a mixing chamber to create a gas–liquid two-phase flow. The droplet formation in effervescent atomization is caused by gas expansion at the exit orifice [10]. When the pressure inside the atomizer is greater than the ambient pressure, the bubble rapidly expands and bursts due to the sudden pressure drop within a very short period of time after it exits the atomizer. Thus, the liquid film breaks into liquid filaments or smaller liquid drops.

In studying the atomization process of an effervescent atomizer, researchers have focused mainly on the internal flow and the spray characteristics beyond the exit. Avulapati et al. [11] observed that the spray was more unstable at low gas liquid ratio (GLR) of 1.7%. It tended to be stable at high GLR of 10%, where annular flow was observed. Kourmatzis et al. [12, 13] used a high-speed camera to record the near-field atomization. When the GLR reached 0.4%, the internal flow pattern changed from bubble to slug flow. At this point, the liquid column at the exit started to break apart due to the expansion of bubbles. Li et al. [14] found that the flow pattern transition in the mixing chamber was closely related to the droplet distribution through experiments. The annular flow produced a thinner liquid film and finer droplets. Konstantinov et al. [15] analyzed different atomization methods. Compared to other traditional atomization methods, smaller droplets are observed in effervescent atomization. The external field achieves the best atomization performance with bubbly flow in an orifice. Ochowiak et al. [16] proposed that the discharge coefficient (the ratio of the actual mass flow rate of the fluid to the theoretical mass flow rate of the fluid) of an effervescent atomizer decreased with an increase of liquid viscosity. At the same time, the lower the GLR, the greater the effect of viscosity. Hammad et al. [17] designed a variety of effervescent atomizers with distinct structures. It was observed that the discharge coefficient was not affected by the internal flow pattern. Moreover, the discharge coefficient was more sensitive to viscosity at low GLR.

In judging the effectiveness of atomization, many factors need to be taken into account. The experimental results of Sun et al. [18, 19] revealed that the design of the effervescent atomizer has an impact on the instability of the spray. The spray was more consistent when the air inlet was distant from the orifice. Additionally, a narrow orifice could generate a more consistent atomization cone angle. Huang et al. [20] measured the droplet size and velocity with the aid of an LDV/PDA (laser doppler velocimetry/ phase doppler anemometry) system. The droplets were minute and the axial velocity was high under high operating pressure. Zaremba et al. [21] summarized the mechanism of droplet breaking. As the gas flow increased, the frequency of bubble breakup was higher, resulting in a more uniform spray. At the same time, the droplet size along the central axis of the spray was relatively small. Ramamurthi et al. [22] observed that in slug flow the atomization effect was poor due to the intermittent flow of large bubbles. The annular flow gradually stabilized the atomization cone angle, which caused the Sauter mean diameter (SMD) to gradually decrease. Mohammadi et al. [23] conducted experimental and numerical studies on the spray characteristics and droplet distribution. Both the GLR and the inlet pressure had a significant influence on the droplet diameter. Additionally, an increase of liquid flow rate caused the density of the larger droplet size to increase rapidly.

A large amount of experiments and numerical simulations have been conducted on effervescent atomizers. However, there are only a few reports on the influence of ambient pressure on the distribution characteristics of external flow field. In the constant volume bomb experiment of internal combustion engine, it usually presents as pressure atomization without air injection, with a high ambient pressure but only for microsecond-level experiments for spray evolution or spray pattern [24,25,26]. For the effervescent atomizer, the addition of gas assistance causes the ambient pressure to fluctuate. PDA has a great advantage for high measurement accuracy. However, the single point measurement of phase Doppler image (PDI) or PDA requires a considerable amount of time to complete the target measurement points. When the nozzle flow rate reaches tens or even hundreds of grams per second, it is considered a very large flow rate for the effervescent atomizer in the experiment. The spread of the droplets is so intense that it covers the surface of the optical window with droplets, making it difficult to carry out routine measurements. It brings great challenges for the design of constant volume bomb and ambient pressure adjustment.

