energies

Article Experimental and Simulation of Diesel Fueled with Biodiesel with Variations in Heat Loss Model

Daniel Romeo Kamta Legue 1,2,* , Zacharie Merlin Ayissi 2,3,4,* , Mahamat Hassane Babikir 1, Marcel Obounou 1,2 and Henri Paul Ekobena Fouda 1

1 Department of Physics, Energy—Electrical and Electronic Systems, University of Yaounde 1, Yaoundé P.O. Box 812, Cameroon; [email protected] (M.H.B.); [email protected] (M.O.); [email protected] (H.P.E.F.) 2 Laboratory E3M, University of Douala, Douala P.O. Box 2701, Cameroon 3 Nationale Higher Polytechnique School, University of Douala, Douala P.O. Box 2701, Cameroon 4 Department of Automotive Engineering and Mécatronics, ENSPD, University of Douala, Douala P.O. Box 2701, Cameroon * Correspondence: [email protected] (D.R.K.L.); [email protected] (Z.M.A.)

Abstract: This study presents an experimental investigation and thermodynamic 0D modeling of the combustion of a compression-ignition engine, fueled by an alternative fuel based on neem biodiesel (B100) as well as conventional diesel (D100). The study highlights the effects of the engine load at 50%, 75% and 100% and the influence of the heat loss models proposed by Woschni, Eichelberg and Hohenberg on the variation in the cylinder pressure. The study shows that the heat loss through the cylinder wall is more pronounced during diffusion combustion regardless of the nature of the fuels tested and the load range required. The cylinder pressures when using B100 estimated at 89 bars are

 relatively higher than when using D100, about 3.3% greater under the same experimental conditions.  It is also observed that the problem of the high pressure associated with the use of biodiesels in

Citation: Legue, D.R.K.; Ayissi, Z.M.; can be solved by optimizing the ignition delay. The net heat release rate remains roughly the Babikir, M.H.; Obounou, M.; Ekobena same when using D100 and B100 at 100% load. At low loads, the D100 heat release rate is higher Fouda, H.P. Experimental and than B100. The investigation shows how wall heat losses are more pronounced in the diffusion Simulation of Fueled combustion phase, relative to the premix phase, by presenting variations in the curves. with Biodiesel with Variations in Heat Loss Model. Energies 2021, 14, 1622. Keywords: biodiesel; load; heat loss; cylinder pressure; heat release rate; python https://doi.org/10.3390/en14061622

Academic Editor: Fabio Bozza 1. Introduction Received: 5 February 2021 Automobile pollution accounts for a large percentage of global pollution [1]. This Accepted: 24 February 2021 Published: 15 March 2021 pollution is largely caused by the use of fossil oil derivatives as fuel vehicles. Spark-ignition and compression-ignition engines are the most widely used as a con-

Publisher’s Note: MDPI stays neutral verter of the internal energy of fuels. They use petrol and diesel, respectively, as fuel. Both with regard to jurisdictional claims in types of engines convert the internal energy of the fuels into thermal energy which is used published maps and institutional affil- in mechanical form to drive motor vehicles. Generally, heavy-duty vehicles, about 90% of iations. the vehicles in use, are mostly diesel [2]. Self-ignition combustion offers better volumetric efficiency, which means that the diesel engine using this mode of combustion exploits a known energy potential. However, diesel engines present a serious problem for global health [3,4]. The intrinsic chemical composition of this fuel is largely responsible for this phenomenon. The combustion mode fossil fuels should be improved with regard to the Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. level of pollutants emitted. Indeed, the emission of nitrogen oxides would be relatively This article is an open access article responsible for pathologies linked to the proliferation of certain types of malignant tumors. distributed under the terms and In fact, this engine generally operates with poor and non-homogeneous mixtures, which conditions of the Creative Commons leads to a relatively high level of nitrogen oxides (NOx) and particulate matter (PM) [1,5,6]. Attribution (CC BY) license (https:// The two major pollutants, particularly nitrogen oxides, are strongly dependent on the creativecommons.org/licenses/by/ temperature of the , which is a function of the cylinder pressure re- 4.0/). sulting from the high imposed by the performance research of this type

Energies 2021, 14, 1622. https://doi.org/10.3390/en14061622 https://www.mdpi.com/journal/energies Energies 2021, 14, 1622 2 of 17

of engine. The mechanism of formation of these pollutants is explicitly described by the Zeldovich mechanism [1,3,7]. The combustion of diesel engines offers a wide area of investigation [4,8,9]. Experi- mental work is being carried out. Ducted (DFI) is proposed in the literature as a strategy to improve the fuel/gas load mixture of the compression-ignition engine relative to conventional diesel combustion (CDC) [5–7]. The concept of DFI is to inject each fuel spray through a small tube into the combustion chamber to facilitate the creation of a leaner mixture in the self-ignition zone, compared to a fuel jet not surrounded by a duct. The experiments are interesting. Nilsen et al. [5] studied the effects on emissions and engine efficiency using a two-hole injector tip for charging gas mixtures containing 16 and 21% mol oxygen. DFI seems to confirm that it is effective in reducing engine soot emissions. Soot and NOx are reduced with increasing dilution. Christopher [6] conducted an investigation where DFI and CDC were directly compared at each operating point in the study. At the low-load condition, the intake charge dilution was swept to elucidate the soot and NOx performance of DFI. The authors mentioned that DFI likely has slightly decreased fuel conversion efficiencies relative to CDC. All these experimental studies are interesting and very promising, but they are still in the laboratory domain and require expensive instruments. For economic reasons, research is increasingly oriented towards modeling engine combustion. The evaluation of wall heat losses, which are responsible for energy losses in thermal engines, is likely to optimize the operation of this type of engine. Modeling is based on control parameters such as rotational speed, compression ratio, engine load, combustion and injection models [7,10–12]. Modeling consists of reproducing physical phenomena using mathematical equations. This method offers a real-time saving and a significant reduction in costs. However, it is important to validate the results obtained from the modeling or simulation systems in order to give the results a formal character. Zero-dimensional (0D) thermodynamic models of combustion are widely used in the literature. Caligiuri et al. [13] implemented a triple Wiebe model in order to describe and predict the heat release rate and ignition delay of dual-fuel combustion. The Aktar model has been successfully implemented and validated. Prakash correlation relating to the ignition delay was used. A methodological approach based on the prediction of the ignition delay of diesel engines has been implemented. Hariram et al. [14] conducted an investigation, and this experimental and theoretical study addressed the problem related to the effects of beeswax biodiesel mixtures with fossil diesel on combustion parameters. The zero-dimensional thermodynamic model was used as a numerical implementation approach. The variation in cylinder pressure, the net heat release rate and the ignition delay were addressed based on Webe’s triple function. The code developed was successfully validated. These models allow evaluating the performance of thermal engines by the use of correlations based on thermodynamic laws. The advantage of zero-dimensional thermodynamic models is that they are easy to use and do not require large computer memory capacities. The use of thermodynamic postulates makes them accessible and efficient. Thermodynamic 0D models allow the study of both fossil fuel combustion and alternative fuels. The polluting nature of fossil fuels and the depletable nature and recurrent price fluctuations of fossil energy sources have led researchers for years to focus increasingly on alternative energy sources such as biofuels [4]. However, the production of biofuels has so far remained relatively low in relation to demand, given the many structural constraints, hence the need to maximize energy savings by optimizing the energy converters that use these fuels. Around 60% of energy in thermal engines is lost in several forms. However, engine losses remain a real problem as they account for almost 40% of the energy lost [15–17]. A numerical study of the heat loss through the wall would allow a better understanding of this phenomenon and improve the combustion and, by deduction, the efficiency of engines. Energies 2021, 14, 1622 3 of 17

