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Selection of an Appropriate Pre-Injection Pattern in a Marine Diesel Engine Through a Multiple-Criteria Decision Making Approach

In the present work, a numerical model was developed to analyze a commercial diesel engine. The adequacy of this model was validated using experimental results. This model was employed to study several pre-injection strategies. Particularly, the pre-injection rate, duration and starting instant were analyzed in the ranges 5% to 25%, 1° to 5° and −22° to −18°, respectively. The effect on consumption and emissions of NOx, CO, and HC wereas evaluated. Since some of these configurations have opposite effects on consumption and/or emissions, it is necessary to develop a formal tool to characterize the most appropriate injection pattern. To this end, a multiple-criteria decision making approach was employed. It was found that the injection duration must remain as low as possible due to significant reductions in NOx. The most appropriate injection pattern resulted 1° pre-injection duration, 20% pre-injection rate, and −19° pre-injection starting instant. This configuration leads to increments of 6.7% in consumption, 3.47% in CO, and 3.83% in HC but reduces NOx by 34.67% in comparison with the case without pre-injection.


Introduction
It is well known that diesel engines are efficient thermal machines but emit significant levels of harmful gases such as CO 2 , Particulate Matter (PM), NO x , CO, HC and SO x [1]. Between these, PM and NO x are especially important in diesel engines. Smoke emissions, related to PM, mostly composed of soot, are related to several diseases but are not globally regulated [2]. On the other hand, ever increasing NO x emission limits have been imposed by regional and international authorities [3]. According to this, several procedures have been developed in the recent years to reduce NO x emissions in diesel engines such as EGR, water injection, modification of the injection parameters and after-treatments [4][5][6][7]. Between these measurements, this paper focuses on multiple injection strategies using pilot injections. This strategy affects mixing and combustion [8]. Several works about the advantages and disadvantages of pilot injections can be found in literature. One of the main disadvantages is that soot can increase because pilot injections aggravate spray characteristics and particulates can be formed at the rich region [9,10]. In order to avoid this problem, some authors recommend combining multiple injections with other systems such as EGR [11] or high injection pressures [12], while other researchers indicate that it is possible to obtain both NO x and particulate reduction using only multiple injections. In this regard, Carlucci et al. [13] analyzed the pilot injection timing and duration and found that NO x emission levels are mainly influenced by the pilot duration, whereas smoke emission is influenced by both variables. Tanaka et al. [14] analyzed the time and quantity of the pilot injection. Benajes et al. [15] analyzed the effect of the dwelling time, i.e., the time between two consecutive injections, obtaining reductions

Materials and Methods
The engine analyzed in the present work is the Wärtsilä 6 L 46. This is a four-stroke diesel engine with six cylinders. Each cylinder presents two intake and two exhaust valves. The fuel injector has 10 holes and is placed at the center of the cylinder head. The fuel is injected directly into the cylinder since it is a direct injection engine.
The geometry and mesh were realized using SolidEdge and Gambit softwares, respectively. A grid independence study was carried out to provide its adequacy. The software OpenFOAM was employed for the CFD simulations. OpenFOAM was chosen because it is an open software which allows a complete manipulation of the code. The simulation started at 360 • Crank Angle After Top Dead Center (CA ATDC) and the whole cycle was analyzed. As boundary conditions, the heat transfer from the cylinder was modelled as a combined convection-radiation. The RANS (Reynolds-averaged Navier-Stokes) equations of conservation of mass, momentum and energy were solved. The k-ε was employed as the turbulence model due to its robustness and reasonably accuracy for a wide range of turbulent flows. As fuel droplet breakup, the Kelvin-Helmholtz and Rayleigh-Taylor breakup models [46] were employed, and the Dukowicz model [47] for the heat-up and evaporation. Regarding the chemical kinetics, a reaction mechanism was programmed by combining the following three kinetic schemes: Fuel Consumption (SFC) obtained numerically and experimentally at several loads are indicated in Figure 1. This figure shows a reasonable correspondence between numerical and experimental results. The in-cylinder pressure obtained numerically and experimentally at 100% load is shown in Figure 2. This figure also shows a satisfactory correspondence between experimental and numerical results. A certain error was inevitable due to both numerical and experimental handicaps. On the one hand, the instruments employed to characterize experimental measurements have a certain tolerance and, on the other hand, numerical errors are introduced due to the discretization processes and the hypothesis assumed to simplify the governing equations.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 13 Figure 1. This figure shows a reasonable correspondence between numerical and experimental results. The in-cylinder pressure obtained numerically and experimentally at 100% load is shown in Figure 2. This figure also shows a satisfactory correspondence between experimental and numerical results. A certain error was inevitable due to both numerical and experimental handicaps. On the one hand, the instruments employed to characterize experimental measurements have a certain tolerance and, on the other hand, numerical errors are introduced due to the discretization processes and the hypothesis assumed to simplify the governing equations.

