ANALYSIS OF THE PRE-INJECTION CONFIGURATION IN A MARINE ENGINE THROUGH SEVERAL MCDM TECHNIQUES

Summary The present manuscript describes a computational model employed to characterize the performance and emissions of a commercial marine diesel engine. This model analyzes several pre-injection parameters, such as starting instant, quantity, and duration. The goal is to reduce nitrogen oxides (NO x ), as well as its effect on emissions and consumption. Since some of the parameters considered have opposite effects on the results, the present work proposes a MCDM (Multiple-Criteria Decision Making) methodology to determine the most adequate pre-injection configuration. An important issue in MCDM models is the data normalization process. This operation is necessary to convert the available data into a non-dimensional common scale, thus allowing ranking and rating alternatives. It is important to select a suitable normalization technique, and several methods exist in the literature. This work considers five well-known normalization procedures: linear max , linear max-min , linear sum , vector , and logarithmic normalization. As to the solution technique, the study considers three MCDM models: WSM (Weighted Sum Method), WPM (Weighted Product Method) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The linear max, linear sum, vector, and logarithmic normalization procedures brought the same result: -22º CA ATDC pre-injection starting instant, 25% pre-injection quantity and 1-2º CA pre-injection duration. Nevertheless, the linear max min normalization procedure provided a result, which is different from the others and not recommended.

The characterization of the pressure inside the cylinder of the engine employed the MALIN 6000 performance analyzer. It is a portable pressure transducer that can be connected to the bleed valve, located at the engine head. The characterization of the emissions of NOx, CO, HC and CO2 used the Gasboard-3000 series gas analyzers.
In order to characterize data at different loads, the engine operated two hours at different setups (25%, 35%, 50%, 75% and 100% load). Eight tests for each load condition have been performed.
The free software OpenFOAM was used for the CFD computations. A new solver was programmed using C++ language. The solver has the following characteristics: • it solves the equations of conservation of mass, momentum, and energy in the domain, • for the temporal evolution, it adopts a simple backward Euler scheme, using a constant time step corresponding to 0.1º CA, • the spatial discretization uses a second order scheme, • the PISO algorithm implements the pressure-velocity coupling, • the employed turbulence model is k-ε, • the fuel heat-up and evaporation is computed by the Dukowicz model [34], • the fuel droplet and breakup is computed by the Kelvin-Helmoltz and Rayleigh-Taylor model [35], • the combustion, NOx formation, and NOx reduction are modeled through the schemes developed by Ra and Reitz [36], Yang et al. [37], and Miller and Glarborg [38], respectively. Figure 1 shows the mesh employed for the computational simulations. Fig. 1(a) represents the 3D mesh at TDC (top dead center) position, while Figs. 1(b) and 1(c) a cross section at BDC (bottom dead center) and TDC positions, respectively. The alternative cylinder movement was imposed to the mesh, as well as the opening-closing movement of the valves. This mesh is composed by 50125 elements at TDC and 802527 at BDC, and it is composed by hexahedrons and tetrahedrons. Several mesh sizes have been considered in order to analyze their effects on the results. Table 1 summarizes the results obtained from three meshes of different sizes. The table shows  the number of elements of these meshes at BDC and the error between experimental and  numerical results regarding pressure and emissions of NOx, CO, HC and CO2. Since the results  obtained with the meshes 2 and 3 were similar, the mesh 2 was selected for the computations carried out on the present work. Figs. 2 and 3 show the correspondence between experimental and numerical results . These figures illustrate the emissions, consumption and pressure obtained both numerically and experimentally. As it can be seen, the CFD model shows a good agreement in SFC, HC, CO, and CO2 with respect to experimental results. Regarding NOx emissions, the values obtained numerically are higher than the experimental ones for all engine loads. The main reason is that compression ignition engines, as opposed to spark ignition engines, operate under lean conditions. Most NOx formation kinetic models are based on NO thermal mechanism, which becomes significant at high temperatures, and for that reason they are not able to properly model locally lean, low-temperature regions which are typical in compression ignition engines and less common in spark ignition engines [39,40]. Nevertheless, the numerical model predicts the NOx trend with an average error of 4.9%, and it is thus considered appropriate for the present work.

