# Spreadsheet for teaching reciprocating engine cycles

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Spreadsheet for TeachingReciprocating Engine CyclesF. CRUZ-PERAGON, J.M. PALOMAR, ELOISA TORRES-JIMENEZ, R. DORADODepartment of Mechanical and Mining Engineering, University of Jaen, ETS Ingenieros Industriales, Campus las Lagunillas,23071, Jaen, SpainReceived 26 November 2009; accepted 18 February 2010ABSTRACT: In an advanced heat engine course, we propose using a spreadsheet application to assist in thestudy of a reciprocating engine model, where the uid composition changes and the parameters depend on thetemperature. This application performs the uid cycle analysis of different engines and also provides experienceto students about computational procedures in heat engines. 2010 Wiley Periodicals, Inc. Comput Appl EngEduc; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20438Keywords: thermodynamic cycles; internal combustion engines; simulation programINTRODUCTIONReciprocating engines are a well known type of internalcombustion engines that appear in a wide range of applications.They produce, by combustion of a fuelwithin a cylinder, the energyneeded in automobiles, trucks, aircrafts, ships, and many otherdevices. Taylor [1], Petchers [2], and Cengel and Turner [3] showa detailed discussion about these engines and their applications.Because of their practical use, the analysis and design ofreciprocating engines are included in the curricula of mechanicalengineers. Initial undergraduate courses about heat enginesare usually addressed by assumptions that consider constantsome thermodynamic parameters. These hypotheses give astraightforward understanding of uid changes within a cylinder.A rigorous study of reciprocating engines in an advanced courseinvolves compositionuid changes along the thermodynamic cycleand temperature-dependent parameters.Tomake the previous complex analysis easier for students,wepropose to use a spreadsheet application. This application performsthe uid cycle analysis of different engines taking into account thevariation in uid composition, temperature-dependent parametersand considering the uid as perfect gas. This method also providesexperience to students about computational procedures in heatengines cycles.It is known that computers are very useful tools both inpractical applications and in teaching engineering. Regardingeducational applications, some advantages of computers are: Make tedious operations, therefore students and instructors onlydeal with concepts and complex models.Correspondence to R. Dorado (rdorado@ujaen.es). 2010 Wiley Periodicals, Inc. Motivate students. Graphics, interactive way to manage theinformation, and the possibility to work with models of complexsystems, are useful ingredients to encourage students. Help in self-learning. Students decides where, when, and whatconcepts to explore. This is possible thanks to Internet learningplatforms as for example, Ilias (www.ilias.de), which is thesoftware employed by the University of Jaen. Reduce the efforts to create, supervise, and evaluate the studentslearning.On the other hand, the use of software in education has somedisadvantages: Choose adequate software is a needed and time-consuming step.The election depends on the methodology aims. Develop the application is also time-consuming and requiresknowledge about programming languages. Again the time spentdepends on the software used. Students need training with the interface.Educational software can be developed by instructors (in-house) as for example CyclePad [4], which aim is designingthermodynamic cycles, or it can be constructed using commercialsoftware as the application described by Rivas et al. [5] to analyzeand optimize power cycles and pipe networks.In general, you can adapt in-house software to the goalsof your methodology, but need more effort and time than if youconstruct an