Evaporation and Autoignition Characteristics of JP-10 Droplets with Hyperbranched Polyester as Additive

Abstract

It was found in our previous work that hyperbranched polyester (HPE) can generate radicals and accelerate the chemical reactions of hydrocarbon fuels used as initiators. In this work, the evaporation and autoignition characteristics of JP-10 droplets with or without HPE were investigated using the high-speed backlight imaging technique in detail. The results indicate that the puffing and micro-explosion phenomena of HPE-blended JP-10 droplets can accelerate fuel evaporation and autoignition. When a 0.1% mass concentration of HPE was used, the droplet lifetime was reduced by 16.5% in evaporation at 850 K and 18.0% in autoignition at 900 K. A mechanism of HPE that promotes puffing and micro-explosions was proposed by analyzing droplet images of combustion and SEM images of combustion residues. Overall, this study provides a method for improving the evaporation and autoignition performance of JP-10.

1. Introduction

High-density hydrocarbon fuels are gaining more attention in the aerospace industry because their high energy density can promote the payload size, flight range, and flight speed of aircrafts [1,2,3]. Among high-density hydrocarbon fuels, JP-10 is widely applied in various aerospace thrusters, detonation engines, and cloud explosion weapons because of its excellent features, such as high mass density (0.935 g·mL⁻¹, 20 °C), high volumetric energy density (39.6 MJ·L⁻¹), low freezing point (−79 °C), and low viscosity (40 mPa·s, −18 °C) [4,5].

Jet fuels’ utilization in jet engines converts chemical energy into heat energy through combustion. Consequently, the quality of the combustion process of fuels determines the performance of a jet engine [6,7]. JP-10 has a higher C/H ratio and relatively stable cyclic structure compared with other jet fuels, leading to low levels of combustion completion, decreases in output power, and increases in fuel consumption [8]. To promote the combustion performance of JP-10, impressive works have been undertaken. The use of additives, including metal nanoparticles [9,10,11,12,13,14], nonmetal nanoparticles [15,16,17], and metal oxide nanoparticles [18,19], can improve the ignition and combustion properties of JP-10 due to their catalysis functions. However, these methods are still far from economical and harmful to human health, and the inherent tendency of nanoparticles to aggregate and form agglomerates limits their practicality [20]. Du et al. [21] proposed another method in which boron and 0–78% mass concentrations of ethanol are mixed with JP-10, which causes droplet micro-explosions and thus promotes energy release. However, an excessive concentration of light components changes the original properties of JP-10, which limits its practicality.

Hyperbranched polymers, a subclass of dendrimers, have attracted the interest of polymer technologists worldwide. The unique properties of hyperbranched polymers include their highly branched three-dimensional structures, endogenous cavities, and abundant end groups on their surfaces [22,23,24,25]. Quan et al. [26,27] synthesized a series of hyperbranched polyesters as flow improvers, reducing heavy oil’s viscosity by 56.16%. In previous work [28,29,30], we synthesized a series of hyperbranched polymers that exhibited excellent properties as fuel-cracking initiators and antioxidants. Among these additives, hyperbranched polyester (HPE) holds great potential in hypersonic applications due to its superb cracking performance and universal applications in high-density hydrocarbon fuels.

However, the effect of hyperbranched polyesters as additives on the burning process of JP-10 has yet to be systematically studied. In this work, the influence of hyperbranched polyester on the evaporation, autoignition, and micro-explosion properties of the high-density hydrocarbon fuel JP-10 was studied with a high-speed backlight imaging technique and SEM. This work provides a way to promote the evaporation and combustion of high-density hydrocarbon fuel.

2. Experimental Method

2.1. Materials

1,1,1-tris(hydroxymethyl)propane (TMP, 98 wt%) and 2,2-bis(hydroxymethyl)-propionic acid (MPA, 98 wt%) were purchased from Energy Chemical Reagent Corporation, Shanghai, China. Palmitic acid and p-toluenesulfonic acid (p-TSA, 98 wt%) were purchased from Aladdin Shanghai Aladdin Biochemical Technology Company Limited, Shanghai, China. exo-tetrahydrodicyclopentadiene (JP-10, 98.5 wt% by GC–MS) was purchased from Yangli Petrochemical Company Limited, Nanjing, China.

2.2. Synthesis of Hyperbranched Polyester

The synthesis and characterization of HPE were reported in our previous study [30]. In short, as shown in Scheme 1, a yellow transparent solid hyperbranched polyester, HPEP, can be obtained via the polycondensation of TMP and MPA. In this work, the weight-averaged molecular weight of HPEP was found to be around 2000.

