Liquid Penetration Length
Figure 7 compares measured and calculated liquid penetration length for the divergent and the convergent nozzle as a function of time after start of injection (aSOI) for different injection pressure values. The liquid penetration length was defined here as a distance between the nozzle tip and the farthest droplet of the spray tip along the injector axis (vertical axis of spray chamber). Each measured data point shown in Fig. 7 corresponds to an average of 20 injection shots; the shaded band shows the standard deviation of the experimental data.
The calculated spray penetration lengths at all investigated injection pressures for both nozzles show overall good agreement with the experiments (objective 1). When fuel is injected into the spray chamber a gas-phase recirculation zone and turbulence are created through momentum transfer from the liquid jet to the gas-phase. In the simulation results the correct exchange of momentum between the liquid and gas phases and the correct aerodynamic forces acting on the droplets that strongly influence the atomization process is ensured by fine-tuning the penetration length to match experimental data. However, some deviation in penetration length is also observed at lower injection pressure. One of the possible reasons behind such a deviation for low injection pressure values could be the inaccurate values of the arithmetic mean diameter shown in Fig. 9. In general, at all injection pressures the convergent nozzle shows faster penetration rate suggesting a faster disintegration of the spray via secondary breakup than the divergent nozzle.
Overall, the spray-tip penetration results clearly show increasing penetration length with increasing injection pressure and decreasing injection duration. A short injection duration provides more possibilities to adjust the injection timings, for instance in stratified operation mode and for multiple injections strategies. Also, in the case of early injection a high injection pressure helps by creating more turbulence to create a homogeneous fuel-air mixture. However, the increasing liquid penetration might also lead to issues of wall wetting or liquid fuel film formation at very high injection pressures and therefore fuel injection timing needs to be proper specified. The Authors will discuss this issue in detailed in forthcoming publication.
Mean Droplet Sizes
Figure 8 shows measured and calculated droplet sizes in terms of the arithmetic mean droplet diameter (D10) and the Sauter mean diameter (SMD or D32) for both nozzles at different injection pressures. The results exhibit the impact of injection pressure on the droplet sizes (objective 2). The measured data are time-averaged droplet diameters at probe location 80 mm downstream of the injector tip. In general, the numerical model accurately captures the mean diameter for both nozzles at all injection pressures except for lower injection pressures. The possible reason behind such disagreement is a considerably high contribution of normal (RT) instabilities (refer Fig. 5) at lower injection pressure compared to those at high injection pressures which are associated to higher shear (KH) instabilities. The results confirm the well-known result that droplet sizes decrease with increasing injection pressure, irrespective of nozzle shape. Moreover, the droplet mean diameters (D10 and D32) for the divergent nozzle exceed those for the convergent nozzle, irrespective of injection pressure. However, the arithmetic mean droplet diameter (D10) varies less than the SMD. At high injection pressures droplets quickly reach their stable diameter below which no secondary breakup occurs. Due to its definition, the SMD is quite sensitive to the presence of large droplets. This leads to a decreasing decay of SMD values with increasing injection pressure. A small SMD values (or small droplet size) means a large contact surface area of the droplets, which is beneficial for faster evaporation under real engine conditions.
Droplet size distributions provide a more detailed picture of the spray than D10 and D32. Here, the local droplet size distributions were measured experimentally using Phase Doppler Interferometry (PDI). The sampling location was 80 mm downstream of the injector tip and the sampling time window was at full needle open condition, so the contribution of the large initial droplets was not taken into account. More details about the droplets sampling time window can be found in the “Appendix”. In the simulations a corresponding sampling point with a radius of 2 mm was used to determine the droplet size distributions. Figure 9 presents a quantitative comparison between experimental and simulated droplet size distributions at different injection pressures for both the convergent and the divergent nozzle. Reasonable agreement between experimental and simulated size distributions can be observed for all injection pressures. The results indicate that the droplet-size distribution becomes narrower with increasing injection pressure.
For both nozzles, the droplet size distributions at 1500 bar show the highest probability of small droplets. The distribution profiles confirm the above discussed (Fig. 8) finding that the droplet sizes decrease as the fuel injection pressure increases, irrespective of nozzle shape. Accordingly, the ratio of smaller droplets at 1000 bar is lower than at 1500 bar but higher than in the 600 and 200 bar case. Furthermore, the droplet size distributions at pressures 200 bar show comparatively higher probabilities of large droplets. The droplet sizes are more widely distributed and are shifted towards larger droplet sizes (right side).