Furthermore, the correlation between diameter and velocity is of great importance for the analysis of the atomization process and engineering application. Nevertheless, most of the current data on droplet size only concentrate on SMD [27, 28]. Studies by Frederik et al. [10] and Nielsen et al. [29] showed that the SMD had no direct relation to the mixing chamber structure. But the mixing chamber structure has an effect on the flow pattern and thus influence the droplet diameter. Sovani et al. [30] summarized that the SMD was most significantly influenced by GLR. Cejpek [31] concluded that SMD is also mainly affected by GLR. Meanwhile, the empirical formula of SMD about GLR is obtained. Liu [32] found that the increase of injection pressure and GLR can reduce the SMD in the experiment. Wittner [28] also found that the droplet size decreases with the increase of injection pressure. However, due to the large momentum of liquid–gas interaction, the effect of injection pressure on SMD decreases with the increase of GLR. In fact, the injection pressure will increase with the increase of liquid and gas flow. Furthermore, the change of GLR is also by adjusting the flow of liquid and gas in the experiments. Therefore, GLR can better describe the experimental conditions. In this paper, the effects of GLR and ambient pressure on the diameter distribution, axial velocity distribution and diameter-velocity correlation of an effervescent atomizer are explored experimentally. The time distribution of the droplet size and axial velocity is analyzed. Additionally, the effect of the GLR and ambient pressure on the probability density of the droplet size is systematically examined.

2 Experimental Methods

As illustrated in Fig. 1, the experimental system consists of a gas–liquid supply system, an atomization system, an optical measurement system, and a data acquisition system. The structural parameters and conditioning process of the chamber have been thoroughly discussed in [33, 34]. The experiment was filmed through an observation window of an ambient pressure tank. In analyzing measurements of the PDI system, the orifice exit is taken as the origin. The measuring section is set along the injection direction (z-direction). The sampling interval is chosen according to the spray angle. In the experiment, Artium's PDI-300 MD PDI system is utilized. The droplet size measurement range of the system is 0.5–2000 μm, with an accuracy of 0.5 μm. The velocity measurement range is 0–300 m/s, with a measurement accuracy of 1%. The reasons for selecting this system has been introduced in reference [35]. To guarantee the accuracy of the measurement results, the number of collected droplets at each measured point was more than 5000.

Fig. 1
figure 1

Schematic of the experimental setup

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The effervescent atomizer utilized in the experiment is depicted in Fig. 2. The application object of the nozzle in this paper is the torch igniter. The torch igniter requires a stable and uniform spray process. Studies have shown that the flow pattern of outside-in-gas (OIG) atomizer is mostly bubbly flow. An intermittent flow of gas–liquid alternating occurs at the orifice exit, resulting in unstable atomization [5, 6]. The outside-in-liquid (OIL) atomizer is dominated by annular flow pattern, which provides a more stable spray [36]. Therefore, the nozzle used in this experiment is OIL. The center of the liquid chamber is equipped with an air inlet chamber with a diameter of 3 mm. The bottom wall of the inlet chamber has 4 rows of evenly distributed air outlets with diameters of 0.6 mm, amounting to 16 in total. The outlet is connected to the gas–liquid mixing chamber. Pure water and air were employed as experimental working media. In the experiment, the gas enters the inlet chamber from the top. Simultaneously, pure water enters the gas–liquid mixing chamber from the liquid inlet. Due to the pressure gradient, the gas is forced into the liquid from the outlet to form a two-phase flow. Finally, the gas–liquid two-phase flow is discharged from the orifice with a pressure gradient. The gas duct of the effervescent atomizer is constructed of stainless steel. The gas–liquid mixing chamber is made of stainless steel and transparent acrylic organic glass. The gas mass flow and liquid mass flow is controlled by a venturi tube and liquid cavitation tube during the experiment, respectively. And they are displayed and recorded with a flowmeter, respectively. The liquid flow rate has a constant value of 20 g/s. For axial cross-sectional data measurements, four absolute ambient pressures (0.1, 0.6, 1.2, and 1.8 MPa) and five different GLRs (0.5%, 1%, 2%, 4%, 6%) were chosen for the experiment.

