spreadsheet for teaching reciprocating engine cycles

11
Spreadsheet for Teaching Reciprocating Engine Cycles F. CRUZ-PERAG ´ ON, J.M. PALOMAR, ELOISA TORRES-JIMENEZ, R. DORADO Department of Mechanical and Mining Engineering, University of Ja´ en, ETS Ingenieros Industriales, Campus las Lagunillas, 23071, Ja´ en, Spain Received 26 November 2009; accepted 18 February 2010 ABSTRACT: In an advanced heat engine course, we propose using a spreadsheet application to assist in the study of a reciprocating engine model, where the fluid composition changes and the parameters depend on the temperature. This application performs the fluid cycle analysis of different engines and also provides experience to students about computational procedures in heat engines. © 2010 Wiley Periodicals, Inc. Comput Appl Eng Educ; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20438 Keywords: thermodynamic cycles; internal combustion engines; simulation program INTRODUCTION Reciprocating engines are a well known type of internal combustion engines that appear in a wide range of applications. They produce, by combustion of a fuel within a cylinder, the energy needed in automobiles, trucks, aircrafts, ships, and many other devices. Taylor [1], Petchers [2], and C ¸ engel and Turner [3] show a detailed discussion about these engines and their applications. Because of their practical use, the analysis and design of reciprocating engines are included in the curricula of mechanical engineers. Initial undergraduate courses about heat engines are usually addressed by assumptions that consider constant some thermodynamic parameters. These hypotheses give a straightforward understanding of fluid changes within a cylinder. A rigorous study of reciprocating engines in an advanced course involves composition fluid changes along the thermodynamic cycle and temperature-dependent parameters. To make the previous complex analysis easier for students, we propose to use a spreadsheet application. This application performs the fluid cycle analysis of different engines taking into account the variation in fluid composition, temperature-dependent parameters and considering the fluid as perfect gas. This method also provides experience to students about computational procedures in heat engines cycles. It is known that computers are very useful tools both in practical applications and in teaching engineering. Regarding educational applications, some advantages of computers are: Make tedious operations, therefore students and instructors only deal with concepts and complex models. Correspondence to R. Dorado ([email protected]). © 2010 Wiley Periodicals, Inc. Motivate students. Graphics, interactive way to manage the information, and the possibility to work with models of complex systems, are useful ingredients to encourage students. Help in self-learning. Students decides where, when, and what concepts to explore. This is possible thanks to Internet learning platforms as for example, Ilias (www.ilias.de), which is the software employed by the University of Jaen. Reduce the efforts to create, supervise, and evaluate the students learning. On the other hand, the use of software in education has some disadvantages: 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 requires knowledge about programming languages. Again the time spent depends 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 designing thermodynamic cycles, or it can be constructed using commercial software as the application described by Rivas et al. [5] to analyze and optimize power cycles and pipe networks. In general, you can adapt in-house software to the goals of your methodology, but need more effort and time than if you construct an application with commercial software. Moreover, with general commercial software students need less training, because it has more familiar interface. They are also more motivated due to the applicability in their professional career. The goal of this work is to analyze lowly idealized reciprocating engine cycles using a computer model. Instead of an in-house program as CyclePad, that can be perfect in a general 1

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Page 1: Spreadsheet for teaching reciprocating engine cycles

Spreadsheet for TeachingReciprocating Engine CyclesF. CRUZ-PERAGON, J.M. PALOMAR, ELOISA TORRES-JIMENEZ, R. DORADO

Department of Mechanical and Mining Engineering, University of Jaen, ETS Ingenieros Industriales, Campus las Lagunillas,23071, Jaen, Spain

Received 26 November 2009; accepted 18 February 2010

ABSTRACT: In an advanced heat engine course, we propose using a spreadsheet application to assist in thestudy of a reciprocating engine model, where the fluid composition changes and the parameters depend on thetemperature. This application performs the fluid 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.20438

Keywords: thermodynamic cycles; internal combustion engines; simulation program

INTRODUCTION

Reciprocating engines are a well known type of internalcombustion engines that appear in a wide range of applications.They produce, by combustion of a fuel within 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 fluid changes within a cylinder.A rigorous study of reciprocating engines in an advanced courseinvolves composition fluid changes along the thermodynamic cycleand temperature-dependent parameters.

