Figure 11 shows the dispersion angles (θ) at different injection pressures and charge densities using the 60% penetration criterion. The angles increase with a higher charge gas density because of larger air mass entrainment into the spray. Results from Figure 11 also indicate that gasoline-like fuels exhibit similar or greater dispersion compared to ULSD. Although the physical properties for both gasolines are very similar, RON92 has an appreciably larger angle than RON60. Based on previous work, the non-vaporizing dispersion angle is expected to correlate as follows (Naber and Siebers, 1996; Tang et al., 2017a): t a n ( θ 2 ) = A ( ρ a ρ f ) B (1)

Given that constants A and B are typically fixed for a given injector design, and ρ f is the fuel density, one would expect the dispersion angle to scale in the following order from smallest to largest: ULSD-RON92-RON60. Figure 12 shows that the unexpected order for RON92 dispersion angle is maintained even when using the alternative 45 d o definition. The differences become more pronounced with this criterion because it focuses on the near-nozzle region, whereas the 60% penetration definition captures more of the far-field spray phenomena as well (Tang et al., 2018). Evaporation could also impact the dispersion angle measurements. However, Figure 2 indicates that no significant vaporization is expected for either gasoline at an ambient vessel temperature of 40°C (313 K). Furthermore, Table 1 shows that RON60 and RON92 have the same IBP and would likely be equally impacted by evaporation effects at this condition.

One possible explanation for the discrepancy could be related to injector hardware. The measurements for ULSD and RON60 were performed with one injector, while the experiments for RON92 were conducted with another. Although the nozzle geometry targets were the same for both, there is always some level of manufacturing tolerance that could lead to variation in the rate of injection and subsequent spray behavior. To investigate this further, the dispersion angles for each fuel were separately correlated using Eq. 1 and plotted in Figure 13. The RON92 results fall on a different fit line which indicates distinctive injector behavior. This is also clearly shown in Table 4 which summarizes the fit line coefficients for each fuel. ULSD and RON60 have very similar coefficients, while the B-coefficient for RON92 is distinctly different.

Finally, Figure 14 shows that injection pressure does not have a significant impact on the spray dispersion angle for all fuels. This further validates that density ratio (ρ_a/ρ_f ) is the main parameter describing non-vaporizing dispersion for high-pressure sprays. However, there may be some more complex, secondary fuel effects that are not completely captured by the simple correlation in Eq. 1. Evidence for this is provided by the difference in data spread observed for ULSD versus RON60 and RON92 across different injection pressures using the 45d_o criterion (see Figure 12) (Tang et al., 2018).

Figure 15 compares the non-vaporizing spray penetration among fuels at a charge gas density of 23 kg/m³. Below an injection pressure of 2,500 bar, both gasoline-like fuels show a slower penetration rate than ULSD. This is an expected result given their dispersion angles are larger than diesel. Eq. 2 was developed in prior work to describe the penetration (S) of high-pressure, single-hole diesel sprays and can be used to explain this behavior (Naber and Siebers, 1996): S = C v ⋅ 2 C a a ⋅ t a n ( θ 2 ) ⋅ ( P i n j − P a ) ρ a ⋅ d o ⋅ t (2) C _v and C _a are the velocity and area coefficients of the orifice, respectively, and are related to the discharge coefficient (i.e., C d = C v C a ). The a-term is assigned a constant value of 0.66 while t represents elapsed time. Although there has been some recent evidence that discharge coefficients may change slightly when using gasoline instead of diesel (Tzanetakis et al., 2021), the current analysis assumes no dependence on fuel type for simplicity. Therefore, it is clear from this expression that sprays with a larger dispersion angle should exhibit slower penetration rates. Essentially, a greater degree of spray dispersion or radial spreading should be accompanied by a slower rate of axial penetration.

Another result from Figure 15 is that RON60 and RON92 exhibit very similar penetration rates. This seemingly conforms to the original hypothesis that both gasolines should have similar non-reacting spray characteristics due to their similar physical properties. However, this is not an expected outcome given the difference observed in their dispersion angles (see Figures 11, 12). Based on Eq. 2, RON92 is expected to have a slower penetration rate compared to RON60 at a given operating condition. As previously discussed, this inconsistency could be due to the use of a different injector build for RON92 experiments.

