Journal of Marine Science and Engineering

Article A Diesel Modelling Approach for Real-Time Simulators

Marco Altosole 1,*, Ugo Campora 2, Massimo Figari 1, Michele Laviola 1 and Michele Martelli 1

1 Department of Electrical, Electronic, Telecommunications Engineering and , University of Genoa, Polytechnic School, 16145 Genoa, Italy; massimo.fi[email protected] (M.F.); [email protected] (M.L.); [email protected] (M.M.) 2 Department of Mechanical, Energy, Management and Transportation Engineering, University of Genoa, Polytechnic School, 16145 Genoa, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-010-353-2387

 Received: 31 March 2019; Accepted: 2 May 2019; Published: 11 May 2019 

Abstract: A turbocharged numerical model, suitable for real-time ship manoeuvre simulation, is presented in this paper. While some engine components (mainly the turbocharger, intercooler and manifolds) are modelled by a filling and emptying approach, the cylinder simulation is based on a set of five-dimensional numerical matrices (each matrix is generated by means of a more traditional thermodynamic model based on in-cylinder actual cycle). The new cylinder calculation approach strongly reduces the engine transient computation time, making it possible to transform the simulation model into a real-time executable application. As a case study, the simulation methodology is applied to a high speed four stroke turbocharged marine diesel engine, whose design and off design running data are available from the technical sheet. In order to verify the suitability of the proposed model in real-time simulation applications, a propulsion plant simulator is developed. Numerical results in ship acceleration and deceleration manoeuvres are shown, reducing the simulation running time of 99% in comparison with the corresponding in-cylinder actual cycle engine model.

Keywords: real-time simulation; ship propulsion; diesel engine; cylinder dynamics; computation time

1. Introduction For ship propulsion controller development and tuning [1–3], or for crew training purposes [4–6], it is essential to have reliable simulators that are able to predict in real time the behaviour of all the system components involved (engine, mechanical power transmission, , rudder, hull, etc.). In the last fifteen years, the authors have gained experience in the use of Real Time Hardware in the Loop (RT HIL) simulation for the design of the propulsion control systems of important Italian vessels [1–3,7]. RT HIL simulation consists of an in-test setup where the real hardware controller can exchange data with the ship propulsion models (mainly the engine and propeller) that are simulated in real-time. From a practical point of view, the adoption of this approach required us to face two challenges: running the model in real time mode and interfacing it with the real controller. This was successfully achieved for ship propulsion applications equipped with marine gas turbines [3]. The main engine is one of the most, if not the most, critical propulsion component to be simulated, requiring good precision and possibly a low computation time. Speed and accuracy are the crucial factors for making a model real-time capable, depending on the technological limits of the current computer processors.

J. Mar. Sci. Eng. 2019, 7, 138; doi:10.3390/jmse7050138 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, 138 2 of 19

In comparison with a marine , a simulation process of a turbocharged diesel engine (the most usual prime mover in marine propulsion systems) presents more difficulties in reproducing chemical and thermodynamic phenomena without significantly increasing the simulation running time. In the literature, different approaches for marine diesel engine simulation are proposed. To strongly reduce the computation time, the engine behaviour is estimated by performance maps in [8–11] or empirical correlations in [12,13]. The engine torque or power are determined as a function of a reduced number of input parameters, such as rotational speed and fuel rate, while the engine and relative subsystem (turbocharger) dynamics are taken into account by means of time constants. A little more sophisticated approach is used in [14–16], where an ideal dual combustion cycle is considered for in-cylinders phenomena calculations, and simple or more complex performance maps are used for turbocharger compressor and turbine behaviour. However, the best diesel engine simulation results, in terms of in-cylinders phenomena computation, are obtained by a fully thermodynamic actual cycle simulation approach, where the cylinder thermodynamic processes, including combustion, are calculated as crank angle functions. In these models, a “single- zone” [17–20] or a “dual-zone” [21–23] combustion scheme is adopted. Further possible approaches involve quasi-dimensional combustion models [24,25] or CFD (Computational Fluid Dynamics) analyses [26], while other specific methodologies can be developed for the engine emissions assessment [27]. For the turbocharger (TC) system modelling, a thermodynamic approach (based on steady state TC compressor and turbine performance maps, dynamic mass ad energy equations for the manifolds and intercooler simulation) increases the simulation running time very slightly; on the contrary, the same cannot be stated as far as the in-cylinders phenomena assessment. For this engine component, the actual cycle approach requires a complicated step-by-step calculation procedure, based on the crank-angle variation, that strongly increases the computation time. In this paper, a more simple numerical methodology is proposed for the cylinder performance representation, in order to considerably reduce the running time during the diesel engine transients simulation without affecting the results accuracy in comparison with the actual cycle in-cylinders approach. The basic idea is to replace the traditional thermodynamic equations of the cylinder with appropriate multidimensional numerical maps, in order to simplify the calculation process during the simulation, but still creating a dynamic model for the prediction over time of the main characteristics of the engine. An alternative approach could be represented by the application of an Artificial Neural Network (ANN) [28,29] although the training of an ANN, reproducing the engine behaviour over time, requires many samples of engine transients (both in accelerations and deceleration conditions). In this regard, the proposed method, based on numerical tables and physical equations (especially for turbocharger dynamics) can avoid the use of ANN together with its long training procedure. However the article does not want to deal with a certain numerical technique, but it wants to present an alternative structure of a diesel engine model to achieve a faster simulation. The model has been then used to simulate two twin turbocharged high-speed diesel powering a motor yacht equipped with two fixed pitch . The model validation is based on the comparison with the engine manufacturer steady state data and with the acceleration and deceleration manoeuvre simulation results, achieved by an actual cycle “single zone” diesel engine model previously developed by the authors [23]. As for computation speed, in this paper it will be shown that the running time required by the new simulator is about 1% of the fully thermodynamic one [23]. This result is essential for the development of a diesel engine real-time simulator, since a fast simulation process can be more easily transformed into a real-time executable application.

2. Thermodynamic Diesel Engine Simulator The real-time diesel engine simulator comes from the fully thermodynamic cylinder’s actual cycle model [23], developed in a Matlab/Simulink environment and consisting of the following modules (Figure1): J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 3 of 21

J. Mar.- Sci.inlet Eng. 2019 manifold, 7, 138 and intercooler; 3 of 19 - exhaust gas manifold; - turbocharger (TC) compressor; - cylinders; - TC turbine; - inlet manifold and intercooler; - TC shaft dynamics. - exhaust gas manifold; A filling and emptying method is adopted in each simulator module, describing the pertinent -subsystem turbocharger behaviour (TC) by compressor; means of component performance maps, and algebraic and differential -equations. TC turbine; The fluid is modelled as an ideal gas while the specific internal energy and enthalpy are -both functionTC shafts dynamics. of temperature and fluid composition. A brief description of the engine simulator is reported in the following, however a more detailed explanation can be found in [23].

