A Design-Oriented Model for Transmission Loss Optimization in Marine DOCs

Abstract

The even more restrictive regulations imposed on chemical and acoustic emissions of ships necessitate the installation of after-treatment systems onboard. The spaces onboard are limited, and the Exhaust Gas Cleaning Systems (EGCSs) have big dimensions, so an appropriate integration and optimization of EGCSs allows to save space and comply with international regulations. Moreover, in the available literature, there is a lack of guidelines about the design of integrated EGCSs. This study aims to develop an ad hoc optimization methodology that uses combined Computational Fluid Dynamics (CFD)–Finite Element Method (FEM) simulations, surrogate models, and Genetic Algorithms to optimize the acoustic properties of EGCSs while considering the limits imposed by the efficiency of chemical reactions for the abatement of NO_x and SO_x. The developed methodology is applied to a Diesel Oxidation Catalyst (DOC), and the obtained results lead to a system that integrates the silencing effect into the DOC.

1. Introduction

Maritime transport is of great importance for the global economy, as, together with its related activities (e.g., shipbuilding, refitting, and port activities), it accounts for around 80% of worldwide trade [1].

Due to the extensive use of Heavy Fuel Oil (HFO), which has a high sulfur content (S wt% up to 3.5), maritime transport accounts for approximately 10–15% of global sulfur (SO_x) and nitrogen oxides (NO_x) emissions, leading to increasing concerns about the real impact of maritime emissions. SO_x at high concentration can harm trees and plants by damaging foliage and decreasing growth and can contribute to acid rain, which can harm sensitive ecosystems. SO_x can also react with other compounds in the atmosphere to form small particles, contributing to particulate matter (PM) pollution. NO_x, which formation depends on the combustion temperature, reacts with volatile organic compounds (VOCs), creating ground-level ozone and contributing to smog. NO_x also contributes to acid rain and climate change, as, when NO_x interact with other gases in the atmosphere, it enhances the greenhouse effect, the process in which gases trap the sun’s heat and make the Earth warmer.

The combustion of fossil fuels by merchant ships also releases carbon dioxide (CO₂), a major greenhouse gas (GHG) contributing to climate change and leading to global warming, rising sea levels, extreme weather events, and other climate-related impacts.

The International Maritime Organization (IMO), consistently takes part in the global fight against climate change in support of the United Nation Sustainable Development Goal 13 to take urgent action to combat climate change and its impacts. The IMO has already limited SO_x and NO_x in the past years, especially in the Emission Control Areas (ECAs) such as SECAs (Sulfur Oxides Emission Control Areas) and NECAs (Nitrogen Oxides Emission Control Areas) [2]. In 2023, the IMO adopted the GHG strategy [3], which identifies levels of ambition for the reduction of GHG emissions for the international maritime transport sector, identifying the technological innovation and the global introduction of alternative fuels and/or energy sources for international maritime transport as strategies to achieve the pre-established targets.

The international regulations apply not only to newly built ships but also to those already in navigation. While it may be relatively easy to design new ships with alternative propulsion and energy production systems, this is not true for existing ships using traditional fuels. The refitting of the entire propulsion system is expensive in terms of time and costs, as well as also requiring a refitting of the internal spaces, the location of the machinery, and the storage systems. Thus, especially for ships already built, the adoption of Exhaust Gas Cleaning Systems (EGCSs) to be compliant with international regulations is of paramount importance.