applicationwith commercial software.Moreover,withgeneral commercial software students need less training, becauseit has more familiar interface. They are also more motivated dueto the applicability in their professional career.The goal of this work is to analyze lowly idealizedreciprocating engine cycles using a computer model. Instead ofan in-house program as CyclePad, that can be perfect in a general12 CRUZ-PERAGON ET AL.Table 1 Engines TestedModel Engine type S (mm) (mm) Max. torque (Nm) r Max. power (kW) Max. speed (rpm)Villiers Four-stroke SI 69.8 69.8 8.69 5.1:1 2.12 3,000Sachs Two-stroke SI 57 58 9.8 7:1 4.5 4,500Petter AA1 Four-stroke CI 58 69.4 8.2 17:1 2.6 3,600S, length stroke; , Piston diameter; r, compression ratio; SI, Spark ignition; CI, compression ignition.course of thermodynamics for undergraduates [6,7], we proposeusing a Microsoft Excel spreadsheet because the denition ofmodels, like reciprocating engine cycles for an advance course,is easier. You do not need program languages knowledge toimplement complex applications that admits different inputoutputdata formats, and almost all students are familiar with the software,so that no training is needed.The main limitations of spreadsheets are the model size andthe precision of number representation [8], but for medium sizeapplications they serve as a handy tool for constructingmany typesof simulations [9]. Oke [10] shows a review of the literature aboutspreadsheet engineering applications. The proposed applicationhas a medium size and the precision provides by the software isenough for teaching purposes.The paper is organized as follows: Experimental DataSection is devoted to describe three engines tested in order toobtain input data examples for the mathematical model. Theassumptions and themodel implementation are discussed inModelParameters and Assumptions Section and Calculation ProcedureSection, respectively. Results Section analyzes the engines ofExperimental Data Section via the proposed application. Finally,main conclusions are drawn in Conclusion Section.EXPERIMENTAL DATAThree different one-cylinder engines were analyzed to performthis study. Those engines were tested in a stationary test bench.All dimensions of each engine component and performance weredetermined and they are presented in Table 1. The present workis based on the study of these three engines, but the methodimplemented can be applied to any other engine by consideringits geometry and operating conditions.MODEL PARAMETERS AND ASSUMPTIONSEngineRelated to the engine, the following parameters have to be dened:engine type (SI or CI), conguration (four-stroke or two-stroke),length stroke S (m), piston diameter (m), connecting rod lengthL (m), and compression ratio r.One more parameter is required which depends on engineconguration: in case of four-stroke engine it is the intake valveclosure delay (crankshaft angle degree) and in case of two-strokeengine it is the exhaust valve closure delay (crankshaft angledegree).An analytical model to predict the energy loosed bymechanical friction [11] was included (Fig. 1).FuelFuel main characteristics have to be dened in the application:type of fuel, lower caloric value LCV (kJ/kg) and fuel densityc (kg/L). The most common fuels, from methane (CH4) to0,40,50,60,70,80,91,01,11,200,10,20,30,40,50,60,70,80,910 1000 2000 3000 4000MECHANICAL LOOSES MEAN PRESSURE (bar)MECHANICAL LOOSES (kW)CRANKSHAFT ROTATIONAL SPEED (rpm)Power (kW)Mean pressure (bar)Polynomial (Power (kW))Polynomial (Mean pressure (bar))1,11,21,31,41,51,61,71,81,900,10,20,30,40,50,60,70,80,910 1000 2000 3000MECHANICAL LOOSES MEAN PRESSURE (bar)MECHANICAL LOOSES (kW)CRANKSHAFT ROTATIONAL SPEED (rpm)Power (kW)Mean pressure (bar)Polynomial (Power (kW))Polynomial (Mean pressure (bar))a bFigure 1 Predicted mechanical looses: (a) two-stroke SI engine; (b) four-stroke SI engine.TEACHING RECIPROCATING ENGINE CYCLES 