Study on Dynamic Characteristics of Single Droplet Impingement on Heated Liquid Film

Received: October 26, 2022
Revised: December 30, 2022
Accepted: January 3, 2023

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Cite this article:

Wu, H., Liu, C., Cen, C., Huang, C.E., Lin, S.L. (2023). Study on Dynamic Characteristics of Single Droplet Impingement on Heated Liquid Film. Aerosol Air Qual. Res. 23, 220366. https://doi.org/10.4209/aaqr.220366

HIGHLIGHTS

• The impact interaction between single droplet and heated liquid film was explored.
• With the change of We and film temperature, six typical phenomena were found.
• The crown diameter, height, and existence time increase with We and temperature.
• At high We, the proportion of large diameter sputtering droplets decreases.
• The ratio of small-diameter sputtering droplets increases with the temperature.

Keywords: Droplet impingement, Liquid film, Weber number, Temperature, Sputtering

1 INTRODUCTION

The cleaner and more efficient combustion technologies attract more consideration on alternative fuel emissions (Yang et al., 2021), special control technologies (Tabor et al., 2021; Chou et al., 2022; Lin et al., 2022a), and the consideration of carbon neutrality (Lin et al., 2022b; Lv et al., 2022). In direct injection spark ignition (DISI) engines and gasoline direct injection (GDI) engines, fuel is injected directly into the cylinder, and droplets inevitably impact the piston and cylinder surfaces, forming a wall-attached oil film that affects the combustion and emission performance of the engine (Stevens and Steeper, 2001). If the wall-attached oil film persists until the premix burns in the cylinder, it can catch fire and burns into a diffusion flame, known as a pool fire that increased the emissions of soot, unburned hydrocarbon (UHC) (Witze and Green, 1997), elementary and organic carbonaceous species.

For most applications, the solid surface will be covered with a liquid film after the impingement, and the subsequent droplets impingement onto the liquid film instead of the solid surface. Therefore, more attention should be paid to the phenomenon of a droplet hitting the liquid film. The droplet impingement on the liquid film is a complicated process involving heat and mass transfer. The main factors affecting the hydrodynamic characteristics are droplet parameters (diameter, impinging velocity, impinging angle, temperature, density, viscosity, and surface tension) and liquid film parameters (thickness, temperature, flow velocity, and composition) (Yarin, 2006; Liang and Mudawar, 2016).

Ethanol has been widely used as an additive in conventional fuels. The physical and chemical properties, combustion characteristics, and emission profiles of ethanol-fossil fuel blends had been explored (He et al., 2003; Masum et al., 2013). The addition of ethanol to diesel reduced fuel density, cetane number, kinematic viscosity, and aromatic fraction, while increasing the octane number and fuel oxygen content of gasoline blends, shortening ignition delay time, and effectively reducing soot, NO_x and CO₂ emissions (Mao et al., 2022). Therefore, ethanol droplets were used to observe the impact of droplets on the liquid film in this study.

The impinging velocity is related to the impinging energy, which is one of the most important factors affecting the dynamic characteristics of droplet impingement on the liquid film. Chen et al. (2020) observed different phenomena with the increasing Weber number (We = 4.6–17.3), including complete rebound, partial rebound, jetting, and spreading when the droplet impinges on the horizontal liquid film at low speed. As the impinging velocity increases, a cylindrical crown without splashing will be formed (Roisman et al., 2006). Wu et al. (2021) studied the impact of ethanol droplets on the hot glycerol pool, and found the phenomenon of vapor explosion and nuclear boiling phenomenon by changing the impact Weber number and the pool temperature, which can effectively inhibit the generation of the wall-attached fuel layer. Lu et al. (2023) used laser-induced fluorescence (LIF) methods to study the breakup process of the crown structure when a single ethanol droplet impacted the glycerol liquid film. The results showed that at different droplet Weber number, liquid film thickness and liquid film viscosity, the coronal structure fragmentation was divided into three regimes: splash breaking, hole breaking, and mixed breaking.

When a droplet collides vertically with a liquid film, the fluid inside the drop experiences a violent redirection from vertical to radial. Yarin and Weiss (1995) proposed that the formation and expansion of the crown was attributed to the kinematic discontinuity when the droplet contacts the film. Cossali et al. (2004) studied the evolution of the crown. The growing and falling speed of the crown did not change with the increase of We. In other word, the crown thickness increased with time and was independent of We. The ratio of maximum crown height to the time of maximum crown height was not affected with We. The crown became unstable, generated jets at the rim of the crown, split into secondary droplets, and eventually splashed with increasing impingement energy (Rioboo et al., 2003). The generation of secondary droplets is caused by Rayleigh-Plateau instability, and this theory has been verified by sufficient studies (Deegan et al., 2008; Zhang et al., 2010). Yang et al. (2022) concluded that with the increase of the droplet Weber number, the spreading crown length, the maximum crown height, the upstream crown angle, and the number of secondary droplets increased.