EGR (Exhaust Gas Recirculation) and SCR (Selective Catalytic Reduction) systems are the most used marine NO_x emissions control technologies [4,5]. As for SO_x, different strategies allow their emission reduction [6]: the use of alternative fuels (e.g., hydrogen and liquefied natural gas) or the adoption of a different energy source (e.g., electric propulsion). However, such technologies require the refitting of the entire propulsion systems, so, alternatively, the use of conventional fuels with a low sulfur content (e.g., LSFO—Low Sulfur Fuel Oil, S wt% < 1 and ULSFO—Ultra-Low Sulfur Fuel Oil, S wt% < 0.1) is mandatory. However, the use of low sulfur content combustibles significantly impacts the total ship operating costs, over 60% of which is associated with the fuel. Accordingly, an alternative solution is the installation of scrubbers as an EGCS to ensure compliance with SO_x regulations [7]. For the GHG emissions, Onboard Carbon Capture (OCC) is gaining more and more interest as an effective solution to reduce carbon emissions from ships. Two strategies to capture CO₂ emissions from ships during operation can be adopted: for post-combustion systems, OCC involves the cleaning of exhaust gases from CO₂, separating it, and storing it onboard for eventual offloading; for pre-combustion, carbon is separated from the fuel to produce hydrogen and use it in dedicated energy conversion machinery.

Notably, ship emissions are not limited to chemical pollution but involve exhaust gas noise, several regulations and class notations [8,9,10] limit the perceived noise level on ship’s decks and at prescribed distances from the vessels during navigation and port stationing. Silencers are usually installed along the exhaust line to reduce the noise radiated by the exhaust gas.

All the above-mentioned EGCSs allow ships to be compliant with international regulations while continuing the use of well-established maritime fuels. On the contrary, spaces have to be found for the installation of such technologies and all the required equipment for their functioning. Thus, the integration between systems onboard is of paramount importance.

The presented paper proposes a design-oriented model aimed at optimizing the acoustic properties of the EGCS, which employs the Transmission Loss (TL) as the main Key Performance Index (KPI). The proposed ad hoc methodology uses combined CFD–FEM simulations, surrogate models, and Genetic Algorithms (GAs) to optimize the acoustic properties of the EGCSs while considering the limits imposed by the efficiency of chemical reactions for the abatement of chemical pollutions.

The integration between EGCSs and silencers can represent a smart way for space-saving along the exhaust line, thus allowing the installation of all the systems needed for full emission compliance.

This paper applies the proposed methodology to a simplified real case study consisting of a Diesel Genset connected to an exhaust line along which are installed a Diesel Oxidation Catalyst (DOC), followed by a wet scrubber, as a feasible and reliable technical solution to satisfy the limits imposed on NO_x and SO_x emissions.

For diesel engines, platinum (Pt)-based DOC is typically used to abate PM (particulate matter), CO (carbon monoxide) and HCs (hydrocarbons) in the automotive sector [11]. Moreover, in some studies, Pt-based DOCs are used to oxidize the NO [12,13,14], which is the main component (~90% v/v) of the engine-emitted NO_x. Notably, it has also been recognized that the oxidation of NO to NO₂ increases the solubility of the NO_x species in the liquid of the subsequent scrubber [15]. Based on such considerations, in this study, the above-mentioned solution is implemented for a simultaneous abatement of NO_x and SO_x, using the wet scrubber for the abatement of both the pollutants.

In the available literature, only a few studies described or investigated the acoustic performances of EGCSs [4,16,17]. On the contrary, silencer performances are reported extensively, especially in the automotive industry [18,19,20,21]. The acoustic properties of such systems are usually studied using FEM [22,23,24] or CFD [25,26,27] approaches; only a few works proposed a combined approach between FEM and CFD [21,28] to reduce the computational burden of CFD modeling. Moreover, in the available literature, no study is presented that focused on the integration and optimization of the acoustic properties of EGCSs, aiming at reducing the complexity and the volume of marine exhaust lines.

Thus, this work presents a considerable scientific novelty addressing the framework for the study and the optimization of the TL of EGCSs, providing results and general guidelines missing in the available literature.

The implemented optimization process leads to the geometry of the DOC, which remarkably increases its silencing effect while maintaining compliance with the limits imposed by the chemical reactions on both the geometry and the flow characteristics and proving the possibility of system integration and the elimination of the traditional silencer. Such results contribute to the generation of new knowledge that can be used for the optimal design of after-treatment systems at a time when the marine industry is moving toward systems integration, as explained above. The proposed methodology can effectively be adopted for the design of the exhaust line of ships that use traditional fuels, bringing significant benefits, especially to ships already in navigation.