Figure 1. Simulink engineengine model, model where, where M_f M_f= fuel= fuel rate; rate; M_C M_C i = compressori = compressor inlet inlet air mass air mass flow; flow; M_cy M_cyi = cylinders i = cylinders inlet airinlet mass air flow;mass M_cyflow; M_cy o = cylinders o = cylinders gas mass gas mass flow; flow; M_T oM_T= turbine o = turbine outlet outlet gas mass gas massflow; N_Eflow;= N_Eengine = engine speed; speed; N_TC = N_TCturbocharger = turbocharger shaft speed; shaft p_C speed; o = p_Ccompressor o = compressor outlet pressure; outlet pressurep_cy i = ;cylinder p_cy i =inlet cylinder pressure; inlet p_cy pressure; o = cylinder p_cy outleto = cylinder pressure; outlet p_T pressure;i = exhaust p_T gas i manifold = exhaust outlet gas manifoldpressure; Q’_Coutlet= pressure;compressor Q’_C torque; = compressor Q’_E o = engine torque; delivered Q’_E o = torque; engine Q’_T delivered= turbine torque; torque; Q’_T T_C = turbineo = compressor torque; T_C outlet o = temperature;compressor outlet T_cy temperature; i = cylinder T_cy inlet i temperature; = cylinder inlet T_cy temperature; o = cylinder T_cy outlet o = cylindertemperature; outlet T_T temperature; i = turbine T_T inlet i temperature.= turbine inlet temperature.

2.1. BasicA filling Equations and emptying method is adopted in each simulator module, describing the pertinent subsystem behaviour by means of component performance maps, and algebraic and differential The fluid is modelled by the ideal gas equation: equations. The fluid is modelled as an ideal gas while the specific internal energy and enthalpy are both functions of temperature and fluid composition.pV = mRT A brief description of the engine simulator(1) is reported in the following, however a more detailed explanation can be found in [23]. where p is the pressure; V the volume; m the fluid mass; R the gas constant and T the temperature. 2.1. BasicFluid Equations mass and energy stored in each engine component volume are calculated through the continuity and the energy dynamic equation: The fluid is modelled by the ideal gas equation: dV  M  M  (2) dtpV = mRTi o (1)

where p is the pressure; V thed volume;UV  m the fluid mass; R the gas constant and T the temperature. M H  M H  M H Φ  P (3) Fluid mass and energy storeddt in eachi enginei o componento f f volume are calculated through the continuity and the energy dynamic equation: where ρ is the gas density; U the gas specific internal energy; Mi and Mo the mass flow rate at the inlet and outlet section; Hi and Ho the specificd(ρV) enthalpy at the inlet and outlet section; Mf and Hf = (M Mo) (2) dt i −

J. Mar. Sci. Eng. 2019, 7, 138 4 of 19

d(ρUV)   = M H MoHo + M H + Φ P (3) dt i i − f f − where ρ is the gas density; U the gas specific internal energy; Mi and Mo the mass flow rate at the inlet and outlet section; Hi and Ho the specific enthalpy at the inlet and outlet section; Mf and Hf respectively the fuel mass flow rate and lower heating value; Φ the heat flow and P the mechanical power. The turbocharger shaft dynamics equation is:

dω 1 = (Q0 Q0 ) (4) dt J T − C where ω is the angular velocity; J is the total moment of inertia; Q’T and Q’C are the turbine and compressor torque, respectively.

2.2. Thermodynamic Cylinder Module In the thermodynamic module named “cylinders” in Figure1, a single zone actual cycle approach is used to assess in-cylinders phenomena. The in-cylinder calculations use the crank angle θ as an independent variable and start when the inlet valve is open (fresh air charge intake phase) and end at the gas exhaust phase. The flow through the inlet and exhaust valves is determined by Equation (5) for compressible gas through a flow valve restriction:

1   k 1 0.5 ! ! − dm ARpi po k  2k  po k  = C  1  (5) D 0.5    dt ( ) pi k 1 − pi  RTi − In the case of choked flow, the equation used is:

  k+1 dm ARpi 1 2 2(k 1) = C k 2 − (6) dt D 0.5 k + (RTi) 1 where pi and Ti are the pressure and temperature at the inlet section of the cylinder valves; po is the exhaust manifold pressure; AR is the valve open area and k is the ratio of specific heats. The discharging coefficient value CD is assumed to be equal to 0.7. The piston displacement from the top dead centre (x) is determined by the crank angle value through [30]:  ! 1   2 2   1 l 2  x =r1 + sin θ cos θ (7)  r − r2 − −  where r is the crank radius and l the connecting rod length. From the x values, it is possible to calculate the in-cylinder volume V of Equations (2) and (3). Using Equation (3), the air compression process is then determined for each crank angle step variation (dθ). During each calculation step dθ, the convective gas–cylinder wall heat transfer (Φ in Equation (3)) is determined as reported in [31]. The fuel ignition crank angle (θign) is given by:

θign = θinj + θid (8) where θinj is the crank angle corresponding to fuel injection starting. The ignition delay angle θid, is estimated by the following relationship: !   0.388 40 0.69 4.644 − θid = Kid n pcy exp (9) CN Tcy J. Mar. Sci. Eng. 2019, 7, 138 5 of 19

where Kid is the delay constant; n is the engine rotational speed; pcy and Tcy are the in-cylinder pressure and temperature at the fuel injection beginning; and CN is the fuel cetane number. At each calculation step dθ, the heat dQf released in the combustion process is determined by:

dQ f = dmbH f (10) where Hf is the fuel lower heating value and dmb is the fuel mass burned. The latter is obtained through:

dmb = m f dxb (11) with mf being the total fuel mass injected per cycle. The fuel fraction burned dxb in Equation (11), during the calculation step dθ, is determined by the Wiebe equation [22]:   θ θ !Km+1  ign  dxb = 1 exp  Ka −  (12) − − ∆θ  where Ka and Km are numerical constants; θign is the crank angle corresponding to fuel ignition and ∆θ is the total combustion angle length. In each calculation step dθ, the work done onto the piston (dW) is calculated by:

dW = pc dV (13) where pc is the in-cylinder pressure during the cycle computation and dV is the cylinder volume change. The cylinder pressure pcy is found through the ideal gas equation (Equation 1), once the fluid temperature from the energy equation (Equation 3) is known. The brake mean effective pressure (b.m.e.p). is determined by:

b.m.e.p = i.m.e.p. + p.m.e.p. f .m.e.p. (14) − where i.m.e.p is the gross indicate mean effective pressure; p.m.e.p. is the pumping mean effective pressure and f.m.e.p. is the mechanical friction mean effective pressure. The latter is evaluated on the basis of test data provided by the engine manufacturer by means of the procedure described in [15]. Finally, the engine delivered brake torque (Q’E) can be calculated by:

V Q0 = b.m.e.p. (15) E 4π

2.3. Inlet Manifold and Intercooler Module As shown in Figure1, these two components of the engine are simulated through a single module. The mass and energy accumulation in the considered control volume are determined by means of the pertinent dynamic equations (Equations (2) and (3), respectively). The air cooling effect is assessed by a heat exchanger efficiency equation. The overall set pressure drop is determined as a function of the inlet pressure and mass flow rate.

2.4. Exhaust Gas Manifold Module This block, located between the “cylinders” and “TC turbine” modules of the engine simulator of Figure1, works in a very similar mode to the intercooler and air receiver modules, by using the dynamic continuity equation (Equation (2)) and the energy equation (Equation (3)). The exhaust J. Mar. Sci. Eng. 2019, 7, 138 6 of 19

manifold temperature Tex (i.e., the TC turbine inlet gas temperature T_Ti in Figure1) is calculated considering the blow-down effect through the exhaust valve [31], as follows: " ! !# k 1 po Tex =Ti 1 − 1 (16) − k − pi where Ti and pi are the in-cylinder temperature and pressure during the unloading phase and po is the exhaust gas manifold pressure.

2.5. Turbocharger Compressor and Turbine Modules The compressor behaviour is simulated by a numerical table extrapolated from the manufacturer’s datasheet. It reports the pressure ratio and isentropic efficiency values, both depending on the corrected volume flow rate (V’Cc) and the corrected rotational speed (nCc): s Tre f V0Cc = V0C (17) Ta s Tre f nCc = nTC (18) Ta where V’C is the volumetric flow rate; Ta and Tref are the ambient and reference temperature respectively and nTC is the TC rotational speed. From the compressor pressure ratio and efficiency, it is possible to assess the outlet air pressure and adsorbed torque. The turbine simulation approach is very similar to the compressor one, since the turbine gas flow rate and efficiency (needed for the delivered torque computation) are estimated by a steady state map depending on the pressure expansion ratio and the kinematic ratio (i.e., the ratio between the rotor speed and the isentropic expansion velocity).

2.6. Turbocharger Shaft Module The basic Equation (4) is used to calculate the TC shaft angular speed (N_TC) in the “TC shaft dynamics” engine simulator module in Figure1.

2.7. Overall Engine Simulator Input–Output Variables With reference to Figure1, the input variables needed by the engine simulator are the engine speed (N_E) and the fuel mass flow rate in percentage (M_f %), referred to as the maximum continuous rating fuel flow consumption. The main simulation output of the engine model is the shaft torque (Q’_E o).

3. Simplified Cylinder Model The “cylinders” module of the thermodynamic simulator (Figure1) is mainly responsible for the long running time. To speed up the computation time, it was decided to substitute the actual cycle calculation procedure with a simpler methodology. In the new approach, the output results of the “cylinders” module are estimated by five five-dimensional (5-D) matrices, one for each of the following output data: (1) cylinder inlet air flow rate; (2) engine delivered torque; (3) outlet exhaust gas flow rate; (4) outlet exhaust gas temperature; (5) outlet exhaust gas pressure J. Mar. Sci. Eng. 2019, 7, 138 7 of 19 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 7 of 21

FigureIn the 2 whole shows new the five “cylinders” input values module, of a single each table 5-D table evaluates for a faster a sampled computation representation of one of of the a fivefunction considered in five outputvariables data.: inputs are mapped to an output value by looking up or interpolating a table of numerical values, defined in the 5-D matrix.

Figure 2. Example of in-cylinder phenomena modelling by a five-dimensional (5-D) matrix (Simulink Figure 2. Example of in-cylinder phenomena modelling by a five-dimensional (5-D) matrix (Simulink environment). environment). In the whole new “cylinders” module, each table evaluates a sampled representation of a function in fiveThe variables: input values inputs of every are mapped 5-D table to anare outputobviously value the by same looking as the up thermodynamic or interpolating “cylinders” a table of numericalmodule of values,Figure 1, defined i.e.: engine in the speed 5-D matrix. (N_E), percent fuel mass flow (M_f %), cylinder inlet pressure (p_cyThe i), temperature input values (T_cy of every i), and 5-D exhaust table are gas obviously outlet pressure the same (p_Ti as). the thermodynamic “cylinders” moduleThe of data Figure reported1, i.e.: in engine each of speed the 5 (-N_ED matrices), percent are fuel evaluated mass flow by running (M_f %), the cylinder engine inlet simulator, pressure in (thep_cy “cylinders” i), temperature actual (T_cy cycle i), configuration, and exhaust gas for outlet a large pressure range (ofp_Ti engine). revolutions. In particular, in orderThe to data cove reportedr the entire ineach engine of the working 5-D matrices area, the are evaluated engine speed by running N_E is theconsidered engine simulator, in a range in thebetween “cylinders” 45% and actual 110% cycle of the configuration, engine design for value a large (considering range of 5% engine as an revolutions. incremental Instep particular,), while the in orderfuel mass to cover flowthe rate entire M_f % engine is tested working in thearea, range the of engine10–110 speed% (10%N_E as anis consideredincremental in step a range). between 45% and 110% of the engine design value (considering 5% as an incremental step), while the fuel mass 4. Engine Models Application and Validation flow rate M_f % is tested in the range of 10–110% (10% as an incremental step). The described thermodynamic model (characterised by the actual cycle “cylinders” module 4.[31 Engine]) was recently Models applied Application to the and performance Validation simulation of two marine engines by Rolls Royce: the dieselThe engine described RR C25:33L6P thermodynamic and the model natural (characterised gas fed engine by RR the C26:33L8PG actual cycle“cylinders” (where in the module latter, [ 31the]) was“cylinders” recently module applied is to adapted the performance for the natural simulation gas combustion of two marine simulation enginesby [32 Rolls]). These Royce: two the engines diesel engineare characterized RR C25:33L6P by and a the maximum natural gas continuous fed engine rating RR C26:33L8PG (MCR) power (where of in the 2 MW latter, and the “cylinders” 2.16 MW modulerespectively, is adapted at the for same the natural rotational gas combustion speed (1000 simulation rpm). The [32 ]). comparison These two engines between are reference characterized and bysimulation a maximum data, continuousreported in rating[32], show (MCR)ed powera good ofsimulator 2 MW and accuracy 2.16 MW: the respectively,errors are generally at the same less rotationalthan 2% in speed the (1000 MCR rpm). engine The load comparison conditions, between and less reference than 5% and in simulation the other data, examined reported working in [32], showedconditions a goodof the simulator engines. accuracy: the errors are generally less than 2% in the MCR engine load conditions,The two and engine less thanmodels 5% described in the other in examinedthis paper working (i.e. cylinder conditions actual ofcycle the and engines. simplified one) are appliedThe to two the engine simulation models of described the General in this Electric paper (GE) (i.e., cylinder marine 12V actual 228 cycle four and stroke simplified diesel one) engine, are appliedwhose main to the characteristics simulation of the are General reported Electric in Table (GE) 1. marine The comparison 12V 228 four between stroke diesel brake engine, specific whose fuel mainconsumption characteristics (bsfc) are reference reported data inTable and 1simulation. The comparison results between is reported brake in specific Figure fuel 3. consumptionIn particular, (bsfc)engine reference working data conditions and simulation at propeller results and is reportedmaximum in continuous Figure3. In speed particular,s are engineconsidered. working The conditionssimulation ataccuracy propeller between and maximum the actual continuous cycle cylinders speeds module are considered. and the 5-D The matrices simulation approach accuracy is so betweengood that the the actual results cycle appear cylinders coincident module. and the 5-D matrices approach is so good that the results appear coincident. Table 1. General Electric (GE) marine 12V 228 four stroke diesel engine main data. MCR = maximum continuous rating; bsfc = brake specific fuel consumption.

