Thermally induced secondary atomization (TISA) is a complex phenomenon that accelerates phase change in the combustion chamber. It occurs if multi-component fuels, having a wide boiling range, are exposed to high temperatures. Several airlines are recently experimenting with bio- and fossil fuels blends. However, the characteristics of droplet TISA are primarily unknown because of the challenges associated with experimental activities like suspended or falling droplets. In this scenario, numerical models become essential to study TISA. That is why a new multi-component, multi-phase volume of fluid computational fluid dynamics solver was developed to simulate droplets TISA. The solver takes advantage of the OpenFOAM framework and uses the isoAdvector methodology. The bio- and fossil fuels were represented by n-heptane and n-hexadecane, respectively, to simplify the problem. Evaporation was implemented by assuming that the mixture could only boil at that temperature. Surface tension and other relevant mixture properties were considered as a function of species concentration and temperature to replicate all phenomena comprehensively. An analysis of bubble expansion based on the Rayleigh–Plesset equation preceded the breakup tests. The test cases consisted of a droplet suspended in microgravity having a bubble initialized at the interface. The bubble eventually expanded, and the bubble cap collapsed, leading to the micro-explosion. A parametric study of breakup cases under different pressures and at a fixed temperature of 1200 K was performed. The atomization mechanism was tested at 1, 3, 10, and 20 bar and compared. It was observed that while high pressure slows down the process, it finally leads to a higher surface area. This behavior was confirmed by testing two different bubble sizes. Together with the atomization intensity, also the morphology of the particles changed. At atmospheric pressure, the maximum surface area was reached when the droplet had a disk-like shape, while at higher pressures, it evolved in an elongated shape.
The continuous reliance on fossil fuel reservoirs and rising carbon emissions have motivated the adoption of renewable fuels. This trend is reflected in the aviation sector, where companies, such as Air France/KLM, Lufthansa, Japan Airlines, and Air New Zealand, are already testing commercial passenger flights using blends of conventional fuel and bio-derived sustainable aviation fuels (SAF).1 Nevertheless, exploiting renewable fuels in the aviation sector is challenging since the new and current powers must be fully compatible with maintaining existing engines and minimizing changes to logistics and infrastructures. Together with compatibility issues, the new fuel must satisfy safety and quality standards and be characterized by low carbon emissions throughout its lifecycle.2 The International Air Transport Association (IATA) has approved three classes of fuels: Fischer–Tropsch Hydroprocessed Synthesized Paraffinic Kerosene (FT-SPK), produced from any carbonaceous raw material, the Synthesized Paraffinic Kerosene from Hydroprocessed Esters and Fatty Acids (HEFA-SPK), created from animal or vegetable oil, and the Synthesized Iso-Paraffins from Hydroprocessed Fermented Sugars (SIP-SPK), from sugar through fermentation. The HEFA can be blended up to 50% volume with conventional fuel oil.3
A crucial step in the combustion of aviation fuel is the atomization process. HEFAs, for instance, are more viscous than conventional jet fuel; consequently, they produce larger droplets when atomized, lowering the surface area and decreasing combustion efficiency. On the other hand, studies from Pacheco et al.4 showed that droplets of 25% hydroprocessed vegetable oil (HVO), with jet A-1 fuel, presented micro-explosions, which significantly increased the surface area of the droplet, decreasing the time required for its consumption.
Micro-explosions occur when a multicomponent droplet is exposed to high temperatures; the more volatile component vaporizes, forming a bubble that later causes breakup phenomena.5 The thermally induced secondary atomization (TISA) process depends mainly on the Lewis number and the boiling range. The Lewis number, in particular (ratio between thermal conductivity and mass diffusivity), results in larger than one when heat penetrates the droplet at a faster rate than mass diffusion to the external environment.
Dryer6 and others extensively studied micro-explosions for water-in-fuel emulsions. This study adopted the suspended droplet experiment; however, since quartz suspension fiber may lower the limit of superheat in the mixture,7 the experiment was replicated in the form of falling droplets by Lasheras et al., and micro-explosive behavior was observed again. In later experiments, Lasheras et al. studied the combustion of paraffinic mixtures. They observed that the combinations yielded secondary atomization when the components had different normal boiling points.8
III. BUBBLE NUCLEATION AND EXPANSION
Figure 1 shows the evolution of the bubble radius in time [obtained using Eq. (18)] for different values of the liquid pressure. The solution showed that the timescale for bubble growth was shorter than the one observed for the micro-explosion, which was of the order of a few milliseconds.8,26 Consequently, it was possible to consider the bubble growth as instantaneous, thus focusing only on the subsequent breakup.
IV. CASE STUDY
The equation of state used in the work was the Soave Redlich Kwong.29 The computational domain was a cubic box of a size 3R×3R×3R, where R is the radius of the droplet. The mesh was uniform and orthogonal and composed of a total of cells. The boundaries are open; therefore, a Neumann boundary condition is imposed by assuming the derivative of the variables with respect to the space equal to zero across the interface. Mesh convergence was demonstrated in a previous work from the group.14 The time step was set at 1e-6 s.