Results and Discussion
Once the numerical model was validated with experimental measurements, it was used to analyze the results of several pre-injection patterns. Five pre-injection rates were employed: 5%, 10%, 15%, 20% and 25%; five pre-injection durations: 1° Crank Angle (CA), 2° CA, 3° CA, 4° CA and 5° CA; and five pre-injection starting instants: −22° CA ATDC, −21° CA ATDC, −20° CA ATDC, −19° CA ATDC and −18° CA ATDC. These ranges were chosen according to a previous paper [43], in which it  Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 13 Figure 1. This figure shows a reasonable correspondence between numerical and experimental results. The in-cylinder pressure obtained numerically and experimentally at 100% load is shown in Figure 2. This figure also shows a satisfactory correspondence between experimental and numerical results. A certain error was inevitable due to both numerical and experimental handicaps. On the one hand, the instruments employed to characterize experimental measurements have a certain tolerance and, on the other hand, numerical errors are introduced due to the discretization processes and the hypothesis assumed to simplify the governing equations.

Results and Discussion
Once the numerical model was validated with experimental measurements, it was used to analyze the results of several pre-injection patterns. Five pre-injection rates were employed: 5%, 10%, 15%, 20% and 25%; five pre-injection durations: 1 • Crank Angle (CA), 2 • CA, 3 • CA, 4 • CA and 5 • CA; and five pre-injection starting instants: −22 • CA ATDC, −21 • CA ATDC, −20 • CA ATDC, −19 • CA ATDC and −18 • CA ATDC. These ranges were chosen according to a previous paper [43], in which it was obtained that wider ranges lead to excessive increments in NO x emissions or consumption. Taking into account these values of pre-injection rates, durations and starting instants, a total of Appl. Sci. 2020, 10, 2482 4 of 12 125 cases were analyzed. These are summarized in Figure 3. SFC and emissions of NO x , CO and HC were characterized for these 125 cases.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 13 was obtained that wider ranges lead to excessive increments in NOx emissions or consumption. Taking into account these values of pre-injection rates, durations and starting instants, a total of 125 cases were analyzed. These are summarized in Figure 3. SFC and emissions of NOx, CO and HC were characterized for these 125 cases. As indicated previously, a MCDM method was employed. The first step in MCDM approaches consists on defining the decision tree with the relative importance of each parameter, Table 1. Two requirements (general aspects) were considered: consumption and emissions. The second level represents the sub-requirements (specific aspects). The relative importance of each requirement and sub-requirement must be defined too. In the present work, this importance was distributed equally, i.e., the same importance was given to SFC and emissions: 50% (α = 0.5 in per unit basis) for each one. Regarding emissions, the same importance was given to NOx, CO and HC: 33.3% (β = 0.333 in per unit basis) for each one. It is worth mentioning that other scenarios could also be possible in case it is necessary to provide other levels of importance.
where Xi is the value of the sub-requirement i and Xref the value corresponding to the case without pre-injection, i.e., SFC = 172 g/kWh, NOx = 13.3 g/kWh, CO = 4.5 g/kWh and HC = 5.5 g/kWh. Once each indicator was transformed into its variation in per unit basis, the global adequacy index, AI, was computed by Equation (2).
where αi is the weight of each requirement and βi the weight of each sub-requirement in per unit basis. As indicated previously, a MCDM method was employed. The first step in MCDM approaches consists on defining the decision tree with the relative importance of each parameter, Table 1. Two requirements (general aspects) were considered: consumption and emissions. The second level represents the sub-requirements (specific aspects). The relative importance of each requirement and sub-requirement must be defined too. In the present work, this importance was distributed equally, i.e., the same importance was given to SFC and emissions: 50% (α = 0.5 in per unit basis) for each one. Regarding emissions, the same importance was given to NO x , CO and HC: 33.3% (β = 0.333 in per unit basis) for each one. It is worth mentioning that other scenarios could also be possible in case it is necessary to provide other levels of importance. The next step was to calculate the variation of each sub-requirement respect to the case without pre-injection, in per unit basis, Equation (1).