Engine Characteristics Values Cylinder number 12

J. Mar. Sci. Eng. 2019, 7, 138 8 of 19

Table 1. General Electric (GE) marine 12V 228 four stroke diesel engine main data. MCR = maximum J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 8 of 21 continuous rating; bsfc = brake specific fuel consumption.

Engine CharacteristicsBore (mm) Values228.6 Stroke (mm) 266.7 Cylinder number 12 BoreCompression (mm) ratio 228.615.7 MCRStroke brake (mm) power (kW) 2289 266.7 CompressionMCR speed ratio (rpm) 1050 15.7 MCR brakeMCR power bsfc (kW)(g/kWh) 207.9 2289 MCR speed (rpm) 1050 Height (mm) 2734 MCR bsfc (g/kWh) 207.9 HeightLength (mm) (mm) 4687 2734 LengthWidth (mm) (mm) 2121 4687 WidthDry (mm) weight (kg) 18942 2121 Dry weight (kg) 18942

FigureFigure 3. 3.Brake Brake specific specific fuel fuel consumption consumption comparison comparison among among reference reference data, data engine, engine actual actual cycle cycle and and 5-D5-D matrices matrices “cylinders” “cylinders” simulation simulation results. results.

For the sake of completeness, the actual cycle approach was validated in a different application [22] For the sake of completeness, the actual cycle approach was validated in a different application by comparing simulation results and experimental data about: gross indicated mean effective pressure, [22] by comparing simulation results and experimental data about: gross indicated mean effective the in-cylinder pressure, cylinder wall temperature and heat release rate. The comparison was carried pressure, the in-cylinder pressure, cylinder wall temperature and heat release rate. The comparison out for three different engine working conditions (brake mean effective pressure equal to 100%, 75% and was carried out for three different engine working conditions (brake mean effective pressure equal 50% of MCR) at the rated speed. Only for the cylinder heat release rate, the error between simulation to 100%, 75% and 50% of MCR) at the rated speed. Only for the cylinder heat release rate, the error and test data exceeds 1.5% but is still less than 3.5% (further details can be found in [22]). Unfortunately, between simulation and test data exceeds 1.5% but is still less than 3.5% (further details can be found for the engine considered in the present work, only brake specific fuel consumption data are available in [22]). Unfortunately, for the engine considered in the present work, only brake specific fuel for the simulation validation process. consumption data are available for the simulation validation process. 5. Yacht Propulsion Plant Simulator 5. Yacht Propulsion Plant Simulator In order to verify the performance of the above described diesel engine models in transient In order to verify the performance of the above described diesel engine models in transient conditions and to compare the respective simulation accuracy and computation time, both approaches conditions and to compare the respective simulation accuracy and computation time, both are used in a motor-yacht propulsion simulator again developed in a Matlab/Simulink environment. approaches are used in a motor-yacht propulsion simulator again developed in a Matlab/Simulink Table2 shows the main ship characteristics, whose propulsion system is equipped with two fixed pitch environment. Table 2 shows the main ship characteristics, whose propulsion system is equipped propellers, each one driven through a gearbox by a GE marine 12V 228 four stroke diesel engine. with two fixed pitch propellers, each one driven through a gearbox by a GE marine 12V 228 four stroke diesel engine.

Table 2. Motor-yacht characteristics.

Yacht Data Values Length (m) 85.6 Beam (m) 14.3 Draft (m) 4.0

J. Mar. Sci. Eng. 2019, 7, 138 9 of 19

Table 2. Motor-yacht characteristics.

Yacht Data Values Length (m) 85.6 Beam (m) 14.3 Draft (m) 4.0 Max speed (knots) 17 Engine power (kW) 2 2289 × Propeller 2 5 blades ×