3gasoline and diesel, are included in the programme data base. Theirchemical composition (carbon, hydrogen, and oxygen content)is according to the specications of Heywood [12]. From thiscomposition LCV is determined, because the caloric value ofcarbon and hydrogen has been experimentally determined withconsiderable accuracy [13].The combustion efciency (C) is computed by a functionof the equivalence ratio FR, inverse of the excess air factor [12]. Then, the fraction of the fuel energy qfuel (kJ/cylindercycle)converted into heat energy qsup (supplied or added to the cycle)(kJ/cylindercycle) is calculated by the following equation:qsup = qfuel C (1)In two-stroke engines the Equation (1) includes the shorted-circuit fuel in the gas exchange process.ENGINE CYCLE ANALYSISENGINECompression ratio , r 8 dimensionlessLength Stroke, S 58 mmPiston diameter , 58 mmConnecting rod length , L 125 mmTwo-Stroke/Four-Stroke 2SI (O) / CI (D) engine ONumber of cylinders 1Swept or displacement volume, Vd 153,2406065 cm3Total volume, Vt = Vd + Vc 175,1321217 cm3Clearance volume, Vc 21,89151521 cm3Crank radius, R 29 mmR/L Ratio 0,232 mm/mmIntake(Four-stroke) / Exhaust (Two-stroke) closure after BDC 71 crankshaft angleTotal volumen at actual exhaust closure, Vt' 131,5007871 cm3Actual swept or displacement volume, Vd' 109,6092718 cm3Actual compression ratio, r' 6,006929434 cm3Actual bore, S' 41,48598674 mmOPERATINGCONDITIONSRotational speed of the crankshaft, n 3266 rpmBrake Torque, M e 9,17 NmVolumetric efficiency v (Four-Stroke) or 0,8 dimensionlessScavenge ratio, Rs (Two-Stroke)Fuel consumption, Cc 0,63452 ml/sFuel density, c 0,74 kg/lTrapping efficiency, TR (only for Two-stroke engine) 0,688338795 dimensionlessMechanical losses 0,93820268 kWBrake power 3,136274984 kWIdeal air mass per cycle (reference) 0,000207449 kg/cycleSupplied air mass 0,000165959 kg/cycleTrapped air mass 0,000114236 kg/cycleSupplied fuel mass 8,62605E-06 kg/cycleTrapped fuel mass 5,93765E-06 kg/cycleTrapped fuel-air ratio, F 0,051977023 kg fuel/kg airFUEL/COMBUSTIONLOWER CALORIFIC VALUE, LCV 44400 kJ/kgTYPE OF FUEL GasolineNumber of C atoms in the fuel 7,76 C atoms/ moleculeNumber of H atoms in the fuel 13,1 H atoms/ moleculeNumber of O atoms in the fuel 0 O atoms/ moleculeCombustion efficiency, c 98 %Stoichiometric fuel-air ratio (Fe) 0,069755272 kg fuel/kg airStoichiometric air-fuel ratio (Amin) 14,3358341 kg air/kg fuelFuel-air ratio (F = Fr x Fe) 0,051977023 kg fuel/kg airAir-fuel ratio (A = x Amin) 19,2392704 kg air/kg fuelExcess air factor () 1,342040531Equivalence ratio, Fr 0,745133978Fraction of residual gasses in the mixture, xr (reference value) 0,1599 kg/kg mixtureMaximum pressure 50 barHeat fraction added at constant volume (Otto), Fv 0,41599 dimensionlessUniversal gas constant, R 8,3143 kJ/kmol KFigure 2 Example of initial data introduced during a practical session.4 CRUZ-PERAGON ET AL.Operating ConditionsThere is a thermal cycle for each operating condition; therefore,experimental data obtained from tests carried out in an engine testbench have to be included. Some of these data are: engine speed n(rpm), number of revolutions per cycle N (dimensionless), braketorque Me (Nm), fuel consumption Cc (ml/s) and in case of four-stroke engine; the volumetric efciency V, and for two-strokeengine; the scavenge ratio Rs.From volumetric efciency the actual air ow per cycle isdetermined.The following equation, function of the scavenge ratio,gives the trapping efciency (TR) [14]:TR= 1 eRSRS(2)If the engine test bench has not an air ow meter, then it isacceptable to assume a value of V or TR between 80% and 90%at full load operating conditions.Figure 2 shows a screen capture of the spreadsheet withthe initials data included during a practical session. Based on theprevious data, the following parameters (per cylinder and cycle)are determined according to [14]: indicated work per cycle (Wi),effective work per cycle (We), mechanical loss work per cycle(Wm), brake mean effective pressure (bmep), and indicated meaneffective pressure (bmip).CALCULATION PROCEDUREComputational ProcedureThe implemented application main goal is to compute a cyclethat veries a desired efciency. This section explains an iterativeprocedure to achieve that goal.Table 2 Terminology Related to Fluid Composition DeterminationTerm SignicanceMi Molecular mass of i component (kg/kmol)Y Fuel molar ratio H/CR =4/(4+ y)FR Equivalence ratio Molar ratio N/O (for air = 3,773)xb Fraction of burnt gas in fresh mixture (01)C Coefcient determined from the equilibrium constant of thechemical reaction: CO2 +H2 =CO+H2OSTARFV0Xr0P-V CYCLECALCULATIONXRF,gFXrF=Xr0?g=gF?SHOWP-V CYCLEENDgENGINE INPUT DATA& OPERATING CONDITIONXrF=Xr0MODIFY FV0YESYESNONOFigure 3 Computational procedure owchart.TEACHING RECIPROCATING ENGINE CYCLES 5Table 3 Composition of the Fluid Not BurntSpecies i = (gas moles/O2 reactant mol)FR 1 FR > 1Fuel 4 (1 xb) (1+ 2r)FR/MfO2 1 xb FR 1 xbH2O 2 xb (1 r) FR xb [2 (1 rFR)+ c]CO 0 xb cH2 0 xb [2(FR 1) c]CO2 xb r FR xb (r FR c)N2 Sum u (1 xb) {[4 (1+ 2r) FR/Mf ]+ 1+}+ xb bTable 4 Composition of the Burnt FluidSpecies i (gas moles/reactant O2 mol)FR 1 FR > 1CO2 FR r FR r cH2O 2 (1 r) FR 2 (1 r) FR + cCO 0 CH2 0 2(FR 1) cO2 1FR 0N2 Total b (1 r) FR + 1+ (2 r) FR +Recall that the proposed model considers the working uidas a perfect gas with temperature-dependent parameters. Theprocedure is performed according to Heywood [12] and theapproximations provided by the JANAF Tables [15]. The uidcomposition is also determined according to Heywood [12] and itis showed in Tables 24.The total uid mass within the cylinder is composed of air,fuel, and a small part of residual exhaust gasses of the previouscycle. Data on molar basis (Tables 3 and 4) are expressed on massfraction by considering the molecular mass of each component Mi(kg/kmol). Then the fuel and the air mass are known (per cylinderand cycle) and the mass of reactant oxygen will be also known.Themass of residual gases is unknown and it is determined byan iterative method which considers this residual gas as a fractionof the total mass. One more parameter is included: heat fractionreleased at constant volume FV. This parameter allows analyzingthe general dual combustion cycle (also called Sabathe cycle): withFV = 1 the Sabathe cycle reduces to Otto cycle, while with FV = 0it reduces to Diesel cycle.From a certain fraction of residual gases xr and the setof reference values (mass and thermodynamic properties), thecalculation procedure evaluates the thermodynamic cycle iteratingover the values of xr and FV, with the aim of providing a xeddiagram factor g around 80%. This process is described inFigure 3. Note that the thermodynamic cycle is computed in eachiteration of the general algorithm described in Figure 3. The CycleComputation Section explains how to determine the beginning andend points of each process of the cycle.Cycle ComputationThe cycle analysis starts by setting a reference value (pressure,temperature, and mixture mass); this value will correspond to thepoint at intake valve closure delay in case of four-stroke engines,or exhaust valve closure delay in case of two-stroke engines.The previous point is the reference one because in that moment,Figure 4 Actual cycle, dual cycle, and reference point.6 CRUZ-PERAGON ET AL.the mass inside the cylinder will evolve during compression andexpansion stroke.If measurements are possible, the reference will be a pointat the compression stroke of the actual cycle (Fig. 4 shows anexample). For the examples showed in Results Section, we haveestimated the reference point. The proposed application comparesactual and simulated cycle via indicators, such as combustionefciency and diagram factor (once mechanical losses tendencyis known).According to Figure 5, the pressure at the