A Three-Zone Scavenging Model for Large Two-Stroke Uniflow Marine

energies

Article A Three-Zone Scavenging Model for Large Two-Stroke Uniﬂow Marine Engines Using Results from CFD Scavenging Simulations

Michael I. Foteinos 1,* , Alexandros Papazoglou 1, Nikolaos P. Kyrtatos 1, Anastassios Stamatelos 2,* , Olympia Zogou 2 and Antiopi-Malvina Stamatellou 2

1 Laboratory of Marine Engineering, National Technical University of Athens, GR-15780 Athens, Greece; [email protected] (A.P.); [email protected] (N.P.K.) 2 Laboratory of Thermodynamics & Thermal Engines, University of Thessaly, GR-38334 Volos, Greece; [email protected] (O.Z.); [email protected] (A.-M.S.) * Correspondence: [email protected] (M.I.F.); [email protected] (A.S.)

Received: 17 April 2019; Accepted: 4 May 2019; Published: 7 May 2019

Abstract: The introduction of modern aftertreatment systems in marine diesel engines call for accurate prediction of exhaust gas temperature, since it significantly affects the performance of the aftertreatment system. The scavenging process establishes the initial conditions for combustion, directly affecting exhaust gas temperature, fuel economy, and emissions. In this paper, a semi-empirical zero-dimensional three zone scavenging model applicable to two-stroke uniflow scavenged diesel engines is updated using the results of CFD (computational fluid dynamics) simulations. In this 0-D model, the engine cylinders are divided in three zones (thermodynamic control volumes) namely, the pure air zone, mixing zone, and pure exhaust gas zone. The entrainment of air and exhaust gas in the mixing zone is specified by time varying mixing coefficients. The mixing coefficients were updated using results from CFD simulations based on the geometry of a modern 50 cm bore large two-stroke marine diesel engine. This increased the model’s accuracy by taking into account 2-D fluid dynamics phenomena in the cylinder ports and exhaust valve. Thus, the effect of engine load, inlet port swirl angle and partial covering of inlet ports on engine scavenging were investigated. The three-zone model was then updated and the findings of CFD simulations were reflected accordingly in the updated mixing coefficients of the scavenging model.

Keywords: two-stroke engine; uniflow scavenging; 0-D modelling; scavenging model; CFD simulations

1. Introduction During the scavenging process, the burnt gas inside the engine cylinders is expelled and new fresh air is charged. The scavenging process establishes the initial conditions of the combustion process, hence is affecting engine fuel economy and emissions. Commercial vessels, such as tankers, bulk carriers, and containerships are, in most cases, propelled by large two-stroke uniflow scavenged diesel engines. Better propulsion efficiency dictates the matching of the engine to a slow turning, large diameter propeller. In order to achieve low engine revolutions while maintaining a certain mean piston speed the bore to stroke ratio of marine diesel engines was increased. Due to their long stroke, loop or cross flow scavenging was unsuitable for these engines and the uniflow scavenging system was introduced. The air enters the engine cylinders through ports located at the lower part of the liner, when the piston is near the bottom dead center (BDC). After exhaust blowdown the incoming air expels the exhaust gas through the exhaust valve located on the cylinder head. The driving force of the scavenging process is the pressure difference between the scavenge receiver and the exhaust gas

Energies 2019, 12, 1719; doi:10.3390/en12091719 www.mdpi.com/journal/energies Energies 2019, 12, 1719 2 of 20 Energies 2019, 12, x FOR PEER REVIEW 2 of 19 receiver.of the Inlet scavenging ports are process usually is the angled, pressure providing differen thece between incoming the airscavenge with swirl receiver to improveand the exhaust purging of the cylinder.gas receiver. A cross Inlet sectional ports are viewusually of angled, a typical providin large uniﬂowg the incoming scavenged air with marine swirl to diesel improve engine purging is shown in Figureof the1. cylinder. A cross sectional view of a typical large uniflow scavenged marine diesel engine is shown in Figure 1.

FigureFigure 1. Cross 1. Cross sectional sectional view view of of a a uniﬂowuniflow scavenged marine marine diesel diesel engine engine [1]. [1].

BeforeBefore CFD CFD models models became became widely widely available available the the scavenging scavenging processprocess was investigated investigated in in detail detail by experimentsby experiments in scaled in down scaled engine down models. engine Such models. works Such include works visualization, include visualization, pitot tube measurements,pitot tube and hotmeasurements, wire experiments and hot whichwire experiments can be found which in can [2– 4be]. found The e ffinect [2–4]. of inletThe effect port of angle inlet onport scavenging angle efficiencyon scavenging was investigated efficiency inwas [5 ,investigated6]. A review in of[5,6]. the A various review of models the various of the models scavenging of the scavenging process can be foundprocess in [7,8 can]. be found in [7,8]. OverOver the past the past two decadestwo decades computational computational cost cost has has declined declined leading leading to to increased increased popularity popularity ofof CFD CFD modeling. Sigurdson et al., performed a CFD analysis, on a 12-degree sector, including one modeling. Sigurdson et al., performed a CFD analysis, on a 12-degree sector, including one scavenge port, scavenge port, of the MAN B&W 4T50 test engine (MAN B&W, Copenhagen, Denmark) [9]. Lamas of the MAN B&W 4T50 test engine (MAN B&W, Copenhagen, Denmark) [9]. Lamas et al. [10] investigated et al. [10] investigated the scavenging process in the MAN B&W 7S50-MC engine (MAN B&W, the scavengingCopenhagen, process Denmark) in the through MAN B&W CFD simulations. 7S50-MC engine Andersen (MAN et B&W,al. performed Copenhagen, CFD investigation Denmark) throughon CFD simulations.full scale engines, Andersen examining et al. the performed effect of CFDengine investigation load [11] and on variation full scale of engines, in-cylinder examining swirl [12] the on effect of enginescavenging load [11 efficiency.] and variation The effect of in-cylinderof inlet port swirldepth [ 12on] the on swirling scavenging flow efficiency. and scavenging The effect process of inletwas port depthinvestigated on the swirling by [13]. flow The and effect scavenging of piston process covering was half investigated of the inlet byports [13 on]. The the effectin-cylinder of piston swirling covering half offlow the was inlet examined ports on by the [14]. in-cylinder swirling flow was examined by [14]. As theAs borethe bore to stroketo stroke ratio ratio of of marine marine engines engines increased,increased, zonal zonal models models became became preferable preferable for for accurateaccurate engine engine performance performance prediction. prediction. A three-zone A three-zone scavenging scavenging submodel submodel was originally was originally introduced introduced in [15]. Due to the introduction of aftertreatment technologies in marine diesel engines in [15]. Due to the introduction of aftertreatment technologies in marine diesel engines such as selective such as selective catalytic reduction (SCR) systems, accurate exhaust gas temperature prediction catalytic reduction (SCR) systems, accurate exhaust gas temperature prediction became more essential. became more essential. Hence, the original three-zone scavenging model was updated using results Hence,from the CFD original simulations. three-zone The scavengingupdated model model can wasbe used updated in conjunction using results with froma zero-dimensional CFD simulations. The updatedengine and model SCR model, can be in used order in to conjunction investigate the with transient a zero-dimensional response of the engine-SCR engine and system. SCR model, in order to investigate the transient response of the engine-SCR system. 2. The Three-Zone Scavenging Model 2. The Three-Zone Scavenging Model In the original model [15], the cylinder is divided in three zones namely, a pure air zone, a pure Inexhaust the original gas zone, model and a [mixing15], the zone cylinder as presented is divided in Figure in three 2. zones namely, a pure air zone, a pure exhaust gasWithin zone, each and zone a mixing the temperature zone as presented is assumed in Figure uniform2. but differs in the three zones. The Withinpressure each throughout zone the the temperature cylinder is uniform is assumed at each uniform computational but differs step. in Every the three zone zones. is treated The as pressure an open system where the first law of thermodynamics may be applied. throughout the cylinder is uniform at each computationald step. Every zone is treated as an open system −pV +Q +hm = (mu) where the first law of thermodynamics may be applied. dt (1) where p is gas pressure, V is the rate. ofX change. ofX gas volume,. d Q is the rate of change of heat, h is pV + Q + h m = (mu) (1) enthalpy, 𝑚 is rate of change −of mass and usf is internalj energyj dt of the gas. An important assumption sf j

