Influence of Cavitation in Common-Rail Diesel Nozzles on the Soot Formation Process through Measuring Soot Emissions

The influence of cavitation in common-rail diesel nozzles on the soot formation process has been analysed experimentally. The soot formation process was characterized by measuring soot emissions in a single-cylinder engine, which was mounted on a test bench equipped with an opacimeter. In order to do this, operating conditions where the soot oxidation process was equivalent were chosen, whereby differences in the soot formation process were possible to be analysed. The results achieved confirm that cavitation provokes a soot formation process reduction. This reduction can be attributed by combining results of three effects: a reduction of the effective diameter, an increase in effective injection velocity, and an increase in turbulence level inside the nozzle orifice leading to a longer lift-off length. The three effects lead to a decrease in relative fuel/air ratio at the lift-off, therefore explaining the soot formation reduction.


Introduction
Soot emissions are one of the main pollutants from diesel engines, which are regulated by environmental regulations [1][2][3][4][5]. Soot emissions are the result of a balance between the soot formation process and that of soot oxidation [6]. One of the alternatives to decrease these soot emissions is to reduce their formation. According to López et al. [7], Pires et al. [8], and Xu et al. [9], the soot formation process depends mainly on the relative fuel/air ratio at the lift-off length.
Several studies have focused on analysing the influence on the lift-off length and its influence on the soot formation process of diverse parameters, namely, the in-cylinder air density and temperature [10,11], the injection pressure [11,12], the nozzle orifice diameter [13], the nozzle geometry [14], and the oxygen concentration [15]. Concerning the nozzle geometry, a physical phenomenon called cavitation can appear or not, depending on the nozzle geometry and operating conditions, such as injection pressure and backpressure. To be more precise, this physical phenomenon appears due to a local pressure drop at the inlet of the nozzle hole as a consequence of the increase in fuel flow velocity inside the injector, provoked by the high injection pressure levels employed [16]. It is well known that this phenomenon has positive effects on different parameters such as the nozzle effective diameter, the effective injection velocity, and the mixing process. For instance, López et al. [17], investigated the effects of cavitation on the nozzle effective diameter, the effective injection velocity, and the spray cone angle. They reported that the nozzle effective diameter decreases with the increase in the cavitation level, as well as, that cavitation provokes an increase in both injection velocity and spray cone angle, which lead to an improvement in the mixing process. Salvador et al. [18], analysed the hydraulic performance of three diesel nozzles with different degrees of conicity, and observed also an increase in the effective injection velocity, when the cavitation phenomenon appears. Similarly, Guo et al. [19], investigated the effects of the internal flow in an optical diesel nozzle on the spray behaviour under cavitating conditions. They also observed that cavitation provokes a remarkable increase in the spray cone angle.
The positive effects aforementioned provoked by cavitation are the main reason why several works have focused on studying the impact of cavitation on the combustion process. Some of these works studied the impact of cavitation on soot emissions. For instance, Fimml et al. [20] investigated the influence of cavitation in diesel nozzles on the combustion process and they observed remarkable differences in both burn rates and soot emissions, where the soot emissions values of the cavitating nozzle are higher than those of the non-cavitating nozzle. Benajes et al. [21] studied the effects of nozzle orifice convergence, and cavitation on the combustion process. They found that both convergence and cavitation provoke an improvement of the mixing process, hence, reducing soot emissions. Other studies analysed the impact of cavitation on the soot formation process by measuring the soot radiation. For example, Som et al. [22] investigated the influence of the diesel nozzle geometry on the injection and combustion processes through the correlation between the internal flow and spray simulations, and observed that the lift-off length values of the cylindrical nozzle are higher than those of the conical nozzle, provoking a soot formation reduction. Similarly, Maes et al. [23], analysed the influence of cavitation on the mixing and combustion processes, utilizing n-dodecane and two diesel nozzles, one of them promoting the appearance of the cavitation phenomenon, whilst the other one preventing this phenomenon. They found that the soot values of the cavitating nozzle are higher than those of the non-cavitating nozzle, attributing their result to the higher equivalence ratio at the lift-off length. However, they also observed an opposite trend at low temperatures due to the different mixing processes. In a previous work [24] performed by the present authors, the effect of cavitation on the lift-off length and soot formation process was also analysed by measuring the soot radiation and using a non-cavitating nozzle and a cavitating nozzle. They confirmed that cavitation provokes an increase in the effective injection velocity and a decrease in the nozzle effective diameter, finding also that cavitation provokes an increase in the lift-off length. Hence, because of this increased distance, the equivalence ratio at the lift-off length was reduced, leading to a reduction in soot formation. In addition, it is worthy to note that there are very limited studies that analyse these aspects through measuring soot emissions.
In order to clarify these controversial results presented by the last cited authors, it is important to improve the comprehension of the influence of cavitation on the soot formation process. Therefore, the present work aims to address the impact of cavitation on the soot formation process through measuring engine-out soot emissions in a single-cylinder engine with the use of an opacimeter. For doing so, some operating conditions where the soot oxidation process is equivalent will be chosen, whereby it will be possible to analyse differences in the soot formation process. More details about this novel methodology will be presented later. Moreover, the same diesel nozzles presented in [24] will be employed, making use, when necessary, of the results also reported in [24]. Finally, it is expected that cavitation provokes a reduction in soot formation.