2. The Transmission Loss as the KPI

It is common practice to characterize the performances of a silencer, from a designer’s perspective, through either the Insertion Loss (IL) or the TL. The IL is the difference between the acoustic pressure radiated from the source with and without the silencer attached, expressed as follows [26]:

IL = Lp(in) − Lp(out),

(1)

Lp(in) and Lp(out) are the sound pressure levels measured at prescribed points at the silencer’s inlet and outlet, respectively. The IL depends not only on the muffler geometry but also on the source and the radiation impedance.

The TL is the ratio between the sound power of the incident pressure wave at the inlet of the muffler to the sound power of the transmitted pressure wave at the outlet of the muffler, expressed as follows [19]:

TL = 10 · Log₁₀ (Wi/Wt),

(2)

Wi and Wt are the incidents and the transmitted waves’ sound power, respectively. The benefit of using TL as a measure of silencer efficiency is that this parameter concerns the silencer alone; the source or termination properties need not be assessed. Because of this simplification, the TL is the most common parameter used to measure silencer performance [18]. For consistency, the TL is used in this study as the KPI instead of IL. Three methods were employed to assess its value: the decomposition technique, the two-load technique, and the two-source technique [19].

3. The Design Strategy

A Response Surface Methodology (RSM) [29] is used in this study to optimize the TL of the DOC. The RSM involves three fundamental steps:

• design a series of experiments for the measurement of the analyzed response;
• creation of a mathematical model that fits the response;
• analysis of the optimum conditions.

3.1. Design Space Creation

Design of Experiment (DoE) techniques allow for creating the database of TL values as a function of predetermined parameters needed to construct the metamodel. The predictor parameters, with their constraints, constitute the design space. In this study, the constraints imposed on the predictors are established based on chemical considerations; as a matter of fact, to ensure an efficient NO_x oxidation, a series of parameters have to be controlled and respected, e.g., the contact time between exhaust gases and catalyst or adequate cell dimensions, to avoid clogging due to particulate matter [14].

Working with complex systems such as the EGCS, simple fractional design methods or derived ones (e.g., central composite designs or Box–Behnken designs [30]) for the DoE determination of the simulation scenario are not advisable due to the complexity of possible mutual interactions of design parameters on predicted TL values. To this end, the proposed methodology employs an alternative strategy for the TL database creation, adopting a Stratified Latin Hypercube Algorithm [31]. The TL database is generated from multiple calculations using a combined CFD–FEM numerical methodology [32] for all the cases found by the DoE.

3.2. Mathematical Model

After the TL database generation, a surrogate model is necessary for the TL prediction. Here, the proposed methodology employs a model based on multiple linear regressions. Such a choice derives from the nature of the DoE employed for the design space generation and the consequent necessity to deal with a low number of experimental points, thus automatically excluding more advanced models like neural networks or trees. The multiple linear regression can be expressed in vectorial form as follows [33]:

y = bX + e,

(3)

where y is the vector of measured values (TL in this case), X is the matrix of predictor variables, b is the vector of the coefficient estimated by the regression, and e is the error vector. The regression coefficients derive from a stepwise selection process [34] that automatically selects the predictor variables significant to the model. The stepwise multiple linear regression model, implemented in Matlab, can be set to consider both linear and nonlinear terms. In the present case, the model is constructed to contain a fully quadratic model, containing intercept linear and squared terms and all products of pairs of distinct predictors. Furthermore, a pure quadratic model is the maximum nonlinearity permitted by the Design of Experiments technique employed for this analysis. Therefore, additional nonlinear models for Equation (3) (e.g., power or logarithmic) are not considered necessary in this study, as the implemented model is also accurate enough to properly reconstruct the experimental TL, as proven by the high values obtained for R² and R²_adjusted, reported in the following section. These parameters are useful to evaluate the quality of the obtained regressions and can be defined as follows [33]:

R² = 1 − SSE/SST,

(4)

R²_adjusted = 1 − (SSE/dfe)/(SST/dft),

(5)

SSE and SST are the sum of squares errors and the sum of squares total, respectively, and dfe and dft are the corresponding degrees of freedom:

SSE = ∑₁ⁿ (y_i − ỹ_i)²,

(6)

SST = ∑₁ⁿ (y_i − ӯ_i)²,

(7)

dfe = n − p − 1,

(8)

dft = n − 1,

(9)

where n is the number of real-valued responses to fit, p is the number of predictors included in the regression, y_i is the real-valued responses to fit, ỹ_i is the fitted value obtained from the regression, and ӯ_i is the mean value of the real-value responses.