. . where p is gas pressure, V is the rate of change of gas volume, Q is the rate of change of heat, h is . enthalpy, m is rate of change of mass and u is internal energy of the gas. An important assumption Energies 2019, 12, 1719 3 of 20 of this three-zone model is that the mass exchange between the zones takes place only in two ways: scavenge air enters the mixing zone and burnt gas enters the mixing zone. Hence the rate of change of the mas for each zone is defined as: . . . mI = minp mI II (2) − − Energies 2019, 12, x FOR PEER REVIEW . . . 3 of 19 Energies 2019, 12, x FOR PEER REVIEW mII = mI II + mIII II 3 of 19 (3) − − of this three-zone model is that the mass. exchange. between. the zones takes place only in two ways: of this three-zone model is that the massm IIIexchange= mIII betweenII m exvthe zones takes place only in two ways: (4) scavenge air enters the mixing zone and burnt− gas enters− − the mixing zone. Hence the rate of change scavenge. air enters the mixing zone and burnt gas enters the mixing. zone. Hence the rate of change whereof mtheI masII is for the each air masszone is flow defined rate as: from zone I to zone II, minp is the air mass flow through inlet of .the −mas for each zone is defined as: . ports,mIII II is the mass flow rate fromm zone =m III−m to zone II and mexv is the mass flow rate through(2) the − m =m −m (2) exhaust valve. The entrainment of air and exhaust gas in the mixing zone is specified by time varying mm =m=m +m+m (3)(3) mixing coefficients. The air penetration coefficient is defined as: m =−m −m (4) m =−m −m (4) . where m is the air mass flow rate from zone I to zone II, m is the air mass flow through inlet where m is the air mass flow rate from zone I tom zoneI II II, m is the air mass flow through inlet µ = − (5) ports,ports, mm is is thethe massmass flowflow raterate fromfrom zonezone IIIIIIa toto zonezone. IIII andand mm is is thethe massmass flowflow raterate throughthrough thethe minp exhaustexhaust valve.valve. TheThe entrainmententrainment ofof aiairr andand exhaustexhaust gasgas inin thethe mixingmixing zonezone isis specifiedspecified byby timetime varyingvarying Andmixingmixing the exhaust coefficients.coefficients. gas penetration TheThe airair penetrpenetr coeationationfficient coefficientcoefficient is defined isis defineddefined as: as:as: m m μμ == . (5) m (5) m mIII II And the exhaust gas penetration coefficient µisg defined= . −as: . (6) And the exhaust gas penetration coefficient is definedminp as: m m μμ == (6) . m (6) where mIII II is the air mass flow rate from zonem III to zone II. The postulated variation of the air where −m is the air mass flow rate from zone III to zone II. The postulated variation of the air penetrationwhere m coeffi iscient the isair shown mass flow in Figure rate from3. zone III to zone II. The postulated variation of the air penetrationpenetration coefficientcoefficient isis shownshown inin FigureFigure 33..

FigureFigureFigure 2. Schematic 2.2. SchematicSchematic representation representationrepresentation ofof the the three-zonethree-zone modelmodel model onon on aa uniflowuniflow a uniﬂow scavengedscavenged scavenged engine.engine. engine.

11 μaμa μgμg 0.80.8

0.60.6

0.40.4

0.20.2 Penetration Coefficients [-] Penetration Coefficients [-] 00 00 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 Normalized scavenging time τ [-] Normalized scavenging time τ [-] FigureFigure 3. 3. Variation of µμα and μµg at the original model. Figure 3.Variation Variation ofof μα andand μg atg atthe the original original model. model.

Initially, μα = 1 since the air entering the engine cylinders is rapidly mixed with exhaust gases. Initially, μα = 1 since the air entering the engine cylinders is rapidly mixed with exhaust gases. AsAs thethe exhaustexhaust gasgas inin thethe lowerlower partpart ofof thethe cylindercylinder isis displaced,displaced, thethe valuevalue ofof thethe coefficientcoefficient declinesdeclines exponentially,exponentially, asas EqEquationuation (7)(7) shows.shows.

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Initially, µα = 1 since the air entering the engine cylinders is rapidly mixed with exhaust gases. As the exhaust gas in the lower part of the cylinder is displaced, the value of the coeﬃcient declines exponentially, as Equation (7) shows.

κτ µα = e− (λτ + 1) (7) where κ is a model constant and τ is normalized scavenging time defined as: ϕ ϕ τ = − EBF (8) ϕ ϕ IPC − EBF where ϕ is crank angle, ϕEBF is the crank angle at end of backflow and ϕIPC is the crank angle at inlet port closing. The assumed variation of µg is divided in two phases and is also presented in Figure3. Initially, µg = 0 and increases parabollicaly, resembling the entrainment of ambient fluid into jets. In the second mixing phase, the gas penetration coefficient decreases exponentially. The mathematical expression of µg is shown in Equation (9).   2 √τ, 0 < τ < τg∗ µ =  (9) g  k(τ2)  e− ξτ2 + µg τg∗ , 0 < τ2 < 1 where ξ and k are model parameters, τg∗ is the time when the second mixing phase begins and τ2 is normalized scavenging time of the second mixing phase.

3. Scope of Work In this paper, the three-zone scavenging model, originally presented in [15] and applicable to two-stroke uniﬂow scavenged marine diesel engines is updated. The model has been used for many years, in conjunction with a control volume, zero-dimensional engine simulation code, MOTHER (MOtor THERmodynamics) (see Chapter 3). A reliable scavenging model is essential for accurate exhaust gas temperature prediction in engine application. This has become even more important due to the recent applications of DeNOx systems such as SCR [16], exhaust gas recirculation (EGR) [17], and WaCoReG system [18]. Available data concerning the scavenging process of two-stroke engines are scarce compared to four-stroke engines due to the large cost associated with large engine testing and the limited number of test facilities for large engines. To update the original zero-dimensional scavenging model, results from a CFD simulation of the scavenging process were used as baseline. The engine geometry used for this study is from a MAN 50 cm bore size two-stroke marine engine. The speciﬁcations of the engine are presented in Table1.

Table 1. Engine speciﬁcations.

Engine Model MAN B&W 6S50ME Bore 500 mm Stroke 2000 mm No. of Cylinders 6 - PMCR 7620 kW NMCR 115 RPM Scavenging Uniﬂow Ports per cylinder 30

CFD results were produced for four steady state load points along a propeller curve namely 25%, 50%, 75%, and 100%, for two different cases. In the first case inlet ports were fully uncovered by the piston and port angle varied from 0◦ to 30◦ by 10◦ intervals. In the second case port angle was fixed at Energies 2019, 12, 1719 5 of 20

20◦ and a 5% and 10% covering of the inlet port area by the piston at BDC was investigated. Then, the mixing coeﬃcients of the three-zone model were revised using the results from the CFD simulations.

4. The Zero-Dimensional Engine Simulation Code The scavenging model under consideration, is integrated in the NTUA in-house thermodynamic engine prediction code MOTHER. The code is based on the control volume principle. A number of basic engineering elements such as flow receivers (cylinders, plenums), flow controllers (valves, compressors, turbines), and mechanical elements (shafts, gearboxes, clutches and shaft loads) are available. A turbocharged engine can be modelled as several flow receiver elements interconnected by flow controller elements. Flow receivers are treated as open thermodynamic systems and the work, heat and mass transfer, which take place through their boundaries, are calculated by applying the conservation equations in appropriate form to each control volume. The resulting set of differential equations are numerically solved step-by-step for all volumes. MOTHER includes a variety of submodels for the simulation of engine processes such as combustion, heat transfer, friction, and scavenging. The MOTHER code has been used for many years in engine performance simulations [19–22].

5. Implementation of the CFD Model To update the mixing coeﬃcients of the original three-zone model results from a more detailed 2D CFD model were used. Only the scavenging process (not the combustion) was simulated. The simulation is carried out between 76–286 CA degrees, for one typical cylinder. The starting point of the simulation (76 crank angle degrees (CAD)) is well before the uncovering of inlet ports by the piston which takes place at 135 CAD. This was done in order to include the blowdown period in the simulation and be able to validate the CFD model against available pressure diagrams. Convective heat transfer in the cooled upper part of the cylinder and the cylinder head is modeled with the assumption of a constant wall temperature. Piston and lower cylinder liner part cooling was not taken into account. The turbulent ﬂow was simulated by the RANS (Reynolds averaged Navier Stokes) equations [23]. Gas density was calculated using the ideal gas equation. The turbulent viscosity was modeled by the RNG k-ε model [24]. The case is solved in Fluent software as 2-D, axisymmetric with swirl. The bending of the exhaust pipe to enter the receiver is not taken into account and inlet ports are modeled as a continuous opening in the cylinder wall. Mesh generation was carried out in ICEM CFD software (v14.5) [25] (structured mesh). Only the cylinder, intake ports, and exhaust duct were meshed. Quad elements were employed in the mesh generation. The mesh movement was imposed to the valve and piston surfaces by means of the “in-cylinder” dynamic mesh facility existing in Fluent software [26]. Turbulent heat transport was modeled using Reynolds analogy. Gas components were computed by a species transport model. The number of elements varied from about 17,000 at the starting point of the simulation (76 degrees ATDC, about mid-stroke) to 30,000 at bottom dead center. Figure4 shows a cross-section of the mesh at 76 CA degree and 180 CA degree. Energies 2019, 12, 1719 6 of 20 Energies 2019, 12, x FOR PEER REVIEW 6 of 19

Figure 4. ComputationalComputational mesh mesh at 76 crank angle degrees (CAD)—180 CAD.