Equation 2 also indicates that spray penetration rate should increase with higher injection pressure. This is due to the higher initial velocity that gets imparted to the liquid fuel at the nozzle exit via Bernoulli’s principle. Figure 16 confirms that this is indeed the case for RON92 gasoline, while previous work also observed the expected trend for RON60 and ULSD using the same injector configuration (Tang et al., 2017a).

Figure 17 shows the impact of charge gas density on non-vaporizing spray penetration at an injection pressure of 1,500 bar. As predicted by Eq. 2, a higher charge gas density (ρ_a) should result in a slower penetration rate. This is due to larger rates of air mass entrainment with higher charge density. The results in Figure 17 are consistent across all fuels and highlight the slower penetration of RON60 compared to ULSD due to dispersion angle effects. Although the RON92 data is self-consistent (i.e., conditions with higher charge density penetrate more slowly), there is an unexpected ordering of curves against RON60 and ULSD results due to a combination of dispersion angle effects and potentially, injector hardware effects (see previous section).

The spray penetration can be normalized to a non-dimensional form using the following transformations based on Eq. 2 (Naber and Siebers, 1996): x + = C a ⋅ d o ⋅ ρ f / ρ a a ⋅ t a n ( θ / 2 ) ,   S ˜ = x x + (3) t + = C a ⋅ d o ⋅ ρ f / ρ a a ⋅ t a n ( θ / 2 ) ⋅ C v 2 ⋅ ( P i n j − P a ) / ρ f ,   t ˜ = t t + (4) t ˜ = S ˜ 2 + S ˜ 1 + 16 S ˜ 2 4 + ln ( 4 S ˜ + 1 + 16 S ˜ 2 ) 16 (5)

When the actual penetration (x) and time (t) are normalized against their respective length and time scales (x ⁺, t ⁺), the data across different operating conditions, fuel types, and nozzle geometries should all collapse onto a single curve. The scaling calculations in Eqs 3, 4 were performed using specifications from Table 2, estimating the C _v based on its relationship to discharge coefficient ( C v = C d / C a ), and assuming an average value of C _a = 0.95 taken from similar single-hole nozzles characterized in prior work (Naber and Siebers, 1996). The a-term was also set to 0.66 as prescribed in this previous study. If experimental results adhere to the established physical theory of non-vaporizing sprays, then the normalized penetration data should collapse onto the correlation described in Eq. 5. Figure 18 shows that this is indeed the case for all three fuels over a wide range of injection pressures and charge gas densities.

Figure 19 shows a scatter plot of dispersion angle versus charge gas density under vaporizing conditions. Angles were determined using the 60% penetration criterion and only represent dispersion of the fuel vapor envelope, not the liquid portion of the spray. As predicted by Eq. 2, the angle generally increases with charge density due to a greater rate of air mass entrainment into the spray. Interestingly however, there does not seem to be any discernable trend with respect to fuel type.

To investigate this further, Figure 20 shows the unique power-law fit for each fuel’s dispersion angle according to Eq. 2. The RON60 and ULSD data were acquired on the same injector, so differences between the two correlations are most likely the result of evaporation effects caused by their vastly different volatility. Based on the original hypothesis of RON92 and RON60 gasoline having similar non-reacting spray characteristics, it is expected they would share similar vaporizing dispersion angles. Although the power law fit for RON92 does not support this claim, additional data at density ratios beyond 0.02 and 0.04 would be needed to make a fair comparison with the other fuels.

Table 5 summarizes the power law coefficients for the half-angle correlation in Eq. 2. Much more variation is observed across fuels with a generally lower R ² value compared to the non-vaporizing data in Table 4. Since these angle measurements were based on the fuel vapor envelope, the correlation between dispersion angle and liquid fuel density may not likely be as strong under these conditions.

The vapor dispersion angle for all three fuels is plotted against charge temperature in Figure 21. Unlike the other results reported in this section, this data was collected with the same nozzle and thus free from any potential injector build impacts on RON92 dispersion angle. As previously observed in Figure 19, there is no statistically significant trend with respect to fuel type for RON60 and ULSD. Within the uncertainty of measurements, the dispersion angle also remains relatively flat with respect to charge temperature. However, RON92 exhibits a larger angle than the other two fuels below 1100 K. Scaling of the dispersion angle also does not follow the order expected due to liquid density (see Table 1 and Eq. 1). These results indicate that a more complex physical model including volatility parameters may be needed to better describe vapor dispersion. For example, RON92 is more volatile than RON60 for 60% of the distillation curve and has a higher RVP (see Table 1 and Figure 2). These differences may have an influence on vapor dispersion angle, especially at the lower end of charge gas temperatures.