Wang et al. (2020) and Zhu et al. (2019) carried out a fundamental research on the fuel droplet impingement on oil film. The effects of different droplet We, liquid film viscosity, and liquid film thickness on the impingement behavior were investigated. The morphology after impingement was categorized into rings, stable crown, delayed splash crown, and prompt splash crown. The results showed that the dimensionless crown height and diameter increased with the increase of We and decrease with the increase of oil film viscosity. Low oil film viscosity, high We, and thin oil film were all conducive to splashing. Vander Wal et al. (2006) also came to the same conclusion. Cossali et al. (1997) identified two mechanisms of splashing, depending essentially on the liquid viscosity: a) the prompt splashing, which occurred in a low Ohnesorge number (Oh), was characterized by secondary atomization already in the jetting phase; b) the late splashing with a high Oh, when secondary atomization occurred only from the jets protruded from the fully developed crown. Rioboo et al. (2003) determined the splash-crown and crown-deposition limits for liquid droplets impacting wetted solid walls. At higher K (= We Oh^–0.4) values, splashing was observed. There were significant differences between the dynamic phenomenons resulted from the droplet-solid surfaces and droplet-liquid film impingement. Therefore, the study to reveal more dynamic information from the droplet-to-hot liquid film impingement on liquid film needs further exploration.

At present, many researchers have conducted comprehensive studies on the behavior of droplets hitting the liquid film, and the experiments were conducted at room temperature. However, what cannot be ignored is that the temperature difference between droplets and liquid film may affect their behaviors and characteristics. There is also a lack of impingement regime map for droplet-to-heated liquid film. Thus, the purpose of the present work is to comprehensively study the impingement dynamics of droplets on the heated liquid film surface, while the ethanol droplets and heated glycerol liquid film were employed. The experiment was conducted under different We and liquid film temperatures. The respective morphologies of droplets impinging on the heated film will be described. The accurate physical description and scientific explanation of the droplets impinging behavior are valuable to the theoretical supplement of hydrodynamics and thermodynamics.

 
2 MATERIALS AND MEHTODS

 
2.1 Testing System

The experimental system diagram is shown in Fig. 1. The apparatus comprises a high-speed camera, a lighting system, a plate with a heater, a droplet generator, and a computer. A high-speed digital camera (MacroVis EoSens) with a Tamron 180 mm micro-lens was employed to record the dynamic process of a single droplet impingement on the liquid film, while 640 × 658-pixel resolution, 3272 fps, and 80 µs exposure time were set as working condition, 1 pixel is 0.262 mm. A 500W LED light was placed on the opposite side of the high-speed video camera to illuminate the behavior of the droplet impingement. A polycarbonate light diffusion plate was placed between the experimental object and the light source to get a uniformly distributed light. A trigger was installed under the needle of the syringe to ensure a complete record of the experiment. A step signal generated by the photoelectric switch would be detected by the detector when the droplet fell through the trigger and subsequently sent to the delay control system to control the trigger time of the camera. The camera and the experimental platform were placed horizontally.

Fig. 1. The experimental system diagram.

 
2.2 Experiment Design and Operation Condition

The entire experiment was carried out at room temperature and at atmospheric pressure. Pure ethanol (purity ≥ 99.7%, Macklin Inc.) was slowly pushed at 0.04 mm s^–1 with a syringe driven by an injection pump to produce droplets. The relevant properties of ethanol are shown in Table 1. The droplet diameter D₀ was 2.05 mm (accuracy within ± 0.25%). The distance between the needle and the liquid film surface was set to 1, 5, 10, 14, 18, and 22 cm to get different impinging velocities in the ethanol droplets. The velocities of the droplet contacting the liquid film calculated by a MATLAB code were 0.38, 0.93, 1.36, 1.57, 1.77, and 1.98 m s^–1. The MATLAB code first processed the recorded image to get the distance between the center of the droplet and the surface of the liquid film and droplet equivalent diameter. The interval time between each frame can be known by the shooting speed of the camera, and the average velocity of the droplet between twenty consecutive frames before touching the heated surface can be got by the stepwise method. The impinging velocity, the velocity at which the droplet contacts the liquid film, can be calculated by the fitting equation of velocity to the droplet center position. Thus, the We(s) were calculated to be 10, 61, 130, 172, 220, and 275, respectively.