5.1. Numerical Procedure 5.1. Numerical Procedure The PISO (Pressure Implicit with Splitting of Operators) algorithm was chosen for pressure-velocity The PISO (Pressure Implicit with Splitting of Operators) algorithm was chosen for pressure- coupling [26]. A second order scheme was selected to discretize the continuity, momentum, energy velocity coupling [26]. A second order scheme was selected to discretize the continuity, momentum, and mass fraction equations. The time derivatives were discretized through a ﬁrst order fully implicit energy and mass fraction equations. The time derivatives were discretized through a first order fully scheme with a constant time step corresponding to 0.1 degrees crank angle. implicit scheme with a constant time step corresponding to 0.1 degrees crank angle. 5.2. Initial and Boundary Conditions—Validation 5.2. Initial and Boundary Conditions—Validation The ﬂow through the inlet ports was assumed fully axisymmetric, with a radial and a tangential The flow through the inlet ports was assumed fully axisymmetric, with a radial and a tangential component (swirl). A pressure boundary condition was employed at engine inlet. A turbulence component (swirl). A pressure boundary condition was employed at engine inlet. A turbulence intensity of 5% was selected. The inlet air temperature and CO2 concentration were set at 313 K and intensity of 5% was selected. The inlet air temperature and CO2 concentration were set at 313 K and 0% respectively. A pressure boundary condition was employed at engine outlet. Initial conditions for 0% respectively. A pressure boundary condition was employed at engine outlet. Initial conditions for the gas in the cylinder (76◦ CA) are shown in Table2. They were produced using the zero-dimensional, the gas in the cylinder (76° CA) are shown in Table 2. They were produced using the zero- engine performance prediction code MOTHER [19]. The engine under consideration was modelled dimensional, engine performance prediction code MOTHER [19]. The engine under consideration under steady conditions using the MOTHER software and validated against available measured data. was modelled under steady conditions using the MOTHER software and validated against available After submodel calibration, the accuracy of MOTHER calculations against measured data is better measured data. After submodel calibration, the accuracy of MOTHER calculations against measured than 3% over the whole operating range of an engine and it has been validated with over 50 engine data is better than 3% over the whole operating range of an engine and it has been validated with types [27–29]. over 50 engine types [27–29]. Table 2. Initial conditions for the CFD model. Table 2. Initial conditions for the CFD model. Engine Load 100% 75% 50% 25% Engine Load 100% 75% 50% 25% N [RPM] 115.3 105 91.5 73 N [RPM] 115.3 105 91.5 73 pcyl at 76◦ CA [bar] 14.8 11.7 8.81 5.6 pcyl at 76° CA [bar] 14.8 11.7 8.81 5.6 Tcyl at 76◦ CA [K] 1239 1186 1163 1020 pscavTcyl[bar] at 76° CA [K] 3.90 1239 3.15 1186 2.20 1163 1.48 1020 pexhpscav[bar] [bar] 3.80 3.90 3.08 3.15 2.15 2.20 1.45 1.48 COp2 exhmass [bar] fraction 0.133 3.80 0.129 3.08 0.129 2.15 0.115 1.45 H2O mass fraction 0.049 0.0475 0.0475 0.0423 CO2 mass fraction 0.133 0.129 0.129 0.115 Air mass fraction 0.358 0.376 0.376 0.444 H2O mass fraction 0.049 0.0475 0.0475 0.0423 Air mass fraction 0.358 0.376 0.376 0.444

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Energies 2019, 12, x FOR PEER REVIEW 7 of 19 The comparison of engine indicator diagrams with the average pressure computed by the CFD modelThe is acomparison good overall of checkengine of indicator the CFD model’sdiagrams accuracy. with the In average this study pressure the CFD computed computed by pressurethe CFD diagrammodel is comparesa good overall well withcheck the of validatedthe CFD model’s 0-D model, accuracy. for the In engine this study cycle partthe CFD of the computed CFD computation pressure (76–286diagram degrees compares CA) well for all with four operationthe validated points 0-D (25–100% model, load,for the along engine the propeller cycle part curve). of the The CFD flow throughcomputation the cylinder (76–286 is degrees driven byCA) a pressurefor all four diff erenceoperation between points the (25–100% scavenge load, receiver along and the the propeller exhaust receiver,curve).The known flow through as the scavenging the cylinder gradient is driven or ∆byp a across pressure engine. difference Higher between dimension the CFDscavenge models receiver with advancedand the exhaust turbulence receiver, submodels known as may the require scavenging a certain gradient degree or ofΔp correction across engine. of scavenging Higher dimension gradient byCFD modification models with of theadvanced mass flow-rate turbulence [30 ].submodels In the present may caserequire the exhausta certain receiver degree pressureof correction as well of asscavenging the inlet pressuregradient areby modification given as boundary of the conditionsmass flow-rate and thus[30]. theIn the mass present flow-rate caseis the computed. exhaust Figurereceiver5 shows pressure the as e ff wellect of as the the scavenging inlet pressure gradient are ongiven some as important boundary scavenging conditionsparameters, and thus the namely, mass flow-rate is computed. Figure 5 shows the effect of the scavenging gradient on some important trapping efficiency (ηtr), charging efficiency (ηch), scavenging efficiency (ηsc), massflow of air entering . scavenging parameters, namely, trapping efficiency (η ), charging efficiency (η ), scavenging the cylinders (minp), and the mass of delivered air retained (mair,ret). The definition of each efficiency is givenefficiency below: (η), massflow of air entering the cylinders (m ), and the mass of delivered air retained (m,). The definition of each efficiency is givenm below:air,ret ηtr = (10) m,m η = air,del m (10) ,mair,ret ηch = (11) m, ρ η = Vref inl V ∙ ρ · (11) mair,ret ηmsc = (12) , mtr η = (12) m where mair,del is the mass of delivered air, Vref is the reference cylinder volume, ρinl is the density at where m is the mass of delivered air, V is the reference cylinder volume, ρ is the density the engine, inlet and mtr is the mass of the total trapped cylinder charge. at theAs engine shown inlet in Figure and m5 the is CFD the mass model of is the sensitive total trapped to the scavenging cylinder charge. gradient and the mass flow-rate is computedAs shown correctly in Figure without 5 the CFD any correctionsmodel is sensitiv needed.e to The the trapping scavenging effi ciencygradient and and the the air mass mass flowflow rate throughis computed the inletcorrectly ports without are the mostany corrections affected quantities needed. byThe a trapping change in efficiency∆p. Thus, and the the selection air mass of theflow simplest rate through possible the CFD inlet configurationports are the most (2-D axisymmetricaffected quantities with swirl)by a change leads toin aΔ goodp. Thus, agreement the selection with theof the 0-D simplest mass flow-rate possible results, CFD configuration succeeding in (2-D an eaxisymmetricfficient hybrid with computation. swirl) leads to a good agreement with the 0-D mass flow-rate results, succeeding in an efficient hybrid computation.