Nozzles and Fuel
Two nozzles with three orifices, which were installed in a piezoelectric diesel injector holder were used. One of them prevents the appearance of the cavitation phenomenon, whilst the other one exhibits and promotes this phenomenon. The nozzles studied have different degrees of conicity. The degree of conicity is characterized by the k-factor, which is defined by Equation (1) [17]: where d out is the nozzle orifice outlet diameter and d in is the nozzle orifice inlet diameter. In a previous study by Payri et al. [24], both nozzles were first used. In Table 1, the geometrical details of the nozzles which were determined by utilizing the silicone methodology [25] are synthetized. Table 1. Geometrical details of the nozzles employed in the study [24].

Single-Cylinder Engine and Opacimeter
The single-cylinder engine is equivalent to the engines used in passenger cars. It is derived from the PSA Peugeot-Citroën engine DV6-TED4. In addition, it has a multivalve cylinder head (four valves per cylinder). The technical specifications of the single-cylinder engine are described in Table 2. The engine was mounted in a test bench, with the components necessary for its proper operation, as is shown in Figure 1. More details about the test bench are available in [26]. In addition, in Table 3, the operating conditions employed in the tests are described. The opacimeter used was an AVL 415. Its measuring principle consists in passing a sample of exhaust gases through a white paper filter with a known light reflection index, and subsequently through a photoelectric cell. The darkening degree of the paper previously mentioned depends mainly on the soot concentration, which is the parameter finally determined. Hence, the smoke measurement is based on the comparison of the light reflection index. The scale of the equipment is comprised between a minimum value (0 FSN) and the absolutely black paper (10 FSN), where FSN (Filter Smoke Number) is the unit assigned to the scale, previously mentioned. By means of Equation (2) it is possible to convert the FSN unit into mg/m 3 [27].
It is worthy to note that Equation (2), which is similar to that developed by Christian et al. [28], has been used in the present research for the units conversion. In addition, it is important to mention that the sample is extracted at nearly atmospheric pressure from the exhaust system, and the amount of sample is controlled directly by the equipment. Besides, the gas sample is cooled down up to ambient temperature before passing through the paper filter. The soot emission index (I soot ) can be expressed in g/kg f uel by Equation (3) [27].
whereṁ f is the mass flow rate of fuel,ṁ a is the mass flow rate of air, and ρ re f is the reference density, which is 1.2 kg/m 3 , value obtained at the temperature and pressure in that the opacimeter performs the measurement. In the present work the ρ re f has been assumed constant. It is worthy to note that in the present work, the soot emissions measured in the engine are converted to the mass values through Equation (3).

Combustion Diagnostic Model
The combustion diagnostic model called CALMEC [29] was employed. Zero-dimensional and single-zone are the main characteristics of this model, as well as the fact that it is based on the solution of the first law of thermodynamics for an open system, and on the state equation. For simplicity, in this model it is considered that pressure and temperature are uniform inside the cylinder. The main parameters obtained from the model were the Heat Release Fraction (HRF), which is associated with the thermal energy released during the combustion process and it depends on both crank angle and some additional information related to each engine cycle. More specifically, the start of combustion, defined as the crank angle position in which 2% of cumulated heat has been released, was obtained. Additional information related to the CALMEC model is available in [29].

Hydraulic Characterization
From the hydraulic characterization of the diesel nozzles previously performed and reported by Payri et al. [24], flow characteristics parameters such as velocity coefficient C v , which characterizes the effective injection velocity, and nozzle effective diameter d e f f were determined. The flow characteristic parameters are described in Table 4.