Subsequently, the hydroxy groups of HPEP were grafted with palmitic acid to make the polyester soluble. A chloroform–methanol mixture was used as a solvent for the recrystallization of crude HPE to remove excessive palmitic acid, and the precipitation was dried under vacuum to obtain a yellow solid HPE.

HPE at mass concentrations of 0.1%, 0.3%, and 0.5% was added into JP-10 (named 0.1%, 0.3%, and 0.5% HPE-blended JP-10 fuel, respectively) to form a uniform, transparent solution.

2.3. Experimental Apparatus

A schematic diagram of the high-speed backlight imaging apparatus is shown in Figure 1. It shows fuel droplets’ evaporation, ignition, and combustion behavior from room temperature to 1273 K at standard atmospheric pressure. A muffle furnace was used as a high-temperature heat source with a temperature accuracy of 1 K. A 50 × 50 mm transparent quartz window was opened in the front and back of the muffle furnace for high-speed camera imaging, and a 40 mm diameter circular window was opened at the top. The fuel droplet was suspended on a zirconia ceramic rod with a diameter of 0.2 mm. Due to the low thermal conductivity of zirconia (2.0–2.5 W·m⁻¹·K⁻¹, 373–1773 K) [31] and high droplet carrier diameter ratio, the effect of the rod on the droplet-burning process was considered to be negligible [32]. The rod was driven by a stepper motor and sent into the muffle furnace from the outside. In addition, a liquid-cooled plate with condensed water was set at the top of the muffle furnace to isolate the influence of hot air flow on the fuel droplet. A microsyringe generated fuel droplets with a diameter of 0.5–3.0 mm. A CP70-2-M/C-1000 color high-speed camera produced by Optronis and an F017 SP 90 mm F/2.8 Di MACRO 1:1 VC lens produced by Tamron were used to shoot the droplet’s burning process. The specs of the high-speed camera included a spatial resolution of 832 × 800 pixels, a frame rate of 3000 FPS, and an exposure time of 5 μs. The timing of all events (the rotation of the liquid cooling plate, the translation of slide, and camera shooting) was controlled with a microcontroller system with a temporal resolution of 1 ms.

The droplet image captured by the high-speed camera was binarized by MATLAB. After removing the support rod, the black pixels were calculated to obtain the projection area $S_t$ of the droplet. Due to the influence of gravity, the droplet was ellipsoidal. Thus, the projected area $S_t$ was equalized according to Equation (1) to obtain the droplet diameter $D_t$:

$$D_t=\sqrt{\frac{4S_t}{\pi }}$$

(1)

The uncertainty in this research was mainly caused by the droplet volume errors generated by the microsyringe. Therefore, the initial droplet diameter $D_0$ was calculated from the picture taken with the high-speed camera after the droplet was stabilized, and all initial droplet diameters were $D_0$ = 2.20 ± 0.05 mm.

2.4. D²-LAW and Film Theory

During the equilibrium evaporation and combustion stages, the square-normalized diameter of a fuel droplet conforms to the D²-Law [33,34]:

$$\frac{D_t^2}{D_0^2}=-K\frac{t}{D_0^2}+1$$

(2)

The D²-Law is only valid with the assumption that the relative velocity between a droplet and a free stream can be neglected, as can the buoyancy effect. If true, then the evaporation or combustion constant K of droplets can be derived and expressed as Equation (3):

$$K=\frac{8k_g}{c_{pg}{\rho }_l}\mathit{ln}\left(1+B\right)$$

(3)

However, when the suspension method is used to investigate the combustion of a single droplet, the experimental environment is similar to actual combustion under actual working conditions. Specifically, the droplet enters the combustion chamber through the nozzle at high speed and has convection with the air.

There are several approaches to simplifying the convection problem in droplet burning, among which the “film theory” is the most efficient and straightforward [33]. The droplet model of film theory is shown in Figure 2. The evaporation and combustion process of a droplet is assumed to be divided into two stages. In the first stage, evaporation and combustion are not considered, and the droplet is regarded as a sphere with only convective airflow heat transfer. In the second stage, convection is not considered, and evaporation and combustion only occur in an imaginary film formed in the first stage. The heat and mass transfer boundary at infinity is replaced by the film boundary, and then the droplet model in a stagnant medium is used to solve droplet-burning problems.