Figure 5. Effect of ∆p on scavenging efficiency and mass of air entering the cylinder (100% load). Figure 5. Effect of Δp on scavenging efficiency and mass of air entering the cylinder (100% load). As regards validation of the flow and temperature field, the amount of validation data for a CFD As regards validation of the flow and temperature field, the amount of validation data for a CFD model of a full size operating two-stroke marine engine is limited because of the high cost, size, and model of a full size operating two-stroke marine engine is limited because of the high cost, size, and manpower required for such experiments [30]. Nevertheless, existing data from similar engines have manpower required for such experiments [30]. Nevertheless, existing data from similar engines have been employed for validation, with the necessary adaptations made according to the similarity laws. been employed for validation, with the necessary adaptations made according to the similarity laws. As regards the validation process for the flow field, Figure6 shows a comparison with literature data As regards the validation process for the flow field, Figure 6 shows a comparison with literature data on steady state, cold flow measurements with Particle Image Velocimetry on an engine cylinder with on steady state, cold flow measurements with Particle Image Velocimetry on an engine cylinder with D = 190 mm and swirl number Sm = 0.33 [31]. The measurements are presented in [31] as axial and D = 190 mm and swirl number Sm = 0.33 [31]. The measurements are presented in [31] as axial and tangential (swirl) velocity components Vz and Vθ respectively as functions of radius, normalized tangential (swirl) velocity components Vz and Vθ respectively as functions of radius, normalized with the bulk flow velocity, Wb, for various axial positions. For comparison, Figure 6 presents the CFD model predictions for the normalized Vz and Vθ components at 25% load, 195 degrees CA, at the same

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with the bulk ﬂow velocity, Wb, for various axial positions. For comparison, Figure6 presents the Energies 2019, 12, x FOR PEER REVIEW 8 of 19 CFD model predictions for the normalized Vz and Vθ components at 25% load, 195 degrees CA, at the same normalized axial positions. Only one measured axial position is inserted in the graph for normalized axial positions. Only one measured axial position is inserted in the graph for comparison. comparison. The computed variation of the tangential velocity component with cylinder radius have a The computed variation of the tangential velocity component with cylinder radius have a shape shape similar to a Lamb–Oseen vortex, for z/D < 2 (z = 0 corresponds to the upper end level of intake similar to a Lamb–Oseen vortex, for z/D < 2 (z = 0 corresponds to the upper end level of intake ports). ports). The vortex core is seen as a sharp linear increase from r = 0. The vortex then has a smooth The vortex core is seen as a sharp linear increase from r = 0. The vortex then has a smooth transition transition to a curve proportional to 1/r for larger values of r [32]. Overall, the CFD computations agree to a curve proportional to 1/r for larger values of r [32]. Overall, the CFD computations agree with with the published experimental results on similar engines [31,33]. the published experimental results on similar engines [31,33].

Figure 6. The mean tangential velocityvelocity componentcomponent VVθ and the mean axial velocityvelocity componentcomponent VVzz at various axial distances from the outletoutlet comparedcompared withwith PIVPIV measurementmeasurement [[31].31]. 5.3. Calculation of Zone Masses Based on CFD Results 5.3. Calculation of Zone Masses Based on CFD Results The CFD model employed a species transport equation, which calculated a passive scalar, directly The CFD model employed a species transport equation, which calculated a passive scalar, correlated to the CO2 mass concentration in the cylinder charge. Computational cells with the directly correlated to the CO2 mass concentration in the cylinder charge. Computational cells with highest CO2 mass concentration are allocated to zone III and the respective cells with zero CO2 mass the highest CO2 mass concentration are allocated to zone III and the respective cells with zero CO2 concentration are allocated to zone I. The remaining volume in the cylinder corresponds to zone II. mass concentration are allocated to zone I. The remaining volume in the cylinder corresponds to zone Volumes were subsequently converted to masses by employing the respective densities for air and II. Volumes were subsequently converted to masses by employing the respective densities for air and exhaust gas. This procedure was performed at a 5 crank angle degree interval starting from 135 CA exhaust gas. This procedure was performed at a 5 crank angle degree interval starting from 135 CA degrees (beginning of scavenging) until 225 CA degrees (end of scavenging). The mixing coefficients degrees (beginning of scavenging) until 225 CA degrees (end of scavenging). The mixing coefficients of the three-zone model were then revised so that results of the 0-D model would be close to results of the three-zone model were then revised so that results of the 0-D model would be close to results from CFD simulations. from CFD simulations. An example of the CO2 mass fraction evolution during scavenging is shown in Figure7. An example of the CO2 mass fraction evolution during scavenging is shown in Figure 7. The The resulting evolution of masses for this case is shown in Figure8. Initially, the cylinder is resulting evolution of masses for this case is shown in Figure 8. Initially, the cylinder is filled with filled with exhaust gas. As scavenging commences, zone III continuously decreases in size, since a part exhaust gas. As scavenging commences, zone III continuously decreases in size, since a part of the of the exhaust gas leaves the cylinder through the exhaust valve and another part is transferred to the exhaust gas leaves the cylinder through the exhaust valve and another part is transferred to the mixing zone. The mixing zone increases rapidly in the beginning of scavenging, since it receives fresh mixing zone. The mixing zone increases rapidly in the beginning of scavenging, since it receives fresh air from the air zone and exhaust gas from the exhaust gas zone. However, when the exhaust gas zone air from the air zone and exhaust gas from the exhaust gas zone. However, when the exhaust gas disappears, the mixing zone starts to decrease since now a part of it is escaping the cylinder through zone disappears, the mixing zone starts to decrease since now a part of it is escaping the cylinder the exhaust valve. The air zone increases slowly at first, since most of the incoming air is mixed with through the exhaust valve. The air zone increases slowly at first, since most of the incoming air is exhaust gases, but increases faster after 180 CAD and eventually becomes larger than the mixing zone. mixed with exhaust gases, but increases faster after 180 CAD and eventually becomes larger than the mixing zone.

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140140 150150 160160 170170 180180 190190 200200 210210 220220 CO2CO mass2 mass CADCAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD CAD fractionfraction [%] [%]

Figure 7. CO2 mass fraction field at 10° intervals between 140–220 CAD (100% load, 10° port angle). FigureFigure 7. 7.CO CO22mass massfraction fractionﬁeld field at at 10 10◦°intervals intervals between between 140–220 140–220 CAD CAD (100% (100% load, load, 10 10◦°port portangle). angle).

1.21.2 M1 M1 M2 M2 1 1 M3 M3 0.80.8 0.60.6 Mass [kg] Mass 0.4[kg] Mass 0.4 0.20.2 0 0 130130 150 150 170 170 190 190 210 210 230 230 CrankCrank Angle Angle [deg] [deg]

Figure 8. Evolution of the mass of each zone as predicted by the CFD model. FigureFigure 8. Evolution 8. Evolution of the of massthe mass of each of each zone zone as predicted as predicted by the by CFDthe CFD model. model. 6. CFD Results 6. CFD6. CFD Results Results Results from the 2D CFD model were employed to enhance understanding of the scavenging Results from the 2D CFD model were employed to enhance understanding of the scavenging processResults and update from thethe three-zone2D CFD model model. were The scavengingemployed to process enhance during understanding the time the inletof the ports scavenging remain process and update the three-zone model. The scavenging process during the time the inlet ports open,process can and be described update the by three-zone two processes: model. mixing The of scavenging incoming air process with exhaust during gasthe and time displacement the inlet ports of remain open, can be described by two processes: mixing of incoming air with exhaust gas and exhaustremain gasopen, by thecan incomingbe described air. Theby sourcestwo processes: of mixing mixing are: of incoming air with exhaust gas and displacementdisplacement of exhaust of exhaust gas gasby theby theincoming incoming air. air.The The sources sources of mixing of mixing are: are: The jet impingement of air into the cylinder through the inlet ports • • •The DiThe jetff usion impingementjet impingement between of exhaust air of intoair gasinto the and thecylinder aircylinder at through the through interface the theinlet between inlet ports ports the two zones • • •Diffusion FlowDiffusion separation between between exhaust at theexhaust inlet gas gasport’sand and air edges atair the at and theinterface formationinterface between between of recirculation the thetwo two zoneszones. zones • ••Flow Flow separation separation at the at theinlet inlet port’s port’s edges edges and and formation formation of recirculation of recirculation zones. zones. In this section, the effect of engine load, inlet port angle, and inlet port covering on scavenging In this section, the effect of engine load, inlet port angle, and inlet port covering on scavenging will beIn presented. this section, the effect of engine load, inlet port angle, and inlet port covering on scavenging willwill be presented.be presented. 6.1. Effect of Engine Load 6.1.6.1. Effect Effect of Engine of Engine Load Load Four load points that lie on a typical propeller curve passing from the MCR (maximum continuous rating)FourFour pointload load werepoints points investigated. that that lie lieon ona The typicala propellertypical pr opellerpr demandopeller curve lawcurve passing obeys passing thefrom followingfrom the theMCR relationMCR (maximum (maximum between continuousenginecontinuous speed rating) rating) and point produced point were were power:investigated. investigated. The The propeller propeller demand demand law law obeys obeys the thefollowing following relation relation betweenbetween engine engine speed speed and and produced produced power: power: P = c Nβ (13) · P=c∙NP=c∙N (13)(13) where P is engine power, N is engine speed, c is the propeller law coefficient and β usually lies between wherewhere P is P engine is engine power, power, N isN engine is engine speed, speed, c is c the is thepropeller propeller law law coefficient coefficient and and β usually β usually lies lies 3 and 4. Engine load influences the scavenging process in two ways. At increased load, the engine betweenbetween 3 and 3 and 4. Engine 4. Engine load load influences influences the thescaven scavengingging process process in two in two ways. ways. At increasedAt increased load, load, the the speed increases which leads to a reduced time that the inlet ports remain open. This is shown in engineengine speed speed increases increases which which leads leads to a to reduced a reduced time time that that the theinlet inlet ports ports remain remain open. open. This This is shown is shown Table3, where scavenging time is normalized with reference to the scavenging time at 25% load. in Tablein Table 3, where 3, where scavenging scavenging time time is normalized is normalized with with refe referencerence to the to thescavenging scavenging time time at 25% at 25% load. load. It It is observedis observed that that at 50% at 50% load load scavenging scavenging time time is reduced is reduced by 20%,by 20%, at 75% at 75% it decreases it decreases at 70% at 70% and and will will