beginning ofthe compression process (point 1) is evaluated following therelationships for an adiabatic process. The next points aredetermined considering the nature of each process and thethermodynamics properties as temperature dependent. Output dataobtained are summarized in Figure 5. Those results will be usedto determine the convergence of the calculation process showed inFigure 3.Process 12: Adiabatic Compression. Once the point 1 is known,the end point of the theoretical compression process (point 2)is calculated by an iterative method. According to Figure 6,compression process starts by choosing any value for the adiabaticindex (ratio of constant pressure and constant volume heatcapacities). After that, the mean value of the adiabatic indexC YC LER eference PointP ref, V ref, T ref, m ref, x ref, h ref, U ref, S ref, C p,ref, C v,ref, refRelationships adiabatic processP1Thermodynamic PropertiesCOMPRESSION 1-2Point 2 (P 2, V 2, T 2,...)CONSTANT VOLUMEHEAT ADDITION (2-3)Point 3 (P 3, V 3, T 3,...)CONSTANT PRESSUREHEAT ADDITION (3-4)EXPANSSION 4-5CYCLE RESULTSE NDV1F V, q supTHEORETICAL WORKAND EFFICIENCY(Wt, t)gFExhaustV1 to V2xrFPoint 1P 1, V 1, T 1, m 1, x1, h 1, U 1, S 1, C p,1, C v,1, 1Point 4 (P 4, V 4, T 4,...)Point 5 (P 5, V 5, T 5,...)Wt, tWiFigure 5 Cycles computation.TEACHING RECIPROCATING ENGINE CYCLES 7COMPRESSIONEXPANSSIONT0=jAdiabatic EquationPi+1Ideal gas lawCF=C0?ENDPoint jPi, Vi, Ti, mi, xihj, uj, sj, cp,j, cv,j, jVj+1TF=(hj+1-hj)/(uj+1-uj)xj+1=xjPoint j+1Pi+1, Vi+1, Ti+1, mi+1, xi+1hj+1, uj+1, sj+1, cp,j+1, cv,j+1, j+1T0=TFNOYESTi+1Thermodynamic propertiesFigure 6 Procedure to evaluate the compression and expansion process.between points 1 and 2 is determined by establishing the relationbetween the enthalpy increment and the internal energy increment.If the adiabatic index obtained is not equal to the rst onechosen, then the iteration process continues and point 2 isrecalculated, but now using the last adiabatic index obtained.The calculation process nishes when the index converges ina stable value (see Fig. 6). In case of SI engines, the methodconsiders a mixture of air, residuals gases, and vaporized fuelduring the compression process, while the mixture considered fora CI engine is a blend of air and residual gases (see Tables 2and 3).Process 23: Heat Addition at Constant Volume. Once point 2 isdetermined, point 3 is calculated considering that the increase ininternal energy is the heat added at constant volume (see Fig. 7).Then the internal energy of point 3 will be known. The remainingproperties are determined iteratively.8 CRUZ-PERAGON ET AL.HEAT ADDITIONCONSTANT VOLUMEcv,0=cv,jqsup,v=mjcv,0TTi+1Ideal gas lawcv,F=cv,0?ENDPoint jPi, Vi, Ti, mi, xihj, uj, sj, cp,j, cv,j, jqsup,vcv,F=(uj+1-uj)/(Tj+1-Tj)xj+1Vj+1=VjPoint j+1Pi+1, Vi+1, Ti+1, mi+1, xi+1hj+1, uj+1, sj+1, cp,j+1, cv,j+1, j+1cv,0=cv,FNOYESPi+1Thermodynamic propertiesFigure 7 Calculation procedure to evaluate the heat addition at constantvolume.Since heat released in this process is equal to a mean value ofthe specic heat capacity at constant volume cv between two pointsmultiplied by the increase in temperature, the iteration methodworks in the same way as in process 12, but now iterating oncv (kJ/kg K) between points 2 and 3 instead of iterating on theadiabatic index. If evaluating an Otto cycle, then point 3 will takethe same properties as point 2.Process 34: Heat Addition at Constant Pressure. Point 4represents the thermodynamics properties of the uid insidethe cylinder at the end of combustion process, in which fuelheat is released at constant pressure (see Fig. 8). This heatadded is equal to a mean value of the specic heat capacityat constant pressure cp (kJ/kg K) multiplied by the increase intemperature between points 3 and 4. After obtaining a stablevalue of cp, rest of thermodynamic properties are determined. Thedrawback is the unknown cylinder volume