Several published articles have reported on the sensitivity between biodiesel and en- gine load compared to conventional ; however, these do not show the specificity of the impact of the load on the cylinder pressure, taking into account the heat loss through the cylinder wall and the type of fuel used. This reasearch proposes a comparative study of the cylinder pressures generated by the combustion of diesel and neem biodiesel. The study is conducted taking into account the correlations between the heat loss through the cylinder wall. The heat release produced allows representing the phenomenology of the heat loss through the cylinder wall by dissociating the gross heat release rate from the net heat release rate during a combustion phase.

2. Modeling of Zero-Dimensional Thermodynamic Combustion A modeling of the amount of energy released by combustion and a deduction of the cylinder pressure produced during the closed part of the cycle are proposed. The chemical formulation of the fuel is the form CxHyOz. The complete combustion equation of the fuel is given by Equation (1). The first principle of thermodynamics is applied in Equation (2) [18]. y C H O + a(O + 3.77N ) → xCO + H O + (3.77a)N (1) x y z 2 2 2 2 2 2

dU = δW + δQW + ∑ hjdmj (2) where dU represents the variation in the internal energy of the system, δW is the work supplied by the piston to the system, δQW is the heat loss through the cylinder wall. The term ∑ hjdmj represents the energy due to the variation in mass. The heat loss through the cylinder wall is modeled using three characteristic postulates: Woschni, Eichelberg and Hohenberg. By transforming and simplifying Equation (2), the differential Equation (3) is obtained as a function of the crankshaft angle (θ)[19].

( dp γp dV (γ−1) dQ dθ = V dθ + V dθ dT h 1 dQ 1 dp i (3) dθ = T(γ − 1) pV dθ − V dθ

where p and T represent the pressure and the cylinder temperature, γ is the specific heat ratio, θ is the crankshaft angle and V is the cylinder volume. The expression of this volume is governed by Equation (3) [19–21].

πD2S q 2 V(θ) = (1 − cos(θ) + λ − λ2 − sin2(θ) + ) (4) 8 CR − 1 The variation in the cylinder volume V in relation to the crankshaft angle can be deduced [19]. dV(θ) πD2S cosθ = (1 − p )sinθ (5) dθ 8 λ2 − sin2θ where λ is the ratio of the rod length, D is the cylinder bore, CR is the compression ratio and S is the stroke. dQ The term dθ is the heat release rate of the system expressed as follows [19]: dQ γ dV 1 dp = p + V (6) dθ γ − 1 dθ γ − 1 dθ

By entering the experimental combustion data into Equation (6), the heat release profile in the engine can be reconstructed as recommended by many authors using the analysis model [11,14,22]. The evolutions of the heat release profile(s) for an engine speed of 1500 rpm correspond to the load ranges: 25%, 50%, 75% and 100%. These loads correspond to 1.1, 2.5, 3.3 and 4.5 kW, respectively. Energies 2021, 14, 1622 4 of 17

Four steps make up the modeling of the heat release, which are characteristic of dQw the different terms used: the energy lost at the walls dθ integrates the heat exchange coefficient of the three models mentioned above; the energy released by combustion takes dQcomb into account the internal energy of the fuel dθ and two other terms due to exchanges with the surroundings (inlet and outlet mass flow). The system is considered closed, and both terms are taken as zero. The system of Equation (7) is proposed. ( dQcomb = m ∗ LCV ∗ dxb dθ inj dθ (7) dQw 1 dθ = hc A(θ)(T − Tw) ω The terms appearing in Equation (7) are defined by Equation (8) at the heat exchanger surface as a function of the engine geometry. The characteristic fraction of fuel burned as a function of the crankshaft angle variation is given by Equation (9).

 D2  L q A(θ) = π ∗ + π ∗ D ∗ (λ + 1 − Cosθ − λ2 − Sin2(θ) (8) 2 2 " #  θ − θ m+1 x = 1 − exp −a 0 (9) b ∆θ

The fraction of fuel burnt in relation to the crankshaft angle θ is evaluated. minj is the mass of the injected fuel, Tw is the wall temperature, ω is the engine rotation frequency, LCV is the characteristic lower calorific value of the fuel used and hc is the convective heat loss coefficient depending on the heat loss model used, expressed in kW/m2K. The different heat loss coefficients through the walls are proposed [20].

−0.2 0.8 −0.55 0.8 hc = 3.26 ∗ D ∗ p ∗ T ∗ W (10)

−0.06 0.8 −0.4 0.8 hc = 0.013 ∗ V ∗ P ∗ T (VP + 1.4) (11)

−3 1 0.5 0.5 hc = 7.799 ∗ 10 ∗ VP 3 ∗ p ∗ T (12) Equations (10)–(12) represent the coefficients of Woschni, Hohenberg and Eichelberg, respectively. VP is the average piston speed. The term W is deduced from Equation (13):

Vd ∗ Ta W = 2.28 ∗ VP + C1 ∗ (p(θ) − pm) (13) pa ∗ Va

with C1 = 0.00324. On the other hand, pm represents the motored pressure, and subscript “a” is the reference condition n ∗ S V = (14) p 30 where n is the engine speed (rpm).