Fig. 2
figure 2

Internal structure of effervescent atomizer

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3 Results and Discussion

3.1 Effect of GLR on Spray Characteristics

Figure 3 show the effect of GLR on the distribution of the droplet size and axial velocity along the radial direction at an axial distance z = 40 mm. The change of radial distance is quantitatively represented by the equivalent distance \({\text{R}}\text{/}{\text{R}}_{0}\), where, \({\text{R}}\) is the radial distance from the outside of spray to the axis, mm; \({\text{R}}_{0}\) is the orifice diameter, mm. Under the same GLR, the maximum droplet diameter is in the center of the spray. The axial velocity distribution shows similar distribution characteristics. In the central region, the breakup of the liquid is mainly dependent on the explosive effect of the bubble and the aerodynamic effect between the droplets and the ambient air. The energy produced by the explosion of the bubbles not only produces droplets of different sizes, but also imparts radial velocity to the droplets [21]. And the axial velocity of the droplets is increased. Smaller droplets are easier to follow the gas to move outward. During the process of outward movement, the droplets are broken again under the action of aerodynamic force. As a result, the droplet diameter gradually shows smaller along the radial direction. Meanwhile, the kinetic energy of droplets decreases for the resistance of air, and the velocity gradually decreases. With the increase of the GLR, the droplet diameter in the central region of the spray decrease. The curve is becoming more gentle in its downward trend.

Fig. 3
figure 3

The distribution of droplet size and axial velocity at axial distance z = 40 mm for various values of GLR

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Figures 4 and 5 show the effect of GLR on the time distribution and probability density of the droplet size at the section at an axial distance z = 40 mm. And the droplet size distributions here are number based distributions. The red dotted line represents the value of D32. As can be seen from Fig. 4, most of the droplet sizes for different GLR are in the range 30–100 μm. However, the fraction of droplets within this range is different. The higher the GLR, the larger the fraction of droplets in that size range. As shown in Fig. 5, the diameter of droplets is mainly concentrated around 65 μm, with only 2.2% of the total droplets having this diameter at GLR of 0.5%. However, when the GLR is 6.0%, the droplets with a diameter of 59 μm account for 5.6% of the total. In addition, it can be seen from the Fig. 4 that the D32 significantly decreases with the increase of GLR. The number of large droplets significantly decreases with the increase of GLR. And large droplets will increase the value of D32 in the calculation formula of D32. As a result, the D32 decreases from 236.2 μm under the lowest GLR of 0.5% to 174.6 μm under the highest GLR of 6%. The value of D32 has decreased by up to 35.2%.

Fig. 4
figure 4

Time distribution of droplet size at axial distance z = 40 mm for various values of GLR (\({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Fig. 5
figure 5

Probability density of droplet diameter at z = 40 mm for various values of GLR (\({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Figure 6 is a time distribution diagram of the effect of GLR on the axial velocity of droplets at z = 40 mm. As can be seen from the figures, the droplet velocity increases significantly as GLR increases. As the gas flow rate increases, the pressure in the mixing chamber increases accordingly, resulting in an increase of the internal–external pressure difference. This, in turn, leads to an increase in the velocity of the outlet and the energy of the bubbles. Consequently, the bubbles have greater bursting energy after ejecting from the orifice, significantly increasing the droplet velocity outside the orifice [37].

Fig. 6
figure 6

Time distribution of axial velocity at z = 40 mm for various values of GLR (\({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Figure 7 illustrates the relationship between droplet velocity and droplet size at z = 40 mm for GLR values of 0.5 to 6%. The horizontal and vertical red dotted line lines represent the average velocity and D32, respectively. As can be seen from the figure, the smaller the droplet size in the spray field, the higher the average velocity for all values of GLR. It is noteworthy that this is contrary to the characteristics of droplets in swirl injectors and gas–liquid swirl coaxial injectors. The larger the droplet at the outlet of such an injector, the greater the inertia. Since small droplets have less inertia, their velocity decreases rapidly under the influence of aerodynamic drag. For the effervescent atomizer, by contrast, the fragmentation of the outlet liquid film is mainly achieved by the explosion of bubbles after the bubbles left the orifice [38]. The increase of gas flow represents the increase of inlet velocity. Therefore, the liquid film will have a greater velocity difference with the air after leaving the nozzle exit, resulting in stronger shear force. This causes the liquid film to break into smaller droplets. And the initial velocity is higher. Furthermore, the expansion effect of bubbles will also be more intense for the increase of internal and external pressure difference. Additionally, the inertia of small droplets is smaller than that of large droplets, so the velocity change is more obvious. Therefore, small droplets have very broad velocity distributions.