to satisfy the previouscomputed thermodynamic properties (point 4). Thus, we look fora crankshaft angle which leads to a volume of the combustionchamber similar to that obtained with the calculated mass atpoint 4.Process 45: Adiabatic Expansion. Finally, we analyze theadiabatic expansion to the point 5 in the same way as inHEAT ADDITIONCONSTANT PRESSUREcp,0=cp,jqsup,p=mjcp,0TTi+1Ideal gas lawThermodynamic Propertiescp,F=cp,0?ENDPoint jPi, Vi, Ti, mi, xihj, uj, sj, cp,j, cv,j, jqsup,pVj+1cp,F=(hj+1-hj)/(Tj+1-Tj)xj+1Crankshaft AnglePj+1=PjPoint j+1Pi+1, Vi+1, Ti+1, mi+1, xi+1hj+1, uj+1, sj+1, cp,j+1, cv,j+1, j+1cp,0=cp,FNOYESFigure 8 Calculation procedure to evaluate the heat addition at constantpressure.compression process, that is, iterating on the adiabatic index of theexpansion (Fig. 6). For points 35, it is considered the compositionof gases given in Tables 3 and 4.Gas Exhaust Process Approach. To obtain the mass fraction ofcombustion residuals, the following assumptions are considered:from points 5 to 1 gases are expanded at constant volumefollowing an ideal process, and spontaneous opening without gasexchange, but with heat loss. From this point, the exhaust processis considered as adiabatic and quasi-stationary. In order to matchthe rst law of thermodynamics according to those considerations,temperature in point 1 should remain constant. Thus, the retainedmass is calculated from the perfect gas law, at volume V2, withpressure P1 and temperature T1. The fraction of residual gasses inthe mixture xr is the ratio of that retainedmass to the constant massof the closed system. This approximation is close to those whereexhaust process is evaluated with numerical methods validated byreal chamber pressures over crankshaft angle [16].Since we know the theoretical and indicated work and theheat added to the cycle, the diagram factor (g) is computed as theratio of the indicated thermal efciency to the theoretical thermalefciency [14].TEACHING RECIPROCATING ENGINE CYCLES 905101520253035404510 30 50 70 90 110 130 150PRESSURE (bar)VOLUME (cm3)P-V DIAGRAM. FUEL-AIR CYCLE213 45ba Reference POINT POINT PROCESS PROCESS POINT PROCESS POINT POINTCYCLE intake/exhaust closure 1 2 2 a 4 2 a 3 3 3 a 4 4 5Degree () 251 251 360 Heat added 360 374,7 469Degree (rad) 4,380776423 4,380776423 6,283185307 (kJ/ciclo) 6,283185307 6,539748707 8,185594192Pg (bar) 1 1 11,99061791 0,258358883 38,11823517 38,11823517 4,659002665Vg (cm3) 131,5007871 131,5007871 21,89151521 Pmax (bar) u (kJ/kg) 21,89151521 h(kJ/kg) 24,9600172 131,5007871Tg (K) 329,5679537 329,5679537 657,8608009 50 1404,938831 2037,445121 396,2647986 2323,030854 1495,886435Mass (kg) 0,000143437 0,000143437 0,000143437 n 0,000143437 0,000143437 0,000143437 0,000143437u(kJ/kg) -61,12501639 -61,12501639 175,757544 Otto 1580,696375 1580,696375 h4 (kJ/kg) 1895,415935 1003,751454h(kJ/kg) 30,5535403 30,5535403 358,7599508 fraction u3 (kJ/kg) 2162,461954 2558,726753 2558,726753 1430,882094 (T) 1,365849499 1,365849499 1,321133461 0,78 1,261740228 1,257152334 1,276361783COEFICIENT 1-2 cv 2-3 cp 3-4 4-5ITERATIONS 1,385523738 1,385523738 1,01837837 1,01837837 1,387551105 1,387551105 1,264875616 1,264875616VALUES MEAN VALUE CHECK MEAN VALUE CHECK MEAN VALUE CHECK MEAN VALUE CHECKDEGREE 4 CALCULATION ACTUAL ERRORdegrees cm3 cm3 cm3374,7 24,97228962 24,9600172 0,012272421We Wm Wi W comp. W exp. Wnet Qfuel Qsup.kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle0,057616809 0,017235812 0,074852621 -0,033977676 0,127899177 0,0939215 0,382996738 0,258358883c t e m i g0,98 0,245227938 0,150436814 0,769736698 0,195439317 0,796970029Figure 9 Two-stroke SI engine. Airfuel cycle: (a) Results. (b) PV cycle.RESULTSThe three tested engines of Experimental Data Section are used asexamples for practical sessions, their characteristics and operatingconditions are the input of the spreadsheet. Figure 2 shows theinput sheetwith the