2.1. Ignition Delay Model The ignition of the fuel is not spontaneous; it is controlled by the Hardenberg and Haze model whose mathematical formulation is given by relation 14 [23–25]:

"   0.63#  1 1 21.2 ID = 0.36 + 0.22V p exp EA − (15) RT 17.190 p − 12.4

where EA is the activation energy, where, R is the universal gas constant. Energies 2021, 14, x FOR PEER REVIEW 5 of 17 Energies 2021, 14, 1622 5 of 17

2.2. Détermining the Heat Release Rate 2.2. Détermining the Heat Release Rate The net heat release rate (Net HRR) represents the thermal energy useful for engine The net heat release rate (Net HRR) represents the thermal energy useful for engine operation [26–28]. It is transformed into mechanical energy by the piston during operation [26–28]. It is transformed into mechanical energy by the piston during combus- combustion inside the combustion chamber. The gross heat release rate (Gross HRR) is, in tion inside the combustion chamber. The gross heat release rate (Gross HRR) is, in fact, the fact, the thermal energy transformed into mechanical work, and the energy losses in the thermal energy transformed into mechanical work, and the energy losses in the walls are walls are associated with it. The combustion of the fuel heats the cylinder walls by associated with it. The combustion of the fuel heats the cylinder walls by convection, and a convection, and a finite amount of calorie is transmitted to the cooling water, constituting finite amount of calorie is transmitted to the cooling water, constituting a heat loss. A curve a heat loss. A curve representing the difference between the total combustion energy and representing the difference between the total combustion energy and the useful thermal energythe useful is generated. thermal energy The characteristic is generated. curves The ofcharacteristic conventional curves diesel of D100 conventional combustion diese are l comparedD100 combustion with those are of compared biodiesel with B100. those of biodiesel B100.

2.3.2.3. ExperimentalExperimental SetupSetup TheThe experimental experimental devicedevice isis anan air-cooledair-cooled single-cylinder single-cylinder motor motor of of the the Lister Lister PeterPeter 0100529-TS10100529-TS1 seriesseries type,type, whosewhose technicaltechnical characteristicscharacteristics areare confinedconfined toto TableTable1 .1. It It is is a a naturallynaturally aspirated,aspirated, four-strokefour-stroke engineengine withwith direct direct injection. injection. CoolingCooling isisby by ambient ambient air. air. This This equipmentequipment isis locatedlocated atat DepartmentDepartment ofof EnergeticEnergetic SystemSystem andand Sustainable Sustainable Development Development (DSEE)(DSEE) of ofEcole Ecole des des Mines Mines de de Nantes Nantes(EMN) (EMN) France. France. Figure Figure1 1shows shows the the experimental experimental device device usedused during during the the study. study.

TableTable 1. 1.Engine Engine characteristics. characteristics.

ListerLister-Petter-01005299-TS1-Petter-01005299-TS1 Sé Sérierie Injection PressureInjection Pressure (Bar)(Bar) 250250 Piston Diameter/StrokePiston Diameter/Stroke (mm)(mm) 95.3/88.995.3/88.9 ConnectingConnecting Rod Length Rod Length (mm)(mm) 165.3165.3 3 Engine CapacityEngine Capacity (m ) (m3) 630630 Compression Ratio - 18 Compression Ratio - 18 Injection Timing (◦CA) 15◦ Before TDC Engine PowerInjection Timing (kW)(°CA) 4.515°à 1500Before trs/min TDC Engine Power (kW) 4.5 à 1500 trs/min

FigureFigure 1.1. Experimental setup setup.. Legend Legend;; 1. 1. Diesel Diesel fuel fuel tank tank;; 2. Biodiesel 2. Biodiesel tank tank;; 3. High 3. High-frequency-frequency acquisition system and computer; 4. Brake dumb dynamometer; 5. Diesel monocylindric motor; 6. acquisition system and computer; 4. Brake dumb dynamometer; 5. Diesel monocylindric motor; Debimeter and air flow sensor; 7. Three-way valve with a purge system; 8. Diesel burette; 9. 6. Debimeter and air flow sensor; 7. Three-way valve with a purge system; 8. Diesel burette; 9. Biodiesel burette. Biodiesel burette. The variation in the load was obtained by modifying the effective power of the engine The variation in the load was obtained by modifying the effective power of the engine by a dynamometer as well as the quantity of fuel admitted into the cylinders. The engine by a dynamometer as well as the quantity of fuel admitted into the cylinders. The engine

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load was varied at 25%, 50%, 75% and 100%. Effective power of 4.2 kW corresponds to the maximum engine load (100%). The fuel supply system consists of two different fuel tanks, (1) and (2), that lead to the three-way valve (7). Each way of this valve was equipped with a stop valve. One tank was filled with conventional diesel fuel D100 (1) and the other (2) with the neem oil methyl ester biodiesel B100. The fuel change during the test was conducted in advance by the shutdown of the second fuel supply and the systematic purge by a system incorporated into the three-way valve. It took ten minutes, with the engine running, to begin measurements without the relative accidental risk of mixing the two fuels. The acquisition of the cylinder pressure was carried out using the Indwin AVL engine rotating at 1500 rpm. The angular position of the crankshaft and the engine speed were obtained via an AVL 364C encoder, attached to the crankshaft. The encoder measures only parameters with frequencies greater than 90 kHz. Table2 presents the test matrix table, which summarizes the main characteristics of the test carried out, and Table3 presents the relative errors of the different sensors used.

Table 2. Main characteristics of the test.

Fuels Engine Speed rpm Engine Load kW Injection Timing ◦CA Diesel 1500 1.18 2.13 3.38 4.59 15 Biodiesel

Table 3. Main characteristics of the test.

Parameters Errors Engine torque ±0.1 N.m Engine speed ±3 rpm Injection timing ±0.05 ◦CA Cylinder pressure ±0.5 of the measured value LCV ±0.25% of the measured value Admission air flow ±0.1% of the measured value Fuel flow ±0.5% of the measured value Injection pressure ±2 bars Inlet air temperature ±1.6 ◦C Exhaust air temperature ±1.6 ◦C

2.4. Fuel Characteristics The experimentation resulting from the work of Ayissi et al. [29] was successfully repeated under the same conditions. The neem oil obtained was characterized in order to calibrate its properties and use it in a heat engine. The characteristic performance values obtained were mostly those found by the authors. These were adopted and are reported in Table4.

Table 4. Fuel characteristics.

Fuel Properties (B100) (D100) Density (kg/m3) 883.3 830 Cetane Number 51.3 48 Lower Heating Value LCV (MJ/kg) 39.7 42.5

2.5. Numerical Method Figure2 presents a synoptic view of the overall methodological organization of the digital study. The end-of-compression characteristic parameters were considered and retained as well as the characteristics of the . The intrinsic properties of the fuels were taken into account. A numerical code was developed. The characteristic equations of the implemented models were solved by the Runge–Kutta method. Energies 2021, 14, x FOR PEER REVIEW 7 of 17

Energies 2021, 14, 1622 fuels were taken into account. A numerical code was developed. The characteristic 7 of 17 equations of the implemented models were solved by the Runge–Kutta method.

Figure Figure2. Digital 2. Digitaldiagram. diagram.

