Spreadsheet for teaching reciprocating engine cycles

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<ul><li><p>Spreadsheet for TeachingReciprocating Engine CyclesF. CRUZ-PERAGON, J.M. PALOMAR, ELOISA TORRES-JIMENEZ, R. DORADO</p><p>Department of Mechanical and Mining Engineering, University of Jaen, ETS Ingenieros Industriales, Campus las Lagunillas,23071, Jaen, Spain</p><p>Received 26 November 2009; accepted 18 February 2010</p><p>ABSTRACT: 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.20438</p><p>Keywords: thermodynamic cycles; internal combustion engines; simulation program</p><p>INTRODUCTION</p><p>Reciprocating 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.</p><p>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.</p><p>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.</p><p>It is known that computers are very useful tools both inpractical applications and in teaching engineering. Regardingeducational applications, some advantages of computers are:</p><p> Make tedious operations, therefore students and instructors onlydeal with concepts and complex models.</p><p>Correspondence to R. Dorado (rdorado@ujaen.es). 2010 Wiley Periodicals, Inc.</p><p> Motivate students. Graphics, interactive way to manage theinformation, and the possibility to work with models of complexsystems, are useful ingredients to encourage students.</p><p> 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.</p><p> Reduce the efforts to create, supervise, and evaluate the studentslearning.</p><p>On the other hand, the use of software in education has somedisadvantages:</p><p> Choose adequate software is a needed and time-consuming step.The election depends on the methodology aims.</p><p> Develop the application is also time-consuming and requiresknowledge about programming languages. Again the time spentdepends on the software used.</p><p> Students need training with the interface.</p><p>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.</p><p>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.</p><p>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</p><p>1</p></li><li><p>2 CRUZ-PERAGON ET AL.</p><p>Table 1 Engines Tested</p><p>Model Engine type S (mm) (mm) Max. torque (Nm) r Max. power (kW) Max. speed (rpm)</p><p>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</p><p>S, length stroke; , Piston diameter; r, compression ratio; SI, Spark ignition; CI, compression ignition.</p><p>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.</p><p>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.</p><p>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.</p><p>EXPERIMENTAL DATA</p><p>Three different one-cylinder engines were analyzed to performthis study. Those engines were tested in a stationary test bench.</p><p>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.</p><p>MODEL PARAMETERS AND ASSUMPTIONS</p><p>Engine</p><p>Related 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.</p><p>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).</p><p>An analytical model to predict the energy loosed bymechanical friction [11] was included (Fig. 1).</p><p>Fuel</p><p>Fuel 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) to</p><p>0,4</p><p>0,5</p><p>0,6</p><p>0,7</p><p>0,8</p><p>0,9</p><p>1,0</p><p>1,1</p><p>1,2</p><p>0</p><p>0,1</p><p>0,2</p><p>0,3</p><p>0,4</p><p>0,5</p><p>0,6</p><p>0,7</p><p>0,8</p><p>0,9</p><p>1</p><p>0 1000 2000 3000 4000</p><p>MEC</p><p>HA</p><p>NIC</p><p>AL </p><p>LOO</p><p>SES </p><p>MEA</p><p>N P</p><p>RES</p><p>SUR</p><p>E (b</p><p>ar)</p><p>MEC</p><p>HA</p><p>NIC</p><p>AL </p><p>LOO</p><p>SES </p><p>(kW</p><p>)</p><p>CRANKSHAFT ROTATIONAL SPEED (rpm)</p><p>Power (kW)</p><p>Mean pressure (bar)</p><p>Polynomial (Power (kW))</p><p>Polynomial (Mean pressure (bar))</p><p>1,1</p><p>1,2</p><p>1,3</p><p>1,4</p><p>1,5</p><p>1,6</p><p>1,7</p><p>1,8</p><p>1,9</p><p>0</p><p>0,1</p><p>0,2</p><p>0,3</p><p>0,4</p><p>0,5</p><p>0,6</p><p>0,7</p><p>0,8</p><p>0,9</p><p>1</p><p>0 1000 2000 3000</p><p>MEC</p><p>HA</p><p>NIC</p><p>AL </p><p>LOO</p><p>SES </p><p>MEA</p><p>N P</p><p>RES</p><p>SUR</p><p>E (b</p><p>ar)</p><p>MEC</p><p>HA</p><p>NIC</p><p>AL </p><p>LOO</p><p>SES </p><p> (kW</p><p>)</p><p>CRANKSHAFT ROTATIONAL SPEED (rpm)</p><p>Power (kW)</p><p>Mean pressure (bar)</p><p>Polynomial (Power (kW))</p><p>Polynomial (Mean pressure (bar))</p><p>a b</p><p>Figure 1 Predicted mechanical looses: (a) two-stroke SI engine; (b) four-stroke SI engine.