Energies 2019, 12, 1719 10 of 20

Energies 2019, 12, x FOR PEER REVIEW 10 of 19 It is observed that at 50% load scavenging time is reduced by 20%, at 75% it decreases at 70% and willfurther further decrease decrease at 63% at 63% when when reaching reaching 100% 100% load. load. The The second second load load dependent dependent factor aaffectingﬀecting scavenging isis boostboost pressurepressure whichwhich increasesincreases withwith increasedincreased engineengine load.load.

Table 3.3. Engine operating conditions at didifferentﬀerent loadload points.points.

EngineEngine Load Load 100% 100% 75% 75% 50%50% 25% 25% N [RPM]N [RPM] 115.3 115.3 105 105 91.591.5 73 73 P [kW]P [kW] 7620 7620 5710 5710 3800 3800 1900 1900 pscav p[bar]scav [bar] 3.90 3.90 3.15 3.15 2.20 2.20 1.48 1.48 pexh [bar] 3.80 3.08 2.15 1.45 pexh [bar] 3.80 3.08 2.15 1.45 ∆p [bar] 0.1 0.07 0.05 0.03 Δp [bar] 3 0.1 0.07 0.05 0.03 ρscav [kg/m ] 4.34 3.54 2.47 1.66 Scavengingρscav time [kg/m with3 reference] to 25% load4.34 0.633.54 0.7 0.82.47 1 1.66 Scavenging time with reference to 25% load 0.63 0.7 0.8 1 Since, scavenge temperature remains relatively invariable, due to the presence of the scavenge air Since, scavenge temperature remains relatively invariable, due to the presence of the scavenge cooler, increased scavenge pressure leads to increased air density. According to [11] mixing of air with air cooler, increased scavenge pressure leads to increased air density. According to [11] mixing of air exhaust gas increases with increased engine load due to the increased difference in density between with exhaust gas increases with increased engine load due to the increased difference in density the two gases. This is also confirmed in Figure9 for two CA instances, 175 and 210 CAD. between the two gases. This is also confirmed in Figure 9 for two CA instances, 175 and 210 CAD. In both cases mixing between air and exhaust gas is more intense for higher engine load (larger In both cases mixing between air and exhaust gas is more intense for higher engine load (larger green area in Figure9) and air manages to displace a smaller amount of exhaust gas (blue area ends green area in Figure 9) and air manages to displace a smaller amount of exhaust gas (blue area ends at a lower axial position). A recirculation zone is formed at the cylinder wall above the scavenge at a lower axial position). A recirculation zone is formed at the cylinder wall above the scavenge ports, where pockets of exhaust gas are trapped between zones of fresh air. These pockets increase in ports, where pockets of exhaust gas are trapped between zones of fresh air. These pockets increase in size with increasing engine load, thus more exhaust gas is mixed with the incoming fresh air with size with increasing engine load, thus more exhaust gas is mixed with the incoming fresh air with increasing engine load in this configuration. increasing engine load in this configuration. 175 CAD 210 CAD

25% 50% 75% 100% 25% 50% 75% 100% CO2 mass Load Load Load Load Load Load Load Load fraction [%]

FigureFigure 9.9. COCO22 mass fraction ﬁeldfield at 175 and 210 CAD forfor the four available engineengine loadsloads ((θθ == 20◦°).

6.2. Effect Effect of Inlet Port Angle InletInlet portsports are inclined withwith respectrespect toto the local radius,radius, in order to induce a tangential component toto thethe flowflow enteringentering the the engine engine cylinders. cylinders. This This creates creates turbulence turbulence which which is is beneficial beneficial for for the the mixing mixing of fuelof fuel with with scavenge scavenge air. air. The The swirl swirl could could also also reduce reduce the the recirculation recirculation zones zones that that areare formedformed nearnear thethe inletinlet portsports duedue toto flowflow separation.separation. Moreover, the coldcold scavengescavenge air coolscools thethe cylindercylinder linerliner andand thethe exhaust valve.valve. IncreasedIncreased in-cylinderin-cylinder swirl swirl increases increases the the tangential tangential velocity velocity at at the the cylinder cylinder liner liner and and as aas result a result increases increases the the convective convective heat heat transfer transfer coe coefficient.fficient. Four portport inclinationinclination anglesangles werewere investigated:investigated: θ == 0◦°, 10◦°, 30°◦,, and 20◦° which is the industryindustry standard. The geometric swirl number ΩΩ was used to quantify the port induced swirlswirl [[12].12].

A Ω= tan( θ) (14) nA

where Acyl is the cross-sectional area of the cylinder, Ainp is the area of one scavenge port and ninp is the number of scavenge ports. Visualization for 25% engine load and various port angles is shown in

Energies 2019, 12, 1719 11 of 20

Acyl Ω = tan(θ) (14) ninpAinp where Acyl is the cross-sectional area of the cylinder, Ainp is the area of one scavenge port and ninp is Energies 2019, 12, x FOR PEER REVIEW 11 of 19 theEnergies number 2019, 12 of, x scavenge FOR PEER REVIEW ports. Visualization for 25% engine load and various port angles is shown11 of 19 in Figure 10. As expected, for θ = 0 , a jet-like ﬂow develops, which at 175 CAD (40 CAD after the Figure 10. As expected, for θ = 0°, ◦a jet-like flow develops, which at 175 CAD (40 CAD after the beginning of scavenging) has reached the top of the cylinder. The jet is surrounded by a mixing zone Figurebeginning 10. As of scavenging)expected, for has θ reached= 0°, a jet-likethe top flowof the develops, cylinder. whichThe jet atis surrounded175 CAD (40 by CAD a mixing after zone the located near the cylinder liner wall. As the port angle and induced swirl increases, the fresh air front beginninglocated near of thescavenging) cylinder linerhas reached wall. As the the top port of anthegle cylinder. and induced The jet swirl is surrounded increases, theby afresh mixing air zonefront moves from the cylinder axis towards the liner walls forming a V-shaped air front. locatedmoves fromnear the cylinder lineraxis towards wall. As thethe linerport wallsangle formingand induced a V-shaped swirl increases, air front. the fresh air front moves from the cylinder axis towards the liner walls forming a V-shaped air front. 175 CAD 210 CAD 175 CAD 210 CAD

CO2 mass ° ° ° ° ° ° ° ° θ = 0 θ = 10 θ = 20 θ = 30 θ = 0 θ = 10 θ = 20 θ = 30 CO2 mass θ = 0° θ = 10° θ = 20° θ = 30° θ = 0° θ = 10° θ = 20° θ = 30° fraction [%] fraction [%] FigureFigure 10.10. COCO22 mass fraction fieldfield at 175 and 210 CAD for the four investigated portport anglesangles (25%(25% load).load). Figure 10. CO2 mass fraction field at 175 and 210 CAD for the four investigated port angles (25% load). AsAs farfar asas mixingmixing isis concerned,concerned, itit isis observedobserved thatthat largerlarger valuesvalues ofof portport angleangle favourfavour thethe mixingmixing ofof airairAs with far exhaustas mixing gas gas is (air (airconcerned, penetration penetration it is to observed to the the mixi mixing thatng zone) larger zone) but values but hinder hinder of theport the penetration angle penetration favour of exhaust ofthe exhaust mixing gas gasofto airthe to with themixing mixingexhaust zone. zone. gas This (air Thisis inpenetration isaccordance in accordance to withthe mixi the with ngfindings the zone) findings ofbut [12]. hinder of This [12 the]. is This alpenetrationso isverified also verified ofby exhaust the masses by thegas massestocalculated the mixing calculated by zone.the byCFD This the model. is CFD in accordance model. As the As port thewith angle port the angleincrfindingseases increases of the [12]. mass the This massin is zone al inso zone Iverified increases I increases by slowerthe masses slower (see (seecalculatedFigure Figure 11), by11since ),the since it CFD loses it losesmodel. more more airAs to the air the toport mixing the angle mixing zone, incr zone, whileeases while the masszone the zoneIIIin masszone III massdecreasesI increases decreases slower, slower slower, since (see sinceFigureless exhaust less 11), exhaust since gas isit gas losestransferred is transferredmore airto theto tothe mixing the mixing mixing zone. zone, zone. while the zone III mass decreases slower, since less exhaust gas is transferred to the mixing zone.

