Behaviors of Multi-Droplets Impacting on a Flat Wall

Abstract

Microscopic characteristics of fuel spray are very important for atomization and mixture formation. The droplet size, number density, velocity distribution as well as minimum distance reveal the quality of spray and atomization, which affects the subsequent combustion and emissions for different engines such as vehicle, marine and aircraft. Moreover, in the internal combustion engine, the spray-wall impingement is difficult to avoid, which is the main source for soot emissions. Nowadays, regulations for emissions become straight by governments. Therefore, it is urgent for us to alleviate the energy and emissions crisis. In this study, the droplets behaviors will be characterized under the related engine working state. Firstly, the experimental setup and measurement were explained in detail. Then, images process method was induced to calculate the droplet size, velocity and distance among them. Finally, results of the impinging spray were presented. One thing should be noted, as the dense region is not available to detect the droplets by the observation. Therefore, a spray “slicer” was designed and applied to cut the spray slim. Finally, multi-droplets were generated, and the results can be concluded as well. All the results could provide insights into the impacting behaviors for better understanding the droplet dynamics.

1. Introduction

Droplet-wall interactions are widely used in the gas-turbine and internal combustion engines under a range of different conditions [1]. After injected into the cylinder, droplets with various velocities travel along the spray axis to impact on the piston head or cylinder wall to form fuel film as well as breakup into small ones splashing off the wall [2]. Moreover, the rebounding and splashing droplets coalesce and collide with each other in the air by the help of vortex, which may impinge on the cylinder wall again or eventually adhere on it [3]. Especially, for the cold-start operation, the liquid film on the wall surface significantly contributes to the soot emissions [4]. Therefore, understanding the mechanism of impinging spray is essential for better design and optimization on the engine performance. Specially, the investigations on droplet characteristics could contribute to model the impinging behaviors for separating the deposit/splash droplets under a series of pressure and temperature conditions.

Recently, droplets impacting on the wall becomes a hotpot for investigations, especially after Moreira et al. [5] put forward the question that “How much of single droplet impact research is useful?”. As a fundamental study, the single drop-wall impacting can clearly explain the relationship between the splashing behavior and non-dimensional parameters, such as Reynolds, Weber, Ohnesorge and K numbers [6]. Previously, Walzel [7] firstly described the droplets impinging behavior. Then, the splashing characteristics was formulated by Yarin and Weiss [8]. Followed by them, Mundo et al. [9] firstly applied K number to separate droplets behaviors of “splashing” and “no-splashing”. Then, Bai et al. [10] characterized the different impingement regimes of the incident drops by Weber number. Then it was refined and developed well by other scholars [11, 12, 13] Recently, Cen et al. [14] studied the dynamic break-up of the alternative biofuel impacting on the hot wall under the film boiling regime with different Weber number. They found that droplet breakup was dominated by Rayleigh instability, and the timing of jet break-up agreed well with the theory of Rayleigh instability. Qin et al. [15] investigated the splashing behaviors of an impacting drop on the hot surface to compare the effects of fuel viscosity and surface roughness. Liu et al. [16] studied the spreading dynamics of a single droplet impacting on a heated surface. They found that impacting behavior such as “depositing”, “rebounding” and “breakup with atomization” were sensitive to both surface temperature and Weber number.

According to the literature surveys above, although many investigations were performed on the drop-wall interaction. It is still necessary to conduct an in-depth study on the multi-droplets wall-impingement. This study aims to fill the research gap. The target is to investigate the characteristics of multi-drops impingement on the wall experimentally under various conditions. Particle image analysis (PIA) technique was implemented to obtain the microscopic observations. Firstly, the spray droplets were checked by a single hole injector. Then, a spray “slicer” was introduced to make the multi-droplets impinging on the wall. Moreover, the thickness of “slicer” was defined. Finally, 0.4 and 0.04 mm in thickness of the “slicer” were determined to test at the spray tip and quasi-steady state.