The numerical simulation techniques to assess the ship performance were already described and validated in [33]. However, a brief description of the yacht propulsion plant simulator is repeated hereinafter. The open water propeller data (Wageningen series) have been adopted for the propeller modelling. By equations: 2 4 Tp = ρsw Kt Np D (19) 2 5 Q’p = ρsw KQ Np D (20) where the propeller thrust Tp and torque Q’p are functions of the thrust Kt and torque KQ coefficients (both depending on the propeller advance coefficient), the propeller diameter D and rotational speed Np; ρsw is the sea water density. Once propeller torque is calculated, the propeller speed Np is determined by the shaft dynamics equation: ! dNp 1 Q0p = Q0E Q0 f (21) dt 2π Jpolar − ηr − where Jpolar is the total inertia polar moment of the all rotational masses (engine, gearbox and propeller plus added water mass); Q’E is the main engine brake torque; Q’p is the open water propeller torque; ηr is the propeller shaft efficiency and Q’f represents the gear frictional losses (considered as a percentage of the engine delivered torque). The gearbox is modelled by the gear ratio, mechanical efficiency and inertia. Ship dynamics are evaluated in one degree of freedom, taking into account only the hull surge motion. Ship speed Vs is calculated by solving the differential equation: ! dVs 1 Rt = zTp (22) dt ms + m − 1 tp ad − where ms and mad are the ship mass and added water mass; z is the number of the working propellers and Tp the single propeller thrust; tp is the thrust deduction factor and Rt the hull total resistance, depending on Vs. In this application, the engine throttle valve is controlled by a proportional and integral action of the governor. The bridge lever position requires the propeller speed, that is compared with the effective one. The speed error is then the input data of the engine governor, whose output is the fuel mass flow rate (M_f % in Figure1). The fuel pump and injection system delays are modelled by a time constant.

6. Yacht Manoeuvre Simulation Boat acceleration and deceleration manoeuvres are simulated to compare behaviour and computation time of the actual cycle “cylinders” method with the 5-D matrices approach. Many simulation values reported in the following figures are normalized on the basis of the MCR engine running conditions. The first transient considered for the engine simulators comparison is yacht acceleration due to the lever step increase from two up to 10, as visualized in Figure4. The fuel mass flow rate percentage managed by the engine governor increases over time, as shown in Figure5. J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 10 of 21 J.J. Mar. Mar. Sci. Sci. Eng. Eng.2019 2018, 7, ,6 138, x FOR PEER REVIEW 1010 of of 19 21

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 10 of 21

Figure 4. Bridge lever position. FigureFigure 4. 4.Bridge Bridge lever lever position. position.

Figure 4. Bridge lever position.

FigureFigure 5. 5.Fuel Fuel mass mass flow flow rate rate time time variation. variation. Figure 5. Fuel mass flow rate time variation. FiguresFigures6 and6 and7 show 7 show simulation simulationFigure results 5. results Fuel inmass thein flowthe engine enginerate time working working variation. area area and and TC TC compressor compressor map. map. TheThe transient transientFigures trajectories6 trajector and 7 showies determined determined simulation by by results the the engine engine in the actual actual engine cycle cycle working cylinders cylinders area model modeland TC (dashed (dashed compressor black black lines) maplines). Figures 6 and 7 show simulation results in the engine working area and TC compressor map. andTandhe 5-D transient5-D matrices matrices trajector method methodies (continuous determined (continuous red by red lines)the lines)engine are practicallyare actual practically cycle coincident. cylinders coincident. The model sameThe (dashed same consideration consideration black lines) can The transient trajectories determined by the engine actual cycle cylinders model (dashed black lines) beandcan substantially be5-D substantially matrices stated method stated for the (continuous for other theengine other red engine and lines) ship and are characteristics ship practically characteristics illustratedcoincident. illustrated in The Figures same in 8Figures– 17consideration. In detail,8–17. In and 5-D matrices method (continuous red lines) are practically coincident. The same consideration thecandetail two be, substantially simulationthe two simulation approaches stated forapproaches the show other larger showengine di fflargererences and ship difference in characteristics compressions in compression ratioillustrated (around ratio in Figures 0.8%), (around air 8– flow0.8%)17. In, can be substantially stated for the other engine and ship characteristics illustrated in Figures 8–17. In rateair (around flow rate 0.5%), (around turbine 0.5%), inlet turbine temperature inlet (around temperature 1%) and (around turbocharger 1%) and rotational turbocharger speed rotational (0.6%). detaildetail, the, the two two simulation simulation approaches approaches show show larger larger differencedifferences inin compressioncompression ratio ratio (around (around 0.8%) 0.8%), , airspeed A flow second(0.6%). rate transient (around 0.5%), example, turbine considered inlet temperature for the two-engine (around simulator 1%) and comparison, turbocharger is rotational a yacht decelerationair flow due rate to (around the telegraph 0.5%), turbine decrease inlet from temperature step 10 to four, (around as represented 1%) and turbocharger in Figure 18 . rotational Figure 19 speedspeed (0.6%). (0.6%). shows the pertinent fuel mass flow rate percentage time variation.

Figure 6. Ship acceleration in the engine map. FigureFigure 6. Ship6. Ship acceleration acceleration in in the the engine engine map. map. Figure 6. Ship acceleration in the engine map.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 11 of 21 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 11 of 21 J. Mar. Sci. Eng. 2019, 7, 138 11 of 19 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 11 of 21

Figure 7. TC acceleration in the compressor map. Figure 7. TC acceleration in the compressor map. FigureFigure 7. TC7. TC acceleration acceleration in in the the compressor compressor map.map.

Figure 8. Engine power time history. FigureFigure 8. 8.Engine Engine power power timetime history.history. Figure 8. Engine power time history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 12 of 21 Figure 9. Engine torque time history. Figure 9. Engine torque time history. Figure 9. Engine torque time history. Figure 9. Engine torque time history.

Figure 10. Compressor outlet pressure time history.. Figure 10. Compressor outlet pressure time history

Figure 11. Compressor air flow rate time history.

Figure 12. Turbine inlet pressure time history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 12 of 21 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 12 of 21

Figure 10. Compressor outlet pressure time history. J. Mar. Sci. Eng. 2019, 7, 138 Figure 10. Compressor outlet pressure time history. 12 of 19

Figure 11. Compressor air flow rate time history. FigureFigure 11. 11.Compressor Compressor air air flow flow raterate timetime history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 13 of 21 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 13 of 21 FigureFigure 12. 12.Turbine Turbine inlet inlet pressure pressure time time history.history. Figure 12. Turbine inlet pressure time history.

Figure 13. Turbine inlet temperature time history. FigureFigure 13. 13.Turbine Turbine inlet inlet temperature temperature time time history.history.

FigureFigure 14. 14.TC TC speed speed time time history. history. Figure 14. TC speed time history.

Figure 15. Engine speed time history. Figure 15. Engine speed time history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 13 of 21

Figure 13. Turbine inlet temperature time history.

J. Mar. Sci. Eng. 2019, 7, 138 Figure 14. TC speed time history. 13 of 19

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 14 of 21

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 14 of 21

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 14 of 21 FigureFigure 15. 15.Engine Engine speed speed time time history.history.

Figure 16. Propeller thrust time history.