To make the previous complex analysis easier for students, wepropose to use a spreadsheet application. This application performsthe fluid cycle analysis of different engines taking into account thevariation in fluid composition, temperature-dependent parametersand considering the fluid 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 ([email protected]).© 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 application with 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 general

1

Page 2: Spreadsheet for teaching reciprocating engine cycles

2 CRUZ-PERAGON ET AL.

Table 1 Engines Tested

Model 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 3,600

S, 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 definition ofmodels, like reciprocating engine cycles for an advance course,is easier. You do not need program languages knowledge toimplement complex applications that admits different input–outputdata 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 constructing many 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 the model implementation are discussed in ModelParameters 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 DATA

Three 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 ASSUMPTIONS

Engine

Related to the engine, the following parameters have to be defined:engine type (SI or CI), configuration (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 engineconfiguration: 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).

Fuel

Fuel main characteristics have to be defined in the application:type of fuel, lower calorific value LCV (kJ/kg) and fuel densityϕc (kg/L). The most common fuels, from methane (CH4) to

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CRANKSHAFT ROTATIONAL SPEED (rpm)

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a b

Figure 1 Predicted mechanical looses: (a) two-stroke SI engine; (b) four-stroke SI engine.

Page 3: Spreadsheet for teaching reciprocating engine cycles

TEACHING RECIPROCATING ENGINE CYCLES 3

gasoline and diesel, are included in the programme data base. Theirchemical composition (carbon, hydrogen, and oxygen content)is according to the specifications of Heywood [12]. From thiscomposition LCV is determined, because the calorific value ofcarbon and hydrogen has been experimentally determined withconsiderable accuracy [13].

The combustion efficiency (�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/cylinder·cycle)converted into heat energy qsup (supplied or added to the cycle)(kJ/cylinder·cycle) 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 ANALYSIS

ENGINECompression ratio , r 8 dimensionlessLength Stroke, S 58 mmPiston diameter , Φ 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 cm3

Total volume, Vt = Vd + Vc 175,1321217 cm3

Clearance volume, Vc 21,89151521 cm3

Crank radius, R 29 mmR/L Ratio 0,232 mm/mmIntake(Four-stroke) / Exhaust (Two-stroke) closure after BDC 71 º crankshaft angleTotal volumen at actual exhaust closure, Vt' 131,5007871 cm3

Actual swept or displacement volume, Vd' 109,6092718 cm3

Actual compression ratio, r' 6,006929434 cm3

Actual bore, S' 41,48598674 mm

OPERATINGCONDITIONSRotational speed of the crankshaft, n 3266 rpm

Brake Torque, M e 9,17 NmVolumetric efficiency η v (Four-Stroke) or 0,8 dimensionless

Scavenge ratio, Rs (Two-Stroke)Fuel consumption, Cc 0,63452 ml/s

Fuel density, ϕc 0,74 kg/lTrapping efficiency, ηTR (only for Two-stroke engine) 0,688338795 dimensionless

Mechanical losses 0,93820268 kWBrake power 3,136274984 kW

Ideal air mass per cycle (reference) 0,000207449 kg/cycleSupplied air mass 0,000165959 kg/cycleTrapped air mass 0,000114236 kg/cycle

Supplied fuel mass 8,62605E-06 kg/cycleTrapped fuel mass 5,93765E-06 kg/cycle

Trapped fuel-air ratio, F 0,051977023 kg fuel/kg air

FUEL/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, ηc 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 = λ x Amin) 19,2392704 kg air/kg fuelExcess air factor (λ) 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 K

Figure 2 Example of initial data introduced during a practical session.

Page 4: Spreadsheet for teaching reciprocating engine cycles

4 CRUZ-PERAGON ET AL.

Operating Conditions

There 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 (N m), fuel consumption Cc (ml/s) and in case of four-stroke engine; the volumetric efficiency �V, and for two-strokeengine; the scavenge ratio Rs.

