Evaporation, Autoignition and Micro-Explosion Characteristics of RP-3 Kerosene Droplets under Sub-Atmospheric Pressure and Elevated Temperature

Abstract

The evaporation, autoignition and micro-explosion characteristics of RP-3 kerosene droplets under sub-atmospheric pressure (0.2–1.0 bar) and elevated temperature (473–1023 K) were experimentally investigated using high-speed camera technology. The results showed that the droplet evaporation rate increased monotonically with increasing temperature and pressure under 573–873 K and 0.2–1.0 bar. The decrease of temperature and pressure was obviously detrimental to the successful autoignition of droplets and increased the ignition delay time. Autoignitions at 0.2 bar were very difficult and required an ambient temperature of at least 973 K, which was about 150 K higher than the minimum ignition temperature at 1.0 bar. Sub-atmospheric pressure environment significantly inhibits the formation of soot particle clusters during the autoignition of droplet. Reducing pressure was also discovered to reduce the likelihood of micro-explosions at 673, 773 and 823 K but increase the bubble growth rate and droplet breakage intensity. Strong micro-explosions with droplet breakage time close to 1 ms were observed at 0.6 bar and 773/823 K, showing the characteristic of bubble inertia control growth.

1. Introduction

Ramjet is a new type of advanced aeronautical science and technology used for high-speed flight. With the development of technology, the research of ramjet engine tends to work at high altitude, high-speed and wide range. At higher altitudes as the air there is thin, the ramjet ingests low mass flow rate of air with reduced values of pressure in the combustion chamber [1]. When the inlet pressure of the combustion chamber is reduced to less than one atmosphere, combustion stability and work efficiency will deteriorate [2]. However, most of the current studies on the evaporation and combustion characteristics of liquid fuel under elevated temperature are conducted at elevated pressure [3,4,5,6] or atmospheric pressure [7,8,9] environments. The research work in sub-atmospheric pressure and elevated temperature environment is still rare. Investigating the evaporation and combustion characteristics of liquid fuel under sub-atmospheric pressure and elevated temperature is essential to improve the working stability of ramjet at high altitude.

The evaporation behavior of liquid fuel droplets at elevated temperature is one of the basic mechanisms of engine spray combustion. The study of single droplet evaporation is very necessary for characterization and understanding of spray combustion. In the past studies, the ambient temperature and pressure range were mostly between 400–1200 K and 1–30 bar [3,4,6,8,9,10]. The current maximum ambient pressure reached 50 bar [11]. The reference oils used in the experiments are mostly kerosene [3], biomass oil [7], diesel [12] and alkanes (n-heptane [6], n-decane [13], n-dodecane [14] and n-hexadecane [6], etc.). Additives include ethanol [15], water [16], energetic substances (benzyl azide) [17] and nanoparticles (aluminum nanoparticles [8,9,10], graphite oxide nanoparticles [18]). Hashimoto et al. [7] investigated the evaporation characteristics of palm methyl ester droplets at high ambient temperatures, and the droplet lifetime was found to decrease with increasing ambient temperature caused by fact of Spalding transfer number increases with increasing ambient temperature. Ghassemi et al. [3] investigated the evaporation characteristics of kerosene droplets at elevated pressure and temperature, and evaporation rate was found to increase first and then decrease with increasing pressure. The maximum value appears at 2 MPa. Therefore, changes in temperature and pressure have a significant effect on droplet evaporation characteristics. Droplet heating and evaporation models have also been studied extensively and can be subdivided into the following groups [19]: (1) models based on the assumption that the droplet surface temperature is uniform and does not change with time [20]; (2) infinite thermal conductivity models [21]; (3) models taking into account finite liquid thermal conductivity (conduction limit models) [22,23]; (4) models taking into account both finite liquid thermal conductivity and the re-circulation (effective conductivity models) [24]; (5) models describing the re-circulation inside droplets in terms of vortex dynamics (vortex models) [25]; (6) models based on the full solution of the Navier–Stokes equation [26].