Figure 11. Evolution of mass of air zone and exhaust gas zone for various port angles at 50% load. FigureFigure 11.11. Evolution of mass of air zone and exhaust gasgas zonezone forfor variousvarious portport anglesangles atat 50%50% load.load. 6.3.6.3. EEffectﬀect ofof InletInlet PortPort CoveringCovering inin PartPart byby thethe PistonPiston CrownCrown 6.3. Effect of Inlet Port Covering in Part by the Piston Crown TheThe coveringcovering of of the the inlet inlet ports ports by theby pistonthe piston results results in an increasein an increase of the velocityof the velocity of the air of entering the air The covering of the inlet ports by the piston results in an increase of the velocity of the air theentering cylinder. the Ascylinder. a result, As the a result, jet-like the nature jet-like of incomingnature of ﬂowincoming is enhanced. flow is enhanced. This results This in the results formation in the enteringformation the of cylinder. exhaust Asgas a recirculation result, the jet-like zones nature at the ofsharp incoming edges flowof the is inletenhanced. ports, Thiswhere results pockets in the of formationexhaust gas of areexhaust trapped gas withinrecirculation fresh air. zones Hence, at the mi sharpxing of edges air with of the exhaust inlet ports, gas is where increased pockets due ofto exhaustport covering. gas are trapped within fresh air. Hence, mixing of air with exhaust gas is increased due to port covering.On the contrary, increased port covering does not favour the entrainment of exhaust gas to the mixingOn zone. the contrary, In Figure increased 12, at 210 port CAD covering the exhaust does ga nots zone favour (red the zone) entrainment is slightly of larger exhaust for gasincreased to the mixinginlet port zone. covering. In Figure This 12, is at seen 210 CADalso in the Figure exhaust 13 gawheres zone the (red evolution zone) is ofslightly zones larger I and forIII increasedmasses is inletpresented port covering.for the 25% This load is caseseen andalso variable in Figure inlet 13 portwhere covering. the evolution Zone I increasesof zones Imore and slowlyIII masses when is presented for the 25% load case and variable inlet port covering. Zone I increases more slowly when

Energies 2019, 12, 1719 12 of 20 of exhaust gas recirculation zones at the sharp edges of the inlet ports, where pockets of exhaust gas are trapped within fresh air. Hence, mixing of air with exhaust gas is increased due to port covering. On the contrary, increased port covering does not favour the entrainment of exhaust gas to the mixing zone. In Figure 12, at 210 CAD the exhaust gas zone (red zone) is slightly larger for increased inletEnergiesEnergies port 2019 2019 covering., ,12 12, ,x x FOR FOR PEER PEER This REVIEW REVIEW is seen also in Figure 13 where the evolution of zones I and III masses1212 of of 19 is19 presented for the 25% load case and variable inlet port covering. Zone I increases more slowly when inletinlet portsports are are partlypartly covered covered by by the the piston piston due due to to increased increased entrainment entrainmententrainment of ofof air airair to toto the thethe mixing mixingmixing zone. zone.zone. OnOn thethe otherother hand, hand, thethe massmass ofof zone zone IIIIII decreases decreases at at aa slowerslower raterate when when inletinlet portsports are are partlypartly covered covered sincesince inin thisthis casecase mixingmixing isis retarded.retarded.

175175 CADCAD 210 210 CADCAD

C = 0 C = 0.05 C = 0.1 C = 0 C = 0.05C = 0.1 CO2 mass fraction [%] C = 0 C = 0.05 C = 0.1 C = 0 C = 0.05C = 0.1 CO2 mass fraction [%]

Figure 12. CO2 mass fraction field at 175 and 210 CAD for the three investigated inlet port coverings FigureFigure 12.12. COCO22 mass fraction ﬁeldfield atat 175175 andand 210210 CADCAD forfor thethe threethree investigatedinvestigated inletinlet portport coveringscoverings (25% engine load and 20° port angle). (25%(25% engineengine load load and and 20 20°◦ port port angle).angle).

Figure 13. Evolution of mass of air zone and exhaust gas zone for various port coverings at 25% load. FigureFigure 13. 13. Evolution Evolution of of mass mass of of air air zone zone and and exhaust exhaust gas gas zone zone for for various various port port coverings coverings at at 25% 25% load. load. As Figures 12 and 13 show, no notable differences between the 5% and 10% covering can be AsAs FiguresFigures 1212 andand 1313 show,show, nono notablenotable differdifferencesences betweenbetween thethe 5%5% andand 10%10% coveringcovering cancan bebe identified for the 25% load case. identifiedidentified forfor thethe 25%25% loadload case.case. 7. The Updated Three-Zone Scavenging Model 7.7. TheThe UpdatedUpdated Three-ZoneThree-Zone ScavengingScavenging ModelModel In this section, the expressions for the evolution of the air and gas penetration coefficient for the In this section, the expressions for the evolution of the air and gas penetration coefficient for the two investigatedIn this section, cases the will expressions be presented. for the The evolution case of varyingof the air port and angle gas penetration will be designated coefficient as Casefor theI. two investigated cases will be presented. The case of varying port angle will be designated as Case I. Thetwo caseinvestigated of varying cases inlet will port be covering presented. by The the pistoncase ofwill varying be designated port angle as will Case be II.designated as Case I. TheThe casecase ofof varyingvarying inletinlet portport coveringcovering byby thethe pistonpiston willwill bebe designateddesignated asas CaseCase IIII..

7.1.7.1. AirAir PenetrationPenetration CoefficientCoefficient InIn the the three-zone three-zone model, model, it it is is assumed assumed that that scaven scavengingging happens happens in in two two phases. phases. In In the the first first phase, phase, whenwhen scavenge scavenge air air rushes rushes in in engine engine cylinders, cylinders, air air is is rapidly rapidly mixed mixed with with exhaust exhaust gases gases and and the the mixing mixing mechanism is dominant. Hence, during the first phase the air penetration coefficient, μα has a large mechanism is dominant. Hence, during the first phase the air penetration coefficient, μα has a large valuevalue whichwhich decreasesdecreases slowly.slowly. DuringDuring thethe secondsecond phase,phase, displacementdisplacement becomesbecomes thethe dominantdominant mechanism of scavenging and μα decreases exponentially. The mathematical expression of the air mechanism of scavenging and μα decreases exponentially. The mathematical expression of the air penetrationpenetration coefficientcoefficient isis shownshown below:below:

Energies 2019, 12, 1719 13 of 20

7.1. Air Penetration Coefficient In the three-zone model, it is assumed that scavenging happens in two phases. In the first phase, when scavenge air rushes in engine cylinders, air is rapidly mixed with exhaust gases and the mixing mechanism is dominant. Hence, during the first phase the air penetration coefficient, µα has a large value which decreases slowly. During the second phase, displacement becomes the dominant mechanism of scavenging and µα decreases exponentially. The mathematical expression of the air penetration coefficient is shown below: Energies 2019, 12, x FOR PEER REVIEW 13 of 19   aτ2 + b, 0 < τ < τ  a∗ µ = µ (τ ) ∗ (15) α aτµ +(τ b ) , 0α

[-] 100% α 0.8 75% 50% 0.6 25%

0.4

0.2

Air Penetration Coef. μ Coef. Air Penetration 0 0 0.2 0.4 0.6 0.8 1 Normalized scavenging time τ [-]

FigureFigure 14. 14. AirAir penetration penetration coefficient coeﬃcient evolution evolution for for different diﬀerent engine engine load load points points (θ (=θ 20°= 20 and◦ and C = C 0).= 0).

TheThe mathematical mathematical expression expression of ofeach each model model pa parameterrameter is isgiven given below. below. The The expressions expressions were were producedproduced using using non-linear non-linear regression regression fitting. ﬁtting. The The coefficients coeﬃcients of ofeach each equation equation were were produced produced using using iterativeiterative least least square square estimations. estimations.