In film theory, the evaporation/combustion constant K can be expressed as:

$$K=\frac{4k_{g}Nu}{c_{pg}{\rho }_l}\mathit{ln}\left(1+B\right)$$

(4)

The Nusselt number can be expressed as [35]:

$$Nu=\frac{h{D}_0}{k_g}\approx 2+\frac{0.555R{e}^{\frac{1}{2}}{Pr}^{\frac{1}{3}}}{{\left[1+\frac{1.232}{ReP{r}^{\frac{4}{3}}}\right]}^{\frac{1}{2}}}$$

(5)

In fact, for a droplet in a stationary medium (Nu = 2), Equation (4) degenerates to Equation (3). By substituting Equation (5) into Equation (4), the evaporation/combustion constant K under convective environments can be obtained:

$$K=\frac{4h{D}_0}{c_{pg}{\rho }_l}\mathit{ln}\left(1+B\right)$$

(6)

3. Result and Discussion

3.1. Thermal Stability of HPE

The thermal properties of HPE were determined with TGA, and the results are given in Figure 3. As shown in Figure 3, the 5% mass loss temperature of HPE was 570 K and the 95% mass loss temperature of HPE was 715 K. Additionally, the boiling point of JP-10 was 458 K (1 atm) [36], which was lower than the decomposition temperature of HPE. During the evaporation/combustion process of the HPE-blended JP-10 droplet, the droplet temperature remained at the boiling point due to the phase transition of JP-10, and HPE did not decompose at this temperature. Consequently, HPE could maintain its structure during the evaporation/combustion process of the HPE-blended JP-10 droplet.

3.2. Evaporation and Autoignition Process of JP-10 Droplets Blended with HPE

Figure 4 shows the probabilities of puffing or micro-explosions with different HPE concentrations of the JP-10 droplets at 700–950 K, where each data point represents the statistical probability of at least 20 experiments. In the low-temperature ranges (T = 700 K and 750 K), all fuel droplets only underwent normal evaporation (shown in Figure 5(A1–A5)). No autoignition, puffing, or micro-explosions occurred under these conditions. In the medium temperature range (T = 800 K and 850 K), normal evaporation was observed in the feedstock JP-10 droplets while puffing was observed in the JP-10 droplets blended with HPE. The puffing phenomenon, as shown in Figure 5(B1–B5), was manifested in local explosions of the main droplet and the ejection of some micro-droplets. In addition, the main droplet also produced a certain degree of deformation (shown in Figure 5(B5)). The reason for puffing is that the light components on the droplet’s surface continuously evaporated and the heavy components on the droplet surface remained and formed an oil film, which prevented the diffusion of the light components inside the droplet. Puffing occurred when the bubbles inside the superheated droplet exceeded the pressure limit of the heavy component liquid film. Puffing can effectively increase the contact area between fuel droplets and air, thereby improving fuel droplets’ evaporation and combustion performance [7]. In addition, the evaporation of the JP-10 droplets was not always accompanied by puffing in the medium-temperature range in this study. Specifically, the probability of puffing was found to be positively correlated with temperature and HPE concentration. In the high-temperature range (T = 900 K, 925 K, and 950 K), autoignition was observed in the JP-10 droplets while puffing still did not occur in the feedstock JP-10 droplets (shown in Figure 5(C1–C5)). At 900 K, puffing occurred with a high probability in the autoignition process of the 0.1% HPE-blended JP-10 droplets (shown in Figure 5(D1–D5)). However, micro-explosions instead of puffing occurred in all JP-10 droplets blended with higher mass concentrations of HPE. The micro-explosion process is shown in Figure 5(E1–E5), which demonstrates that many small bubbles generated inside the droplet did not locally explode but continued to converge and eventually formed a larger bubble (shown in Figure 5(E1,E4)). As the light component continued to diffuse, the large bubble exceeded the surface’s heavy component oil film pressure limit and a violent micro-explosion occurred (shown in Figure 5(E2,E5)). Compared with puffing, a micro-explosion is caused by a large bubble composed of many small bubbles that has a destructive effect on a whole fuel droplet and then leads to chain puffing and chain micro-explosions. Therefore, micro-explosions can improve fuel droplets’ evaporation and combustion performance. Additionally, the main difference between puffing and micro-explosions is that puffing is the process during which the partial breakup of the parent fuel droplet occurs (as caused by small bubbles) while a micro-explosion is the complete breakup of the parent fuel droplet into small droplets caused by a large bubble.

3.3. Effect of the Initial Diameter of Feedstock JP-10 Droplet on the Evaporation Constant K at 500–800 K

Figure 6 shows the evolution of the droplet diameter square for the JP-10 droplets at 500–900 K. In the 500–800 K temperature range, the evaporation process of the JP-10 fuel droplets could be divided into two stages: transient heating and equilibrium evaporation. At the transient heating stage, due to the combined influence of droplet evaporation and thermal expansion, the JP-10 droplet diameter nonlinearly decreased. As the droplet temperature gradually increased, the droplet entered the equilibrium evaporation stage. This specific performance shows that $D_t^2/D_0^2$ linearly decreased with time, which conformed to the classical D²-Law. At the equilibrium evaporation stage, the evaporation constant K could be obtained by linear fitting $D_t^2/D_0^2$ with t$/D_0^2$ (Equation (2)). In addition, the evaporation rate of fuel droplets significantly increased with increases in temperature, and the JP-10 fuel droplets spontaneously combusted at 900 K.