A very important performance indicator of liquid fuel is autoignition delay time. Under high temperature environment, the droplet will quickly evaporate to produce combustible steam. When the temperature is high enough, combustible steam mixes with air and spontaneous ignition occurs. Law [27,28] first proposed to use Damköhler number as a criterion to determine whether the droplet ignited, and compared it with experimental data. The ignition criterion of Law states that a droplet of given properties vaporizing in a prescribed atmosphere can achieve ignition if the Damköhler number of the system exceeds a critical point. Influence of pressure and temperature on autoignition time under elevated pressure and temperature, has been experimentally studied by Khan et al. [4]. Their results show that the autoignition delay time of kerosene fuel droplet decreases with an increase in ambient temperature and pressure.

Puffing and micro-explosion were first discovered by Ivanov et al. [29] in 1962 when they studied the combustion characteristics of emulsified droplets. Micro-explosion is not only of scientific significance, but also beneficial to the atomization of liquid droplets in engineering applications. It is an important secondary breakup process of liquid droplets. These values have attracted the attention of scientists and been widely studied [30,31,32]. At present, it is generally believed that the micro-explosion is caused by the large difference in boiling points of the components in the droplet. The components with lower boiling points locally overheat inside the droplet [33,34,35,36]. Then the bubbles nucleate and grow, finally breaking through the action of droplet surface tension and causing puffing or breaking. Shang et al. [37] investigated the combustion and micro-explosion characteristics of n-alkane droplets, and they found that micro-explosion is strongly occurring when the components are sufficiently different in thermal properties and the concentrations of all components are equivalent. The effect of pressure on micro-explosion remains highly controversial. Ghassemi et al. [6] observed that the bubble formation and probably explosion of droplet is suppressed when environment pressure increases. However, Wang and Law [38] discovered that the increasing pressure enhances the possibility of micro-explosion of droplet.

The combustion characteristics of RP-3 kerosene at sub-atmospheric pressure and room temperature have been studied in our previous study [39]. In order to better understand the characteristics of droplets in elevated temperature combustion chamber of engine, the evaporation, ignition and micro-explosion characteristics of RP-3 kerosene at sub-atmospheric pressure (0.2–1.0 bar) and elevated temperature (473–1023 K) were experimentally studied by using a self-designed device.

2. Materials and Methods

A schematic of the experimental apparatus is shown in Figure 1. Experiments were carried out in a 0.064 m³ (length of 0.4 m) pressure-controlled stainless-steel chamber with four quartz windows for optical measurements. The pressure chamber was divided into elevated temperature zone and normal temperature zone. It was filled with air as an oxidizing agent.

The elevated temperature zone was generated by a furnace with an internal volume of 0.8 L (0.1 × 0.1 × 0.08 m). Compared to previous studies [5,35], the cavity volume is large enough to allow droplet combustion behavior to be unaffected. The top of the furnace was designed with a cylindrical channel with a diameter of 18 mm for liquid droplets to pass through. The size of 3 × 6 cm quartz glass window was designed around the electric furnace for optical measurement. A K-type thermocouple and four silicon carbon heating rods were placed in the furnace chamber for temperature control. In order to control the temperature around the droplet more accurately, the thermocouple temperature measuring point was located 1 cm below the center position of the inner cavity. Beside the thermocouple at the bottom of the furnace, a gas passage was connected to an air pump for air purge after the droplet combustion is complete.

In the normal temperature zone, some motion mechanisms and wires were placed. A micro-pipette was used to produce a 1.35 ± 0.1 mm fuel droplet and place it on the end of a 0.2 mm diameter zirconia ceramic rod. Compared with commonly used thermocouple [35,39] and SiC ceramic rod [5,9] [5.2 W/(mK)], the zirconia ceramic rod has much lower thermal conductivity [1–2 W/(mK)], which can reduce heat transfer to the droplet. A stepper motor was used to drive the slider to transport the droplet. The slider movement speed was about 40 cm/s, so that the droplet movement time to the center of the furnace cavity was controlled within 0.325 s. To prevent natural convection of high temperature air from affecting the droplet, an aluminum water-cooled sheet was placed below the droplet. The droplet transport channel is blocked before the experiment starts, and when the droplet needs to be transported, a stepper motor (NEMA17) rapidly drives the water cooler to rotate 90 degrees to open the droplet transport channel. In order to reduce the time of the whole process, the operation of stepper motors is automated by programming the controller.