3.3. Optimized Operating Conditions

The final scope of the process is to find the optimal set of parameters that maximize the TL values of the DOC in a defined frequency range. The GA is a method for solving constrained and unconstrained optimization problems [35]. GA are mostly used for optimization problems that cannot be properly represented by standard optimization algorithms, including problems in which the objective function is discontinuous, non-differentiable, stochastic, or highly nonlinear [36]. The GA iteratively modifies a population of solutions (Figure 1). At each time step, select individuals from the current population as parents and use them to produce children for the next generation, until the convergence to an optimal solution is reached.

The GA creates three types of children for the next generation:

• Elite are the individuals in the current generation with the best fitness values;
• Crossovers are created by combining a pair of parents;
• Mutations are created by introducing random changes to a single parent.

The algorithm stops when a given stopping criterion is met (e.g., the fitness function for the best point in the population is less than or equal to a given limit, the maximum number of generations is reached, the maximum computational time is exceeded, and the average relative change in the fitness function value is less than a certain value).

The optimization procedure is implemented using a Matlab script, and an Augmented Lagrangian Genetic Algorithm (ALGA) [37] is applied to solve nonlinear constrain problems. The optimization problem, solved by the ALGA algorithm, can be expressed as follows:

min_x (f(x)),

(10)

Such that

c_i(x) ≤ 0,

(11)

where f(x) is the objective function, and c_i(x) represents the nonlinear inequality constraints.

4. The Computational Procedure

The combined methodology used to simulate the TL of the DOC was assessed by the authors in a previous study [32], and for the sake of clarity, it is briefly illustrated here and schematically represented in Figure 2. The process involves the following steps:

• A steady-state CFD analysis to evaluate the flow field and its characteristics (i.e., velocity, temperature, and pressure).
• A mesh mapping to transfer the obtained data from the CFD mesh to the acoustic one.
• FEM–acoustic analysis to evaluate the TL, considering the influence of the flow field.

The software STAR-CCM+ is used to perform the CFD simulations. RANS (Reynolds-Averaged Navier–Stokes) model is used to solve the Navier–Stokes equations, setting the k–ε turbulence model and considering for the working medium air as compressible ideal gas with physical properties dependent on the temperature. The segregated approach is used, adopting SIMPLE (Semi-Implicit Method for Pressure Linked Equation). The no slip condition is imposed to the walls, while the experimentally measured data (see next section) are used as boundary conditions at the inlet and at the outlet of the calculation domain. The prism layer is generated with a total thickness of 5.83 mm and 6 prism layers with a stretching factor of 1.5 in order to obtain a wall y⁺  ≤  1. A trimmer mesh with a base size of 8 mm is set based on the mesh sensitivity study performed (Figure 3), using as the target value the flow velocity measured at the outlet of the DOC and comparing the Grid Independence Index (GCI) to evaluate the independence of the obtained results by the mesh size [38,39]. Refinement areas are set in the proximity of the inlet/outlet and the monoliths. A perusal of Figure 3 shows that the bigger the mesh size the higher the discrepancy with the experimental data. The calculated velocity at the outlet of the DOC decreases when the mesh size is increased.

The software Actran VI is used for FEM simulations, implementing a Direct Frequency Response analysis. The geometry is discretized with a tetrahedral mesh with 10 linear elements for the smallest wavelength, which is proven to ensure reliable results [32] and represent the common practice in FEM acoustic simulations. Surface refinements are also set at the inlet/outlet of the monoliths. At the inlet, the duct modes [32] are used to model the incident wave, imposing a plane wave propagation in the frequency range of interest. In order to avoid reflection, free mode propagation is set in the direction opposite to the excitation. At the outlet, the anechoic condition is modeled using the duct modes and by setting free mode propagation. Fluid characteristics are imported from the CFD simulations through a mesh mapping performed using the i-CFD module of Actran.