The atomization process progressed in three steps: pinching, crown formation, and ejection. The first step occurred when the liquid meniscus above the droplet became thinner, rupturing into a hole. The two leading causes of pinching were expansion of the bubbles and boiling at the surface caused by the hot external environment. Another reason for the bubble motion was the Marangoni effect, originated by surface tension gradients in the liquid. A recent work demonstrated that in most cases, boiling is not a major cause of pinching although it contributes to its occurrence.14 When pinching occurs, instabilities propagate along the crater crest; those instabilities form crown-like structures and eventually evolve into liquid filaments. The liquid filaments anticipate the ejection of droplets that occur through amplification of Plateau–Rayleigh instabilities. Micro- and nano-droplets formation occurs because of Rayleigh–Taylor instability in the liquid filaments. Figure 2 shows the filament formation in an azimuthal view of droplets at atmospheric pressure. The crown formation generates the droplets; however, the formation of those secondary droplets was not the main cause of surface area increase; instead, the surface area increased mainly because of the shape assumed by the parent droplet during the process. Secondary droplets spread at velocities in the order of . The secondary particles rapidly changed phase as their temperature rose while projected to the hot external atmosphere. The temperature of secondary droplets quickly reached the boiling point of the mixture. Figure 3 shows the liquid temperature of the droplet, highlighting the much higher temperature reached by the small structures, which basically boiled immediately as they left the parent droplet. Conversely, the temperature of the parent droplet increased at a lower rate. The crown formed from instabilities propagating at its crest and enlarged following the ejection of the higher pressure internal vapor until it folded on itself. In the case in Fig. 4, the particle became almost a disk, while ejection took place. Figure 4 demonstrates the crown folding after 0.002 s, when the crater reached its maximum diameter and the ejection was initiated. Because of computational power requirements, the ejection step was not completely simulated.
A. Pressure effect
Pressure was observed to have a major effect on the evolution of the droplet after ejection. Pinching occurred later in time, as also noted by Law et al.5 and reported in their work. Slower pinching could be attributed to a lower relative gradient between the internal vapor and the external environment, which eventually reduced the stress on the bubble cap. Another important effect of high pressure was the limited expansion of the droplet, which maintained a more rounded but elongated shape throughout the breakup.
Breakup time was defined as the time between pinching and the occurrence of the maximum surface area; in both cases, this time gradually increased with pressure, as expected. In fact, pressure acted as a binding force, first, compressing the liquid and later slowing the ejection of gas from the internal bubble to the external environment. Larger bubbles also slowed the atomization process at low pressures, while they performed very much the same when the pressure was higher than 10 bar. The atomization process of a large bubble was intrinsically slower as multiple pinching zones and ejection occurred simultaneously.
Finally, a last numerical experiment was performed to verify the influence of droplet size. A case, where the droplet had a diameter of 200 μm and the bubble a diameter of 120 μm, was tested at 10 bar and at the usual temperature of 1200 K (Fig. 9). The outcome was a faster atomization compared to the larger particle with the same surface area ratio between bubble and droplet. This result was expected as the pressure inside a smaller bubble is higher compared to other cases. Also, the temperature of the liquid increases faster given the shorter characteristic length heat has to travel.
Numerical simulations were used to demonstrate and quantify the effect of pressure on thermally induced secondary atomization. A binary mixture of n-heptane and n-hexadecane was considered as a surrogate. It was assumed that the significant difference in the boiling temperature would trigger bubble formation. The evolution of the critical nuclei was then studied by solving the Rayleigh–Plesset equation, but at all pressures considered, the characteristic time of bubble expansion was substantially shorter than the time required for breakup.
As pressure increased, the onset of breakup occurred later, and the entire process was substantially slower. The onset of breakup, in particular, required a time higher than one order of magnitude in the cases of breakup at 20 bar, compared to the simulation at 1 bar. Compared to an almost instantaneous breakup (order 0.01 s) in the case at atmospheric pressure, in cases at 10 and 20 bar, the droplets reached their maximum surface area after almost 0.7 s. It was also observed that the maximum surface area reached under pressure was substantially higher in the case with a smaller (0.6 mm) bubble initialized, reaching almost two times the initial surface. The effect of pressure on the extent of the atomization process was greatly reduced when the bubble was larger. Breakup time with the larger bubble was slower at a low pressure and slightly faster at higher pressure. The latter behavior could have been caused by the lower pressure excess of the inner bubble, given the larger size. To conclude, it was demonstrated that pressure has a potentially beneficial effect in the atomization of fuel blends. However, further analysis is required to generalize the observations made in this work, as, for instance, the size of the analyzed droplets was larger than those actually generated in combustion devices such as aircraft turbines.
This work was sponsored by the Clean Combustion Research Center at King Abdullah University of Science and Technology (KAUST). Computational resources were provided by the KAUST Supercomputing Laboratory (KSL).
Conflict of Interest
The authors have no conflicts to disclose.
Paolo Guida: Conceptualization (lead); Software (lead); Validation (lead); Writing – original draft (equal). Alberto Ceschin: Conceptualization (supporting); Methodology (equal); Software (supporting); Validation (equal); Visualization (lead). Chiara Canciani: Conceptualization (equal); Data curation (supporting); Investigation (equal); Visualization (supporting); Writing – original draft (equal). Hong G. Im: Conceptualization (supporting); Supervision (supporting); Writing – review & editing (supporting). William L. Roberts: Conceptualization (supporting); Supervision (lead); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.