A black/white high-speed camera (IDT Y4-S1) was used to capture changes in droplet diameter. The shooting speed of 100–10,000 frames/s was adopted according to the speed of evaporation and combustion process. The exposure time was set to 200 μs. The lens used was Sigma 200 mm Macro Lens.

Droplet image captured by the high-speed camera was first binarized by MATLAB. Then, a self-designed MATLAB code was used to remove the rod image and evaluate the droplet projection area $S_p\left(t\right)$ in the shooting direction at each moment, so as to obtain the droplet diameter results calculated by $D\left(t\right)=\sqrt{4S_p\left(t\right)/\pi }$. Chinese RP-3 kerosene was chosen as the fuel for the experiment. It typically consists of 52.2% of alkanes, 39.9% of naphthenes, and 7.9% of aromatic hydrocarbons, by mass [39]. The fractions with more than 2% content measured by chromatography-mass spectrometry are shown in

Table 1. RP-3 Aviation kerosene chromatography-mass spectrometry component ratio (>2%) [40].

Chemical Name	Chemical Formula	Boiling Point/K (1 bar)	Mass Fraction/%
Nonadecane	C19H40	602.9	12.61
Hexane,2,5-dimethyl-	C8H18	382.1 ± 0.9	5.44
Cyclohexane,1,3-dimethyl-,cis-	C8H16	393 ± 1	5.27
Heptane,3-methyl-	C8H18	392 ± 1	4.21
Pentadecane	C15H32	540 ± 20	4.17
Hexadecanoic acid, methyl ester	C17H34O2	690	3.23
Undecane,5-methyl-	C12H26	480.9	3.12
Cyclohexane,1,3,5-trimethyl-	C9H18	411 ± 3	2.42
Octane,3-methyl-	C9H20	417 ± 1	2.36
Tetradecane	C15H32	523 ± 10	2.33
1-Hexene,2,5,5-trimethyl-	C9H18	405 ± 7	2.32

.

3. Results and Discussion

3.1. D²-Law

3.1.1. General Behavior

In Figure 2, the diameter change in droplet evaporation at 0.4 bar and 773 K is divided into two stages. They are nonlinear stage and d²-law evaporation stage, respectively. The droplet diameter is controlled by both thermal expansion and evaporation in the nonlinear stage. As the temperature inside the droplet reaches a relatively stable state, the droplet diameter change will be mainly controlled by evaporation. The square of the droplet diameter decreases linearly under the action of evaporation in this stage called d²-law evaporation stage. The evaporation rates ($C_v$) can be calculated by linear fitting of the square diameter curve in the d²-law evaporation stage.