Pure glycerol (purity 99.7%, Tianjin Zhiyuan Chemical Reagent Co., Ltd.) was used as the composition of the liquid film. The boiling point of glycerol is 290°C, and its other properties are also displayed in Table 1. The liquid film was laid flat on a 50 mm × 50 mm stainless steel plate with a surface average roughness of Ra = 1.6 µm. The steel plate was placed on a thermostat heater, whose maximum heating temperature is 450°C and heating size is 150 × 100 mm. Under constant temperature conditions, the temperature error of each point was ± 1°C. To reduce the error, two K-type contact thermocouples were used to detect changes in wall surface temperature. The thermocouples were placed on the surface of the thermostat heater, and the value of the thermocouples indicated the liquid film temperature. The temperature change range of the liquid film was 70–175°C with an interval of 5°C, which was controlled by the thermostat heater. Since the spreading area of the liquid film was constant, the thickness of the liquid film was controlled by the film volume. The thickness in this experiment was a fixed value of 0.4 mm. Tropea and Marengo (1999) already identified four different liquid surfaces, including the thin film, liquid film, shallow pool, and deep pool. According to their calculation standards, the liquid film in this experiment is a thin liquid film, and the impinging characteristics are affected by wall roughness. To ensure the reliability of the experiment, the liquid film was replaced after each impingement, and each condition was repeated at least five times.

 
3 RESULTS AND DISCUSSION

3.1 Phenomena and Analysis of Droplet Impact on Liquid Film

The spreading process of droplet-impingement on a liquid film surface (We = 10, T = 80°C) is indicated in Fig. 2. The time when the droplet contacts the liquid film is defined as 0 ms. It can be seen from the second picture that the droplet will not immediately fuse with the liquid film after contacting the liquid film (1.0 ms). This is because there is a thin layer of air between the droplet and the liquid film, which hinders the fusion. When the air trapped between the droplet and the free surface is expelled, the droplet is in contact with the liquid film and the capillary pressure rises, causing the droplet to deposit and spread rapidly (1.5 ms–4.3 ms) and merge completely at 9.2 ms. There is no crown or jet formation during the deposition process, and only capillary waves can be observed on the liquid film surface.

Fig. 2. The phenomenon of deposition-spreading.

When the temperature of the liquid film increases, the droplet no longer spreads on the liquid film, but rebounds from the film. Fig. 3(a) indicates a case of this phenomenon (We = 10, T = 120°C). As soon as the droplet contacts the liquid film, an air layer is still formed, as shown at 1.5 ms. However, the droplet does not fuse with the liquid film but spreads and deforms into a flat column on the surface of the liquid film (4.6 ms). This is because the droplet close to the surface of the hot liquid film evaporates to produce a vapor layer, and the corresponding vapor flow induces a pressure that prevents the droplet from directly contacting the liquid film (van Limbeek et al., 2019). During the spreading process, the droplet’s kinetic energy is converted into surface energy. When the droplet reaches its maximum spread, the top of the droplet moves upward under the action of the surface energy (10.4 ms), and finally, the entire droplet rebounds from the liquid surface (23.2 ms). During the rebound process, the surface energy of the droplet is continuously transformed into potential energy. When the droplet rebounds to the maximum height, it falls back to the liquid film for a second rebound (45.5 ms–65.1 ms). After several rebounds, the kinetic energy of the droplet is gradually consumed. In addition, the pressure generated by the vapor layer is not enough to overcome the gravity of the droplet, causing the droplet to contact the liquid film and spread rapidly (184.0 ms). The droplet exchanges a lot of heat with the liquid film and the wall surface, and it can be observed that the droplet boils, accompanied by sputtering of small droplets (215.1 ms). This is due to the enormous number of small bubbles generated by the vaporized core on the wall. The bursting of the bubble produces a rapid shock wave, causing the liquid near the bubble to be sputtered, as shown at 228.9 ms.

Fig. 3. The phenomenon of (a) rebounding-sputtering and (b) rebounding-floating.