The droplet size distributions for the divergent nozzle show larger droplet diameters compared to the convergent nozzle. However, it should be noted that the orifice diameter of the nozzles is different. Moreover, the droplet size distributions at injection pressures of 1000 and 1500 bar are quite similar, indicating that raising the injection pressure above 1000 bar may not result in further improvements of spray atomization with respect to creating smaller droplets. It might be possible that droplets reach a limiting low value at 1000 bar here, and all the energy gained from injection pressures above 1000 bar would be converted mainly into kinetic energy. This will be investigated in detail in a forthcoming publication.
In summary, increasing injection pressure has a substantial influence on droplet sizes. The mean droplet sizes are strongly reduced compared to the lowest pressure shown. The droplet size distributions also show a higher probability of finding smaller droplets at high injection pressures.
Spray-Induced Turbulence
The origin and transfer of a turbulent kinetic energy within the spray jet is investigated here with the aim to characterize the impact of nozzle design and injection pressure on turbulence generation (objective 3). Figure 10 shows the turbulent kinetic energy spectra for the divergent and the convergent nozzle. The spectra are calculated by sampling the velocity field data at a point 30 mm downstream the nozzle. The velocity data is collected at every time step after the fuel jet reaches the sampling location. Then, the spectra are constructed by postprocessing the velocity signal using the Fast Fourier Transformation (FFT). Note that the LES results shown are consistent with the traditional view of an equilibrium turbulence energy cascade (Pope 2000).
The spectra do not allow any specific conclusions here, but it can be observed that the divergent nozzle spray creates higher turbulent kinetic energy levels than the convergent nozzle spray at almost all frequencies.
Similar turbulence kinetic energy spectra were calculated for a point outside the spray core region (not shown). The purpose of such calculation was to identify the capability of the spray to generate turbulence outsize the spray-jet region. Similar results as shows in Fig. 10 were observed for both nozzles. The results indicate that the divergent nozzle spray has more potential to develop turbulence kinetic energy compared to the convergent nozzle spray not only in the spray core region but in the whole domain.
When the liquid fuel is injected into ambient gas at high velocities the gas flow quickly becomes turbulent due to strong momentum exchange between the liquid spray and the gas phase. A turbulent flow is comprised of eddies of different scales. One of the potential benefits of ultra-high fuel injection pressures is to enhance the spray-induced turbulence which can be used to promote efficient fuel-air mixing. The large scales of turbulence are characterized by the integral length scale. Therefore, in this work, the integral length scale of spray-induced eddies is calculated at different locations inside the spray chamber by means of the velocity correlation, as:
$$\begin{aligned} L_\delta = \int _{0}^{q} \frac{{u_\alpha ^{'}}(z)~{u_\alpha ^{'}}(z+r)}{ {u}_\alpha ^{'} (z)^2 } dr. \end{aligned}$$
(16)
Here, \({u_\alpha ^{'}}\) is the velocity fluctuation in \(\alpha\) direction, r is the distance between the two velocity vectors, and q is the length of the probe line. This two-point correlation function relates the velocity fluctuations of two velocity vector components to each other as a function of their distance r (Pope 2000). However, this classical two-point correlation is reasonable for homogeneous, isotropic turbulence with sufficient statistical data (e.g. via time or ensemble averaging) which is often not available when investigating highly transient sprays. Therefore, we use an alternative definition (Janas et al. 2017) that includes vortex and subsequent coherent structures:
$$\begin{aligned} L_\delta = \int _{0}^{q} \frac{{u_\alpha ^\delta }(z)~{u_\alpha ^\delta }(z+r)}{ {u}_\alpha ^{\delta } (z)^2 } dr, \end{aligned}$$
(17)
where, \(u^\delta\) is the deviation of the instantaneous (filtered) velocity \(\tilde{u}\) from the spatial mean value \(\bar{\tilde{u}}\) along a probe line. The modified function to calculate the integral length scale (Eqn. 17) is evaluated at 3 different vertical locations: x* = 0 mm, x* = 10 mm and x* = 30 mm (illustrated in Fig. 11). Figure 12 shows the integral length scale at different injection pressures for both nozzles at three probe locations. As a general trend it can be observed that higher fuel injection pressures tend to generate larger turbulence structures quicker than lower injection pressures. This is particularly obvious for the divergent nozzle. The final scale of the integral length scale does not depend much on the fuel injection pressure for a given nozzle type particularly along the spray axis (x* = 0 mm). However, the integral length scales at radial locations (x* = 10 mm and x* = 30 mm) clearly show the impact of higher injection pressures such as substantially larger length scale at the highest pressure compared to the lowest pressure. Similar trends can be observed for the convergent nozzle with steeper gradients during the creation of large turbulent eddies by the spray. The spray from the divergent nozzle creates slightly larger turbulence length scales which might have the potential to survive longer.