Soot Formation Process Characterization from the Soot Emissions
The soot formation process will be characterized from the soot emissions measurement. For this, a single-cylinder engine and an opacimeter, previously described in Section "Single-cylinder engine and opacimeter", will be employed. With regard to the testing methodology, different aspects can be highlighted: (1) the operating condition employed in the engine when using the conical and cylindrical nozzles were the same: the operating conditions have been previously described in Table 3. (2) In order to work with an identical global fuel/air ratio (FAR) in both nozzles and with both p rail levels of 76 MPa and 146 MPa, the same fuel mass has been injected. (3) An injection pulse of around 2 ms has been used to ensure a diffusion combustion phase, i.e., combustion controlled by mixing. (4) Finally, in order to vary the relative position of the combustion process in the cycle, when utilizing the studied nozzles and p rail levels of 76 MPa and 146 MPa, a sweep of injection timings was performed.

Methodology for Analysis of the Results
The methodology is based on establishing a criterion allowing to ensure an equivalent oxidation process in the cases to be compared, to analyse possible differences in the soot formation process. To do so, Molina's work [27] will be considered, where T b−75% is proposed as the temperature representative of oxidation at end-of-combustion, when 75% of the total heat has been released, and this parameter correlated quite well with the final soot emissions at a given operating point, particularly when the start of injection (SOI) was swept. In the present work, since cases with the same injected fuel mass and under the same engine operating conditions are compared, the same T b−75% is achieved if the cases taken for comparison have the same CA75, i.e., with the same position of the combustion process in the cycle, where 75% of the fuel mass has been burned. Besides, this also guarantees the same oxygen content in the compared cases, these two parameters (temperature and oxygen concentration) being the main controllers of the soot oxidation process. With this methodology, an equivalent soot oxidation capacity is warranted, and differences in the soot formation process could be observed when analysing the final soot emissions.
The CA75 was obtained through the heat release fraction, which was determined by employing the combustion diagnostic model, CALMEC previously described in the "Combustion diagnostic model" section. The evolution of the HRF (non-dimensional) as a function of the crank angle is shown in Figure 2, for several injection timings viz. −2.4°, −0.4°, +1.6°, +3.6°, +5.6°, +7.6°, +9.6°, and +11.6°After Top Dead Center (ATDC), when using the conical nozzle and a p rail level of 146 MPa. As a conclusion, it can be ensured that the oxidation process will be equivalent in two cases with the same CA75, and this will allow us to analyse possible differences in the soot formation process. Figure 3 shows the smoke behaviour versus CA75, for different injection timings when using the conical and cylindrical nozzles and p rail levels of 76 MPa and 146 MPa.  Figure 4 shows the evolution of the I soot (as was shown in Equation (3)) versus CA75, for several injection timings using the conical and cylindrical nozzles, and for p rail levels of 76 MPa and 146 MPa. Moreover, a fitting curve for I soot values is also shown in the figure. This fitting was performed up to where both nozzles showed similar behaviour. These fittings were carried out for two reasons: (1), to filter the possible experimental variations and, (2), to obtain values of CA75 not tested through performing interpolation and/or extrapolation. Finally, in Figure 4, a region highlighted with a grey rectangle is also shown, which corresponds to the range where the results will be analysed. Before analysing the results, it is worthy to highlight that the parameter of higher influence on the soot formation process is the equivalence fuel/air ratio at the lift-off (F rLOL ), as it was mentioned in the introduction section, whose functional dependence is the following [30]:

Effects of Cavitation on the Soot Formation Process
where LOL is the lift-off length, which is defined as the distance from the nozzle orifice exit and the start the flame; L f lame is the flame length, which is defined as the distance from the nozzle orifice exit and the flame tip. The functional dependence is defined by Equation (6) [31]: where (m a /m f ) st is the stoichimetric air-fuel ratio, YO 2 is the oxygen mass fraction, d e f f is the effective diameter, and finally ρ a and ρ f are the air and fuel density, respectively. Considering that most of the terms in Equation (6) are constant when taking them at CA75, the final expression for L f lame is: Equation (8) is obtained from combination of Equations (5) and (7).
where K is a constant of proportionality, ( ∆p · C v ) is proportional to the effective injection velocity, and T a is the air temperature. It should be noted that the proportionality constant can differ from one nozzle to the other. As a first approach, the same value will be assumed for both nozzles, and later, in view of the results, this assumption will be revised. Combining Equations (8) and (9), and considering also that all tests were carried out at the same in-cylinder conditions (air temperature and density, and oxygen mass fraction), and that the comparison will be performed at the same p rail level, the F rLOL is scaled by Equation (10).
It is worthy to note that F rLOL is determined employing the d e f f and C v values previously described in Table 4. Figure 5a shows the evolution of I soot versus F rLOL , for different cases with the same CA75, viz. CA75 = 12, CA75 = 14, CA75 = 16, and CA75 = 18, covering the region marked in Figure 4, using the conical and cylindrical nozzles. Whilst, in Figure 5b, the values of I soot presented in Figure 5a are normalized by the value of I soot from the conical nozzle, hence all values of I soot for the conical nozzle are 1. This manner to proceed was already applied systematically in the work preceding this one [24]. Despite the complexity involved in the analysis of the final soot emissions, which are the result of a balance between the soot formation process and that of soot oxidation, there are two points to highlight from the results presented in Figure 5b. For the observation, attention will be focused on the I soot behaviour in both the conical and cylindrical nozzles, but individually in each of the p rail levels tested. The two points to highlight are: (1) the cylindrical nozzle produces more soot compared to the conical one. These results were also observed by Kong et al. [34], when they analysed the influence of nozzle geometry on the combustion process using a single-cylinder engine. This behaviour can be attributed to the larger effective diameter of the cylindrical nozzle compared to that of the conical nozzle, which leads to a higher F rLOL [24]. (2) It is noted that, as the cavitation intensity increases in the cylindrical nozzle, which is associated to the p rail level, the soot formation is reduced.
This behaviour can be due to two reasons: (1) cavitation provokes a reduction in the effective diameter, therefore decreasing the equivalence fuel/air ratio at the lift-off length; (2) it also produces an increase in C v , hence increasing the lift-off length and diminishing the corresponding equivalence fuel/air ratio [24]. It is worthy to note that the experimental and analysis methodology used in the present study has allowed isolating the effect of cavitation on soot formation from other effects, such as the nozzle diameter or permeability, thus reaching the statements previously described.
Moreover, it can be seen in Figure 5b that, if all straight lines connecting the red dots are extrapolated (see the grey lines), these ones cross the y = 1 value (i.e., conical nozzle's reference) in x > 1 values. This indicates that with cavitation, an additional effect takes place, apart from the reduction of d e f f and the increase in C v . Thanks to this additional effect, it is possible to have the same soot formation with a higher d e f f or a lower C v than those of the conical nozzle. As already indicated in a previous study by Payri et al. [24], and based on Equation (8), this additional effect can be an increase in the lift-off length provoked by cavitation, which most probably is caused by the higher turbulence level of the flow exiting the nozzle orifice, leading to a stabilization of the lift-off further downstream. In a previous work [24], the hypothesis previously described was first raised and partially confirmed by LOL visualization results. Now, in the present work, with a significantly different approach, the hypothesis appears again, reinforcing its validity a bit more. In other words, this result indicates that the proportionality constant in Equation (9) is not the same for both nozzles. If the correct proportionality constant would be used for each nozzle, the point where all lines converge in Figure 5b would be placed at point (1,1). Based on this, it can be concluded that the LOL increases in a factor of 1.08 when cavitation appears.

Conclusions
In the present work, the effects of cavitation on the soot formation process through measuring soot emissions, which are the result of a balance between the soot formation process and that of soot oxidation have been explored. To do so, a novel methodology has been employed, which consists in choosing cases with the same CA75, where there is an equivalent soot oxidation process. Hence differences in the soot formation process were possible to be analysed. Now, the main conclusions reached in the present work will be described.
The cylindrical nozzle produces more soot formation compared to the conical nozzle in about 84% and 77.5% for the level of p rail of 76 MPa and 146 MPa, respectively. Moreover, as the cavitation intensity increases in the cylindrical nozzle, which is associated with the p rail level, the soot formation is reduced by about 53.2% from 76 MPa to 146 MPa. This reduction can be attributed by combining results of three effects, namely: a reduction of the effective diameter, an increase in C v , and an additional effect observed on the soot formation process when cavitation phenomenon appears, which most probably is related to an increase in turbulence level inside the nozzle orifice; leading to a lift-off length increases in a factor of 1.08. The three effects lead to a reduction in equivalence fuel/air ratio at the lift-off length by about 3.7%, therefore explaining the soot formation reduction.

Acknowledgments:
The authors would like to thank Gabriel Alcantarilla and Santiago Molina, who are members of CMT-Motores Térmicos, for the support in performing the experimental measurements in the single-cylinder engine.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: Outlet of the nozzle orifice rail Common-rail re f Reference