where X i is the value of the sub-requirement i and X ref the value corresponding to the case without pre-injection, i.e., SFC = 172 g/kWh, NO x = 13.3 g/kWh, CO = 4.5 g/kWh and HC = 5.5 g/kWh. Once each indicator was transformed into its variation in per unit basis, the global adequacy index, AI, was computed by Equation (2).
where α i is the weight of each requirement and β i the weight of each sub-requirement in per unit basis. The minimum value of the AI is the most adequate solution. It was determined using an in-house code programmed using the open software GNU Octave. For the parameters analyzed in the present work, the minimum AI is −0.0122, corresponding to −19 • CA ATDC pre-injection starting instant, 20% pre-injection rate and 1 • CA pre-injection duration. The results are detailed in Appendix A. As can be seen in this appendix, the minimum AI value was obtained in the ninety-first case analyzed. On a per-unit basis, SFC varies by 0.067; NO x −0.3467, CO 0.0347 and HC 0.0383, corresponding to an SFC increment of SFC 6.7%; NO x reduction of 34.7%, CO increment of 3.47% and HC increment of 3.83% in comparison with the case without pre-injection. Despite the increments in SFC, CO and HC, these solution results are the most appropriate because the increments are low and the NO x reduction is too significant.
The results shown in Appendix A indicate that the influence of CO and HC in the AI is not too important due to the low variation of these emissions with the pre-injection rate, duration and starting instant. On the other hand, SFC and NO x emissions are more sensitive. A representative quantity of pre-injection is necessary, specifically 20%, due to the important reduction on NO x emissions. Nevertheless, if this pre-injection rate is increased, it leads to important increments in SFC and, to a lesser extent, CO and HC emissions. Regarding the pre-injection instant, early pre-injections are appropriate to reduce NO x but the increase increment in SFC is considerable; for this reason, a -19 • CA ATDC was obtained. Finally, the injection duration mainly affects to NO x and short injections lead to considerable NO x reductions. The goal of NO x reduction using pre-injections is to control the combustion temperature. It is well known that high combustion temperatures promote NO x formation [56]. In order to control the combustion temperature, it is necessary to rigorously inject the fuel at the optimum instant. It is worth mentioning that in practical applications it is not possible to reduce the injection duration at the desirable level. For instance, the present engine is a four-stroke medium-speed model which runs at 500 rpm, which corresponds to 0.00033 s to reach 1 • CA. Some current piezo-injectors are able to switch on and off in tens of microseconds but solenoid or electromagnetic injectors have longer response times. For this reason, pre-injections shorter than 1 • CA were not analyzed in the present work. Using 1 • CA pre-injection duration, the AI is represented in Figure 4. As can be seen, the minimum value of AI, −0.0122 is reached using 20% pre-injection rate and −19 • CA ATDC pre-injection starting instant, as indicated above.
house code programmed using the open software GNU Octave. For the parameters analyzed in the present work, the minimum AI is −0.0122, corresponding to −19° CA ATDC pre-injection starting instant, 20% pre-injection rate and 1° CA pre-injection duration. The results are detailed in Appendix A. As can be seen in this appendix, the minimum AI value was obtained in the ninety-first case analyzed. On a per-unit basis, SFC varies by 0.067; NOx −0.3467, CO 0.0347 and HC 0.0383, corresponding to an SFC increment of SFC 6.7%; NOx reduction of 34.7%, CO increment of 3.47% and HC increment of 3.83% in comparison with the case without pre-injection. Despite the increments in SFC, CO and HC, these solution results are the most appropriate because the increments are low and the NOx reduction is too significant.