From volumetric efficiency the actual air flow per cycle isdetermined. The following equation, function of the scavenge ratio,gives the trapping efficiency (�TR) [14]:

�TR= 1 − e−RS

RS(2)

If the engine test bench has not an air flow 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 PROCEDURE

Computational Procedure

The implemented application main goal is to compute a cyclethat verifies a desired efficiency. This section explains an iterativeprocedure to achieve that goal.

Table 2 Terminology Related to Fluid Composition Determination

Term Significance

Mi 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 ψ = 3,773)xb Fraction of burnt gas in fresh mixture (0–1)C Coefficient determined from the equilibrium constant of the

chemical reaction: CO2 + H2 = CO + H2O

STAR

FV0

Xr0

P-V CYCLECALCULATION

XRF,ηgF

XrF=Xr0?

ηg=ηgF?

SHOWP-V CYCLE

END

ηg

ENGINE INPUT DATA& OPERATING CONDITION

XrF=Xr0

MODIFY FV0

YES

YES

NO

NO

Figure 3 Computational procedure flowchart.

Page 5: Spreadsheet for teaching reciprocating engine cycles

TEACHING RECIPROCATING ENGINE CYCLES 5

Table 3 Composition of the Fluid Not Burnt

Species �i = (gas moles/O2 reactant mol)

FR ≤ 1 FR > 1

Fuel 4 (1 − xb) (1 + 2r)FR/Mf

O2 1 − xb FR 1 − xb

H2O 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 + ψ}+ xb �b

Table 4 Composition of the Burnt Fluid

Species �i (gas moles/reactant O2 mol)

FR ≤ 1 FR > 1

CO2 FR r FR r − cH2O 2 (1 − r) FR 2 (1 − r) FR + cCO 0 CH2 0 2(FR − 1) − cO2 1 − FR 0N2 � �

Total �b (1 − r) FR + 1 + ψ (2 − r) FR + ψ

Recall that the proposed model considers the working fluidas a perfect gas with temperature-dependent parameters. Theprocedure is performed according to Heywood [12] and theapproximations provided by the JANAF Tables [15]. The fluid

composition is also determined according to Heywood [12] and itis showed in Tables 2–4.

The total fluid 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.

The mass 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 fixeddiagram 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 Computation

The 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.

Page 6: Spreadsheet for teaching reciprocating engine cycles

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 combustionefficiency 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 are

determined 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 1–2: 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 index

C YC LE

R eference PointP ref, V ref, T ref, m ref, x ref, h ref, U ref, S ref, C p,ref, C v,ref, γ ref

Relationships adiabatic process

P1

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COMPRESSION 1-2

Point 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 4-5

CYCLE RESULTS

E ND

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F V, q sup

THEORETICAL WORKAND EFFICIENCY

(Wt, ηt)

ηgFExhaustV1 to V2

xrF

Point 1P 1, V 1, T 1, m 1, x1, h 1, U 1, S 1, C p,1, C v,1, γ 1

Point 4 (P 4, V 4, T 4,...)

Point 5 (P 5, V 5, T 5,...)

Wt, ηt

Wi

Figure 5 Cycles computation.

Page 7: Spreadsheet for teaching reciprocating engine cycles

TEACHING RECIPROCATING ENGINE CYCLES 7

COMPRESSIONEXPANSSION

γT0=γj

Adiabatic Equation

Pi+1

Ideal gas law

γCF=γC0?

END

Point jPi, Vi, Ti, mi, xi

hj, uj, sj, cp,j, cv,j, γj

Vj+1

γTF=(hj+1-hj)/(uj+1-uj)

xj+1=xj

Point j+1Pi+1, Vi+1, Ti+1, mi+1, xi+1

hj+1, uj+1, sj+1, cp,j+1, cv,j+1, γj+1

γT0=γTFNO

YES

Ti+1

Thermodynamic properties

Figure 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 first onechosen, then the iteration process continues and point 2 isrecalculated, but now using the last adiabatic index obtained.The calculation process finishes 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 for

a CI engine is a blend of air and residual gases (see Tables 2and 3).