7.1.1. Parameter a 7.1.1. Parameter a This parameter, expresses the rate of decrease of mixing coefficient during the first phase of This parameter, expresses the rate of decrease of mixing coefficient during the first phase of scavenging. It increases with increased engine load and port covering and decreases with increased scavenging. It increases with increased engine load and port covering and decreases with increased port angle. This means that during the first phase of scavenging, mixing decreases more rapidly with port angle. This means that during the first phase of scavenging, mixing decreases more rapidly with increased port angle and slower for increased engine load and port covering. increased port angle and slower for increased engine load and port covering.  . 2.2  0.03 0.37N N − , θ [10, 30] 0.03 − 0.37 Nmcr , θ ∈ [10,30] a=(I) a =  − ∈ (17) (I)  N0, θ [ 0, 10] (17) 0 , θ ∈ [0,10] ∈ 0.8 .N − 0.2 (II) a = 1.1 Ν1.42 +.0.5 C (18) (II) a = 1.1 − 1.42 − Nmcr+0.5∙C · (18) Ν

7.1.2. Parameter b Model parameter b, expresses the initial value of the mixing coefficient during IPO. This parameter was found to be increasing with increasing with engine load, port angle and port covering. N . (I) b = 0.8 − 0.05 +0.2∙Ω. (19) N

N . (II) b = 2.8 − 1.9 +0.5∙C (20) N

7.1.3. Parameter d

Energies 2019, 12, 1719 14 of 20

7.1.2. Parameter b Model parameter b, expresses the initial value of the mixing coeﬃcient during IPO. This parameter was found to be increasing with increasing with engine load, port angle and port covering.

1.5 N − (I) b = 0.8 0.05 + 0.2 Ω0.8 (19) − Nmcr ·

0.1 N − (II) b = 2.8 1.9 + 0.5 C (20) − Nmcr ·

7.1.3. Parameter d This parameter, expresses how steep the exponential decline of the air penetration coeﬃcient is. It was observed to increase with engine load and port covering and decrease with increased inlet port angle. This means that with increased engine load and port covering, µα decreases slower, while as inlet port angle increases µα decreases more rapidly.

N 2.5 (I) d = 0.28 + 0.035 0.29 Ω0.35 (21) Nmcr − ·

N 2.2 (II) d = 0.1 + 0.16 C0.1 (22) Nmcr ·

7.1.4. Parameter τa∗

Parameter τa∗ expresses the time instant when the second mixing phase commences. This parameter was found to increase with port angle, and be independent of engine load or inlet port covering.

0.7 (I) τ∗ = 0.27 + 0.3 Ω (23) a ·

(II) τ∗ = 0.42, C (24) a ∀ 7.2. Gas Penetration Coefficient The model assumes that the entrainment of exhaust gases to the mixing zone is divided in two phases. In the first phase, the evolution of mixing resembles the one of entrainment of ambient fluid into jets and increases parabolically. The initial phase of increasing mixing will be terminated due to jet interaction and confinement as well as due to the displacement of the exhaust gas. In the second phase, mixing of exhaust gas decreases and µg drops exponentially. The mathematical expression of µg is shown in Equation (25), where σ and kg are model parameters and τ2. is normalized scavenging time of the second mixing phase.  q  τ  σ , 0 < τ < τg∗  τg∗ µg =  (25)  kg(τ2)  e− µg τg∗ (1 + τ2) , 0 < τ2 < 1

The duration of the first mixing phase τg∗ . was estimated at 15–20% of total scavenging time hence, τg∗ = 0.17. . The evolution of the gas penetration coefficient as a function of normalized scavenging time τ for different engine load points is shown in Figure 15. Energies 2019, 12, x FOR PEER REVIEW 14 of 19

This parameter, expresses how steep the exponential decline of the air penetration coefficient is. It was observed to increase with engine load and port covering and decrease with increased inlet port angle. This means that with increased engine load and port covering, μα decreases slower, while as inlet port angle increases μα decreases more rapidly. N . (I) d = 0.28 + 0.035 −0.29∙Ω. (21) N

N . (II) d=0.1 +0.16∙C. (22) N

∗ 7.1.4. Parameter τ ∗ Parameter τ expresses the time instant when the second mixing phase commences. This parameter was found to increase with port angle, and be independent of engine load or inlet port covering. ∗ . (I) τ =0.27+0.3∙Ω (23) ∗ (II) τ = 0.42, ∀ C (24)

7.2. Gas Penetration Coefficient The model assumes that the entrainment of exhaust gases to the mixing zone is divided in two phases. In the first phase, the evolution of mixing resembles the one of entrainment of ambient fluid into jets and increases parabolically. The initial phase of increasing mixing will be terminated due to jet interaction and confinement as well as due to the displacement of the exhaust gas. In the second phase, mixing of exhaust gas decreases and μg drops exponentially. The mathematical expression of

μg is shown in Equation (25), where σ and kg are model parameters and τ is normalized scavenging time of the second mixing phase.

⎧ τ ∗ 𝜎 ∗ , 0 < τ < τ μ = τ (25) ⎨ () ∗ ⎩e μτ(1+τ) , 0 < τ <1 ∗ The duration of the first mixing phase τ was estimated at 15%–20% of total scavenging time ∗ hence,Energies τ2019=0.17, 12, 1719. The evolution of the gas penetration coefficient as a function of normalized15 of 20 scavenging time 𝜏 for different engine load points is shown in Figure 15.

[-] 100% g 0.8 75% 50% 0.6 25%

0.4

0.2

0 Gasμ Coef. Penetration 0 0.2 0.4 0.6 0.8 1 Normalized scavenging time τ [-]

FigureFigure 15. 15.GasGas penetration penetration coefficient coeﬃcient evolution evolution for fordifferent diﬀerent engine engine load load points points (θ (=θ 20°= 20 and◦ and C = C 0).= 0).

In reality, the transition from one mixing phase to the next, that takes place in∗ τg∗ would be quite In reality, the transition from one mixing phase to the next, that takes place in 𝜏 would be quite smoother. However, the presented expression was preferred since it provided a better prediction of the smoother. However, the presented expression was preferred since it provided a better prediction of evolution of each mass. the evolution of each mass. 7.2.1. Parameter σ

This parameter expresses the peak value of the gas penetration coeﬃcient during the ﬁrst phase of mixing. Increased values of σ indicate increased mixing of exhaust gas. Since mixing increases with load, σ also increases with load. On the other hand, for increased inlet port angle, the recirculation zones that are formed act as a barrier towards the entrainment of exhaust gas to the mixing zone [9]. As a result, σ decreases with increased port angle. As far as port covering by the piston is concerned, σ decreases with port covering, since port covering was found to hinder the entrainment of exhaust gas to the mixing zone. N 5 (I) σ = 0.75 + 0.4 0.7 Ω (26) Nmcr − · N 5 (II) σ = 0.45 + 0.4 0.6 C0.4 (27) Nmcr − ·

7.2.2. Parameter kg

Model parameter kg expresses how rapidly the entrainment of exhaust gas to the mixing zone declines. Increased values of kg indicate decreased mixing. This parameter increased with engine load and port angle and decreased with inlet port covering.

3 N 0.5 (I) kg = 6.5 + 0.5 + 5 Ω (28) Nmcr ·

4 N 0.6 (II) kg = 10.5 + + 2 C (29) Nmcr ·

8. Validation of the Updated Three-Zone Model Against CFD Results The revised zero-dimensional three-zone model was validated against results from CFD simulations. The predicted masses at each zone using the updated 0-D model were compared to the masses predicted by the 2-D CFD model. Validation results are presented in Figures 16 and 17 where CFD results are presented with solid line and results of the updated 0-D model are presented with dashed line. In both cases, the updated model manages to accurately predict the qualitative evolution of scavenging, as predicted by the CFD model. In both presented cases the updated 0-D Energies 2019, 12, x FOR PEER REVIEW 15 of 19

7.2.1. Parameter σ This parameter expresses the peak value of the gas penetration coefficient during the first phase of mixing. Increased values of σ indicate increased mixing of exhaust gas. Since mixing increases with load, σ also increases with load. On the other hand, for increased inlet port angle, the recirculation zones that are formed act as a barrier towards the entrainment of exhaust gas to the mixing zone [9]. As a result, σ decreases with increased port angle. As far as port covering by the piston is concerned, σ decreases with port covering, since port covering was found to hinder the entrainment of exhaust gas to the mixing zone. Ν (I) σ = 0.75 + 0.4 −0.7∙Ω (26) N Ν (II) σ=0.45+0.4 −0.6∙C. (27) N

7.2.2. Parameter kg

8. Validation of the Updated Three-Zone Model Against CFD Results The revised zero-dimensional three-zone model was validated against results from CFD simulations. The predicted masses at each zone using the updated 0-D model were compared to the masses predicted by the 2-D CFD model. Validation results are presented in Figures 16 and 17 where Energies 2019, 12, 1719 16 of 20 CFD results are presented with solid line and results of the updated 0-D model are presented with dashed line. In both cases, the updated model manages to accurately predict the qualitative evolution ofmodel scavenging, slightly overestimatesas predicted by the the mass CFD of themodel. air zone In both and predictspresented the cases dissipation the updated of the exhaust0-D model gas slightlyzone slightly overestimates faster than the the mass CFD of model. the air zone and predicts the dissipation of the exhaust gas zone slightly faster than the CFD model.