Figure 7 shows the evaporation constant K with initial droplet diameter D₀ at temperatures of 500–800 K. As the temperature increased, the evaporation constant K gradually increased. At the same temperature, the evaporation rate constant K linearly increased with the initial droplet diameter D₀. This phenomenon has also been reported by other scholars [37].

Film theory can satisfactorily explain this phenomenon. Equation (6) shows a linear correlation between the evaporation constant K and the initial droplet diameter D₀. Compared with the classical droplet model without convection, the film theory states that a larger initial droplet diameter is more conducive to convective heat transfer under forced airflow. In other words, large droplets have a larger Nusselt number, which increases the evaporation constant K. As the temperature increases, the slope of the $K-D_0$ fitting line gradually increases. This is because the evaporation constant K is directly affected by the $h,c_{pg},{\rho }_l,\mathrm{a}\mathrm{n}\mathrm{d}B$ of the whole droplet-burning system (shown in Equation (6)), and the temperature of the environment can affect them. Under the experimental conditions of this study, high temperatures caused the specific heat capacity and Spalding transfer number to increase and the density to decrease. The influence of temperature on the convective heat transfer coefficient is more complicated. Many properties, such as viscosity, thermal conductivity, and convection state, affect it [38]. Various factors are coupled, so high temperatures make the effect of the initial droplet diameter D₀ on the evaporation constant K more significant. In addition, the main reason for the non-zero linear intercept in Figure 7 is the influence of the carrier background area.

3.4. Effect of HPE Additives on JP-10 Droplets’ Evaporation and Autoignition

Figure 8 shows the evaporation curves of the JP-10 blended with different mass concentrations of HPE at 800 K. It can be seen in the curve of the JP-10 without puffing that the evaporation curve of the feedstock JP-10 had a sharp inflection point at the end of the equilibrium evaporation stage. With the increase in HPE concentration, the droplet’s evaporation rate slowed, and the curve became softer at the end of droplet evaporation. Specifically, the intersection of the linear line in the equilibrium evaporation stage and the baseline was no longer a sharp intersection but a gentle curve. The above phenomena were caused by the addition of HPE, and the evaporation rate-slowing stage after the equilibrium evaporation stage is named the residual component evaporation stage. At this stage, the light component JP-10 had evaporated almost completely, and HPE (and its cracking products) had a higher concentration. Additionally, the curves of 0, 0.1%, and 0.5% HPE-blended JP-10 without puffing show that the relative occurrence time of the residual component evaporation stage advanced and the relative duration increased with the increase in HPE concentration.

At 800 K, the puffing phenomenon occurred in the evaporation of the HPE-blended JP-10 droplets, as shown in the evaporation curve with a transient fluctuation in Figure 8. Puffing increased the contact area between the droplets and air, accelerated the evaporation process, and reduced the lifetime of the droplets. In addition, it is worth noting that the residual component evaporation time of the JP-10 droplets with puffing was significantly lower than that of the JP-10 droplets without puffing, which may have been because the small droplets ejected from the puffing process took away residual components from the surface of the droplet.

Figure 5(C2) shows the autoignition process of the JP-10 droplets at 900 K. As JP-10 burned, soot shells formed around the JP-10 droplets, mainly due to the insufficient combustion of JP-10. Excessive droplet volume and low oxygen concentration may be the main reasons for this phenomenon. Figure 5(D1–D5,E1–E5) shows the puffing and micro-explosions of the HPE-blended JP-10 droplets during combustion. Numerous micro-droplets ejected from the main droplet at high speed destroyed the soot shell around the main droplets, and then secondary flames developed around the micro-droplets.

After the combustion of JP-10, some soot aggregates remained on the zirconia ceramic rod. An SEM image of soot aggregates is shown in Figure 9. Figure 9(A1,A2) shows the blank comparison of clean zirconia ceramic rods. Figure 9(B1,B2) shows the residual soot aggregate after feedstock JP-10 combustion. These soot aggregates were isolated or irregularly connected with other soot aggregates, and the size was generally near tens of nanometers, similar to the SEM images taken by other scholars [39]. Figure 9(C1,C2) shows the residual soot aggregate after HPE-blended JP-10 droplet combustion. The main soot aggregates were connected by nanometer-level regular bands to form a network structure with other soot aggregates. These soot aggregates were the combustion residues of HPE. In addition, there were many nanometer-sized cavities on the micron-sized network structure. Additionally, many irregular JP-10 combustion residues, similar to those shown in Figure 9(B1,B2), were attached to the micron-sized porous network structure.