data of the two-strokeSI engine tested. Figure 9portraits the cycle, graphic, thermodynamic properties, energy, andefciency for the previous engine. The same can be done for thefour-stroke SI and the CI engines. In the last case, the mechanicallosses are unknown, so it has been taken into account those fromthe four-stroke SI engine. Figure 10 shows the cycle graphics ofthe four-stroke engines.Thismethodology also performs lower complexity cycles.Anideal cycle can be simulated using air as working uid, consideringit behaves as perfect gas and its specic heat capacities areconstant and independent of temperature. A medium complexitymethod can consider the variation of specic heat capacities ontemperature.The procedure requires the student to be aware of all steps inthe process, interacting with the terms needed in various iterations.This allows checking the intermediate and nal results variationwhen the same parameter is modied, for example, when totalfraction delivery, heat released at constant volume or mass fractionof combustion residuals are modied.Results for other current engines are drawn in Table 5. Notethat the spreadsheet computes theoretical parameters; therefore,the results are bounded values of the actual ones.CONCLUSIONThe study of engine thermodynamic cycles has an increasingdifculty, as they are relaxing simplifying assumptions. Thecalculation models that consider the working uid as a mixtureof air and fuel lead to solve a differential equation system, whichcan be very complex for the student. The aim of the present study10 CRUZ-PERAGON ET AL.0510152025303510 60 110 160 210 260 310 360PRESSURE (bar)VOLUME (cm3)P-V DIAGRAM. FUEL-AIR CYCLE010203040506070809010010 60 110 160 210PRESSURE (bar)VOLUME (cm3)P-V DIAGRAM. FUEL-AIR CYCLE1523 415234a bFigure 10 Four-stroke PV cycles (a) SI engine (b) CI engine.Table 5 Spreadsheet Parameters for 2 Current EnginesData Engine modelInput data 1.4MPI (1,368 cm3) Lister Petter LPW4for Alfa Romeo vehicle, model MiTo for stationary applicationsFuel Gasoline DieselNumber of cylinders (L) 4 4Bore (mm) 72 86Displacement (mm) 84 80Compression ratio (dimensionless) 10.8:1 18.5:1Data maximum power: power(kW), torque (Nm), speed (rpm),brake-specic fuel consumption(g/kWh)77, 113.12, 6,500, 260 29.5, 93.8, 3,000, 227.7Data maximum Torque: power(kW), torque (Nm), speed (rpm),brake-specic fuel consumption(g/kWh)54.45, 130, 4,000, 220 21.15, 101, 2,000, 213Rod length (mm) 1,54.7 (real data) 126.5 (estimated)Volumetric efciency V (%) 90%Spreadsheet results Max. torque Max. power Max. torque Max. powerBrake mean effective pressure (MPa);engine efciency e (%)1.2; 28.4 1.04; 26.1 0.685; 40.1 0.635; 37.55Indicated mean effective pressure(MPa); indicated efciency i (%)1.39; 33 1.3; 32.7 0.795; 46.7 0.764; 45.26Friction mean effective pressure(MPa); mechanical efciency m (%)0.19; 85 0.26; 80 0.11; 86 0.13; 83Theoretical mean effective pressure(MPa); thermodynamic cycleefciency t (%)1.54; 36.5 1.546; 38.8 0.92; 54.5 0.9; 53.5Diagram factor g (%) 90.5 84 86 84.7is to facilitate the study and understanding of complex enginethermodynamic cycles using a spreadsheet.Onone hand, the use of this tool allows knowing the equationsgoverning the studied process, and how each parameter inuencesthe process in a quick and interactive way. On the other hand, thisapproximation is carried out using computational tools which willgreatly facilitate the calculation process and can be a basis formorecomplex researches or engineering practical works.Spreadsheets and mathematical programming languages arepresented as a powerful tool for students and instructors, as theydecisively contribute in the teachinglearning process and theachievement of its objectives.TEACHING RECIPROCATING ENGINE CYCLES 11ACKNOWLEDGMENTSThis research is supported by the University of Jaen.REFERENCES[1] C. F. Taylor, The internal-combustion engine in theory and practice.Volume 2: Combustion, fuels, materials, design. Revised edition.MIT Press, Cambridge, USA. 1985.