3. Results3. Results and Discussions and Discussion 3.1. Experimental3.1. Experimental Evaluation Evaluation of Cylinder of Cylinder Pressure Pressure FigureFigure 3 shows3 shows the increase the increase in the in experimental the experimental cylinder cylinder pressure pressure based based on the on the crankshaftcrankshaft angle anglewhen when using using B100 and B100 D100 and D100at 100% at 100% load. load. A similarity A similarity between between the the increaseincrease in the cylinder in the cylinder pressu pressurere curves curves of biodiesel of biodiesel B100 and B100 D100 and is D100 observed. is observed. However, However, there is an estimated pressure increase of 3.3% when using B100 at 100% load. A faster there is an estimated pressure increase of 3.3% when using B100 at 100% load. A faster pressure increase in B100 compared to D100 is also observed. pressure increase in B100 compared to D100 is also observed.

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FigureFigure 3.3. ComparisonComparison ofof experimentalexperimental pressurespressures ofof B100B100 andand D100D100 atat 100%100% load.load.

HighHigh cylindercylinder pressurepressure isis characteristiccharacteristic ofof goodgood fuelfuel vaporizationvaporization asas wellwell asas relativelyrelatively betterbetter oxygenationoxygenation ofof fuel.fuel. ThisThis observationobservation hashas alsoalso beenbeen mademade inin thethe literature.literature. Indeed,Indeed, thethe studiesstudies ofof TarabetTarabet [[1818],], MohamedMohamed etet al.al. [[2424]] andand EvangelosEvangelos [[3030]] demonstrateddemonstrated thisthis quitequite clearly.clearly. TheThe transesterificationtransesterification processprocess helpshelps reducereduce thethe viscosityviscosity ofof biodiesel.biodiesel. TheThe operationoperation of of the the engine engine under under high high loads loads would would sufficiently sufficiently reduce reduce the the effects effects of of the the viscosityviscosity of of biodiesel biodiesel on on the the kinetics kinetics of of combustion. combustion. The The increase increase in in cylinder cylinder pressure pressure duringduring biodieselbiodiesel combustioncombustion is probablyprobably duedue toto thethe relativerelative simplicitysimplicity ofof thethe molecularmolecular structurestructure ofof thethe hydrocarbonshydrocarbons thatthat B100B100 contains.contains. ThisThis molecularmolecular structurestructure wouldwould bebe eveneven moremore advantageousadvantageous at at high high load load since since the the high high heat heat inside inside the the cylinder cylinder would would contribute contribute to theto the destructuring destructuring of the of the macromolecules macromolecules of biodiesel, of biodiesel, which which is relatively is relatively less complex less complex after theafter transesterification the transesterification process. process. This predisposition This predisposition of biodiesel of biodiesel to good to combustion good combustion could promotecould promote the rapid the appearancerapid appearance of radicals of radicals inside in theside drops the drops close close to the to stoichiometry the stoichiometry and catalyzed by the high cylinder temperature. This spatial–temporal consideration would suit and catalyzed by the high cylinder temperature. This spatial–temporal consideration the premix combustion process with the consequence of the increase in the pressure peak would suit the premix combustion process with the consequence of the increase in the in the cylinders. The intramolecular presence of residual oxygen atoms would be another pressure peak in the cylinders. The intramolecular presence of residual oxygen atoms factor in raising the pressure peak in the cylinders as biodiesel is relatively oxygenated and would be another factor in raising the pressure peak in the cylinders as biodiesel is the kinetics of combustion are easy. This high-pressure peak would be one of the reasons relatively oxygenated and the kinetics of combustion are easy. This high-pressure peak that increases the NOx level in post-combustion gases of an engine fueled with biodiesel would be one of the reasons that increases the NOx level in post-combustion gases of an generally [5,6,26]. Chiavola et al. [22] and Tarabet [18] mentioned it. The faster pressure engine fueled with biodiesel generally [5,6,26]. Chiavola et al. [22] and Tarabet [18] increase in B100 biodiesel compared to diesel is characteristic of a short ignition period. mentioned it. The faster pressure increase in B100 biodiesel compared to diesel is Mohamed et al. and Evangelos [20,21,27] made the same observation in similar studies. characteristic of a short ignition period. Mohamed et al. and Evangelos [20,21,27] made 3.2.the same Cylinder observation Pressure Evaluation in similar Consideringstudies. the Heat Loss through the Cylinder Wall Patterns of B100 and D100 at 100% Load 3.2. CylinderFigures 4Pressure and5 show Evaluation the evolution Considering of the the cylinder Heat Loss pressure through duringthe Cylinder the combustion Wall Patterns ofof B100 and and D100 D100, at respectively.100% Load Under the constraint of three heat loss models, namely, Eichelberg,Figures Hohenberg 4 and 5 show and the Woschni, evolution the of time the evolution cylinder ofpressure the cylinder during pressure the combustion is simu- latedof B100 taking and intoD100 account, respectively. the heat Under loss through the constraint the cylinder of three wall heat and loss associated models, withnamely the, experimentalEichelberg, Hohenberg pressure curve. and A Woschni, relative similarity the time between evolution the ofnumerical the cylinder and experimental pressure is pressuresimulated curves taking for into both account B100 and the D100heat loss combustions through the is observed. cylinder wall The peaksand associated characteristic with ofthe the experimental temporal variation pressure in the curve. cylinder A relative pressure similarity of the three between numerical the models numerical are evalu- and atedexperimental at 90, 92 and pressure 85 bars, curves respectively, for both forB100 the and Eichelberg, D100 combustion Hohenbergs is and observed. Woschni The models. peaks Thecharacteris result oftic the of experimental the temporal set variation is 89 bars. in The the overestimationcylinder pressure of cylinder of the pressuresthree numerical by the implementedmodels are evaluated models compared at 90, 92 toand the 85 experimental bars, respectively study, isfor explained the Eichelberg, by the factHohenberg that the numericaland Woschni models models take. The into result account of thethe heatexperimental loss through set is the 89 cylinder bars. The wall. overestimation The difference of observedcylinder pressures in the variations by the implemented in the pressure models peaks compared of the implemented to the experimental models, although study is varyingexplained from by onethe correlationfact that the to numerical another, remains models confinedtake into to account the intervals the heat encountered loss through in thethe literature.cylinder wall. The difference observed in the variations in the pressure peaks of the

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Energies 2021, 14, 1622 9 of 17 implementedimplemented models, models, althoughalthough varyingvarying from from oneone correlation correlation toto another,another, remainremainss confinedconfined toto thethe intervalsintervals encounteredencountered inin thethe literature.literature.

Figure 4. Cylinder pressure of B100 at 100%. FigureFigure 4.4. CylinderCylinder pressurepressure ofof B100B100 atat 100%.100%.

Figure 5. Cylinder pressure of D100 at 100%. FigureFigure 5.5. CylinderCylinder pressurepressure ofof D100D100 atat 100%.100%.