The mechanism of the puffing and micro-explosions of JP-10 droplets with HPE as an additive is shown in Scheme 2. The micron-sized porous network structure formed by HPE at a high temperature can provide many nucleation sites, thus promoting bubble nucleation inside JP-10 droplets [39]. In addition, the light component JP-10 on a droplet’s surface rapidly evaporates, and the heavy component HPE gathers in large quantities to form a thicker liquid film, thus blocking the escape of bubbles inside the droplet [40]. Under the synergistic effect of these two mechanisms, the droplet enters a superheated state. Then, it undergoes puffing or a micro-explosion, thereby improving the evaporation and combustion performance of JP-10 droplets.

3.5. Effect of HPE Additives on JP-10 Droplets’ Ignition and Lifetime

Figure 10 shows the variation in the ignition delay with different HPE concentrations at 800–950 K. As the temperature increased, the ignition delay of the JP-10 droplets gradually decreased, which followed the Arrhenius equation. The addition of HPE did not significantly affect the ignition delay of the JP-10 droplets.

Adding HPE to JP-10 made the evaporation and autoignition of the JP-10 droplets more complicated. The process could be divided into the following stages: transient heating, puffing/micro-explosion, equilibrium evaporation/combustion, and residual component evaporation/combustion. However, the evaporation/combustion constant K only applied to the equilibrium evaporation/combustion stage, which was insufficient for evaluating the total evaporation and combustion performance of JP-10. Therefore, the droplet lifetime was defined as shown in Equation (7). The droplet lifetime $t_d$ can be used to measure the time of the entire droplet evaporation/combustion process. Thus, $t_d/d_0^2$ was used to measure the evaporation and combustion performance of the JP-10 droplets.

$$t_d=\mathrm{m}\mathrm{i}\mathrm{n}\{t|\frac{D_t^2-D_{Inf}^2}{D_{Inf}^2}<0.01\}$$

(7)

Figure 11 shows the variation in the droplet lifetime with different HPE concentrations at 750–950 K. Overall, the droplet lifetime decreased with increasing temperature. At 750 K, the droplet lifetime of JP-10 slowly increased with increases in HPE concentration. At 800 K, puffing occurred in the HPE-blended JP-10 droplets, which promoted the evaporation process of the droplets and significantly shortened the droplet lifetime. At 850 K, 0.1%, 0.3%, and 0.5% of HPE as additives greatly accelerated the evaporation of the JP-10 droplets, reducing the droplet lifetime by 16.5%, 20.1%, and 30.6%, respectively. At 900 K, puffing and micro-explosions occurred in the 0.1%, 0.3%, and 0.5% HPE-blended JP-10 droplets during combustion, reducing the droplet lifetime by 18.0%, 12.4%, and 15.2%, respectively. Micro-explosions always occurred in the 0.3% and 0.5% HPE-blended JP-10 droplets, and the droplet lifetime was lower than that of the feedstock JP-10 droplets without micro-explosions. In other words, HPE could effectively improve the evaporation and combustion of the JP-10 droplets.

4. Conclusions

In summary, hyperbranched polyester (HPE) was used as an additive for JP-10. The evaporation and autoignition of feedstock and HPE-blended JP-10 droplets were experimentally examined. The following conclusions can be drawn from this study:

• The evaporation constant K of JP-10 droplets is linearly correlated with the initial droplet diameter D₀, and the fitting slope is positively correlated with temperature. Film theory can explain this phenomenon well. The main reason for this phenomenon is that large initial droplet diameters can improve the convective heat transfer ability of droplets.
• Low concentrations of HPE (0.1~0.5%) can cause droplets to exhibit puffing at low temperatures and micro-explosions at high temperatures, which increases the contact area between JP-10 droplets and the air, reduces the effect of the delayed evaporation or autoignition of residual components, shortens the droplet lifetime, and improves the evaporation and combustion performance of JP-10 droplets.
• A mechanism of puffing and micro-explosions induced by HPE is proposed: inside a droplet, the micron-sized porous network structure of HPE provides numerous nucleation sites and thus promotes bubble nucleation. On the droplet’s surface, the heavy component HPE aggregates to form a liquid film and thus blocks the escape of bubbles inside the droplet. These effects synergistically cause JP-10 droplets to exhibit puffing and micro-explosions.