2. Experimental system and image processing method

The experimental setup is shown in Figure 1. It consists of three parts, including an injection system, an optical system and one constant volume chamber. Fuel was injected into the chamber, then developed and impinged on a flat wall by a high-pressure common rail. The high-pressure constant volume chamber was equipped with four glass-windows to transmit the observation light. Similar to the shadow method, particle image analysis (PIA) was applied in this research, which was also used in our published literatures [17, 18]. Therefore, here only a brief introduction is shown. A double pulsed Nd: YAG laser of 532 nm wavelength was used to illuminate the spray. And microscopic behaviors of spray can be observed through a charge-coupled device (CCD) camera (Flowtech Research Inc., FtrNPC). Moreover, a microscope was used to connect the camera to obtain the tiny droplets clearly with three teleconverters (Kenko Tokina, N-AF 1.4X TELEPLUS MC4*3) connected to amplify the micro-image. Besides, owing to the dense drops along the spray axis, a house-designed spray “slicer” was designed and applied to get the slim spray, as depicted in Figure 2. The spray “slicer” made of steel with length of each slicer at 30 mm and height at 3 mm. And the distance between two slicer was defined as the thickness, which could be adjusted from 0.04 to 1 mm.

Figure 1.

Experimental apparatus.

Figure 2.

Schematic of spray “slicer”.

Table 1 lists the experimental conditions. On mini-sac injector with a single hole of 0.135 mm in diameter and 0.65 mm in hole length was used, resulting in the length-to-diameter (L/D) ratio at 4.8. Toluene was used as the tested fuel with density being 866 kg/m³ under the room temperature. The properties such as viscosity and surface tension under the room temperature are 5.89 × 10–4 N·s/m² and 0.0285 N/m, respectively. The injection mass of toluene was kept constant at 4.0 mg. The chamber was filled with nitrogen to conduct the experiment under the non-evaporation condition. And the ambient pressure was changed between 0.1 and 0.5 MPa, leading to the gas density at 1.19 and 5.95, respectively. Besides, the injection pressure was set among 10, 20 and 30 MPa with injection duration at 2.9,2.1 and 1.7 ms. A flat wall made of quartz glass was used as the impingement wall, as shown in Figure 3. The impingement distance from the nozzle exit to the wall was decided at 22 mm. And the impingement angle was determined at 45 deg. between the spray axis and the wall surface. One thing should be noted that the roughness of the flat wall was measured at Ra7.0 μm by a portable high-performance surface roughness and waviness measuring instrument (Kosaka Laboratory Ltd., SE300).

Injector Parameters
Injector Type	Mini-sac with a single hole
Hole Length (mm)	0.65
L/D Ratio	4.8
Hole Diameter (mm)	0.135
Fuel Properties @ 298 K
Test Fuel	Toluene
Density (kg/m^3)	866
Dynamic Viscosity (N·s/m^2)	5.89 × 10^−4
Surface Tension (N/m)	0.0285
Conducted Conditions
Injection Mass (mg)	4.0
Ambient Gas	Nitrogen
Injection Pressure (MPa)	10, 20, 30
Injection Duration (ms)	2.9, 2.1, 1.7
Ambient Temperature (K)	298
Ambient Pressure (MPa)	0.1 and 0.5
Ambient Density (kg/m^3)	1.95 and 5.95
Impinging Conditions
Impingement Wall	Flat wall, quartz glass
Wall Roughness (μm)	Ra = 7.0
Wall Temperature (K)	298
Impingement Distance (mm)	22
Impingement Angel (deg)	45

Table 1.

Experimental conditions.

Figure 3.

Image processing.

The image processing is shown in Figure 3. Firstly, the resolution can be calculated by the help of a micro-scale ruler. For filtering the spherical droplets, some refined criteria should be defined, such as roundness, pixel number and diameter. After detecting the spherical droplets, the distance between droplets can be obtained. Furthermore, with the interval timing between these two frames at 0.4 μs, the velocity of each droplet can be calculated. Moreover, in order to make the statistical results reasonable, at least 100 repeated tests were conducted under the same condition to make sure more than 5000 particles are available for statistics. Finally, the droplet size, velocity, distance and non-dimensional results can be gotten. The details about the algorithm can be seen in the article of Wang et al. [19].

3. Results and discussion

3.1 Impinging spray and droplet behaviors

Microscopic spray development before impingement under 0.1 and 0.5 MPa are presented in Figure 4. It can be seen that all the images are arranged along the spray axis and then rotated 45 deg. at counterclockwise connected. Under P_amb = 0.1 MPa, when fuel spray at the near field region, less droplets can be seen. With development at 2–4 mm from the origin, it is clear to see the liquid column. With longer penetration development at 8–10 mm, better atomization can be seen that liquid sheet located in the core with droplets at the periphery. At further locations, more ligaments and clear droplets can be captured. Besides, increased the ambient pressure to 0.5 MPa, more atomized droplets can be obtained because of the strong sheer force to promote droplets collision, leading to dense spray when compared to that of 0.1 MPa. In this case, although PIA could obtain the microscopic spray clearly at periphery, it is still difficult to clear observe the drops at the dense spray regions.