TheThe threethree wallwall lossloss modelsmodmodelsels studiedstudied representrepresent fairlyfairly wellwell thethe combustioncombustion ofof thethe modelmodel fuelsfuels inin thethe compression-ignitioncompressioncompression--ignitionignition configuration.configuration.configuration. InIn the the specificspecific specific case case of of of B100 B100 B100 combustion combustion combustion illustrated illustrated in in Figure Figure4 4 4at at at 100% 100% 100% load, load, load, the the the characteristiccharacteristic curves curves ofof thethe the threethree three modelsmodels models studiedstudied studied keepkeep keep thethe the samesame same spatialspatial spatial positionposition position duringduring during thethe ◦ theinitialinitial initial 1212 °CA°CA 12 CAofof combustion.combustion. of combustion. BetweenBetween Between thethe beginning thebeginning beginning ofof thethe of rise therise riseinin cylindercylinder in cylinder pressurepressure pressure andand anditsits peak,peak, its peak, aa gapgap a gap ofof 77 of barsbars 7 bars isis observed isobserved observed betweenbetween between thethe the cumulativecumulative cumulative numericalnumerical numerical curvescurves and and thethe experimentalexperimental curve.curve. ThisThis gapgap whichwhich benefitsbenefitsbenefits thethe simulatedsimusimulatedlated correlationscorrelations isis probablyprobably due duedue toto thethe factfactfact that thatthat the thethe simulated simulatedsimulated models modelmodel takess taketake into intointo account accountaccount the thethe heat heatheat loss lossloss through throughthrough thecylinder thethe cylindercylinder wall inwall the in physical the physical materialization materiali ofzation the spatiotemporal of the spatiotemporal evolution evolution of the cylinder of the pressure. cylinder wall in the physical materialization of the spatiotemporal evolution of the◦ cylinder pressure.pressure.The cylinder pressure of the Woshni model begins a declination around 12 CA after the startTheThe ofcylindercylinder the rise pressurepressure in the cylinder ofof thethe WoshniWoshni pressure. modelmodel The beginsbegins initiated aa declinationdeclination pressure drop aroundaround falls 1212 below °°CACA afterafter the characteristic values of the experimental cylinder pressure. This underestimation of the thethe startstart ofof thethe riserise inin thethe cylindercylinder pressure.pressure. TheThe initiatedinitiated pressurepressure dropdrop fallsfalls belowbelow thethe time evolution of the cylinder pressure by the correlation proposed by Woshni could be characteristiccharacteristic valuesvalues ofof thethe experimentalexperimental cylindercylinder pressure.pressure. ThisThis underestimationunderestimation ofof thethe assimilated by the fact that it does not take into account the piston speed. The piston timetime evolutionevolution ofof thethe cylincylinderder pressurepressure byby thethe correlationcorrelation proposedproposed byby WoshniWoshni couldcould bebe displacement would present the cylinder surface at the temperature gradient generated assimilatedassimilated by by the the fact fact that that it it does does not not take take into into account account the the piston piston speed. speed. The The piston piston by combustion, which would more or less increase the heat loss through the cylinder wall. Hohenberg’s model is the one that retains the highest pressure peak of all the correlations implemented.

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displacement would present the cylinder surface at the temperature gradient generated displacement would present the cylinder surface at the temperature gradient generated Energies 2021, 14, 1622 by combustion, which would more or less increase the heat loss through the cylinder10 wall of 17. by combustion, which would more or less increase the heat loss through the cylinder wall. Hohenberg’s model is the one that retains the highest pressure peak of all the correlations Hohenberg’s model is the one that retains the highest pressure peak of all the correlations implemented. implemented. In the specific case of Figure 5, it is observed that the curves of the numerical models InIn thethe specificspecific casecase ofof FigureFigure5 ,5 it, it is is observed observed that that the the curves curves of of the the numerical numerical models models remain confused during the first 10 °CA before seeing the declination in the characteristic remainremain confusedconfused duringduring thethe firstfirst 1010◦ °CACA beforebefore seeingseeing thethe declinationdeclination inin thethe characteristiccharacteristic curve of the Woshni model. At this load range, all the models shown decline below the curvecurve ofof thethe WoshniWoshni model.model. AtAt thisthis loadload range,range, allall thethe modelsmodels shownshown declinedecline belowbelow thethe experimental cylinder pressure around 17 °CA. Heat losses at 75% load could be experimentalexperimental cylinder cylinder pressure pressure around around 17 ◦ CA.17 Heat°CA. losses Heat at losses 75% load at 75% could load be minimized could be minimized in the post-combustion period. A similar observation is made at 100% load, inminimi the post-combustionzed in the post period.-combustion A similar period. observation A similar is madeobservation at 100% is load, made under at 100% the sameload, under the same simulation conditions, although the declination◦ occurs at 25 °CA. simulationunder the same conditions, simulation although conditions, the declination although occurs the declination at 25 CA. occurs at 25 °CA. 3.3. Cylinder Pressure Evaluation Taking into Account the Heat Loss through the Cylinder Wall 3.3.3.3. CylinderCylinder PressurePressure EvaluationEvaluation TakingTaking into into Account Account the the Heat Heat Loss Loss through through the the Cylinder Cylinder Wall Wall PatternsPatterns WhenWhen EngineEngine IsIs FueledFueled withwithB100 B100 atat 25%,25%, 50%,50%, 75%75% andand 100%100% Load Load Patterns When Engine Is Fueled with B100 at 25%, 50%, 75% and 100% Load FiguresFigures6 6––88 show show the the evolution evolution of of the the cylinder cylinder pressure pressure at at 75%, 75%, 50% 50% and and 25% 25% load, load, Figures 6–8 show the evolution of the cylinder pressure at 75%, 50% and 25% load, respectively.respectively. A A decrease decrease in in the the cylinder cylinder pressure pressure proportional proportional to theto the load load is observed is observed at all at respectively. A decrease in the cylinder pressure proportional to the load is observed at measuringall measuring points. points. The The decrease decrease in the in massthe mass of fuel of fuel allowed allowed would would be at be the at origin the origin of this of all measuring points. The decrease in the mass of fuel allowed would be at the origin of observationthis observation during during the combustion the combustion of B100. of B100. this observation during the combustion of B100.

Figure 6. Cylinder pressure of B100 at 75% load. FigureFigure 6.6. CylinderCylinder pressurepressure ofof B100B100 atat 75%75% load.load.

Figure 7. Cylinder pressure of B100 at 50% load. FigureFigure 7.7. CylinderCylinder pressurepressure ofof B100B100 atat 50%50% load.load.

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FigureFigure 8.8. CylinderCylinder pressurepressure ofof B100B100 atat 25%25% load.load.