</p></li><li><p>TEACHING RECIPROCATING ENGINE CYCLES 3</p><p>gasoline 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].</p><p>The combustion efciency (C) is computed by a functionof the equivalence ratio FR, inverse of the excess air factor </p><p>[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:</p><p>qsup = qfuel C (1)</p><p>In two-stroke engines the Equation (1) includes the shorted-circuit fuel in the gas exchange process.</p><p>ENGINE CYCLE ANALYSIS</p><p>ENGINECompression 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 cm3</p><p>Total volume, Vt = Vd + Vc 175,1321217 cm3</p><p>Clearance volume, Vc 21,89151521 cm3</p><p>Crank 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 cm3</p><p>Actual swept or displacement volume, Vd' 109,6092718 cm3</p><p>Actual compression ratio, r' 6,006929434 cm3</p><p>Actual bore, S' 41,48598674 mm</p><p>OPERATINGCONDITIONSRotational speed of the crankshaft, n 3266 rpm</p><p>Brake Torque, M e 9,17 NmVolumetric efficiency v (Four-Stroke) or 0,8 dimensionless</p><p>Scavenge ratio, Rs (Two-Stroke)Fuel consumption, Cc 0,63452 ml/s</p><p>Fuel density, c 0,74 kg/lTrapping efficiency, TR (only for Two-stroke engine) 0,688338795 dimensionless</p><p>Mechanical losses 0,93820268 kWBrake power 3,136274984 kW</p><p>Ideal air mass per cycle (reference) 0,000207449 kg/cycleSupplied air mass 0,000165959 kg/cycleTrapped air mass 0,000114236 kg/cycle</p><p>Supplied fuel mass 8,62605E-06 kg/cycleTrapped fuel mass 5,93765E-06 kg/cycle</p><p>Trapped fuel-air ratio, F 0,051977023 kg fuel/kg air</p><p>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, 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 K</p><p>Figure 2 Example of initial data introduced during a practical session.</p></li><li><p>4 CRUZ-PERAGON ET AL.</p><p>Operating Conditions</p><p>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 (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.</p><p>From volumetric efciency the actual air ow per cycle isdetermined.The following equation, function of the scavenge ratio,gives the trapping efciency (TR) [14]:</p><p>TR= 1 eRS</p><p>RS(2)</p><p>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.</p><p>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</p><p>(Wm), brake mean effective pressure (bmep), and indicated meaneffective pressure (bmip).</p><p>CALCULATION PROCEDURE</p><p>Computational Procedure</p><p>The implemented application main goal is to compute a cyclethat veries a desired efciency. This section explains an iterativeprocedure to achieve that goal.</p><p>Table 2 Terminology Related to Fluid Composition Determination</p><p>Term Signicance</p><p>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 = 3,773)xb Fraction of burnt gas in fresh mixture (01)C Coefcient determined from the equilibrium constant of the</p><p>chemical reaction: CO2 +H2 =CO+H2O</p><p>STAR</p><p>FV0</p><p>Xr0</p><p>P-V CYCLECALCULATION</p><p>XRF,gF</p><p>XrF=Xr0?</p><p>g=gF?</p><p>SHOWP-V CYCLE</p><p>END</p><p>g</p><p>ENGINE INPUT DATA&amp; OPERATING CONDITION</p><p>XrF=Xr0</p><p>MODIFY FV0</p><p>YES</p><p>YES</p><p>NO</p><p>NO</p><p>Figure 3 Computational procedure owchart.</p></li><li><p>TEACHING RECIPROCATING ENGINE CYCLES 5</p><p>Table 3 Composition of the Fluid Not Burnt</p><p>Species i = (gas moles/O2 reactant mol)FR 1 FR &gt; 1</p><p>Fuel 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 b</p><p>Table 4 Composition of the Burnt Fluid</p><p>Species i (gas moles/reactant O2 mol)</p><p>FR 1 FR &gt; 1</p><p>CO2 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 +</p><p>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 uid</p><p>composition is also determined according to Heywood [12] and itis showed in Tables 24.</p><p>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.</p><p>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.</p><p>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.</p><p>Cycle Computation</p><p>The cycle analysis starts by setting a reference value (pressure,temperature, and mixture...</p></li></ul>

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