3.1.2. Temperature Influence

Figure 3 shows the change of normalized D² in the evaporation process at 1.0/0.4 bar and 473–973 K. It can be discovered that the d²-law is not always valid for the evaporation process. Different from other higher temperatures, the normalized D² significantly deviated from the d²-law at 473 K. This phenomenon is mainly due to the multicomponent characteristics of RP-3 kerosene. Among the main components of RP-3 kerosene shown in Table 1, the boiling points of nonadecane (602.9 K), pentadecane (540 ± 20 K), Undecane, 5-methyl- (480.9 K), hexadecanoic acid, methyl ester (690 K) and tetradecane (523 ± 10 K) are all higher than 473 K, while the boiling points of the remaining components are lower than 473 K. Therefore, the evaporation rates of different components at 473 K differ greatly. The volatile components within droplets vaporize more quickly, which causes rapid depletion of volatile components on the droplet surface and increase the concentration of non-volatile components. As a result, the droplet evaporation rate gradually decreases, no longer following d²-law. It can be found that the normalized D² deviates from the d²-law obviously at 473 K. Under this condition, the evaporation rate showed the law of gradually decreasing. However, the changes in the normalized D² of other droplets at 573–873 K still basically conform to the d²-law. Ghassemi et al. [3] pointed out and discussed that evaporation of multi-component fuel droplets such as kerosene at high ambient temperatures follows the d²-law. The thermal diffusion rate is much higher than the mass diffusion rate at 573–873 K. The evaporation process is controlled by mass diffusion of the components. This means that during droplet evaporation, the concentration of non-volatile components on the droplet surface will rise rapidly and reach a relatively stable level. It results in a relative stability of the droplet surface boiling point and evaporation rate. Diagrams of droplet evaporation process at different temperatures are shown in Figure 4.

The multicomponent properties of kerosene also induce micro-explosion of droplets during evaporation at higher temperatures. The bubbles grow in the droplet until they break through the surface tension and explode. Due to the presence of bubbles in the droplet, the change of normalized D² deviates from the d²-law, as shown in Figure 3a. During the micro-explosion, the normalized D² increases first and then decreases rapidly, and the whole process lasts for a short time. Micro-explosions occurring during evaporation are usually of low intensity and thus do not affect the calculation of evaporation rates. The micro-explosion phenomenon will be further discussed later.

3.1.3. Pressure Influence

Figure 5a shows the effect of different pressures on the normalized D² at 473 K. Reducing the pressure decreases evaporation rate at all ambient temperatures. This is due to the deterioration of the heat transfer performance between the droplet surface and the environment at low pressure. The normalized D² under all pressures at 473 K do not conform to the d²-law. In order to better demonstrate the influence of pressure on the normalized D² curve, the data in Figure 5a were derived after 6th degree polynomial fitting. Except for the initial thermal expansion phase, its physical meaning is the instantaneous evaporation rate, as shown in Figure 5b. For 473 K, reducing the pressure was found to reduce the amount of change in the evaporation rate. This is most probably due to the fact that the decrease in pressure reduces the difference between the boiling points of the different components, thereby inhibiting the rise in the droplet surface temperature, which inhibits the change in the evaporation rate.

3.2. The Evaporation Rate

3.2.1. Temperature Influence

Evaporation rates at all pressures are shown in Figure 6, it can be seen that the evaporation rates all increases rapidly with the increase of ambient temperature. This trend can be understood by the equations of the d²-law [41].

$$\frac{d{D}^2}{dt}=-\frac{8{\lambda }_g}{{\rho }_l{c}_{p,g}}\ln \left(B+1\right)=-C_v$$

(1)

here, ${\lambda }_g$ and $c_{p,g}$ denote the thermal conductivity [W/(m K)] and the specific heat of gas [J/(kg K)] of gas. ${\rho }_l$ denotes the density of liquid (kg/m³). B is Spalding transfer number [42]. B can be expressed in two ways as follows.

$$B_M=\frac{Y_{fuel,s}}{1-Y_{fuel,s}}$$

(2)

$$B_T=\frac{c_{p,g}(T_{ambient}-T_s)}{h}$$

(3)

here, $Y_{fuel,s}$ and $T_s$ denote fuel vapor mass fraction and temperature (K) on the surface of droplet. $T_{ambient}$ is the environment temperature (K). And $h$ denotes the heat of evaporation (J/kg). $B_M$ and $B_T$ are called as the Spalding mass and heat transfer numbers [43]. $B_M$ and $B_T$ are equal under steady state conditions. As the ambient temperature $T_{ambient}$ rises, $B_T$ obviously increases. Therefore, evaporation rates, $C_v$ in Equation (1) and Figure 6, both increase with temperature.