TheThe experimentalexperimental pressurepressure decreasesdecreases byby 10%10% andand 6%6% proportionallyproportionally toto thethe passagepassage fromfrom 100%100% toto 75%75% loadload andand fromfrom 75%75% toto 25%25% loadload successively.successively. ThisThis dropdrop inin experimentalexperimental pressurepressure isis evaluatedevaluated atat 22.5%22.5% between between 100% 100% andand 25%25% load. load. This This decrease decrease in in cylinder cylinder pressurepressure couldcould bebe attributed attributed to to the the reduction reduction in in effective effective power power characterized characterized by by the the decreasedecrease inin thethe quantityquantity ofof fuelfuel admittedadmitted intointo thethe cylinders.cylinders. However,However, withwith regardregard toto thethe evolutionevolution ofof thethe pressurepressure curvescurves whateverwhatever thethe typetype ofof modelmodel implemented,implemented, thethe thermalthermal losseslosses wouldwould bebe moremore importantimportant duringduring thethe ascendingascending phasephase ofof thethe piston.piston. ConsideringConsidering thethe specificspecific combustioncombustion ofof B100B100 atat 75%75% load,load, thethe statisticalstatistical differencesdifferences ◦ betweenbetween thethe simulated simulated pressure pressure curves curves and and the the experimental experimental curve, curve, between between 20 and 20 30 andCA, 30 are°CA the, are smallest, the smallest, all loads all combined. loads combined. This observation This observation visible in visible Figure in6 wouldFigure indicate 6 would thatindicate the heat that lossesthe heat are losses less important are less important at this phase at this of phase engine of operation. engine operation. The rising The part rising of thepart numerical of the numerical pressure pressure curves shows curves the shows largest the deviations largest deviations from other from load other points load studied. points Atstudied. this load At this range, load the range, Woschni the modelWoschni underestimates model underestimates the approximation the approximation of the cylinder of the pressure value. cylinder pressure value. The 50% load range seems to present the best compromise between the estimated The 50% load range seems to present the best compromise between the estimated values of wall losses according to the models studied. This load range would be relatively values of wall losses according to the models studied. This load range would be relatively close to the nominal operating rating of the test engine. close to the nominal operating rating of the test engine. Indeed, when compared with other load ranges studied, a better compromise is Indeed, when compared with other load ranges studied, a better compromise is observed between the evolutions of the combustion models and the experimental curve. observed between the evolutions of the combustion models and the experimental curve. The deviations observed during the other load ranges evaluated remain minimized for the The deviations observed during the other load ranges evaluated remain minimized for Woschni, Eichelberg and Hohenberg correlations. the Woschni, Eichelberg and Hohenberg correlations. At 25% load, the three models have curves representing the temporal evolution of the At 25% load, the three models have curves representing the temporal evolution of cylinder pressure which are in agreement. This observation can be seen more clearly in Figurethe cylinder8. This pre observationssure which could are in be agreement. explained by This a small observation parametric can be difference seen more between clearly thein Figure values 8. of This the observation different correlations could be explained implemented. by a small parametric difference between the valuesIn general, of the thedifferent Eichelberg correlations and Hohenberg implemented. models agree on the time evolution of the cylinderIn general, pressure the Eichelberg during the and tests Hohenberg at 50% and models 25% load.agree Thison the rise time in digitalevolution cylinder of the pressurecylinder is pressure characteristic during of the the testsrise deduced at 50% andfrom 25% the heat load. loss This through rise in the digital cylinder cylinder wall duringpressure the is descendingcharacteristic phase of the of rise the deduced pressure from curves the considered. heat loss through The tendency the cylinder for heatwall lossduring to increasethe descending during thisphase phase of the and pressure at this load curves range considered. could be dueThe totendency the fact thatfor heat the gasesloss to have increase more during time to this lick phase the walls and at because this load of range the reduced could be speed due ofto thethe pistonfact that in the its descendinggases have phase.more time to lick the walls because of the reduced speed of the piston in its descendingObservation phase. at high loads shows that the Eichelberg and Hohenberg models show a slightObserva differencetion at in high the loads approximation shows that of the the Eichelberg cylinder and pressure Hohenberg evolution. models However, show a slight difference in the approximation of the cylinder pressure evolution. However, this

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characteristic deviation remains less than 0.6 bar regardless of the time position of the piston. The Woschni model seems to underestimate the time value of the heat loss through thethis cylinder characteristic wall deviationregardless remains of the less engine than load 0.6 bar point regardless compared of the to time the position other two of correlationsthe piston. implemented. The Woschni model seems to underestimate the time value of the heat loss through the cylinder wall regardless of the engine load point compared to the other two 3.4.correlations Evaluation implemented. of Heat Release

3.4. EvaluationThe heat release of Heat at Release different engine loads at 100%, 75% and 50% is evaluated. The heat release curves of the different fuel models D100 and B100 have characteristic curves The heat release at different engine loads at 100%, 75% and 50% is evaluated. The of combustion by auto-ignition. heat release curves of the different fuel models D100 and B100 have characteristic curves of Whatever the load range or the fuel tested, the evolution profiles of net heat release combustion by auto-ignition. rate (Net HRR) and gross heat release rate (Gross HRR) during the premix pressure rise Whatever the load range or the fuel tested, the evolution profiles of net heat release phase remain the same. A relatively significant difference is observed between Net HRR rate (Net HRR) and gross heat release rate (Gross HRR) during the premix pressure rise and Gross HRR when compared with D100 diesel. These differences are evaluated at 10, phase remain the same. A relatively significant difference is observed between Net HRR 10, and 20 J/°CA for 50%, 75% and 100% load, respectively. These differences would mean and Gross HRR when compared with D100 diesel. These differences are evaluated at 10, that heat losses would be greater during combustion of B100 biodiesel. Heat losses in the 10, and 20 J/◦CA for 50%, 75% and 100% load, respectively. These differences would mean premix phase would be minimized based on information from the study. that heat losses would be greater during combustion of B100 biodiesel. Heat losses in the premix phase would be minimized based on information from the study. 3.4.1. Heat Release Curve for 100% Load 3.4.1.Figures Heat Release 9 and Curve10 show for the 100% different Load heat release profiles of D100 diesel and B100 biodiesel,Figures respectively9 and 10 show, for a the 100% different load heat range, release equivalent profiles to of 4.5 D100 kW. diesel The andNet B100HRR convertedbiodiesel, respectively, by the engine for a to 100% mechanical load range, energy equivalent when to B100 4.5 kW. is The used Net as HRR a test converted fuel is approximatelyby the engine 30 to J/ mechanical°CA. Between energy 0 and when 10 °CA B100, this is biofuel used as provides a test fuel an estimated is approximately energy of30 17.32 J/◦CA. J/°CA Between compared 0 and to 10 21.31◦CA, J/ this°CA biofuel for D100. provides No fundamental an estimated difference energy of between 17.32 J/◦ theCA differentcompared Gross to 21.31 HRR J/◦ CAvalues for D100. of the No two fundamental fuels over difference this load between range is the observed. different Gross B100 biodieselHRR values would of the have two better fuels performance over this load at range high loads. is observed. This behavior B100 biodiesel is probably would due have to thebetter oxygenation performance of the at molecule high loads. and This the structural behavior issimplicity probably of due its chemical to the oxygenation composition of [the23–26, molecule30]. At andhigh the temperatures, structural simplicity the relatively of its hi chemicalgher viscosity composition of biodiesel [23–26 ,is30 no]. Atlonger high fundamentallytemperatures, a the handicap relatively for higherthe combustion viscosity of of this biodiesel fuel. This is no would longer justify fundamentally its relatively a goodhandicap combustion. for the combustion of this fuel. This would justify its relatively good combustion.