Fig. 3(b) demonstrates the impinging phenomenon when the temperature of the liquid film further rises (We = 10, T = 165°C). The morphological change of the droplet in Fig. 3(b) in the 65.1 ms is consistent with that of Fig. 3(a). The distinction is that after rebounding several times, the droplet finally floats on the liquid surface until it is consumed by evaporation without sputtering. This is because the temperature difference between the droplet and the liquid film in Fig. 3(b) is large, the heat exchange rate is high, and the pressure generated by the vapor layer suffices to support the droplet to float on the free surface. Therefore, the entire process is called rebounding-floating. The rebound phenomenon was also observed in the experiment of Chen et al. (2020) when the We was 4.6 at an ambient temperature condition. It is worth mentioning that the rebound is remarkably like the Leiden frost phenomenon.

As the We increases, a crown structure will be formed at the point of impingement after the droplet collides with the liquid film. Fig. 4(a) indicates the liquid film evolution observed under the condition of We = 172 and T = 100°C. When a moving droplet hits a stationary liquid film, the fluid inside the droplet undergoes a drastic redirection from vertical to radial. The rapid change toward movement causes a kinematic discontinuity phenomenon, which contributes to the crown’s formation and propagation. (0.6 ms–1.2 ms) (Yarin and Weiss, 1995). There is no splash at the edge of the crown in this study. As the crown develops, the crown grows to a 2.4-ms height, degenerates and spread (2.4 ms–7.0 ms), and finally merges with the liquid film peacefully (157.1 ms). Therefore, the entire process is called stable crown-spreading.

Fig. 4. The phenomenon of (a) stable crown-spreading and (b) stable crown-sputtering.

Fig. 4(b) provides a case with We = 172 and T = 140°C. The morphological development of the crown in Fig. 4(b) is consistent with that in Fig. 4(a) before 7 ms, but the development time of the crown is longer. It can be seen from 4.6 ms that the crown of Fig. 4(b) is still in the process of degradation, while Fig. 4(a) has almost finished the descent. In addition, after the droplet reaches the maximum spreading scale, many small droplets are sputtered upward from the central region of the liquid film (13.1 ms–55.9 ms). This is due to the large temperature difference and large heat exchange between the droplet and the liquid film. On the other hand, the liquid in the middle area is pushed away during the spreading process, making the liquid film thinner, causing nucleate boiling of the droplet liquid in contact with the wall. Therefore, the entire process is called stable crown-sputtering.

Fig. 5 indicates the evolution of the liquid film with splashing, which results from the high We impingement (We = 275, T = 155°C). When a high-speed droplet collides with the liquid film, secondary droplets will be generated from the crown’s edge during the ascent of the crown (0.6 ms–4.6 ms). And because of the violent fluctuations of the liquid film, its structure is destroyed and disappeared during the descent of the crown (7.0 ms–13.1 ms). When the droplet impinging velocity increases, the kinetic energy increases, so more energy is converted to the crown (Pei et al., 2017). As a result, the self-shearing force of the crown is not enough to maintain the stability of the crown structure, and secondary droplets are separated from the edge of the crown. In addition, during the fusion process of the crown and the liquid film, sputtering will also occur, but the diameter of sputtered droplets is significantly reduced. A detailed discussion will be conducted below. The entire process is called splash crown-sputtering.

Fig. 5. The phenomenon of splash crown-sputtering.

To better understand the evolution of these six phenomena, we have drawn a regional distribution map, as shown in Fig. 6. Spreading, rebounding-sputtering, and rebounding-floating only occur when We is 10. Spreading occurs at low temperatures, and rebounding-sputtering occurs at high temperatures. When the temperature further rises, rebounding-suspension occurs, which is due to the change in pressure generated by the vapor layer. When the We increases, the crown is formed. After the development of the crown structure, spreading occurs at lower temperatures, and sputtering occurs at higher temperatures. The critical temperature for sputtering is about 125°C, independent of the We. This is because no matter how high/low the We is, the initial energy of the droplet will be dissipated after the droplet spreads. Only temperature affects the droplet behavior. The higher the temperature, the greater the heat exchange. When the droplet touches the high-temperature wall, nuclear boiling occurs and producing bubbles. The collapse of bubbles sputters a large number of droplets. The decrease of the liquid surface tension/viscosity with the temperature makes sputtering more likely to occur. The splash crown occurs at high temperatures and high We. A high temperature leads to a decrease in the viscosity and surface tension of the liquid film, and a high We increases the instability of the crown, resulting in secondary droplets splashing at the edge of the crown. In addition, the critical We for crown splashing decreases with increasing temperature. The increase in film temperature causes a decrease in viscosity and shear force, so the relatively low We of the droplet can cause splashing. Next, we mainly discuss the characteristics of the crown and the sputtered droplets.