3.2.2. Pressure Influence

Different from the results under elevated pressure [3], the evaporation rate at sub-atmospheric pressure decreases monotonically with the decrease of pressure as shown in Figure 6. The results show that sub-atmospheric pressure inhibits evaporation, which is not conducive to generating enough steam around the droplet to ignite. When the pressure is reduced, the boiling point of each component in the droplet will drop, making the droplet surface temperature $T_s$ drop. According to Equation (3), when the ambient temperature $T_{ambient}$ is constant, the decrease in $T_s$ causes the increase in $(T_{ambient}-T_s)$. $B_T$ increases so that $C_v$ in Equation (1) increases, thereby promoting evaporation. However, the decrease of pressure also leads to the deterioration of heat transfer. The decrease of thermal conductivity ${\lambda }_g$ strongly inhibits evaporation. The combined action of the two makes the evaporation rate decrease monotonically with the decrease of pressure in the experimental temperature range.

3.3. Spontaneous Ignition

3.3.1. Pressure Influence on Spontaneous Ignition Behavior

Figure 7 shows spontaneous ignition process at 973 K and 1.0/0.6/0.2 bar as captured by the high-speed camera. After the droplet enters the high temperature environment, the flammable vapor accumulates around the droplets and diffuses continuously. The combustible steam will flow downward because of the much higher density than air. Therefore, at 1.0 and 0.6 bar, the flammable boundary presents a downward stretching shape, as shown in Figure 7a,b. At 0.2 bar, the flammable vapor boundary showed a circular shape. This is the shape produced by the free diffusion of combustible steam through the air. In addition, the lower the pressure (1.0 > 0.6 > 0.2 bar), the longer the droplet evaporates before ignition (403 < 626 < 919 ms), and the more combustible steam is produced. The combustible steam also has a longer diffusion time. Therefore, the area of combustible steam at 1.0 bar pressure was significantly less than 0.2 bar.

After the spontaneous combustion of combustible steam, the high-speed flame propagation process was observed. The flame first propagated along the boundary where the combustible gas and air are more fully mixed, and then propagated inside the steam. The time of the whole flame propagation process was within 10 ms. In addition, the flame shrinkage was observed. This is because a large area of combustible steam produced by the droplet is ignited and rapidly consumed. The flammable steam that evaporates after this point does not have enough time to diffuse before it is consumed by flame. Under the pressure of 0.2 bar, the natural convection is weak and the diffusion area of combustible steam is large, so the flame shrinkage phenomenon is more obvious, as shown in Figure 7c.

Then, the flame slowly rose due to high temperature, under the action of gravity. The time of this process was about 200 ms. The formation of particles of soot was discovered during the flame lifting process. As can be seen in Figure 7, it exists as a bright spot in a hot flame, leaving the flame and turning to black soot as it cools. It was also observed that the decrease of pressure inhibited the formation of soot during spontaneous ignition. The black smoke formed by the aggregation of soot particles was observed at 1.0 and 0.6 bar pressures. But at 0.2 bar, only sporadic black soot particles were observed. A previous study has also observed a decrease in the concentration of soot generated under sub-atmospheric pressure [39]. This phenomenon is due to that the distance between molecules increases with the decrease of pressure, and the probability of collision between small molecules decreases, making it difficult to form large molecules and large particles.

3.3.2. Temperature and Pressure Influence on Spontaneous Ignition Delay

Ignition time data were obtained by calculating the time between the droplet’s arrival at the center of the furnace and ignition [44]. It takes a certain amount of time (0.325 s) for the droplet to reach its position. During this time, it is impossible to avoid being heated by the high temperature environment. As a result, the measured ignition time will be slightly shorter than the actual time. Since each droplet has exactly the same transport time, the trend of the measured ignition time data should be consistent with the actual ignition time. The criterion for droplet ignition is the observation of bright flame propagation in a high-speed camera, as shown in Figure 7.