In both the simulations, the two monoliths inside the DOC are simulated using simplified models [40]. In Star-CCM⁺, the flow through a porous medium is modeled with the so-called porous region, which is based on the Darcy–Forchheimer law [41]. The flow resistivity has to be set as the input parameter, which is equal to 678 N·s/m⁴ (declared by the manufacturer of the DOC) at 270 °C (exhaust gas temperature) in the presented case. In Actran VI, the monoliths are modeled using the so-called viscous–thermal component, useful to calculate the flow inside a narrow channel. This strategy requires as input parameters the Open Area Ratio (OAR), the temperature and velocity of the flow, and the hydraulic radius of the channel (h_r) [40]. For the presented case, the flow temperature is experimentally measured (270 °C), the velocity field is imported from the CFD simulation, and the OAR and h_r are 0.92 and 0.62 × 10⁻³ m, respectively.

5. The Reference DOC: Characteristics and Experimental Measurements

As mentioned above, DOC catalyzes the oxidation of NO and thus promotes the solubility of NO_x in water, leading to enhanced NO_x abatement in the subsequently closed-loop scrubber. The DOC converter used in this work is schematized in Figure 4. Internally, it features two metallic honeycomb monoliths wash-coated with a Pt/doped-Al₂O₃ catalyst employed for the oxidation reactions. The shape and dimensions of these honeycombs, summarized in

Table 1. Summary of the DOC converter geometrical parameters.

Parameters	Value
D in/out	88.9 [mm]
D catalyst	297 [mm]
L in/out	100 [mm]
L catalyst	510 [mm]
L conical adapters	125 [mm]
L monolith	90 [mm]
Distance between monoliths	60 [mm]
Flow resistivity of the monolith	678 [N·s/m3]
Open area ratio of the monolith	0.92 [-]

, are imposed by the chemical requisites of the process.

A mock-up (Figure 5) composed of a 4-stroke Genset engine Iveco and its exhaust line is used to experimentally test and measure the main characteristics of the DOC, such as TL, velocity, and pressure of the flow at the inlet and at the outlet.

The selected engine is comparable with an emergency diesel generator mounted on cruise ships. For space reasons, it is not possible to test a primary engine in the laboratory; however, all the after-treatment systems are designed for the prescribed engine. The characteristics of the Genset are reported in

Table 2. Genset IVECO 8361SRi26 main characteristics.

Prime Power [kW]	N. of Cylinders	Bore × STROKE [mm]	RPM	Fuel Consumption 75% Load [L/h]
185	6	115 × 130	1500	31.4

, and the experimental measurements are performed with the engine working at 75% of the prime load.

Flow characteristics are measured with a Flowtest ST made by TCR Tecora, which combines a Pitot tube with a thermocouple. The probe is inserted in the same locations as microphones (Figure 5) to a depth such as to measure the center of the exhaust pipe. Three measures are performed for each measuring point, and the values averaged over a period of 5 min are reported in

Table 3. Boundary conditions employed for the CFD analysis.

Velocity Inlet [m/s]	Pressure Outlet [Pa]	Temperature [°C]
44	101,325	543

. The measured data reported are used as input parameters for simulations.

The TL is measured using the two-load technique [19] and GRAS 40SC CCP Probe microphone. Figure 5 reports the scheme of the experimental set-up. When using the two-loads method, the test has to be performed in two configurations to have the data required for TL calculations. The two configurations are realized by changing the load and thus the impedance at the end of the measurements line; in this study, the two loads are represented by an open end and a silencer-containing end.