[2] N. Petchers, Combined heating, cooling & power handbook:Technologies & applications: An integrated approach to energyresource optimization. 1st edition. The Fairmont Press, Inc., USA.2003.[3] Y. A. Cengel and R. H. Turner, Fundamentals of thermal-uidsciences. 2nd edition. McGraw-Hill, New York, 2005.[4] P. B.Whalley, K. D. Forbus, J. O. Everett, L. Ureel, M. Brokowski, J.Baher and S. E. Kuehne, CyclePad: An articulate virtual laboratoryfor engineering thermodynamics. Artif Intell 114 (1999), 297347.[5] A. Rivas T. Gomez-Acebo and J. C. Ramos, The applicationof spreadsheets to the analysis and optimization of systems andprocesses in the teaching of hydraulic and thermal engineering.Comput Appl Eng Educ 14 (2006), 256.[6] K. Tuttle and C. Wu, Intelligent computer assisted instruction inthermodynamics at the US Naval Academy, Proceedings of the 15thannual workshop on qualitative reasoning, SanAntonio, Texas, 2001.[7] C.Wu andD. C. Sherrill, Intelligent computer aided design, analysis,optimization, and improvement of thermodynamic systems. ComputAppl Eng Educ 9 (2001), 220227.[8] R. Bradley, Understanding AS level computing for AQA., NelsonThornes 2004.[9] J. A. Sokolowski and C. M. Banks, Principles of modelingand simulation: A multidisciplinary approach, 1st edition. Wiley-Blackwell, Hoboken, New Jersey, 2009.[10] S. A. Oke, Spreadsheet applications in engineering education: Areview. Int J Eng Educ 20 (2004), 893901.[11] D. E. Richardson, Review of power cylinder friction for dieselengines. J Eng Gas Turbines Power-Trans ASME 122 (2000), 506519.[12] J. B. Heywood, Internal combustion engines fundamentals, 1stedition. McGraw-Hill, New York, 1988.[13] K. Newton, W. Steeds and T. K. Garrett, The motor vehicle, 12thedition. Butterworth-Heinemann, Oxford, 1996.[14] F. Payri and F. Munoz, Motores de combustion interna alternativos.Publicaciones de la Escuela Tecnica Superior de IngenierosIndustriales de la Universidad Politecnica deMadrid, Madrid, Spain,1990.[15] JANAF Thermochemical tables, 2d ed., NSRDS-NB537, U.S.National Bureau of Standards, June 1971.[16] F. Cruz-Peragon, Analisis de metodologas de optimizacioninteligentes para la determinacion de la presion en camara decombustion en motores alternativos de combustion interna pormetidos no intrusivos. PhDDissertation. University of Sevilla, Spain,2005.BIOGRAPHIESFernando Cruz-Peragon is a professor of heatengines in the Department of Mechanical andMining Engineering at Jaen University (Spain).Dr. Cruz-Peragon received his Ph.D. degree inMechanical Engineering from the University ofSevilla in 2005. His research and professionalinterests include reciprocating engines, softwarefor simulation and design of thermal systems, andenergy utilization facilities.Jose Manuel Palomar is a professor of heatengines at the University of Jaen (Spain). Dr.Palomar received his Ph.D. degree in MechanicalEngineering from the University of Sevilla in1998. His areas of eldwork and research includereciprocating engines, software for simulation anddesign of thermal systems and energy utilizationfacilities.Eloisa Torres-Jimenez is a Ph.D. student andan Assistant Professor of heat engines in theDepartment of Mechanical and Mining Engineer-ing at Jaen University in Spain. Her research andprofessional interests include renewable energy,energy save, bio fuels and its application in heatengines.Ruben Dorado Vicente is an Assistant Professorof Mechanical Engineering in the Departmentof Mechanical and Mining Engineering at JaenUniversity in Spain. Dr. Dorado received hisPh.D. degree in 2007 from the University ofCastilla-laMancha. His research and professionalinterests include differential curves and surfaces,computer aided geometric design algorithm andits applications.

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