FigureFigure 9. 9. ProfileProfile of of n netet h heateat r releaseelease r rateate (Net HRR) evolution andand grossgross heatheatrelease release rate rate (Gross (Gross HRR) HRR)for engine for engine speed speed n = 1500 n = rpm1500 atrpm 100% at 100% load accordingload according to D100 to D100 combustion. combustion.

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Figure 10. Profile of net heat release rate (Net HRR) evolution and gross heat release rate (Gross HRR) for engine speed n = 1500 rpm at 100% load according to B100 combustion. Figure 10. ProfileProfile of of n netet h heateat release release rate rate (Net (Net HRR) HRR) evolution evolution and and gross gross heat heat release release rate rate (Gross (Gross HRR) for engine speed n = 1 1500500 rpm at 100% load according to B100 combustion combustion.. 3.4.2. Heat Release Curves Net HRR and Gross HRR for 75% Load 3.4.23.4.2.Figures. Heat Release 11 and Curves12 show Net the HRRdifferent and profilesGross HRR the nfor et 75%heat Loadrelease rate (Net HRR) and the grossFigures heat 11 r eleaseand 12 r showate (Gross the different HRR) for profiles profiles an engine thethe netn etspeed heatheat releaserofelease 1500 rateraterpm (Net at 75% HRR) load. and Betweenthe g grossross 0 andh heateat 10r releaseelease °CA, ther rateate co (Gross mbustion HRR) s of forB100 an and engine D100 speed produce of of 1500 150013.20 rpm rpmand at14.20 at 75% 75% J/ °load. load.CA, ◦ ◦ respectivelyBetween 0 and . The 10 heat°CACA, , lossthe co combustions throughmbustion thes of cylinder B100 and wall D100 as produceproduce a function 13.2013.20 of and and the 14.2014.20 crankshaft J/J/°CACA, , positionrespectively. is evaluated The heat at loss about through 10 J/°CA the cylinderduring B100 wall combustion as a function, representing of the crankshaft 20% position higher respectively. The heat loss◦ through the cylinder wall as a function of the crankshaft thanpositionis evaluated during is evaluated the at combusti about at 10 abouton J/ ofCA 10D100 duringJ/°CA at this during B100 range combustion, B100 of load combustion. A similar representing, representing observation 20%higher 20%was highermade than bythanduring Pankaj during the et combustion theal. [combusti31] and of Muhamedon D100 of D100 at this etat althis range. [ 28range]. of These load. of load Aauthors similar. A similar show observation observationed that at was a was range made made of by 75%,Pankaj the et ignition al. [31] delay and Muhamed of B100 and et al.D100 [28]. increases. These authors This increase showed of that about at a range2 °CA ofin 75%,the by Pankaj et al. [31] and Muhamed et al. [28]. These authors showed◦ that at a range of ignition75%,the ignition the delay ignition delay is significant delay of B100 of and B100 and D100 andhas increases. alsoD100 been increases. Thisobserved increase This by increase ofMuhamed about of 2 about CAet al in .2 [ the27°CA] ignitionat in this the delay is significant and has also been observed by Muhamed et al. [27] at this range of load. rangeignition of load.delay is significant and has also been observed by Muhamed et al. [27] at this range of load.

FigureFigure 11. 11. ProfileProfile of of net net heat heat release release rate rate (Net (Net HRR) HRR) evolution evolution and and gross gross heat heat release release rate rate (Gross (Gross HRR) for engine speed n = 1500 rpm at 75% load according to the B100 combustion analysis FigureHRR) for 11. engine Profile speed of net nh =eat 1500 release rpm r atate 75% (Net load HRR) according evolution to theand B100 gross combustion heat release analysis rate (Gross model. model. HRR) for engine speed n = 1500 rpm at 75% load according to the B100 combustion analysis model.

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FigureFigureFigure 12. 12.12. Profile ProfileProfile of ofof n et netnet h eath heateat release r releaseelease rate r rateate (Net (Net (Net HRR) HRR) HRR) evolution evolution evolution and and and g rossgross gross h eatheat heat release release release rate rate rate (Gross (Gross (Gross HRR)HRR)HRR) for for for engine engine engine speed speed speed n n n= = =1 15005001500 rpm rpmrpm at atat 75% 75%75% load loadload accordingaccording according to to to D100 D100 D100 c combustion. ombustioncombustion. .

3.4.3.3.4.3.3.4.3. The TheThe NetNet Net HRR HRRHRR and andand Gross GrossGross HRR HRR HRR for for for 5 50% 05%0% Load Load Load FiguFiguresFiguresres 1313 13 andand and 1414 14 showshow show the the the different different different profiles profiles profiles of of of the the the evolution evolution evolution of of of the the the n net etnet h heat eatheat r release eleaserelease rrateaterate (Net (Net (Net HRR) HRR) andand and thethe the grossg rossgross heat h eatheat release r eleaserelease rate r aterate (Gross (Gross (Gross HRR) HRR) HRR) for for anfor enginean an engine engine speed speed speed of 1500 of of 1500 rpm1500 rpmatrpm 50% at at 50% load. 50% load. load. These These These two two figures two figures figures indicate indicate indicate that that the that diffusionthe the diffusion diffusion combustion combustion combustion phase phase phase of B100 of of B10 andB100 0 ◦ andD100and D100 D100 starts starts starts with with awith Net a aNet HRR Net HRR HRR of 20 of of and 20 20 and 21 and J/ 21 21CA, J/ J/°CA°CA respectively., respectively., respectively. The The heatThe heat heat loss loss throughloss through through the ◦ thecylinderthe cylinder cylinder wall wall (curvewall (curve (curve representing representing representing the difference) the the difference) difference) is estimated is is estimated estimated at 10 forat at 10 B10010 for for and B100 B100 8 J/and andCA 8 8 ◦ ◦ J/forJ/°CA°CA D100. for for D100. AtD100. 10 At AtCA, 10 10 the°CA °CA Net, the, the HRR Net Net HRR value HRR valueof value B100 of of isB100 B100 12 andis is 12 12 13.5 and and J/ 13.5 13.5CA J/ J/°CA for°CA D100. for for D D100. The100. heatThe The ◦ ◦ heatlossheat loss through loss through through the cylinderthe the cylinder cylinder wall wall values wall values values are as are are follows: as as follows: follows: B100 B100 (10B100 J/ (10 (10CA), J/ J/°CA°CA D100), ),D100 D100 (8 J/ (8 (8 CA).J/ J/°CA°CA). ).