The frequencies of the noise generated by the engine have to be evaluated, as the TL of the exhaust line components has to be maximized, especially in correspondence with these values, and even more important, the hollow of the TL must not coincide with the engine frequencies [42]. The exhaust noise spectrum always contains strong tones associated with the rate of cylinder firings. The lowest tone is the CFR (Cylinder Frequency Rate), which is the firing rate for every single cylinder, while the EFR (Engine Firing Rate) is generally the strongest tone in the exhaust spectrum [43]. For a 4-stroke engine, CFR and EFR can be expressed as follows:

CFR = RPM/120,

(12)

EFR = CFR · N_c,

(13)

where RPM are the revolutions per minute, and Nc is the number of cylinders. In general, the EFR and its harmonics up to the 4th order are considered for TL optimization, since higher-order harmonics do not significantly influence exhaust gas noise [44].

The quality of the correlation between the computational results and the measured data can be performed considering the error E between the numerical result and the experimental measurement and the norm U between the experimental error and the numerical error [45]. Figure 6 reports the comparison between numerical and experimental TL: the trend of the curves is the same, and E has a maximum value of 3.1 dB around 150/200 Hz. At such point, U is equal to 3.3, greater than E, thus highlighting the good correlation between the curves. The discrepancy between the numerical and the experimental data is primary due to the difficult measurement conditions, such as positioning of the probe with high temperatures and pressure or the turbulence of the flow, which are difficult to simulate. Such consideration is also demonstrated by the fluctuation in the experimental TL curve, which is the average between 5 measurements. Moreover, there is the influence of the simplified model adopted in the simulations and previously explained.

The experimental data are reported up to 350 Hz, i.e., the region where the engine frequencies generate the highest acoustic impact. Notably, TL values varying between 8 dB and 14 dB are detected in the frequencies range of interest (i.e., EFR and the related harmonics reported in Figure 6), which is sensibly lower than the values of 30–35 dB that can be achieved in a conventional marine silencer. This clearly highlights the necessity of optimizing the design of the DOC converter to improve its silencing performances.

6. The Preparation of the Database

As previously mentioned, DoE is used in this study to create the database of TL values, choosing the following characteristics as predictor variables: length of the DOC (L), angle of the conical expansion (θ), length of the monoliths (l), length of the interstice between the monoliths (i), DOC diameter (D), length of perforated pipe at inlet/outlet (lf), the adding of perforated plates (np), perforations diameter (Df), flow resistivity of the monoliths (R), and Open Area Ratio (OAR) of the monoliths. Figure 7 shows the predictor variables, while

Table 4. Predictor variables and their limits.

Parameter	Max	Min	Unit
D	598	297	[mm]
θ	45	0	[deg]
L	1020	510	[mm]
l	180	90	[mm]
i	120	60	[mm]
Df	35	10	[mm]
Lf	Lc/2	0	[mm]
R	678	520	[N·s/m3]
OAR	0.98	0.92	[-]

reports the upper and lower limits for each variable. Such limits are imposed by the need to endure prescribed values for the back pressure and the contact time between exhaust gas and catalysts so as not to influence the efficiency of the chemical reactions, respectively.

The value of the generated back pressure, which is a function of parameters such as D and R, also has to be controlled to avoid a negative influence on the engine efficiency [46]. The diameter of the inlet/outlet pipe is maintained constant, dictated by the diameter of the exhaust line pipe. Figure 8 reports the representation of the resulting design space.

The TL database is finally generated employing multiple calculations with the combined FEM–CFD numerical methodology (see previous section) for each case found through DoE.

7. The Optimization of the Reference DOC

As explained above, multiple linear regression is used as a mathematical surrogate model for TL prediction. The regressions on TL values pertain to specific frequencies from 50 to 350 Hz, more precisely in steps of 50 Hz. The frequencies for the regression are selected inside the frequency range where the engine is more influent (EFR in Figure 6). The quality of the obtained regressions is assessed by employing the determination of coefficients R² and R²_adjusted; the values obtained for the implemented regression (

Table 5. R² and R²_adjusted of the multiple linear regressions.

Regression Frequency [Hz]	R2 [-]	R2adjusted [-]
50	0.98	0.98
100	0.98	0.98
150	0.99	0.98
200	0.99	0.98
250	0.98	0.97
300	0.98	0.97
350	0.96	0.95

) are very close to 1, thus assessing both the appropriateness of the use of stepwise multiple linear regression to fit the TL and goodness of the predicted TL.