Figure 4.

Microscopic behaviors of spray and droplets.

Then, typical morphologies at (10, 10) and (14, 14) are shown in Figure 5. Before impingement at (10, 10), both ligaments and droplets can be seen at 0.1 MPa due to the primary breakup. Under 0.5 MPa, intense interactions result in more small size droplets. Transferred to being impingement location at (14, 14). The white solid line represents the surface of the flat wall. At the near wall region, it is too dense to identify the droplets along the spray axis when compared to (10, 10), resulting in only droplets at periphery can be observed.

Figure 5.

Spray morphology under different ambient pressures.

Generally, the atomized droplets are the outcomes of competitions between aerodynamic force and surface tension. The friction in the gas-fuel interface results in the disintegration and instable deformation, finally contributing to the formation of smaller droplets. Therefore, We_g can be used to describe instability of the droplet formations and predicts the behaviors of droplet breakup furtherly, defined as:

$$W{e}_g=\frac{{\rho }_g{v}^{2}d}{\sigma }$$E1

where ρ_g is the ambient gas density with σ being the liquid surface tension. v is the relative velocity between droplet and ambient gas. d represents the droplet diameter.

Previously, Wierzba [7] found the vibrational breakup occurs at a relatively low We_g, and droplets are easy to break up into smaller ones. Therefore, We_g can be applied to indicate the degree of atomization during development, which is divided into four parts: when 0<We_g<1 and 1<We_g<10, it suggests good atomization; when 10<We_g<14, the transient section indicates the further atomization can be expected; when We_g>14, the large droplets still exist.

The diameter-velocity distribution is presented in Figure 6. The scatter number in each sub-figure suggests the number of available droplets. The horizontal axis is droplet size (6–80 μm), and vertical axis is velocity (0–200 m/s). At 0.1 MPa, compared between (10, 10) and (14, 14) in Figures. (a) and (b), results are similar. However, more droplets with larger We_g can be seen when ambient pressure increased to 0.5 MPa in Figures. (c) and (d), suggesting these droplets have the potential for further atomization. Besides, in contrast to Figures. (c) and (d), the number of large We_g decreases significantly, indicating that higher ambient pressure favors fuel breakup and atomization. In other words, it can be concluded that fuel spray development is the process of We_g decreasing with better atomization.

Figure 6.

Diameter–velocity distribution with gas phase weber number.

The number probability of droplet size is calculated in Figure 7. Before impingement (10, 10), two curves are similar but with different peak values, and the peak value of 0.1 MPa is larger than that of 0.5 MPa. However, difference becomes not obvious. Furthermore, the droplet size corresponding to the peak value of curves is the same at 12 μm. One possible reason may be that the scale of atomization is mainly decided by the injector itself, resulting in less relationship with the ambient pressure. In order to discuss the velocity distribution, the probability of velocity is presented in Figure 8. With the increase in ambient pressure, the maximum velocity reduces from 200 to 150 m/s. Besides, the velocity corresponding to the peak value decreases at elevated ambient pressure decreases from 65 to 25 m/s at (10, 10), from 45 to 10 m/s at (14, 14). Besides, different to droplet size distribution, the peak value in velocity decreases sharply under high ambient pressure owing to more energy dispersion. All in all, it can be seen that velocity is sensitive to the location and ambient pressure significantly compared to diameter. And both ambient pressure and spray development decelerate droplets.

Figure 7.

Droplet diameter probability curves.

Figure 8.

Droplet velocity probability.

Sauter mean diameter (SMD = ∑D3/D2) is defined as the diameter of a droplet with the same ratio of volume to surface area, which is widely applied to evaluate the atomization, as shown in Figure 9. Here, SMD and averaged velocity under each condition are compared. SMD decreases with elevated ambient pressure and spray development, resulting in better atomization. The ambient shear force and high gas density should be the main reasons for it. Moreover, the averaged velocity decreases as well because of the resistance force. And the minimum distance of the selected droplets is defined as the shortest distance among them, as shown in Figure 10, which can be applied to represent the spray dispersion. The results of mean minimum distance (MMd) are calculated and depicted here. Similar to SMD and averaged velocity, MMd decreases with ambient pressure increasing but with different reason. That high ambient pressure compacts droplets, making them together due to the high ambient density should be one possible reason for it.

Figure 9.

(a) SMD and (b) averaged velocity.

Figure 10.

Definition and results of mean minimum distances.