Fig. 6. Distribution of impinging phenomena.

 
3.2 Characteristic Indexes of Droplet Impact on Heated Liquid Film

3.2.1 Crown Characteristics

The change of the crown characteristic with the We and time is shown in Fig. 7, and the liquid film temperature is fixed at 120°C. The curve indicates the development process of the crown, and the right end of the curve indicates the disappearance of the crown. The geometric parameters of the crown include the crown diameter D and the crown height H. In this paper, D is the diameter of the top edge of the crown, and H is the distance from the bottom of the crown to the top of the crown. We define the dimensionless crown diameter D^* = D/D₀ and the dimensionless crown height H^* = H/D₀.

 Fig. 7. The effect of We on the crown characteristic parameters.

From Fig. 7(a), as time goes by, during the process of the crown ascending and descending, the crown diameter continues to grow. And the change rate (slope of the curve) increases with the increase of the We, which is caused by the inertial force of the horizontal velocity of the crown. In addition, the crown diameter increases as the We increases, but when the We is higher than 172, the crown diameter changes little with the We. The reasons may be as follows. Under low We, the impinging energy is low, and only a small amount of liquid film at the contact point can be pushed away, resulting in a smaller crown diameter. The larger the We, the more liquid film is pushed away and the larger the crown diameter. Moreover, the liquid film at the contact point is completely pushed away when the We increases to 172, and the steel plate under the liquid film is exposed. When the We continuously increases, the less liquid film is used to form the crown and smaller the crown diameter. However, Liang et al. (2014) indicated that the crown diameter might be independent of We, when We was relatively large (We = 260, 510, and 843). In addition, the maximum crown diameter increases with the increase of We. This is because the larger We, the greater the energy absorbed by the crown so that the crown can continue to expand outward, and the maximum crown diameter increases. Fig. 7(b) shows that the height of the crown first increases and then decreases with time and increases with the increase of We. The larger the We, the more energy the liquid film absorbs during impingement, as well as the higher the crown. Additionally, the crown's existence time increases with the increase of We, which can be explained because the ascent and descent process of a high crown takes a long time.

Fig. 8. Relationship between dimensionless maximum crown height and Weber number.

Fig. 8 indicates the relationship between the maximum dimensionless crown height and the Weber number, and the H^*_max = 0.0026 We is obtained by fitting, indicating that the maximum dimensionless crown height has a linear relationship with the impact Weber number, which is basically consistent with the conclusion obtained by Asadi and Passandideh-Fard (2009) using numerical simulation methods, and the formula fitted by this scholar is H^*_max = 0.0025 We.

The characteristic parameters of the crown vary with temperature and time as shown in Fig. 9, and the We is fixed at 172. It can be seen from Fig. 9(a) that the change of the crown diameter with time has no relation to temperature, but the maximum crown diameter increases with the increase of temperature. This is because the increase in temperature reduces the viscosity and surface tension of the liquid film, which makes the crown easier to expand outward. The change of the crown height with time and temperature is shown in Fig. 9(b). When the temperature increases, the crown height and maintenance time increase. The high viscosity and surface tension at low temperatures will inhibit the growth of the crown height, and the crown will disappear faster. When the temperature rises, the viscosity and surface tension of the liquid film decrease. The energy used to overcome the viscosity and surface tension is reduced, and more energy is used for the formation of the crown.

Fig. 9. The effect of film temperature on the crown characteristic parameters.

3.2.2 Sputtering Characteristics

It has been described in Section 3.1 that sputtering is a phenomenon that occurs at high temperatures and high We. During the experiment, we found that the diameter of sputtering droplets varied with temperature and We. Figs. 10(a) and 10(b) demonstrate the relationship between the dimensional distribution of droplets and We ((a) We = 172, T = 150°C; (b) We = 220, T = 150°C). The image processing selects the phenomenon diagram when the sputtering droplets just fill the window. It can be seen from Fig. 10(a) that at low We, the proportion of large sputtering droplets is high, and 67% of the droplets have a diameter of over 0.1 mm. However, at high We (Fig. 10(b)), it can be obviously observed that the proportion of large-diameter droplets decreases, the proportion of small-diameter droplets increases, and 70% of the droplets have a diameter less than 0.1 mm. This is because the droplet spreads more widely at a high, We, resulting in a thinner liquid film around the contact point. In this way, fewer droplets are brought up during sputtering, and the thin liquid film reduces the heat transfer resistance and increases the heat transfer rate in the central area of the liquid film (Liang et al., 2016). On the other hand, with the increase of the spreading area, the droplet liquid will contact more vaporization cores on the stainless-steel plate, and there are more sputtering positions. These two aspects reduce the diameter of sputtering droplets when bubbles break through the liquid film.