As indicated, the optimization process aims at maximizing the TL in the frequency range of interest. To this end, the area under the TL curve is selected as a representative objective function of the GA optimization. Notice that a GA works by minimizing the objective function (Equation (10)); accordingly, the area is multiplied by −1 before starting the calculation. Given the above experimental results, an additional constrain that the TL cannot be less than 25 dB is addressed. As quoted above, the marine silencer typically ensures a sound abatement of about 30–35 dB; for this reason, a minimum limit of 25 dB for the TL of the DOC is chosen. In the real case scenario, it would be mounted with a scrubber in a series, which would certainly ensure the abatement of 30–35 dB by the whole system. Setting a limit of 30–35 dB for only DOC would result in its over-dimensioning.

As regards the use of the area under the TL instead of its peaks as the objective function, this is due to the fact that it is risky to consider only the peaks and their match with the analytical values of EFR and CFR. The real operating conditions can deviate, however slightly, from the analytically calculated tones, and therefore, it is better to guarantee noise reduction in a narrow band.

Figure 9 reports the convergence diagram of the GA used to find the optimum solution; on the ordinate axis, the fitness value is reported, which is the value of the area under the TL curve multiplied by −1 (see the previous section), while the abscissa axis reports the number of generations to reach the convergence. As shown in the figure, the convergence is reached for a number of generations higher than 10.

The obtained optimal parameters are reported in

Table 6. Optimized combination of parameters to maximize the TL of the DOC.

Parameter	Value	Unit
D	594	[mm]
θ	0	[deg]
L	1020	[mm]
l	180	[mm]
i	60	[mm]
Lf	0	[mm]
R	678	[N·s/m3]

, whereas Figure 10 compares the geometry of the optimized DOC with the reference one. Using the tool of the CAD software Rhinoceros, the overall volumes of both the reference DOC and the optimized one are calculated for comparison. The volume of the optimized DOC is about 10 times bigger than the reference one (0.280 m³ vs. 0.028 m³); however, the standard DOC must be installed along the exhaust line in a series with a silencer, so considering the volume of a typical silencer for the engine mounted on the mock-up (about 0.380 m³), the use of the optimized DOC led to space savings of about 31%.

Figure 11 compares the reference TL of the standard DOC with the optimized one; the TL is increased from a maximum of 20 dB in correspondence with the first harmonic EFR to a minimum of 11 dB in correspondence with the third harmonic of the EFR. The first EFR is proven to be the more energetic, thus providing the highest sound pressure level. The considerable increase of the TL, especially in correspondence of this harmonic of the excitation (i.e., engine noise), proves the applicability of the proposed methodology in a real case scenario to optimize the acoustic properties of EGCSs.

Moreover, the generated back pressure by the optimized DOC is calculated and compared with one of the reference DOC.

Table 7. Generated back pressure: optimized DOC vs. reference DOC.

Reference DOC Back Pressure [Pa]	Optimized DOC Back Pressure [Pa]
1458	1750

reveals that the generated back pressure is increased by about 20%, thus obtaining a value that is much lower than the allowable back pressure for the used Genset Iveco (4900 Pa). As indicated above, achieving low back pressure is essential: the higher its value, the lower the engine’s efficiency. Therefore, the allowable back pressure for the considered engine can never be exceeded.

Finally, Figure 12 shows the velocity field in the optimized DOCs. A perusal of the figure clearly indicates that the different form of the optimized converter generates a quite strong turbulence in the zone preceding the first honeycomb monolith. The premixing of the exhausts results in a more uniform and slower velocity profile within the monolith with respect to the reference DOC (Figure 4). Uniform gas distribution and higher gas residence time in the honeycomb strongly suggest that the optimized DOC should result in more efficient conversions and capability to oxidize NO_x compared to the reference one.