Figure 16. Propeller thrust time history. FigureFigure 16. 16.Propeller Propeller thrust thrust time time history. history.

Figure 17. Ship speed time history.

A second transient example, considered for the two-engine simulator comparison, is a yacht deceleration due to the telegraph decrease from step 10 to four, as represented in Figure 18. Figure FigureFigure 17. 17.Ship Ship speed speed timetime history.history. 19 shows the pertinent fuel mass flow rate percentage time variation. Figure 17. Ship speed time history. A second transient example, considered for the two-engine simulator comparison, is a yacht decelerationA second due transient to the telegraph example, decrease considered from for step the 10 two to- fourengine, as simulatorrepresented comparison in Figure, 18.is aFigure yacht 19deceleration shows the pertinentdue to the fuel telegraph mass flow decrease rate percentage from step time10 to variation.four, as represented in Figure 18. Figure 19 shows the pertinent fuel mass flow rate percentage time variation.

FigureFigure 18. 18.Lever Lever position position in in deceleration deceleration manoeuvre.manoeuvre.

Figure 18. Lever position in deceleration manoeuvre. Figure 18. Lever position in deceleration manoeuvre.

J. Mar.J. Mar. Sci. Eng.Sci. Eng.2019 2018, 7, 138, 6, x FOR PEER REVIEW 1514 of of 21 19

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 15 of 21

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 15 of 21

FigureFigure 19. 19.Fuel Fuel mass mass flow flow rate rate time time history.history.

TheThe simulation simulation results results in in the the engine engine and and TC TC compressor compressormaps maps areare reported in in Figures Figures 20 20 and and 21. 21 . AlsoAlso in this in this case, case, transient transient results results are are coincident coincident for for the the two two engine enginesimulation simulation approaches.approaches. The The same same is validis valid for Figuresfor Figures 22– 2231– too.31 too. In addition, from the point of view of the simulation running time, 250 s of the yacht acceleration manoeuvre are simulated in a MATLAB computation time of 206.95 s by the actual cycle “cylinders” Figure 19. Fuel mass flow rate time history. engine model, versus the 2.04 s of the 5-D matrices approach. The ship deceleration needs to be Figure 19. Fuel mass flow rate time history. performedThe by simulation the simulation results in in 234.17 the engine s and and 2.06 TC s respectively compressor maps for the are two reported methods; in Figures similar 20 results and 21. are foundAlso for inThe other this simulation case, yacht transient propulsion results results in the manoeuvres. are engine coincident and TheseTC for compressor the speed two dataengine maps obviously simulation are reported depend approaches in Figures on the. 20The particular and same 21. computerisAlso valid in processor forthis Figures case, power;transient 22–31 therefore,too results. are the coincident real noteworthy for the two result engine is that simulation the new approaches simulation. The approach same for theis valid engine, for in Figures comparison 22–31 too with. a traditional thermodynamic model, makes the whole ship simulator about one hundred times faster.

Figure 20. Ship deceleration in the engine map.

Figure 20. Ship deceleration in the engine map. FigureFigure 20. 20.Ship Ship deceleration deceleration in in the the engine engine map. map.

Figure 21. TC deceleration in the compressor map.

FigureFigure 21. 21.TC TC deceleration deceleration in in the the compressor compressor map.map. Figure 21. TC deceleration in the compressor map.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 16 of 21 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 16 of 21 J. Mar.J. Mar. Sci. Sci. Eng. Eng.2019 2018, 7,, 138 6, x FOR PEER REVIEW 1615 of of 21 19

Figure 22. Engine power time history.

Figure 22. Engine power time history. FigureFigure 22. 22.Engine Engine power power timetime history.history.

Figure 23. Engine torque time history.

FigureFigure 23. 23.Engine Engine torque torque timetime history.history. Figure 23. Engine torque time history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 17 of 21 FigureFigure 24. 24.Compressor Compressor outlet outlet pressure pressure timetime history.

Figure 24. Compressor outlet pressure time history. Figure 24. Compressor outlet pressure time history.

Figure 25. Compressor air flow rate time history. Figure 25. Compressor air flow rate time history.

Figure 26. Turbine inlet pressure time history.

Figure 27. Turbine inlet temperature time history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 17 of 21 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 17 of 21

Figure 25. Compressor air flow rate time history. J. Mar. Sci. Eng. 2019, 7, 138 16 of 19 Figure 25. Compressor air flow rate time history.

Figure 26. Turbine inlet pressure time history. FigureFigure 26. 26.Turbine Turbine inlet inlet pressure pressure timetime history.history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 18 of 21 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 18 of 21 FigureFigure 27. 27.Turbine Turbine inlet inlet temperature temperature time timehistory. history. Figure 27. Turbine inlet temperature time history.

Figure 28. TC speed time history. FigureFigure 28. 28.TC TC speed speed time time history.history.

FigureFigure 29. 29.Engine Engine speed speed time time history. history. Figure 29. Engine speed time history.

Figure 30. Propeller thrust time history. Figure 30. Propeller thrust time history.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 18 of 21

Figure 28. TC speed time history.

J. Mar. Sci. Eng. 2019, 7, 138 Figure 29. Engine speed time history. 17 of 19

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 19 of 21 FigureFigure 30. 30.Propeller Propeller thrust thrust time time history.history.