The results shown in Appendix A indicate that the influence of CO and HC in the AI is not too important due to the low variation of these emissions with the pre-injection rate, duration and starting instant. On the other hand, SFC and NOx emissions are more sensitive. A representative quantity of pre-injection is necessary, specifically 20%, due to the important reduction on NOx emissions. Nevertheless, if this pre-injection rate is increased, it leads to important increments in SFC and, to a lesser extent, CO and HC emissions. Regarding the pre-injection instant, early pre-injections are appropriate to reduce NOx but the increase increment in SFC is considerable; for this reason, a -19° CA ATDC was obtained. Finally, the injection duration mainly affects to NOx and short injections lead to considerable NOx reductions. The goal of NOx reduction using pre-injections is to control the combustion temperature. It is well known that high combustion temperatures promote NOx formation [56]. In order to control the combustion temperature, it is necessary to rigorously inject the fuel at the optimum instant. It is worth mentioning that in practical applications it is not possible to reduce the injection duration at the desirable level. For instance, the present engine is a four-stroke medium-speed model which runs at 500 rpm, which corresponds to 0.00033 s to reach 1° CA. Some current piezo-injectors are able to switch on and off in tens of microseconds but solenoid or electromagnetic injectors have longer response times. For this reason, pre-injections shorter than 1° CA were not analyzed in the present work. Using 1° CA pre-injection duration, the AI is represented in Figure 4. As can be seen, the minimum value of AI, −0.0122 is reached using 20% pre-injection rate and −19° CA ATDC pre-injection starting instant, as indicated above. The consumption against the pre-injection rate and starting instant is shown in Figure 5. This figure refers to 1° CA pre-injection duration. As can be seen, early pre-injections promote considerable increase increments in SFC, as indicated above. On the other hand, the pre-injection rate also promotes increase increments in SFC considerably. The consumption against the pre-injection rate and starting instant is shown in Figure 5. This figure refers to 1 • CA pre-injection duration. As can be seen, early pre-injections promote considerable increase increments in SFC, as indicated above. On the other hand, the pre-injection rate also promotes increase increments in SFC considerably. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13 . Figure 5. SFC against R and S. Pre-injection duration 1° CA.
NOx emissions against the pre-injection rate and starting instant are indicated in Figure 6. This figure refers to 1° CA pre-injection duration. As can be seen, early pre-injections promote reductions in NOx, but increment SFC, as indicated above. On the other hand, the pre-injection rate considerably reduces NOx but also increments SFC. These figures refer to 1° CA pre-injection duration. As can be seen, both CO and HC are sensitive to the pre-injection rate and starting instant. Nevertheless, the influence of CO and HC in the results is low due to their low variation.  NO x emissions against the pre-injection rate and starting instant are indicated in Figure 6. This figure refers to 1 • CA pre-injection duration. As can be seen, early pre-injections promote reductions in NO x , but increment SFC, as indicated above. On the other hand, the pre-injection rate considerably reduces NO x but also increments SFC.
NOx emissions against the pre-injection rate and starting instant are indicated in Figure 6. This figure refers to 1° CA pre-injection duration. As can be seen, early pre-injections promote reductions in NOx, but increment SFC, as indicated above. On the other hand, the pre-injection rate considerably reduces NOx but also increments SFC. These figures refer to 1° CA pre-injection duration. As can be seen, both CO and HC are sensitive to the pre-injection rate and starting instant. Nevertheless, the influence of CO and HC in the results is low due to their low variation.   These figures refer to 1 • CA pre-injection duration. As can be seen, both CO and HC are sensitive to the pre-injection rate and starting instant. Nevertheless, the influence of CO and HC in the results is low due to their low variation.
NOx emissions against the pre-injection rate and starting instant are indicated in Figure 6. This figure refers to 1° CA pre-injection duration. As can be seen, early pre-injections promote reductions in NOx, but increment SFC, as indicated above. On the other hand, the pre-injection rate considerably reduces NOx but also increments SFC. These figures refer to 1° CA pre-injection duration. As can be seen, both CO and HC are sensitive to the pre-injection rate and starting instant. Nevertheless, the influence of CO and HC in the results is low due to their low variation.