EnergiesFigure 2019, 16.12, xEvolution FOR PEER of REVIEW mass of each zone as predicted by the original 0-D model, the updated 0-D16 of 19 model and the CFD model for the 75% load, θ == 20°,20◦,C C = 0.10.1 case. case.

Figure 17. Evolution of mass of each zone as predicted by the original 0-D model, the updated 0-D Figure 17. Evolution of mass of each zone as predicted by the original 0-D model, the updated 0-D model and the CFD model for the 25% load, θ = 30◦,C = 0 case. model and the CFD model for the 25% load, θ = 30°, C = 0 case. Results of the original 0-D model are also included in the graphs (dotted line) for comparison. In bothResults cases, of the the original original model 0-D signiﬁcantlymodel are also overestimates included in the the evolution graphs (dotted of zone line) I. This for means comparison. that the originalIn both cases, model the predicts original that model less amount significantly of air isoverestimates mixed with exhaustthe evolution gases, of than zone the I.one This predicted means that by the CFDoriginal model. model Moreover, predicts the that original less amount model of predicts air is mixed that thewith dissipation exhaust gase of zones, than III the takes one place predicted about 20by CADthe CFD earlier model. than theMoreover, CFD. As the far or asiginal the mixing model zone predicts is concerned, that the resultsdissipation from of the zone original III takes model place are closeabout to 20 the CAD ones earlier from CFDthan simulationsthe CFD. As until far as the the dissipation mixing zone of zone is concerned, III takes place. results Once from this the happens, original themodel mixing are close zone beginsto the ones to reduce from rapidlyCFD simulations and the original until the 0-D dissipation model results of zone deviate III signiﬁcantlytakes place. Once from CFDthis happens, simulation the results. mixing The zone amount begins of gasto reduce that remains rapidly in and the enginethe original cylinder 0-D at model the end results of scavenging deviate (235significantly CAD) is from very closeCFD insimulation both cases. results. The amount of gas that remains in the engine cylinder at the end of scavenging (235 CAD) is very close in both cases.

9. Conclusions An updated zero-dimensional three-zone model for the simulation of the scavenging process of uniflow scavenged two-stroke diesel engines was presented. In order to gain insight on the scavenging process of the engine and update the model, a CFD model of a large two-stroke marine diesel engine was used. The updated model, takes into account the effect of engine load, port angle, and inlet port covering on the scavenging process. Each of the three zones of the model (air zone, mixing zone and exhaust gas zone), is considered as a control volume. The entrainment of air and exhaust gas in the mixing zone is specified through time varying mixing coefficients. The influence of the different scavenging mechanisms was implicitly taken into account by considering the scavenging process to constitute two different phases. CFD simulations showed that mixing of air with exhaust gas increased with increased engine load. Moreover, increasing inlet port-induced swirl and inlet port covering were found to increase the entrainment of air to the mixing zone but decrease the entrainment of exhaust gases to the mixing zone. These results were compatible with the findings of previous works such as [9,11,12]. The updated three-zone model can be used in conjunction with an engine performance prediction code to simulate the performance and especially the transient exhaust gas temperature of a modern uniflow scavenged two stroke large marine diesel engine. The described updating procedure enabled a higher accuracy of the 0-D model, without increasing the computational time and the complexity, by taking into account the gas flow in the cylinder through detailed CFD simulations. The future objective of this work is to be able to investigate with better accuracy the transient response of such a marine engine with a coupled SCR aftertreatment system when driving a propeller of a ship in heavy weather.

Energies 2019, 12, 1719 17 of 20

9. Conclusions An updated zero-dimensional three-zone model for the simulation of the scavenging process of uniflow scavenged two-stroke diesel engines was presented. In order to gain insight on the scavenging process of the engine and update the model, a CFD model of a large two-stroke marine diesel engine was used. The updated model, takes into account the effect of engine load, port angle, and inlet port covering on the scavenging process. Each of the three zones of the model (air zone, mixing zone and exhaust gas zone), is considered as a control volume. The entrainment of air and exhaust gas in the mixing zone is specified through time varying mixing coefficients. The influence of the different scavenging mechanisms was implicitly taken into account by considering the scavenging process to constitute two different phases. CFD simulations showed that mixing of air with exhaust gas increased with increased engine load. Moreover, increasing inlet port-induced swirl and inlet port covering were found to increase the entrainment of air to the mixing zone but decrease the entrainment of exhaust gases to the mixing zone. These results were compatible with the findings of previous works such as [9,11,12]. The updated three-zone model can be used in conjunction with an engine performance prediction code to simulate the performance and especially the transient exhaust gas temperature of a modern uniflow scavenged two stroke large marine diesel engine. The described updating procedure enabled a higher accuracy of the 0-D model, without increasing the computational time and the complexity, by taking into account the gas flow in the cylinder through detailed CFD simulations. The future objective of this work is to be able to investigate with better accuracy the transient response of such a marine engine with a coupled SCR aftertreatment system when driving a propeller of a ship in heavy weather.

Author Contributions: Conceptualization: N.P.K. and A.S.; Data curation: M.I.F., A.P., and O.Z.; Formal analysis: M.I.F., A.P., O.Z., and A.-M.S.; Funding acquisition: N.P.K.; Investigation: M.I.F., A.P., A.S., O.Z., and A.-M.S.; Methodology: M.I.F., A.P., A.S., and O.Z.; Project administration: N.P.K. and A.S.; Resources: N.P.K. and A.S.; Software: M.I.F., A.P., O.Z., and A.-M.S.; Supervision: N.P.K. and A.S.; Validation: A.P. and O.Z.; Visualization: O.Z. and A.-M.S.; Writing—original draft: M.I.F.; Writing—review and editing: M.I.F., N.P.K. and A.S. Funding: This work has received part funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 634135. The doctoral studies of the first author (MIF) are also supported through funding from the NTUA Special Account for Research Grants. Conflicts of Interest: The authors declare that there is no conflict of interest.

Nomenclature

A Area, m2 a Air penetration coefficientarameter BDC Bottom de center b Air penetration coefficientarameter C Percentage of the inlet port area covered by the piston own CAD Crank ang degrees c Propeller law coefficient d Air penetration coefficientarameter EGR Exhaust gas recirculation h Specific enthalpy, J/kg IPO Inlet port oning kg Gas penetration coefficient parameter . m Mass flow rate, kg/sec MCR Maximum continuous rating, kW N Engine rotational speed, RPM ninp Number of inlet ports p Pressure, r Energies 2019, 12, 1719 18 of 20

P Power, kW Q Heat flow, J Sm Swirl number SCR Selective catalytic reduction T Temperature, K TDC Top dead center u Specific energy, J/kg V Volume, m3 Vθ Tangential velocity component, m/s Vz Axial velocity component, m/s Wb Mean velocity at the axial position, m/s Greek Characters β Propeller law exponent ηch Charging efficiency ηsc Scavenging efficiency ηtr Trapping efficiency θ Inlet port angle, ◦ κ Constant of the original three-zone model λ Constant of the original three-zone model µ Mixing coefficient ξ Constant of the original three-zone model ρ Density, kg/m3 σ Gas penetration coefficient parameter τ Dimensionless scavenging time τ1 Normalized scavenging time for second phase of mixing of air τ2 Normalized scavenging time for second phase of mixing of burnt gas τa∗ End of first mixing phase for the air τg∗ End of first mixing phase for the exhaust gas ϕ Crank angle, ◦ Ω Geometric swirl numr Subscripts a Air air, ret Airetained air, del Air delivered tr Trapped cylinder charge cyl Cylinder EBF End of backflow EFP End of first mixing phase exh Exhst receiver exv Exhaust valve g Exhaust Gas IPC Inlet port closing j Different entries to the control volume MCR Maximum continuous rating, kW scav Scavenge receiver sf Surfaces with different rates of heat traner inp Inleports

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