3.2 Sliced spray behaviors

In this part, the spray behaviors will be discussed at the spray tip for clear observation. Moreover, the spray “slicer” was applied here with the thickness at 0.4 mm.

Firstly, Figure 11 shows the morphology of spray tip at two locations under the injection pressure of 10 and 30 MPa, respectively. At (10, 10), clear droplets, ligaments and even liquid sheets can be seen, indicating the spray slicer improves the atomization. Moved to the impinging location at (14, 14), the splashing crown structures can be seen clearly, which previously reported in the single drop impacting experiment [20, 21]. Besides, the photographing timing is recorded in each image. With an increase in injection pressure, shorter timing is needed due to high momentum energy from the drops.

Figure 11.

Spray morphology under different injection pressures.

Droplet diameter-velocity distribution is presented in Figure 12. The horizontal axis is diameter, and vertical axis is velocity. Besides, SMD is depicted in each image. It is interesting to find the “fish-shape” distribution under all conditions with big “head” and small “tail”. Furthermore, increased the injection pressure from 10 to 30 MPa, distribution becomes wider with higher velocity because of high kinetic energy. In contrast to location effect, the influence of injection pressure plays a much more important role on not only velocity but droplet size. It is evident that increasing injection pressure reduces SMD significantly, when compared it between (10, 10) and (14, 14).

Figure 12.

“Fish-shape” distribution.

The size probability is presented in Figure 13. It is interesting to find the almost half droplet diameter is in the range of 12–20 μm. Moreover, the peak value corresponding to diameter locates in only 12–16, indicating the droplet size is determined largely by the injector itself, instead of the injection pressure. Besides, the peak value increases with spray tip movement and injection pressure owing to better atomization. Furthermore, injection pressure shows lager effect on droplets atomization than that of measurement location.

Figure 13.

Droplet size distribution.

Figure 14 shows the velocity distribution along x and y directions to describe both velocity and direction. Four quadrants are separated to define the velocity direction. Quadrant I indicates the incident droplet moving along the spray axis; Quadrant II indicates droplet splashing off the wall in the direction perpendicular to spray axis; Quadrant III indicates droplet rebounding into the air along the spray axis; Quadrant IV indicates droplet rushing to the wall in the completely opposite direction of Quadrant II. Moreover, the absolute velocity is the distance from one certain dot to the origin. Because of the spray tip, all the droplets show similar rushing direction to the wall in Quadrant I. And almost the same shape can be seen under 10 MPa. But increasing the injection pressure to 30 MPa, droplet velocity can reach to 200 m/s.

Figure 14.

Droplet velocity direction.

Figure 15 shows the diameter-minimum distance. As explained before, minimum distance (Md) could be used to judge the droplet dispersion with larger Md to indicate the better dispersion. All results show similar distribution with little difference. One thing can be concluded from distributions that increased the injection enlarges Md at a certain level. Therefore, in order to discuss the Md clearly, mean minimum distance (MMd) is used in Figure 16 as well as averaged velocity. For averaged velocity, increasing injection pressure accelerates droplet greatly from 83.3 to 137.0 m/s at (10, 10). But this increasing tendency becomes moderate at (14, 14). In addition, averaged velocity decreases slightly with tip movement due to the air drag force. For MMd, both movement and injection pressure enlarge MMd, suggesting better atomization. However, one interesting thing is that different to velocity, MMd is more sensitive to the location instead of injection pressure. Droplets disperse well with the spray development should be one possible reason for it.

Figure 15.

Droplet diameter-Md distribution.

Figure 16.

(a) Averaged velocity and (b) MMd.

3.3 Multi-droplets impacting characteristics

In order to explore the multi-droplets impacting behaviors deeply, the thickness of “slicer” was decreased to 0.04 mm, as shown in Figure 17. At spray tip, droplets can be recognized at thickness of 0.4 and 0.1 mm. However, changed to quasi-steady state, the thickness should be decreased much more. Finally, the thickness was determined at 0.04 mm. And in this part, multi-droplets can be achieved through the “slicer”. Moreover, the impacting and splashing behaviors of droplets will be discussed in detail.

Figure 17.

Comparison in the clear observations with different thickness of “slicer”.