Process 2–3: 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.

Page 8: Spreadsheet for teaching reciprocating engine cycles

8 CRUZ-PERAGON ET AL.

HEAT ADDITIONCONSTANT VOLUME

cv,0=cv,j

qsup,v=mjcv,0∆T

Ti+1

Ideal gas law

cv,F=cv,0?

END

Point jPi, Vi, Ti, mi, xi

hj, uj, sj, cp,j, cv,j, γj

qsup,v

cv,F=(uj+1-uj)/(Tj+1-Tj)

xj+1

Vj+1=Vj

Point j+1Pi+1, Vi+1, Ti+1, mi+1, xi+1

hj+1, uj+1, sj+1, cp,j+1, cv,j+1, γj+1

cv,0=cv,FNO

YES

Pi+1

Thermodynamic properties

Figure 7 Calculation procedure to evaluate the heat addition at constantvolume.

Since heat released in this process is equal to a mean value ofthe specific heat capacity at constant volume cv between two pointsmultiplied by the increase in temperature, the iteration methodworks in the same way as in process 1–2, 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 3–4: Heat Addition at Constant Pressure. Point 4represents the thermodynamics properties of the fluid 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 specific 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 4–5: Adiabatic Expansion. Finally, we analyze theadiabatic expansion to the point 5 in the same way as in

HEAT ADDITIONCONSTANT PRESSURE

cp,0=cp,j

qsup,p=mjcp,0∆T

Ti+1

Ideal gas law

Thermodynamic Properties

cp,F=cp,0?

END

Point jPi, Vi, Ti, mi, xi

hj, uj, sj, cp,j, cv,j, γj

qsup,p

Vj+1

cp,F=(hj+1-hj)/(Tj+1-Tj)

xj+1

Crankshaft Angle

Pj+1=Pj

Point j+1Pi+1, Vi+1, Ti+1, mi+1, xi+1

hj+1, uj+1, sj+1, cp,j+1, cv,j+1, γj+1

cp,0=cp,FNO

YES

Figure 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 3–5, 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 first 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 retained mass 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 efficiency to the theoretical thermalefficiency [14].

Page 9: Spreadsheet for teaching reciprocating engine cycles

TEACHING RECIPROCATING ENGINE CYCLES 9

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CYCLE intake/exhaust closure 1 2 2 a 4 2 a 3 3 3 a 4 4 5Degree (º) 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) Δu (kJ/kg) 21,89151521 Δh(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 1430,882094γ (T) 1,365849499 1,365849499 1,321133461 0,78 1,261740228 1,257152334 1,276361783

COEFICIENT γ 1-2 cv 2-3 cp 3-4 γ 4-5ITERATIONS 1,385523738 1,385523738 1,01837837 1,01837837 1,387551105 1,387551105 1,264875616 1,264875616

VALUES MEAN VALUE CHECK MEAN VALUE CHECK MEAN VALUE CHECK MEAN VALUE CHECK

DEGREE 4 CALCULATION ACTUAL ERRORdegrees cm3 cm3 cm3

374,7 24,97228962 24,9600172 0,012272421

We Wm Wi W comp. W exp. Wnet Qfuel Qsup.kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle kJ/cycle

0,057616809 0,017235812 0,074852621 -0,033977676 0,127899177 0,0939215 0,382996738 0,258358883ηc ηt ηe ηm ηi ηg

0,98 0,245227938 0,150436814 0,769736698 0,195439317 0,796970029

Figure 9 Two-stroke SI engine. Air–fuel cycle: (a) Results. (b) P–V cycle.

RESULTS

The 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 sheet with the data of the two-stroke SI engine tested. Figure 9portraits the cycle, graphic, thermodynamic properties, energy, andefficiency 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.

This methodology also performs lower complexity cycles. Anideal cycle can be simulated using air as working fluid, consideringit behaves as perfect gas and its specific heat capacities areconstant and independent of temperature. A medium complexitymethod can consider the variation of specific 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 final results variationwhen the same parameter is modified, for example, when totalfraction delivery, heat released at constant volume or mass fractionof combustion residuals are modified.