Fig. 7
figure 7

Relationship of axial velocity and droplet size at z = 40 mm for various values of GLR (\({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Figure 8 shows the time distribution of droplet size with \({\text{R}}\text{/}{\text{R}}_{0}\) from axis at z = 40 mm and GLR = 2%. As illustrated in this figure, the mode of droplet size increases from 50 μm in Fig. 8a to 65 μm in Fig. 8e along the spray edge to the axial center (The 'mode' here refers to the highest proportion of droplets.). At the same time, the distribution of droplet size is more dispersed, showing an increasing proportion of large droplets. Figure 9 shows the probability density of droplet size at different radial positions at z = 40 mm and for GLR = 2%. The maximum probability of droplet size density decreases from 10.8% at \({\text{R}}\text{/}{\text{R}}_{0}\)= − 4 to 4.9% at \({\text{R}}\text{/}{\text{R}}_{0}\)= 0. It is evident that the upward trend of the cumulative probability distribution curve of droplet size slows down. It results in the SMD gradually increasing in the radial direction, which is in line with the pattern observed in Fig. 3.

Fig. 8
figure 8

Time distribution of droplet size on the cross section at z = 40 mm (GLR = 2%)

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Fig. 9
figure 9

Probability density of droplet size at z = 40 mm (GLR = 2%)

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Figure 10 shows the time distribution of the axial velocity of droplets on the cross section at z = 40 mm and for GLR = 2%. This phenomenon has two primary causes: Firstly, the bubble detonates at the center of the orifice exit, thus providing the droplets at the center with greater explosive energy and higher speed. Secondly, as the droplet diffuses around, the droplet is impeded by the resistance of the surrounding gas, thus causing its speed to decrease [39, 40]. This behavior can also be found from Fig. 11, which shows the relationship between axial velocity and droplet size. In Fig. 11, the droplet size and velocity at the spray edge are lower than at the axial position.

Fig. 10
figure 10

Time distribution of axial velocity at axial position z = 40 mm (GLR = 2%)

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Fig. 11
figure 11

Relationship between axial velocity and droplet size at axial position z = 40 mm (GLR = 2%)

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3.2 Effect of Ambient Pressure on Atomization Characteristics

Four sets of experiments with varying ambient pressure were conducted for a GLR of 4%. Figure 12 displays the temporal distribution of droplet size at z = 40 mm. In the experiment, the minimum droplet size and the maximum droplet size were 1 μm and 375 μm, respectively. As shown in Fig. 12, the main distribution range of droplet size is 25 to 370 μm. The lower the ambient pressure, the higher the proportion of small droplets. Furthermore, droplet size distribution is highly irregular. As the ambient pressure increases, the number of droplets of different sizes changes drastically, exhibiting an increasing proportion of large droplets. The density of the ambient gas increases with the increase of the ambient pressure, resulting in an increase in the resistance of the liquid film. In addition, the pressure difference between the inside and outside of the orifice is smaller, resulting in less energy for bubble expansion and breaking. Therefore, the droplet diameter will be larger under high ambient pressure. This also causes the D32 to increase with increasing ambient pressure. It can be seen from the Fig. 12 that D32 increased from 198.8 μm at the ambient pressure of 0.1 MPa to 225.7 μm at the ambient pressure of 1.8 MPa.