Figure 18 presents the diameter-velocity distribution at (16, 14) and (18, 14). The horizontal axis is the droplet diameter, with vertical axis being as the velocity. Results of 10, 20 and 30 MPa are depicted by the black, red and blue data, respectively. For the velocity, at (16, 14), the velocity ranges from 0 to 110 m/s. But it decreases to only 50 m/s when the location is transferred to (18, 14). And it is supposed that the energy disperses with the interaction of droplets and fuel film on the wall during the injection, which will be discussed more in the following part. Moreover, for the droplet size, it is clear to see that diameter increases significantly when transferring from (16, 14) to (18, 14). Droplets collision with each other after impacting on the wall should be one possible reason for it.

Figure 18.

Droplet diameter-velocity distribution.

In order to analyze the size distribution statistically, the probability of the diameter is applied and shown in Figure 19. At (16, 14), the peak value corresponding to the diameter increases with higher injection pressure from 20–25%. In contrast to (18, 14), peak value declines obviously, suggesting that droplet size increases from (16, 14) to (18, 14) with spray movement but decreases with increasing injection pressure. Finally, SMD is calculated and depicted in Figure 20. It shows that SMD decreases slightly with an increase in injection pressure at (16, 14). However, larger influence of injection pressure can be seen at (18, 14). The larger-size drops are easy to break up into smaller ones owing to high kinetic energy. While, by comparing the location effect, SMD is enlarged with movement. After impingement on the wall, the splashing droplets may collide and coalesce by others can explain this phenomenon. More details will be discussed through the velocity analysis.

Figure 19.

Probability of diameter at different locations. (a) @(16, 14) (b) @(18, 14).

Figure 20.

SMD at different locations.

Figure 21 shows the velocity-direction distribution. X and Y coincide with the direction presented in Figure 4. And the distance from the origin to one selected droplet presents the magnitude velocity. At (16, 14), almost all the droplets rush into the wall along the spray jet direction. Besides, high injection pressure accelerates droplets. While, changed to (18, 14), droplets change direction in Quadrant II, indicating the splashing direction. And this is the main reason for the low velocity and large size. After impacting on the wall, droplets splashing off the wall results in energy loss. Additionally, some droplets may collide and change the direction as well as coalescence into larger ones. One thing should be pointed that at (16, 14) and (18, 14), droplets locate in all these four quadrants because of the vortex.

Figure 21.

Droplet velocity distribution at different locations.

Next, the averaged velocity was calculated and presented in Figure 22. It shows that at (16, 14), velocity increases significantly with higher injection pressure. Compared with after impingement at (18, 14), only half velocity can be seen due to the interaction consuming energy. Finally, the mechanisms of multi-droplets impacting on the wall is conceived. After impingement, the secondary droplets are generated by the irregular crown structure with the help of the interaction between fuel film and droplets. On one hand, the splashing droplets after impingement collide with each other and then coalesce into larger one. On the other hand, the splashing crown structures also collide owing to the multi-droplets crash into the fuel film, leading to droplets generated from the rim of the crown body. Moreover, the crown bodies collide, then generate droplets splashing off the structure to increase the totally calculated SMD.

Figure 22.

Averaged velocity at different locations.

4. Conclusions

In this study, droplet behaviors were investigated before, during and after impingement on the wall. For clear observation, free and impinging spray (with/without “slicer”) at different thickness of 0.4 and 0.04 mm were characterized to evaluate the droplet size, velocity and distance. Besides, different influences including measurement locations, injection pressures and ambient pressures were considered to better understand the behaviors of multi-droplets impacting on the wall. The following conclusions can be drawn as:

1. We_g can be applied to evaluate the degree of breakup and atomization. Owing to the droplets breakup and atomization, We_g decreases from (10, 10) to (14, 14). Moreover, high ambient pressure can promote this phenomenon. Furthermore, ambient pressures and locations has less effect on the scale of atomization as the diameter corresponding to peak value of probability is constant. However, velocity is more sensitive to the ambient pressure and locations compared with the droplet size.

2. Higher injection pressure widens the distribute in velocity but compacts the diameter distribution. Droplet velocity direction can be obtained and mapped in four quadrants. And Md of droplets is defined and employed to evaluate the droplets dispersion. Higher injection pressure decreases SMD, accelerates droplets and promotes the droplets dispersion owing to high kinetic energy and better atomization.

3. After impacting on the wall, SMD increases but velocity decreases. The multi- droplets impacting on the wall cannot be considered as the superposition of undisturbed single droplet. Not only splashing droplets but also splashing crown structures collide and coalesce to generate secondary droplets with large size and low velocity.

Acknowledgments

The author would like to acknowledge National Natural Science Foundation of China [Grant 51909037] and Foundation of State Key Laboratory of Engines [No. K2022-12].

Conflict of interest

The authors declare no conflict of interest.