Figure 22 shows a plot of vapor penetration for all three fuels over a charge gas temperature range of 800–1200 K. Results indicate that there is no discernable trend with respect to fuel type. This was also observed in previous work which showed a maximum difference of only 5% between the vapor penetration curves of RON60 gasoline and ULSD (Zhang et al., 2017a). Since all the data in Figure 22 was obtained using the same nozzle, there were no potential injector build effects on the RON92 measurements. Hence, it can be confidently said that RON92 exhibits a similar vapor penetration to the other two fuels. The absence of any significant trend with respect to charge gas temperature is consistent with the relatively flat dispersion angles observed over 800–1200 K in Figure 21. However, the differences between RON92 and the other fuels below 1100 K does not seem to impact the penetration. As discussed previously, this may be due to more complex volatility effects that influence the evaporating spray beyond those accounted for in Eqs 1, 2. To better understand these nuanced effects, mixing field measurements using planar laser induced fluorescence (PLIF) or laser induced exciplex fluorescence (LIEF) are planned as part of future work (Parrish and Zink, 2012; Fansler and Parrish, 2014; Chen et al., 2019; Feng et al., 2021).

Under vaporizing conditions, the liquid penetration of the spray reaches a quasi-steady-state length. This occurs at a location downstream of the nozzle orifice where the mass flow rate of fuel exactly matches the evaporation rate (Siebers, 1998; Siebers, 1999). Figure 23 plots the liquid length versus charge temperature at different charge gas densities. For ULSD, the liquid length decreases with increasing charge pressure due to higher gas density and rates of hot air entrainment (i.e., enthalpy) into the spray. This supports higher evaporation rates and shortens penetration. Intuitively, the liquid length of diesel also decreases with charge gas temperature because there is more enthalpy available for evaporation.

As observed in previous work however, RON60 exhibits a strikingly flat liquid length characteristic versus charge temperature (Zhang et al., 2017a). RON92 behaves similarly and seems to validate the original hypothesis regarding similarity of non-reacting spray characteristics among gasoline-like fuels. The results reported in Figure 24 at a constant charge gas density were taken with the same injector and further substantiate the gasoline similarity hypothesis due to the alignment between RON60 and RON92.

To explain why gasoline exhibits a relatively flat penetration curve compared to diesel, the liquid lengths were normalized according to Eq. 3 through Eq. 5 and plotted in Figure 25. The normalized penetrations of RON92 and RON60 fall much closer to the transition regime defined by a normalized time of t ˜ = 1 . This point in the correlation curve represents a transition between the short and long timescale limits describing spray behavior. At shorter timescales, interphase transport processes like mass diffusion and heat conduction become the limiting factor in evaporation of the fuel (Naber and Siebers, 1996; Siebers, 1998; Siebers, 1999). Under these conditions, evaporation is largely a function of physical fuel properties like heat capacity, saturation temperature, thermal conductivity, etc. Thus, it is expected that gasoline-like fuels approaching this regime and sharing similar fuel properties should exhibit similar spray behavior that is also independent of air entrainment rates.

Conversely, Figure 25 shows that ULSD liquid lengths are better described by the longer timescales of the correlation. Interphase transport processes are relatively fast compared to the mixing and air entrainment rates that ultimately limit fuel evaporation in this regime. Under these conditions, the available charge gas enthalpy and entrainment rate of air into the spray directly impact the evaporation rate of fuel. Thus, it is expected that diesel liquid length would be more strongly governed by spray momentum and charge gas properties like density and temperature.

The much lower liquid length exhibited by gasoline-like fuels compared to diesel is of practical significance and can be used to optimize combustion system designs for GCI. In previous work for heavy-duty engine applications, this behavior was leveraged to develop a unique, low-NOx combustion system (Zhang et al., 2019). Using simulation-led design tools, a wide and shallow piston shape was combined with low swirl ratio and a 14-hole injector to produce significantly lower in-cylinder heat transfer losses compared to a conventional geometry-guided (i.e., step-lip), mixing shape, especially at low to medium engine loads. The improved fuel efficiency for this design was determined to be the result of increased air utilization (i.e., faster burning rate) and reduced spray flame interaction with the internal heat transfer surfaces of the combustion chamber.