MCDM analysis
The CFD model described in the previous section was employed to generate the data necessary to carry out the MCDM approach. 125 cases were analyzed, and they are schematically illustrated in Fig. 4. As can be seen, five pre-injection quantities (Q) were employed: 5%, 10%, 15%, 20%, and 25%; five pre-injection durations (D): 1º CA (Crank Angle), 2º CA, 3º CA, 4º CA, and 5º CA; and five pre-injection starting instants (S): -22º CA ATDC (Crank Angle After Top Dead Center), -21º CA ATDC, -20º CA ATDC, -19º CA ATDC, and -18º CA ATDC. These data ranges were chosen in order to define an appropriate engine performance. Pre-injection quantities higher than 25% and pre-injection starting instants before -22º are not recommended [32]. Taking into account the 125 simulations performed, and the four criteria considered: SFC, NOx, CO, and HC, , a m × n data matrix can be constituted with m = 125 rows and n = 4 columns, as shown in Eq. (1). This matrix is highlighted in red color in Table 2. To simplify, this table C.G. Rodriguez, M.I. Lamas, Analysis of the pre-injection configuration in a J.D. Rodriguez, C. Caccia marine engine through several MCDM techniques only exhibits the first, second and last alternative (row). The case number and corresponding pre-injection starting angle, quantity and duration are also shown in this table. An important aspect in MCDM methods is the definition of the weight of each criterion. This refers to the degree of importance of each criterion. Instead of objective methods, subjective ones are recommended to establish the criteria weights, since experts in the field can directly define them. Objective weighting criteria methods are only recommended when there is no agreement between the experts or when the objectivity is extremely important [27,41]. According to this, this study considers two main requirements: consumption and emissions. Equal importance has been assigned to consumption and emissions, i.e., 50% each. Regarding emissions, the importance of NOx, CO and HC was also distributed equally, i.e., 33.3% for each one. To summarize, Table 3 shows these values in per-unit basis. Logically, each column in Table 3 sums to 1 for the requirements. Regarding sub-requirements, the value of the part of the column corresponding to SFC is 1 and the part of the column corresponding to emissions sums to 1. The weight of each criterion is obtained by multiplying the weight of the requirement by the weight of the sub-requirement, leading to 0.5, 0.167, 0.167, and 0.167 for SFC, NOx, CO, and HC, respectively. These weights also sum to 1. Table 3 Criteria weights, per unit basis.

Requirement (α)
Sub-requirement (β) SFC (0. converts the different measurable values into comparable similar ones, and the normalized decision matrix is a m × n matrix given by Eq. (2), whereby each Vij element is the normalized value of Xij. As mentioned above, many normalization techniques are available in the literature. The most employed ones, which will be compared in the present work, are listed in Table 4. This table shows the expressions used to normalize each term of the decision matrix, both for beneficial and non-beneficial criteria. Beneficial and non-beneficial terms refer to criteria for which a higher greater value is preferable or not, respectively. In the present work, all considered criteria are non-beneficial since the goal is to reduce SFC, NOx, CO, and HC as much as possible. Table 4 shows the normalization criteria used in this study: Xj,min and Xj,max are the minimum and maximum grades of the alternatives for each criterion j. Once the decision matrix is normalized, the adequacy index corresponding to each i-th alternative, AIi, was computed through the three procedures described below.

Normalization technique Criteria Expression
Linear max normalization Analysis of the pre-injection configuration in a J.D. Rodriguez, C. Caccia marine engine through several MCDM techniques 8

WSM procedure
This procedure is also knowns as SAW (Simple Additive Weighting) or WLC (Weighted Linear Combination). This method, proposed by Churchman and Ackoff in 1954 [42], is the oldest and most widely used MCDM approach. The adequacy index is given by Eq. (3), and after applying the normalization procedures described, the most appropriate alternative is the one corresponding to the maximum AI.
whereby wj the weight of the j-th criterion.

WPM procedure
This procedure is also known as MEW (Multiplicative Exponential Weighting). This method is quite similar to WSM, and computes the adequacy index as [43]:

TOPSIS procedure
The TOPSIS method, introduced by Hwang and Yoon [44], determines the so called positive ideal solution and the negative ideal solution. By computing the Euclidean distance to these two alternatives, this method provides the solution that is closest to the best one and farthest to the worst one. The main steps of the TOPSIS procedure are the following ones: Step 1: Determining the normalized decision matrix. Although the classical TOPSIS uses the vector normalization technique, the normalization techniques described above have been compared.
Step 2: Weighting the data, given by the following expression: Step where + - Step 4: Calculating the Euclidean distance of each alternative. Eqs (8) and (9) give the distance from the positive ideal solution and negative ideal solution., respectively: Step 5: Calculating the relative closeness to the ideal solution: Step 6: Ranking the alternatives according to the highest Ci. A value of Ci = 1 is the ideal solution and Ci = 0 is the worst solution. Tables 5 to 9 show the normalized matrixes using each of the described methods (i.e.: linear max, linear max-min, linear sum, vector and logarithmic normalization techniques, respectively). The expressions presented in Table 4 produce the normalized values. Since all criteria are non-beneficial, the expressions corresponding to non-beneficial criteria are considered. The minimum and maximum normalized values corresponding to each criterion are also shown at the end of each of the Tables 5-9. As can be seen, the linear max normalization technique provides normalized values between 0 (minimum value) and a number lower than 1 (maximum value). The linear max-min normalization provides a normalized matrix with data within the range [0 1], where 0 is the worst value and 1 the best one. The linear sum and logarithmic normalization techniques provide normalized values considerably smaller than the other ones, and finally the vector normalization technique provides normalized values close to 1.  The results show a strong dependency on the range of the normalized data. According to the expressions shown in Table 4 for the linear max-min method, the initial data are transformed into normalized values within the range [0 1]. Nevertheless, the other methods lead to a much narrower range of the normalized data. The variation of HC and CO emissions with the preinjection starting instant and quantity is considerably small, as shown in Figs. 5 and 6, respectively. These figures represent the HC and CO emission against the pre-injection quantity and starting rate using 1º pre-injection duration. Other pre-injection durations provide similar results and thus are not presented here. As can be seen in Figs. 5 and 6, the variation of HC and CO is too small, and all normalization methods reflect this fact by providing close values in the normalized matrix, except for the linear max-min normalization. Since this method transforms the values corresponding to each criterion within the range [0 1], the importance of these small variations in CO and HC emissions is incremented, i.e., small differences are always transformed to the range [0 1] independently of the initial data range, and thus small differences are extended. Nevertheless, the other normalization methods maintain the irrelevance of CO and HC during the normalization process and pay more attention to the variation of NOx emissions and consumption with the pre-injection starting instant and quantity. The variation of NOx and consumption with the pre-injection rate and starting angle is shown in Figs. 7 and 8, respectively. These figures underline an important dependence of NOx and consumption on the pre-injection rate and starting angle.    Table 10 shows the highest adequacy index using the different normalizations methods analyzed in the present work. As can be seen, the linear max, linear sum, vector and logarithmic normalization methods provide practically the same result, which corresponds to -22º preinjection starting instant, 25% pre-injection quantity and 1º (WSM and WPM) or 2º (TOPSIS) pre-injection duration. Nevertheless, the linear max-min normalization method provides the alternative corresponding to -18º pre-injection starting instant, 5% pre-injection quantity, and 2º pre-injection duration. The linear max-min normalization method provides a different result since, as mentioned above, it transforms the negligible variations of CO and HC into significant values. According to this, this normalization technique leads to a solution with small CO and HC emissions. This alternative is a compromise between the four criteria analysed (NOx, SFC, CO, and HC), providing more relevance to CO and HC than these really have. This alternative leads to a small contribution of pre-injection, with a 5% quantity, due to the increment of SFC, CO, and HC with the pre-injection quantity. Besides, this solution does not lead to important pre-injection advancements also due to the SFC, CO, and HC penalty. Since a 5% pre-injection quantity leads to excessive NOx emissions, this solution is not recommended due to the current legislation about NOx emissions.

Results and discussion
On the other hand, the alternative obtained by the other normalization techniques provides significant NOx reductions with a small increment of SFC in comparison with the case without pre-injection. This solution proposes a high pre-injection percentage (i.e. 25%) due to the effect on NOx reduction. As shown in Fig. 5, advancing the pre-injection starting instant also leads to important NOx reductions, resulting in -22º as pre-injection starting instant. Regarding preinjection duration, low values emerge since short injections provide important NOx reductions. NOx is mainly caused by the high temperatures that are reached during the combustion process [45]. In order to reduce NOx efficiently, the fuel must be rigorously injected at the optimum instant and thus under short injections.

Conclusions
The following conclusions may be drawn from the present work: -Due to the important emissions of NOx produced in the marine field, the present work analyses a NOx reduction policy in a commercial marine diesel engine. The measure proposed is a pre-injection system. Besides NOx, the objective is to maintain SFC and emissions of CO and HC as low as possible. It is worth mentioning that PM emissions should also be included in this model. These were not included due to the difficulties to accurately predict these emissions through CFD. -A total of 125 alternatives with different values of the pre-injection starting instant, quantity and duration were analyzed. -Since the pre-injection starting instant, quantity and duration are conflicting criteria, a MCDM methodology was employed to determine the most suitable pre-injection configuration. -An important step in MCDM is the normalization process. Many normalization methods can be found in the literature, and the five most employed ones were compared in the present work: linear max normalization, linear max-min normalization, linear sum normalization, vector normalization and logarithmic normalization. -3 MCDM approaches were compared: WSM, WPM, and TOPSIS. -It was found that linear max, linear sum, vector, and logarithmic normalization methods provided practically the same result as most appropriate pre-injection pattern: -22º CA ATDC pre-injection starting instant, 25% pre-injection quantity, and 1º (WSM and WPM) or 2º (TOPSIS) pre-injection duration due to the important NOx reductions with a low SFC penalty. Nevertheless, the linear max-min normalization technique provided a very different result: -18º CA ATDC pre-injection starting instant, 5% pre-injection quantity, and 2º preinjection duration. The reason of the discrepancy between the max-min normalization technique and the other normalization techniques lies in the range of the normalized values. The variation of CO and HC emissions in the 125 cases is practically irrelevant, but the linear max-min normalization technique increments the importance of these pollutants since it converts its values into the range [0 1]. On the other hand, the other normalization methods maintain the irrelevance of the variations of CO and HC and thus lead to another optimal configuration. -Among the limiting aspects of MCDM methods, it is worth mentioning that, even if they provide a formal tool for decision making problems, subjectivity is not removed, due to the procedure to stablish the weights. In fact, different MCDM methods and different normalization procedures lead to different results, which means that there is no universal method suitable for all problems.