The influence of temperature and pressure on the ignition time of kerosene droplets are shown in Figure 8. The higher temperature or pressure apparently favored the droplet to ignite earlier. When a fuel droplet enters a high temperature environment, it goes through the initial heating phase and begins to evaporate flammable steam to mix with air. Ignition occurs when the fuel vapor and air reach a combustible ratio and the activation energy is overcome. The time between the exposure of a droplet to high temperatures and the generation of the minimum amount of fuel vapor sufficient for ignition is known as physical delay. The time between generating enough fuel vapor for ignition and overcoming the activation energy for ignition is called chemical delay [45]. The influence of temperature and pressure on ignition time can be caused by two factors. On the one hand, reducing pressure or temperature reduces the evaporation rate, as shown in Figure 6, which increases the physical delay. On the other hand, the decrease of temperature or pressure inhibits the collision between fuel and air molecules and increases the chemical delay. These two aspects above make the effect of pressure and temperature on ignition time seem monotonous.

3.4. Micro-Explosion Characteristics

3.4.1. Temperature Influence on Micro-Explosion

According to the normalized D² change in Figure 3a and Figure 9, reduced temperature was found to inhibit the potential for micro-explosion. The occurrence of micro-explosion of kerosene droplets is closely related to the evaporation characteristics. The necessary condition for micro-explosion is superheat within the droplets, depending on the pattern of the evaporation process [33,34,35]. When the ambient temperature is low (473 K) as shown in Figure 4b, the internal components of the droplet are evenly distributed in the evaporation process, and the temperature difference between the surface and the internal is very small, so it is impossible for micro-explosion to occur in this situation. When the ambient temperature is high (573 K or higher) as shown in Figure 4a, the concentration of non-volatile components on the droplet surface is high, and the surface temperature also increases and conducts to the droplet interior. The temperature inside the droplet is thus increased while the composition remains unchanged. The formation of superheat inside the droplet lays the foundation of micro-explosion. Therefore, when the temperature rises to 673 K above the boiling point temperature of almost all components, the micro-explosion phenomenon begins to appear, as shown in Figure 9. At ambient temperatures of 673, 773 and 823 K, the normalized D² curve was captured to fluctuate significantly in the red dotted box. The micro-explosions captured by the high-speed camera are shown in Figure 10, which reflects the significant effect of temperature change on droplet morphology. At 0.8 bar pressure, the growth rate of bubbles increased significantly when the temperature increased from 673 to 823 K. The maximum diameter of bubbles also increased significantly. However, because the bubble growth rate is not large enough, the final droplet remains intact after puffing under the dominant effect of surface tension. When the pressure is reduced to 0.6 bar, the droplet can still maintain its intact form after bubble puffing at 673 K. However, it can be observed that its maximum bubble diameter has significantly exceeded that at 0.8 bar and 823 K. When the temperature continues to rise to 773 and 823 K, the droplets show violent fragmentation under the inertia of rapid bubble growth. The inertial effect of bubble growth dominates the droplet breaking process at this point.

3.4.2. Pressure Influence on Micro-Explosion

Reducing pressure was discovered to reduce the likelihood of micro-explosions at 673, 773 and 823 K, as shown in Figure 11. The same trend was also reported in previous study of multi-component droplet micro-explosions at 1.0–5.0 bar [38]. It can be concluded from change of the normalized D² in Figure 11 that the micro-explosions occur in d²-law evaporation stage. At this stage, enough superheat will gradually form inside the droplet for formation and growth of gas bubbles. However, due to the decrease of pressure, the boiling point difference between different components of kerosene decreases, which makes it difficult to establish sufficient superheat inside the droplet. This is also consistent with the evaporation phenomenon described in Figure 5b above. They are likely both caused by the change of boiling point of different components of RP-3 at different pressure.