Fig. 12
figure 12

Time distribution of droplet size at axial distance z = 40 mm for various ambient pressures (GLR = 4%, \({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Under the same conditions, the probability density of droplet size at axial distance z = 40 mm from the exit outlet can be seen in Fig. 13. It reveals that droplet size tends to increase with an increase in ambient pressure, thus resulting in fewer droplets of small size. Simultaneously, the slope of the droplet size cumulative probability density curve becomes less steep. Figure 13 summarizes the relationship between droplet distribution and ambient pressure from the data in Fig. 12.

Fig. 13
figure 13

Probability density of droplet size at an axial distance z = 40 mm for various ambient pressures (GLR = 4%, \({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Figure 14 shows the time distribution of axial velocities of droplet size at z = 40 mm from the orifice outlet under the same working condition. As can be observed from Fig. 14, the lower the ambient pressure, the broader the range of droplet velocity and the larger the velocity disparities among droplets. Conversely, the higher the ambient pressure, the more concentrated the droplet velocity distribution and the smaller the velocity differences among droplets. Additionally, as the ambient pressure increases, the droplet velocity decreases significantly [41]. When the ambient pressure increases, the air density around the spray increases. Therefore, the aerodynamic drag of the droplet increases, resulting in greater momentum loss. Thus, the axial velocity decreases with the increase of ambient pressure. Due to the increase of ambient pressure, the pressure difference inside and outside the orifice is smaller, resulting in less energy for bubble expansion and breakage. Therefore, the droplet diameter will be larger under high ambient pressure. The aerodynamic drag around them is relatively weak for the large inertia of the larger droplets, resulting in a smaller change in velocity. Therefore, the velocity distribution is relatively concentrated. For example, under an ambient pressure of 0.1 MPa, the droplet velocities range from 60 to 120 m/s, with a uniform distribution of droplets of different velocities. However, the velocities for an ambient pressure of 1.8 MPa are significantly lower than for an ambient pressure of 0.1 MPa. And they are concentrated in the 20–40 m/s range.

Fig. 14
figure 14

Time distribution of axial velocities at an axial distance z = 40 mm for various ambient pressures (GLR = 4%, \({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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Figure 15 shows the distribution of droplet size and velocity at z = 40 mm for different ambient pressures. As can be seen from Fig. 15, small droplets have a wider velocity distribution than large droplets for different ambient pressures. Taking the ambient pressure of 1.2 MPa as a reference, droplets with a size of 75 μm have velocities in the range of 20–60 m/s, whereas droplets with a size of 300 μm have velocities in the range of 30–60 m/s. Gradually, as the ambient pressure rises, the range of droplet velocities decreases. This is due to the fact that the bubble explosion at the exit outlet produces droplets of varying sizes. Smaller droplets, having less inertia, are more susceptible to change in motion. As a result, the velocity distribution of droplets will be wider. On the other hand, larger droplets, with greater inertia, are less affected by aerodynamic drag. Consequently, the speed of large droplets decreases more slowly and their distribution is more concentrated.

Fig. 15
figure 15

Relationship between axial velocity and droplet size at an axial distance z = 40 mm for various ambient pressures (GLR = 4%, \({\text{R}}\text{/}{\text{R}}_{0}\)=0)

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From the above analysis, it can be seen that for the same ambient pressure, the SMD and axial velocity decrease rapidly as radial distance increases. Furthermore, the droplet size decreases and the velocity decreases at the edge of the spray. The SMD at the axis increases with an increase in ambient pressure [42]. By contrast, the axial velocity decreases as ambient pressure increases. Most important, an increase in ambient pressure reduces the axial velocity differences among droplets.

4 Conclusions

This study focused on the effects of GLR and ambient pressure on the atomization characteristics. The droplet size and velocity distributions were measured by PDI system. In contrast to a centrifugal atomizer, the smaller droplets in the spray field of the effervescent atomizer have a higher velocity, and the larger droplets have a lower velocity. The ascending trend of the cumulative probability curve of droplet size decreases with an increase in GLR. The results showed that the SMD increased steadily along the radial direction away from the axis.

It is observed that the velocity distribution of droplets is more concentrated at high ambient pressure. Simultaneously, the velocity difference between droplets becomes smaller. Correspondingly, the slope of the cumulative probability density curve of droplet size decreases with an increase in ambient pressure.