FigureFigure 31. 31.Ship Ship speed speed timetime history.history. 7. Conclusions In addition, from the point of view of the simulation running time, 250 seconds of the yacht accelerationA methodology manoeuvre to simulate are simulated diesel engine in a MATLAB dynamics computation is proposed time in order of 206.95 to strongly seconds reduce by the the simulationactual cycle running “cylinders” time. Theengine study model, stems versus from the the 2.04 need seconds to use of marine the 5-D propulsion matrices approach simulators. The in realship time, deceleration specifically needs developed to be forperformed control by system the simulation design or trainingin 234.17purposes. seconds and Thermodynamic 2.06 seconds equations,respectively representing for the two in-cylinder methods; phenomena, similar results are are usually found responsiblefor other yacht for propulsion a high computation manoeuvres time,. makingThese the speed development data obviously of complex depend shipon the propulsion particular simulatorscomputer processor in real time power technically; therefore impossible., the real noteworthy result is that the new simulation approach for the engine, in comparison with a Hence the proposed approach is based on the steady state representation of the cylinder behaviour, traditional thermodynamic model, makes the whole ship simulator about one hundred times faster. through the introduction of 5-D matrices, each specifically built for the assessment of inlet air flow6. rate,Conclusions engine torque, exhaust gas flow rate, pressure and temperature. By this method, the whole engine dynamics are mainly due to the turbocharger dynamics; in this regard, the simulation analysisA carried methodology out to reproduceto simulate thediesel propulsion engine dynamics behaviour is proposed of a motor-yacht in order to shows strongly the reduce validity the of thissimulation assumption running (turbocharger time. The performancestudy stems from data the show need di toff erencesuse marine lower propulsion than 1% simulators between thein real two time, specifically developed for control system design or training purposes. Thermodynamic simulation approaches). For the main result, the running time of the whole propulsion simulator is equations, representing in-cylinder phenomena, are usually responsible for a high computation reduced by about 99% if the new approach for the engine dynamics description is adopted instead of time, making the development of complex ship propulsion simulators in real time technically the traditional one (based on the actual cycle in-cylinders calculation model). This faster computation impossible. Hence the proposed approach is based on the steady state representation of the cylinder speed allows to transform more easily the whole ship simulator into a real-time executable application, behaviour, through the introduction of 5-D matrices, each specifically built for the assessment of even if the complex aspects related to the representation of the vessel motions are considered. At the inlet air flow rate, engine torque, exhaust gas flow rate, pressure and temperature. By this method, samethe time, whole the engine model dynamics is able to are perform mainly reliable due to engine the turbocharger dynamics in dynamics ship propulsion; in this applications, regard, the providingsimulation also analysis in-cylinder carried thermodynamic out to reproduce data. the propulsion behaviour of a motor-yacht shows the validityIn addition, of this the assumption physical structure(turbocharger of the performance model allows data toshow simulate difference similars lower diesel than engines 1% (characterizedbetween the for two example simulation by a approaches different number). For the of cylinders)main result, simply the running updating time some of geometrical the whole datapropulsion of turbocharger simulator and is manifolds. reduced by This about kind 99% of design if the option new approach would be for much the moreengine complicated dynamics to obtaindescription in the is case adopted of using instead other numerical of the traditional techniques one such(based as neural on the networks actual cycle (being in- essentiallycylinders “blackcalculation boxes” tomodel be re-trained). This faster every computation time something speed isallows changed). to transform more easily the whole ship simulator into a real-time executable application, even if the complex aspects related to the representation of the vessel motions are considered. At the same time, the model is able to perform reliable engine dynamics in ship propulsion applications, providing also in-cylinder thermodynamic data. In addition, the physical structure of the model allows to simulate similar diesel engines (characterized for example by a different number of cylinders) simply updating some geometrical data of turbocharger and manifolds. This kind of design option would be much more complicated to obtain in the case of using other numerical techniques such as neural networks (being essentially "black boxes" to be re-trained every time something is changed). On the other hand, the method cannot disregard the availability of a fully thermodynamic model, necessary to numerically generate the five 5-D tables of the simplified approach. Moreover the ambient conditions effects (e.g. inlet air temperature) on the diesel engine performance can be more difficulty estimated without a complete thermodynamic model.

J. Mar. Sci. Eng. 2019, 7, 138 18 of 19

On the other hand, the method cannot disregard the availability of a fully thermodynamic model, necessary to numerically generate the five 5-D tables of the simplified approach. Moreover the ambient conditions effects (e.g., inlet air temperature) on the diesel engine performance can be more difficulty estimated without a complete thermodynamic model. Therefore, although some drawbacks still exist in using this method, this research represents an effective answer to an important technical problem linked to the development of ship simulators in real-time.

Author Contributions: Conceptualization, U.C. and M.L.; methodology, U.C. and M.L.; validation, U.C.; formal analysis, U.C. and M.A.; investigation, U.C.; resources, U.C. and M.M.; data curation, U.C. and M.A.; writing—original draft preparation, U.C. and M.A.; writing—review and editing, M.A, U.C., M.F. and M.M.; visualization, M.A. and U.C.; supervision, M.A. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Altosole, M.; Figari, M.; Bagnasco, A.; Maffioletti, L. Design and test of the propulsion control of the “Cavour” using real-time hardware in the loop simulation. In Proceedings of the SISO European Simulation Interoperability Workshop 2007, EURO SIW 2007, Genoa, Italy, 18–20 June 2007; pp. 67–74. 2. Altosole, M.; Benvenuto, G.; Figari, M.; Campora, U.; Bagnasco, A.; D’Arco, S.; Giuliano, M.; Giuffra, V.; Spadoni, A.; Zanichelli, A.; et al. Real time simulation of the propulsion plant dynamic behaviour of the Aircraft Carrier “Cavour”. In Proceedings of the 9th International Naval Engineering Conference and Exhibition: Embracing the Future, INEC 2008, Hamburg, Germany, 1–3 April 2008. 3. Altosole, M.; Benvenuto, G.; Figari, M.; Campora, U. Real-time simulation of a COGAG naval ship propulsion system. In Maritime Industry, Ocean Engineering and Coastal Resources, Proceedings of the 12th International Congress of the International Maritime Association of the Mediterranean, IMAM 2007, Varna, Bulgaria, 2–6 September 2007; Taylor & Francis: London, UK, 2007; Volume 1, pp. 331–337. 4. Papachristos, D.; Nikitakos, N.; Lambrou, M. A Neuroscience Approach in User Satisfaction Evaluation in Maritime Education. TransNav 2013, 7, 319–326. [CrossRef] 5. Laskowski, R.; Chybowski, L.; Gawdzi´nska,K. An Simulator as a Tool for Environmental Education of Marine Engineers. In Advances in Intelligent Systems and Computing, Proceedings of the World Conference on Information Systems and Technologies, WorldCIST 2015, Azores, Portugal, 1–3 April 2015; Rocha, A., Correia, A., Costanzo, S., Reis, L., Eds.; Springer: Cham, Switzerland, 2015; pp. 311–322. [CrossRef] 6. Chybowski, L.; Gawdzi´nska,K.; Slesicki,´ O.; Patejuk, K.; Nowosad, G. An engine room simulator as an educational tool for marine engineers relating to explosion and fire prevention of marine diesel engines. Zeszyty Naukowe Akademii Morskiej w Szczecinie 2015, 43, 15–21. [CrossRef] 7. Michetti, S.; Ratto, M.; Spadoni, A.; Figari, M.; Altosole, M.; Marcilli, G. Ship Control system wide integration and the use of dynamic simulation techniques in the Fremm project. In Proceedings of the International Conference on Electrical Systems for Aircraft, Railway and Ship Propulsion, ESARS 2010, Bologna, Italy, 19–21 October 2010. 8. Hendricks, E. Mean Value Modelling of Large Turbocharged Two-Stroke Diesel Engines. In Proceedings of the SAE International Congress and Exposition (SAE 890564), Detroit, Michigan, 27 February–3 March 1989. 9. Hirst, P.A Simple ‘Field Proven’ Engine Performance Prediction Program. In Proceedings of the Turbocharging and Turbochargers Conference, Birdcage Walk, London, UK, 7–9 June 1994. 10. Theotokatos, G. On the cycle mean value modelling of a large two-stroke marine diesel engine. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ. 2010, 224, 193–205. [CrossRef] 11. Figari, M.; Altosole, M. Dynamic behaviour and stability of marine propulsion systems. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ. 2007, 221, 187–202. [CrossRef] 12. Altosole, M.; Figari, M. Effective simple methods for numerical modelling of marine engines in ship propulsion control systems design. J. Nav. Archit. Mar. Eng. 2011, 8, 129–147. [CrossRef] 13. Winterbone, D.E.; Thiruarooran, C.; Wellestead, P.E. A Wholly Dynamic Model of a Turbocharged Diesel Engine for Transfer Function Evaluation. In Proceedings of the 1977 International Automotive Engineering Congress and Exposition (SAE 770124), Detroit, MI, USA, 28 February–4 March 1977. J. Mar. Sci. Eng. 2019, 7, 138 19 of 19