The bubble growth rate is significantly higher at 0.6 bar compared to 0.8 bar, as shown in Figure 10. And at temperatures above 773 K, as the pressure drops from 0.8 to 0.6 bar, the droplet micro-explosion mode also changes from a puffing mode to a violently broken mode. Bubble growth is generally divided into three stages: (1) Inertia controlled stage; (2) Transition stage; (3) Diffusion controlled stage. Inertia controlled stage and diffusion control stage are the main process of bubble growth, and transition stage is the process of conversion between the two modes. During the inertia controlled stage, the bubble growth characteristics can be described by the following equation [46]:

$$R_b={\left[\frac{2}{3}\frac{{\rho }_g}{{\rho }_l}A\left(T_0-T_b\right)\right]}^{\frac{1}{2}}t$$

(4)

$$P_g-P_{\infty }={\rho }_{g}A\left(T_0-T_b\right)$$

(5)

here, $R_b$ denotes the radius of bubble (m).${\rho }_l$ and ${\rho }_g$ denote the density of liquid and vapor respectively (kg/m³). A is a linearization constant. $T_0$ is the initial temperature at the bubble boundary and $T_b$ is the saturation temperature of the liquid (K). $P_g$ and $P_{\infty }$ denote the vapor pressure inside bubble and the ambient pressure.

During the diffusion controlled stage, the analytical solution of bubble growth in an infinite mono-component liquid can be expressed as [47]:

$$R_b=2b\sqrt{a_{l}t}$$

(6)

$$b=\sqrt{\frac{3}{\pi }}\left\{\frac{\Delta T_s}{\left(\frac{{\rho }_g}{{\rho }_l}\right)\left[\frac{h_{lv}}{c_{p,l}}+\left(\frac{c_{p,l}-c_{p,g}}{c_{p,l}}\right)\Delta T_s\right]}\right\}$$

(7)

here, $c_{p,l}$ and $c_{p,g}$ are, respectively, the specific heat capacities of liquid and vapor at constant pressure [J/(kgK)]. $a_l$ and $h_{lv}$ are the thermal diffusivity of liquid (m²/s) and the latent heat of vaporization (J/kg), respectively. $b$ is a dimensionless bubble growth constant whose value depends on the superheat $\Delta T_s$ (K) and the thermophysical properties. For bicomponent or multicomponent liquids, (4) and (5) remain unchanged, but $\Delta T_s$ has to be multiplied by an effective coefficient of overheating in (7). The effective overheating coefficient is $\frac{c_{1,m}}{c_{1,p}}<1$, which is calculated by multi-component phase equilibrium characteristics [48]. The magnitude of the effective overheating coefficient remains constant as the concentration of components in the liquid are stable. Therefore, in the study of the effects of pressure and temperature, changes in the effective coefficient of overheating can be ignored.

Due to the multi-component properties of kerosene droplets, the increase in temperature and pressure causes an increase in $\Delta T_s$. This increases the rate of bubble growth, resulting in greater droplet deformation. Therefore, temperature was discovered to promote micro-explosions at all pressures in the experiment. However, the effect of pressure on micro-explosions is much more complicated. Reducing pressure not only reduces $\left(T_0-T_b\right)$ and $\Delta T_s$, but also affects the value of ${\rho }_g$ and $P_{\infty }$.

In the inertia controlled stage, $P_g-P_{\infty }$ in Equation (5) increases as $P_{\infty }$ decreases and $P_g$ remains practically constant. Therefore, the environment below atmospheric pressure is favorable for bubble growth in the inertial control stage. In the diffusion controlled stage, the pressure inside and outside the bubble is in a quasi-equilibrium state. The pressure inside the bubble ($p_g$) can be expressed as $p_g=p_{\infty }+p_{s,b}+p_{s,d}$. $p_{\infty }$, $p_{s,b}$ and $p_{s,d}$ are environmental pressure, pressure caused by the surface tension of the bubble and droplet, respectively. It is assumed that the gas in the bubble follows the ideal gas equation. The gas density in the bubble can be calculated by ${\rho }_g=\frac{p_g}{R_{g}T}=\frac{p_{\infty }+p_{s,b}+p_{s,d}}{R_{g}T}$. So, a decrease in ambient pressure ($p_{\infty }$) will lead to a decrease in ${\rho }_g$. The $b$ in (5) increases with the decrease of $p_{\infty }$. Eventually, the bubble growth rate increases. According to the experimental results, $\Delta T_s$ is crucial to the occurrence of micro-explosions. The change of ${\rho }_g$ has a greater influence on the bubble growth rate and droplet breakage strength.