Fig. 10. The effect of We and film temperature on the size distribution of sputtering droplets.

The effect of liquid film temperature on the diameter distribution of sputtering droplets is shown in Fig. 10(c) (T = 140°C, We = 220) and Fig. 10(d) (T = 160°C, We = 220). When the liquid film temperature is 140°C, the 33%, 11%, and 56% of the sputtering droplets have the diameters > 0.1, 0.05–0.1, and < 0.05 mm, respectively. When the temperature rises to 160°C, the droplet sizes decrease significantly, in which the counting contribution of three aforementioned ranges of sizes are 25%, 22%, and 53%, respectively. The proportion of sputtering droplets < 0.5 mm reaches 22%, while the proportion of droplets with a diameter larger than 0.1 mm accounts for 25%, and most droplets are still concentrated in 0.05–0.1 mm. One explanation is that the increase of temperature leads to the decrease of the viscosity and surface tension of the liquid film, which not only makes the droplet spreading area larger and the liquid film thinner, but also makes the droplet easier to separate from the liquid film during sputtering. On the other hand, the higher the temperature, the stronger the heat transfer and droplet boiling, and the smaller the sputtering droplets.

Another characteristic parameter of sputtering is the sputtering time, which is defined as the time from the first sputtering to the last one. The effects of We and temperature on sputtering time are shown in Fig. 11. When We is 275 and the temperature is 130°C, only one sputtering occurs, so the sputtering time is 0. The sputtering time decreases with the increase of We. As described above, a large We leads to a large spreading area, the area where sputtering occurs increases, and multiple positions are sputtered, resulting in a shorter sputtering time. On the other hand, the spreading area makes the liquid film thinner, and the large heat exchange accelerates the sputtering process. The sputtering time only slightly decreases with the increasing temperature, except 130°C. The increase of temperature will not only increase the final spreading area of droplets but also enhance the heat transfer and shorten the sputtering time. The sputtering time at 130°C is obviously lower than 140°C because the temperature is too low, the sputtering is not strong, and the sputtering times are less, so the sputtering time is short.

Fig. 11. The effect of We and temperature on sputtering time.

 
4 CONCLUSIONS

The collision dynamics of a single ethanol droplet with a heated liquid film were experimentally studied by changing the droplet We and liquid film temperature. Some interesting phenomena were recorded, which differ from previous studies because of the temperature difference between the droplet and liquid film. With the increase of We and temperature, six typical phenomena were observed: deposition-spreading, rebounding-sputtering, rebounding-floating, stable crown-spreading, stable crown-sputtering, and splash crown-sputtering. The critical temperature for sputtering is about 125°C, independent of the We.

During the development of the crown, the crown diameter continued to increase, and the crown height first increased and then decreased. The existence time of the crown increased with the increase of We and temperature. The crown diameter increases along with the increasing We, which less than 172. The relationship between the maximum dimensionless height of the crown and the We is H^*_max = 0.0026 We. The changing rate of the crown diameter with time is independent of temperature. The maximum crown diameter and crown height increase with the increase of We and temperature. In addition, at low We, the proportion of large sputtering droplets is higher. At high We, it can be clearly observed that the proportion of large-diameter droplets decreases, and the proportion of small-diameter droplets increases. The sputtering time decreases as the We increases. Except for 130°C, the sputtering time decreases with increasing temperature.

The rebound phenomenon in this paper can well reduce the production of the wall-attached fuel film, and the sputtering phenomenon can damage the wall-attached fuel film, which weakens the formation of soot and unburned hydrocarbons. Therefore, by changing the droplet impact Weber number and liquid film temperature, the occurrence of rebound and sputtering can be controlled, reducing the emission of aerosol particles. The study of droplet impingement on hot liquid film and the accurate physical description and scientific explanation of impinging behavior not only plays a positive role in optimizing cylinder combustion, cooling, and safety technology but also provides a better theoretical basis for mass and heat exchange enhancement in relevant applications in the industrial field.

 
ACKNOWLEDGMENT

This material is based upon work supported by the National Natural Science Foundation of China under Grant No. 52176098. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not reflect the views of the National Science Foundation.