8. Conclusions

The present study addresses the development of an effective calculation framework capable of properly modeling and optimizing the acoustic properties of an EGCS coupled to a marine diesel engine. The methodology combines CFD and FEM simulations and an ad hoc project design to provide solutions for the reduction of exhaust gas noise while minimizing the volume of the exhaust gas treatment system and without reducing the efficiency of chemical pollution abatement. The developed methodology is applied to a real case study represented by an experimental mock-up that uses an advanced EGCS that includes a DOC converter that promotes the oxidation of NO to make the NO_x soluble in water in a subsequent scrubber. The optimization aims to maximize the silencing properties of the DOC to eliminate the traditional silencers. This approach may provide space savings, thus allowing the installation of an integrated systems capable of ensuring compliance with the international regulations of ships’ emissions, both acoustic and chemical. The proposed design process is implemented in Matlab, choosing the TL of the DOC as the KPI. The main steps can be summarized as follows:

• Creation of a database of TL values as a function of the predictor parameters and their constraints using a DoE approach with a stratified Latin Hypercube Algorithm and a combined CFD–FEM methodology;
• Creation of a mathematical model that reproduces the response using multiple linear regression with a stepwise selection process;
• Analysis of an optimum solution based on an objective function, and constraints using an Augmented Lagrangian Genetic Algorithm.

Following this procedure, the optimum combination of geometrical parameters that maximize the TL of the DOC while ensuring the efficiency of the chemical reaction needed for NO_x oxidation is derived. The TL is increased from 8–14 dB up to 20 dB, ensuring a noise reduction of at least 25 dB in the frequency range of interest (10–350 Hz). The optimization procedure is therefore proven to be applicable for the study of acoustic properties of after-treatment systems, considering also the geometrical constraints dictated by the chemical aspects.

The proposed methods and results are applicable in the maritime industry for the design of a marine exhaust line: during the design phase, thanks to its low computational effort and relatively easy usage, the proposed methodology allows the study of system integration and the optimization of acoustic properties, leading to the design of an exhaust line with a lower volume and compliant with the even more stringent emissions regulations. This aspect is of paramount importance not just for the design of new ships but also for the refitting of the ships already in navigation. Emission regulations also involve old ships and the possibility to study a system integration that allows installing the needed after-treatment systems in the available space, so as to not perform a refitting of the entire propulsion system.

Moreover, this work presents a considerable scientific novelty, as, in the available literature, there is a lack of study and general guidelines on the evaluation and optimization of acoustic properties of after-treatment systems used in marine exhaust lines such as scrubbers or catalytic converters. Just a few works consider the acoustic properties of SCR, but under simplified hypotheses (e.g., no flow influence and no viscous dissipation inside components) that can lead to a non-negligible discrepancy with a real case scenario. The marine industry is moving toward systems integration, for example, prototypes of integrated SCRs silencers have already been constructed; thus, the methodologies and results presented in this study contribute to the generation of new knowledge that can be used for the optimal design of after-treatment systems.

The combined CFD–FEM approach presents some limits due to the adoption of simplified models such as steady-state CFD simulations for the evaluation of the flow field and the above-mentioned strategies to model internal components without the need to design and mesh their exact geometry. Moreover, parameters such as surface roughness, that, in the real case scenario, influence the performances of the after-treatments systems or the water spray inside the scrubber are not considered. On the contrary, the methodology does not require the knowledge of parameters difficult to estimate with measurements; thus, the adopted simplification, while leading to a discrepancy with a real case scenario, allows a methodology capable of predicting acoustic properties of after-treatment systems, studying their integration, and also optimizing their performances and volumes in an early design stage.

In the future, the optimization process should be applied to a whole system (i.e., DOC plus real scrubber) to further optimize the design, volume, and operation conditions. Moreover, the influence of the water spray inside the scrubber on the acoustic properties should be evaluated. As for the noise generated by the exhaust gas itself, preliminary simulations using SNGR suggest that the noise generated by flow turbulence is limited to high frequencies and tends to be a local phenomenon (i.e., not carried by the gases up to the exit of the funnel and radiated to the outside). However, further investigation should be performed to properly assess this aspect.