As for the multi-component miscible droplets, the bubble growth rate is lower, and the process from bubble growth to droplet breakage is considered to be mainly controlled by the diffusion growth stage [46]. However, the decrease of $p_{\infty }$ will cause the bubble to be bigger as $P_g$ goes down close to $p_{\infty }$ during inertial control stage. This means that inertia control will occupy more position in the whole bubble growth process. Moreover, the growth rate of bubbles in the inertia control stage is much higher than that in the diffusion control stage. Therefore, the decrease of pressure will promote the transition of bubble growth from slow diffusion control to fast inertia control. The droplet breakage time at 0.6 bar and 823 K is close to the characteristic time of heat diffusion of 1 ms [46], showing the characteristic of bubble inertia control growth.

3.5. Droplet State

Figure 12 contains the droplet state under all experimental conditions in this study. When the pressure is 1.0 bar, the ignition occurred during droplet evaporation at the lowest 823 K. As the pressure decreases, the minimum ignition temperature increased. Ignitions at 0.2 bar were very difficult and required an ambient temperature of 973 K, which was about 150 K higher than the ignition temperature at 1.0 bar. Puffing and micro-explosion phenomena were found in partial evaporation and all combustion conditions. As droplet ignition creates a higher ambient temperature around the droplet, combustion is highly conducive to micro-explosion. When the pressure is lower than atmospheric pressure, the reduction of boiling point difference between different components in kerosene significantly inhibits the micro-explosion, so that the micro-explosion only occurs under 0.6–1.0 bar.

4. Conclusions

The evaporation, combustion and micro-explosion characteristics of RP-3 kerosene were investigated under different sub-atmospheric pressures and elevated temperature. The following conclusions can be drawn from this study:

• Different from other higher temperatures (573–873 K), the normalized D² significantly deviates from the classical d²-law and the evaporate rate decreases gradually under 473 K and 0.2–1.0 bar. For 473 K, lowering the pressure has been shown to reduce the change in the evaporation rate. This may be due to the fact that the difference in boiling points between the different components of the droplet decreases with decreasing pressure;
• The droplet evaporation rate increases monotonically with increasing temperature and pressure under 573–873 K and 0.2–1.0 bar. Temperature has a greater effect on evaporation rate than pressure. The increase of ambient temperature increases the temperature difference between the environment and the droplet surface, which promotes the heat transfer. The decrease of pressure makes the distance between the gas molecules become larger and the heat transfer between the environment and the droplet surface deteriorates;
• The decrease in pressure causes the combustible vapor to be more evenly distributed around the droplet and significantly reduced the formation and aggregation of large soot particles in the process of spontaneous ignition. The decrease of temperature and pressure is obviously detrimental to the successful ignition of droplet and significantly increases the ignition delay time of spontaneous combustion. Ignitions at 0.2 bar are very difficult and required an ambient temperature of at least 973 K, which is about 150 K higher than the minimum ignition temperature at 1.0 bar; and
• A sufficiently high ambient temperature (673 K or higher) is a necessary condition for micro-explosion to occur. The increase of ambient temperature and droplet combustion can effectively promote the occurrence of micro-explosion. Reducing pressure was discovered to reduce the likelihood of micro-explosions at 673, 773 and 823 K, probably due to the boiling point difference among different components of kerosene decreases as the ambient pressure decreases. In addition, the decrease of pressure was discovered to significantly increase the bubble growth rate and droplet breakage intensity. This is probably caused by the fact that pressure reduction can significantly increase the bubble growth rate in both inertial and diffusion-controlled growth stages.