Conclusions
The present work proposes a numerical model to analyze the commercial diesel engine Wärtsilä 6 L 46. Once validated, the numerical model was employed to analyze 125 injection patterns with different values of pre-injection rate, duration and starting instant in the ranges 5% to 25%, 1° CA to 5° CA and −22° CA ATDC to −18° CA ATDC, respectively. Due to this large number of results and the fact that these parameters can lead to different and opposite effects, it is difficult to determine the most adequate injection pattern. According to this, a MCDM approach was employed to select the most appropriate injection pattern. The effects on consumption and emissions of NOx, CO and HC were characterized. It was found that the injection duration must remain as lower as possible due to significant reductions in NOx. The most appropriate injection pattern was shown in the 1° CA preinjection duration, 20% pre-injection rate and −19° CA ATDC pre-injection starting instant. This injection pattern leads to increases in 6.7% in SFC, 3.47% in CO and 3.83% in HC but reduces NOx by 34.67% in comparison with the case without pre-injection. Future works will focus on analyzing other parameters such as number of pre-injections, dwelling time and injection angle, as well as other engines.

Acknowledgments:
The authors would like to express their gratitude to Norplan Engineering S.L. and recommend the courses "CFD with OpenFOAM" and "C ++ applied to OpenFOAM" available at www.technicalcourses.net.

Conflicts of Interest:
The authors declare no conflict of interest. Table A1 lists the results of the 125 cases analyzed by the MCDM approach developed in the present work. Five pre-injection starting instants are included: −22° CA ATDC (Crank Angle After Top Dead Center), −21° CA ATDC, −20° CA ATDC, −19° CA ATDC, and −18° CA ATDC; five preinjection rates: 5%, 10%, 15%, 20%, and 25%; and five pre-injection durations: 1° CA (Crank Angle), 2° CA, 3° CA, 4° CA, and 5° CA. Table A1 also includes the variation of SFC, NOx, CO and HC in per unit basis, as well as the AI obtained for each case analyzed. The minimum AI, which represents the most adequate solution, is highlighted. As can be seen, this minimum value was obtained for the 91th case, corresponding to −19° CA ATDC pre-injection starting instant, 20% pre-injection rate, and 1° CA pre-injection duration, leading to variations of 0.067 in SFC, −0.3467 in NOx, 0.0347 in CO and 0.0383 in HC. In a per cent basis, these values correspond to a SFC increment of 6,7%, NOx reduction

Conclusions
The present work proposes a numerical model to analyze the commercial diesel engine Wärtsilä 6 L 46. Once validated, the numerical model was employed to analyze 125 injection patterns with different values of pre-injection rate, duration and starting instant in the ranges 5% to 25%, 1 • CA to 5 • CA and −22 • CA ATDC to −18 • CA ATDC, respectively. Due to this large number of results and the fact that these parameters can lead to different and opposite effects, it is difficult to determine the most adequate injection pattern. According to this, a MCDM approach was employed to select the most appropriate injection pattern. The effects on consumption and emissions of NO x , CO and HC were characterized. It was found that the injection duration must remain as lower as possible due to significant reductions in NO x . The most appropriate injection pattern was shown in the 1 • CA pre-injection duration, 20% pre-injection rate and −19 • CA ATDC pre-injection starting instant. This injection pattern leads to increases in 6.7% in SFC, 3.47% in CO and 3.83% in HC but reduces NO x by 34.67% in comparison with the case without pre-injection. Future works will focus on analyzing other parameters such as number of pre-injections, dwelling time and injection angle, as well as other engines.

Acknowledgments:
The authors would like to express their gratitude to Norplan Engineering S.L. and recommend the courses "CFD with OpenFOAM" and "C ++ applied to OpenFOAM" available at www.technicalcourses.net.

Conflicts of Interest:
The authors declare no conflict of interest. Table A1 lists the results of the 125 cases analyzed by the MCDM approach developed in the present work.  Table A1 also includes the variation of SFC, NO x , CO and HC in per unit basis, as well as the AI obtained for each case analyzed. The minimum AI, which represents the most adequate solution, is highlighted. As can be seen, this minimum value was obtained for the 91th case, corresponding to −19 • CA ATDC pre-injection starting instant, 20% pre-injection rate, and 1 • CA pre-injection duration, leading to variations of 0.067 in SFC, −0.3467 in NO x , 0.0347 in CO and 0.0383 Appl. Sci. 2020, 10, 2482 8 of 12 in HC. In a per cent basis, these values correspond to a SFC increment of 6,7%, NO x reduction of 34.7%, CO increment of 3.47%, and HC increment of 3.83% in comparison with the case without pre-injection.