FigureFigureFigure 13. 13.13. Profile ProfileProfile of ofof n et netnet h eath heateat release r releaseelease rate r rateate (Net (Net (Net HRR) HRR) HRR) evolution evolution evolution and and and g rossgross gross h eatheat heat release release release rate rate rate (Gross (Gross (Gross HRR)HRR)HRR) for for for engine engine engine speed speed speed n n n= = =1 15005001500 rpm rpmrpm at atat 50% 50%50% load loadload accordiaccording accordingng to to to B100 B100 B100 combustion. combustion. combustion.

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FigureFigure 14. 14.Profile Profile of of net netheat heat releaserelease raterate (Net(Net HRR) evolution and and g grossross h heateat r releaseelease rate rate (Gross (Gross HRR)HRR) for for engine engine speed speed n n = = 1500 1500 rpm rpm at at 50% 50% load load according according to to D100 D100 combustion. combustion.

4.4. Conclusions Conclusions AnAn experimental experimental investigation investigation coupled coupled with with a a thermodynamic thermodynamic 0D 0D simulation simulation of of a a neem-basedneem-based biodiesel, biodiesel, a conventionala conventional diesel diesel and and their their respective respective different different heat releasesheat releases was carriedwas carried out. The out. different The different correlations correlations of Woschni, of Woschni, Eichelberg Eichelberg and Hohenbergand Hohenberg served served as numericalas numerical models model in thes in systemic the systemic simulation simul ofation combustion of combustion phenomenology. phenomenology. The Woshni The correlationWoshni correlation best represents best represents the peak of the the peak cylinder of the pressure cylinder comparison pressure madecomparison with other made implementedwith other models. implemented This correlation, models. This however, correlation, seems to however, relatively seems underestimate to relatively the valueunderestimate of the cylinder the value pressure of the after cylinder bottom pressure dead center.after bot Thetom Eichelberg dead center. and The Hohenberg Eichelberg modelsand Hohenberg represent themodel spatial–temporals represent the evolutionspatial–temporal of the cylinder evolution pressure of the incylinder the same pressure way. Implementationin the same way. of otherImplementation heat losses of through other heat cylinder losses wall through models cylinder such as wall Zainal models or Sitkey such couldas Zainal be exploited or Sitkey for could greater be opennessexploited tofor the gre fieldater ofopenness investigation. to the Thefield investigation of investigation. of theThe cylinder investigation pressure of confirmedthe cylinder that pressure the load confirmed rate has that an influence the load rate on the has value an influence of the peakon the of thevalue cylinder of the pressure. peak of the The cylinder study presented pressure. provides The study a better presented understanding provides a of better the phenomenologyunderstanding ofof parietalthe phenomenolog thermal lossesy of from parietal the combustionthermal losses of alternative from the combustion fuels and its of impact on the performance of combustion ignition engines. The cylinder pressure in the alternative fuels and its impact on the performance of combustion ignition engines. The case of the combustion of biodiesel B100 is estimated at 89 bars against 86 bars for diesel cylinder pressure in the case of the combustion of biodiesel B100 is estimated at 89 bars D100; a gap of 3.3% to the advantage of B100 is thus observed when using this biofuel against 86 bars for diesel D100; a gap of 3.3% to the advantage of B100 is thus observed at 100% load. A faster pressure increase in B100 compared to D100 is also observed. A when using this biofuel at 100% load. A faster pressure increase in B100 compared to D100 study of a parametric variation in the ignition delay associated with this study could better is also observed. A study of a parametric variation in the ignition delay associated with explain its influence on the comparative evolution of the peak cylinder pressure depending this study could better explain its influence on the comparative evolution of the peak on the nature of the fuel. cylinder pressure depending on the nature of the fuel. Author Contributions: Conceptualization, D.R.K.L. and Z.M.A.; methodology, M.O.; software, Author Contributions: Conceptualization, D.R.K.L. and Z.M.A.; methodology, M.O.; software, D.R.K.L. and Z.M.A. and M.H.B.; validation, E.F.H.P., M.O. and Z.M.A.; formal analysis, Z.M.A.; D.R.K.L. and Z.M.A. and M.H.B.; validation, E.F.H.P., M.O. and Z.M.A.; formal analysis, Z.M.A.; investigation, Z.M.A. and D.R.K.L.; resources, M.O.; data curation, D.R.K.L.; writing—original draft investigation, Z.M.A. and D.R.K.L.; resources, M.O.; data curation, D.R.K.L.; writing—original draft preparation, Z.M.A. and D.R.K.L.; writing—review and editing, Z.M.A. and D.R.K.L.; visualization, preparation, Z.M.A. and D.R.K.L.; writing—review and editing, Z.M.A. and D.R.K.L.; visualization, M.H.B.; supervision, E.F.H.P.; project administration, M.O.; funding acquisition, Z.M.A. and D.R.K.L. M.H.B.; supervision, E.F.H.P.; project administration, M.O.; funding acquisition, Z.M.A. and All authors have read and agreed to the published version of the manuscript. D.R.K.L. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Funding: This research received no external funding. Institutional Review Board Statement: Ethical review and approval were waived for this study, due Institutional Review Board Statement: Ethical review and approval were waived for this study, to the fact that the studies not involve humans or animals. due to the fact that the studies not involve humans or animals. Informed Consent Statement: Patient consent was waived due to the reason that the studies not involving humans.

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Informed Consent Statement: Patient consent was waived due to the reason that the studies not involving humans. Acknowledgments: We thank the Department of Energetic System and Sustainable Development of Ecole des Mines de Nantes EMN for giving us the experimental device; the G.C.C. team for always encouraging us in combustion and simulation aspects; and the team members of Energy, Electric and Electronic Systems, University of Yaoundé 1, for welcoming and assisting us. Conflicts of Interest: The authors declare that there is no conflict of interests regarding the publication of this paper.

Abbreviations

θ Crank angle (◦CA) ∆θ Total combustion duration (◦CA) ◦ θ0 Start of combustion ( CA) x Burnt mass fraction W Work done (KJ) U Internal energy CR Compression ratio cv Specific heat at constant volume −2 −1 hc Heat transfer coefficient (W. m .K ) m Masse (Kg) R Gas constant R Gas constant Q Heat transfer (KJ) V Volume (m3) p Pressure (Bar) T Temperature (K) A(θ) Area exposed to heat transfer (m2) D Cylinder bore (m) S Stroke (m) n Engine speed ω Angular velocity (rad/s) Vp Mean piston speed (rad/s) TDC Top dead center (deg) BTDC Before TDC (deg) BDC Bottom dead center (deg) HRR Heat release rate ◦CA Degree crank angle

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