14. Would, J.K.; Bott, P.; Riet, B.J. A Diesel Engine Model for the Dynamic Simulation of Propulsion Systems. Schip en Werf de Zee 1993, 3, 4. 15. Benvenuto, G.; Campora, U. A Computer Model for the Dynamic Simulation of Turbocharged Diesel Engine. In Proceedings of the 1st International Conference on Control and Diagnostics in Automotive Applications, Genoa, Italy, 3–4 October 1996. 16. Watson, N.; Marzouk, M. A Non-Linear Digital Simulation of Turbocharged Diesel Engine Under Transient

Conditions. In Proceedings of the SAE Conference, Detroit, MI, USA, 28 February–4 March 1977. paper n◦ 770123. 17. Medica, V.; Giadrossi, A. Numerical Simulation of Turbocharged Diesel Engine Operation in Transient Load Conditions. In Proceedings of the ASME ESDA Conference, Second Biennial European Joint Conference on Engineering Systems Design and Analysis, London, UK, 4–7 July 1994. 18. Kao, M.; Moskwa, J.J. Turbocharged Diesel Engine Modeling for Nonlinear Engine Control and State Estimation. J. Dyn. Sys. Meas. Control 1995, 117, 20–30. [CrossRef] 19. Benvenuto, G.; Campora, U. A Calculation Procedure of the Real Cycle for Four-Stroke Diesel Engines. In Proceedings of the 52nd A.T.I. National Congress, Cernobbio, Italy, 22–26 September 1997. 20. Larmi, M. Transient Response Model of Low-Speed Diesel Engine in Ice-Breaking Cargo Vessels. Ph.D. Thesis, Acta Polytechnica Scandinavica, Helsinki, Finland, 1994. 21. Ishida, M.; Ueki, H.; Matsumura, N.; Chen, Z.L. Diesel Combustion Analysis Based on Two-Zone Model: Comparison between Model Analysis and Experiment. JSME Int. J. Ser. B Fluids Therm. Eng. 1996, 39, 185–192. [CrossRef] 22. Benvenuto, G.; Campora, U.; Carrera, G.; Casoli, P. A Two-Zone Diesel Engine Model for the Simulation of Marine Propulsion Plant Transients. In Proceedings of the 2nd International Conference on Marine Industry, MARIND 98, Varna, Bulgaria, 28 September–2 October 1998. 23. Campora, U.; Laviola, M.; Zaccone, R. An Overall Comparison Between Natural Gas Spark Ignition and Compression Ignition Engines for a Ro-Pax Propulsion Plant. In Proceedings of the 3th International Conference on Maritime Technology and Engineering, MARTECH 2016, Lisbon, Portugal, 4–6 July 2016; pp. 735–743. 24. Qi, K.P.; Feng, L.Y.; Leng, X.Y.; DU, B.G.; Long, W.Q. Simulation of quasi-dimensional combustion model for predicting diesel engine performance. Appl. Math. Model. 2011, 35, 930–940. [CrossRef] 25. Mrzljak, V.; Medica, V.; Bukovac, O. Simulation of a two-stroke slow speed diesel engine using a quasi-dimensional model. Trans. Famena. 2016, 40, 35–44. [CrossRef] 26. Reitz, R.D.; Rutland, C.J. Development and testing of diesel engine CFD models. Prog. Energy Combust. Sci. 1995, 21, 173–196. [CrossRef] 27. Bolla, M.; Wright, Y.M.; Boulouchos, K.; Borghesi, G.; Mastorakos, E. Soot Formation Modeling of n-Heptane Sprays Under Diesel Engine Conditions Using the Conditional Moment Closure Approach. Combust. Sci. Technol. 2013, 185, 766–793. [CrossRef] 28. Parlak, A.; Islamoglu, Y.; Yasar, H.; Egrisogut, A. Application of artificial neural network to predict specific fuel consumption and exhaust temperature for a Diesel engine. Appl. Therm. Eng. 2006, 26, 824–828. [CrossRef] 29. Bukovac, O.; Medica, V.; Mrzljak, V. Steady state performances analysis of modern marine two-stroke low speed diesel engine using mlp neural network model. Brodogradnja 2015, 66, 57–70. 30. Benson, R.S.; Whiteouse, N.D. Internal Combustion Engines; Pergamon Press International Library: Oxford, UK, 1979. 31. Campora, U.; Figari, M. Numerical Simulation of Ship Propulsion Transients and Full Scale Validation. Proc. Inst. Mech. Eng. Part. M J. Eng. Marit. Environ. 2003, 217, 41–52. [CrossRef] 32. Altosole, M.; Benvenuto, G.; Campora, U.; Laviola, M.; Zaccone, R. Simulation and Performance Comparison Between Diesel and Natural Gas Engines for Marine Applications. Proc. Inst. Mech. Eng. Part. M J. Eng. Marit. Environ. 2017, 231, 690–704. [CrossRef] 33. Altosole, M.; Figari, M.; Martelli, M. Time domain simulation for marine propulsion applications. In Proceedings of the 44th Summer Computer Simulation Conference, 2012 International Simulation Multi-Conference, Genoa, Italy, 8–11 July 2012.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).