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.

CONCLUSION

The study of engine thermodynamic cycles has an increasingdifficulty, as they are relaxing simplifying assumptions. Thecalculation models that consider the working fluid 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 study

Page 10: Spreadsheet for teaching reciprocating engine cycles

10 CRUZ-PERAGON ET AL.

0

5

10

15

20

25

30

35

10 60 110 160 210 260 310 360

PRES

SUR

E (b

ar)

VOLUME (cm3)

P-V DIAGRAM. FUEL-AIR CYCLE

0

10

20

30

40

50

60

70

80

90

100

10 60 110 160 210

PRES

SUR

E (b

ar)

VOLUME (cm3)

P-V DIAGRAM. FUEL-AIR CYCLE

1

52

3 4

1

5

2

3

4

a b

Figure 10 Four-stroke P–V cycles (a) SI engine (b) CI engine.

Table 5 Spreadsheet Parameters for 2 Current Engines

Data Engine model

Input data 1.4 MPI (1,368 cm3) Lister Petter LPW4for Alfa Romeo vehicle, model MiTo for stationary applications

Fuel 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 (N m), speed (rpm),brake-specific fuel consumption(g/kWh)

77, 113.12, 6,500, 260 29.5, 93.8, 3,000, 227.7

Data maximum Torque: power(kW), torque (N m), speed (rpm),brake-specific fuel consumption(g/kWh)

54.45, 130, 4,000, 220 21.15, 101, 2,000, 213

Rod length (mm) 1,54.7 (real data) 126.5 (estimated)Volumetric efficiency �V (%) 90%

Spreadsheet results Max. torque Max. power Max. torque Max. power

Brake mean effective pressure (MPa);engine efficiency �e (%)

1.2; 28.4 1.04; 26.1 0.685; 40.1 0.635; 37.55

Indicated mean effective pressure(MPa); indicated efficiency �i (%)

1.39; 33 1.3; 32.7 0.795; 46.7 0.764; 45.26

Friction mean effective pressure(MPa); mechanical efficiency �m (%)

0.19; 85 0.26; 80 0.11; 86 0.13; 83

Theoretical mean effective pressure(MPa); thermodynamic cycleefficiency �t (%)

1.54; 36.5 1.546; 38.8 0.92; 54.5 0.9; 53.5

Diagram factor �g (%) 90.5 84 86 84.7

is to facilitate the study and understanding of complex enginethermodynamic cycles using a spreadsheet.

On one hand, the use of this tool allows knowing the equationsgoverning the studied process, and how each parameter influencesthe process in a quick and interactive way. On the other hand, thisapproximation is carried out using computational tools which will

greatly facilitate the calculation process and can be a basis for morecomplex researches or engineering practical works.

Spreadsheets and mathematical programming languages arepresented as a powerful tool for students and instructors, as theydecisively contribute in the teaching–learning process and theachievement of its objectives.

Page 11: Spreadsheet for teaching reciprocating engine cycles

TEACHING RECIPROCATING ENGINE CYCLES 11

ACKNOWLEDGMENTS

This 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-fluidsciences. 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), 297–347.

[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, San Antonio, Texas, 2001.

[7] C. Wu and D. C. Sherrill, Intelligent computer aided design, analysis,optimization, and improvement of thermodynamic systems. ComputAppl Eng Educ 9 (2001), 220–227.

[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), 893–901.

[11] D. E. Richardson, Review of power cylinder friction for dieselengines. J Eng Gas Turbines Power-Trans ASME 122 (2000), 506–519.

[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 de Madrid, 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 metodologıas de optimizacioninteligentes para la determinacion de la presion en camara decombustion en motores alternativos de combustion interna pormetidos no intrusivos. PhD Dissertation. University of Sevilla, Spain,2005.

BIOGRAPHIES

Fernando 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 fieldwork 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-la Mancha. His research and professionalinterests include differential curves and surfaces,computer aided geometric design algorithm andits applications.