In summary, the divergent nozzle sprays create more turbulent kinetic energy than the convergent nozzle sprays. Sprays at higher injection pressure quickly generate larger turbulent structures compared to sprays at lower injection pressures. The final integral length scales along the spray axis is almost identical at all injection pressures, however, the impact of higher pressure on length scales is more pronounced at off-axis probe lines.
Air Entrainment
An efficient fuel-air mixing in any direct fuel injection system strongly depends on the entrainment of air into the spray region. Here, the air entrainment is quantified as the mass fluxes across a control line of length 40 mm (see Fig. 3) at different injection pressures (objective 4). The control line was parallel to the spray-axis with an offset of 20 mm. The velocity component on the probe line pointing towards and perpendicular to the spray-axis was considered as air entrainment. The entrainment rate was calculated at the time-step when the liquid penetration reached the bottom of the chamber.
Figure 13 shows simulation results of the spatially resolved normalized air entrainment flux along the control line for the convergent and the divergent nozzle at different fuel injection pressures. Because of different injection pressures, it was not possible to compare the entrainment flux directly, therefore, the comparison was made on normalized (by the maximum value for each nozzles) entrainment flux scale. In previous studies (Tomita et al. 1995) it was observed that air entrainment is higher close to the nozzle than further downstream.
Overall, the results in Fig. 13 confirm the previous study (Tomita et al. 1995). In particular, the spray from the divergent nozzle features the highest entrainment for all injection pressures except 1500 bar close to the nozzle and a continuous decrease further downstream. In comparison, the convergent nozzle starts with relatively low entrainment in the vicinity of the nozzle and reached a maximum value at 20 to 25 mm downstream for all expect the lowest injection pressure. The qualitative differences in the entrainment profiles along the control line for the different nozzles suggest an important impact of the nozzle shape on the large-scale flow structure.
The development of the normalized air entrainment rate during the complete injection process is summarized in Fig. 14. Here, the entrainment rate corresponds to the mean value along the control line. The figure shows both experimental data and simulation results for the convergent and the divergent nozzle at different injection pressures. Note that, the experimental air entrainment values are based on 2D data, however, 3D flow field data has been used to calculate the air entrainment rate in the simulation. The results indicate that the entrainment rate is significantly influenced by the injection pressure, i.e. entrainment rate was increased by injecting the fuel at high pressure. Similar result can be observed for both nozzles types. However, entrainment for the convergent nozzle dies out quickly while it remains persist longer for the divergent nozzle at the respective pressure. This result suggests that the divergent nozzle is more effective in keeping the flow motion. Simulation results also indicate the presence of a small recirculation zone in the beginning indicated by negative flux values. However, no such effect was observed in the measurement data, though, this could be due to resolution in time and space.
Figure 15 shows the total amount of air entrained over the control line (see Fig. 3) during the complete injection process. Interestingly, the divergent nozzle shows overall a higher amount of entrained air at all injection pressures compared to the convergent nozzle. This suggests that the divergent shape of the injector nozzle helps to generate large turbulent structures and subsequently support to entrain more air in the spray-jet. The total entrained air is larger at higher injection pressures irrespective of nozzle shapes. For the divergent nozzle, the entrained air at 1000 bar injection pressure is similar to 1500 bar injection pressure. This important result indicates that an injection pressure above a certain level (here 1000 bar) might not beneficial for overall air entrainment. This will be investigated in detail in subsequent simulation studies.