《船舶柴油机》课程教学资源（文献资料）The theory of compression ignition engines

The theory of1compressionignition enginesContents1.1 5Introduction51.1.1Historical51.1.2Classifications51.2Two-stroke and four-stroke engines61.2.1Two-strokeengines71.2.2Four-strokeengines1.2.3Evaluation of power output of two-stroke7andfour-strokeengines81.2.4Other operatingparameters1.3Airstandardcycles:constantpressure-constant9volume-dualcombustion1.3.1Theoretical expressions for air standard9cycles1.3.2Further comments on air standard cycles13141.4Basic thermodynamics of real gases141.4.1Gasproperties151.4.2Combustion171.4.3Dissociationandreactionkinetics171.5Real diesel engine cyclic processes171.5.1Closed period191.5.2Openperiod211.6Detailed cycle analysis methods211.6.1Closed period221.6.2Open period (gas exchangeprocess)251.6.3Completion ofcalculation sequence25ReferencesThispage has been reformatted by Knovel toprovide easier navigation

This page has been reformatted by Knovel to provide easier navigation. 1 The theory of compression ignition engines Contents 1.1 Introduction 5 1.1.1 Historical 5 1.1.2 Classifications 5 1.2 Two-stroke and four-stroke engines 5 1.2.1 Two-stroke engines 6 1.2.2 Four-stroke engines 7 1.2.3 Evaluation of power output of two-stroke and four-stroke engines 7 1.2.4 Other operating parameters 8 1.3 Air standard cycles: constant pressure—constant volume—dual combustion 9 1.3.1 Theoretical expressions for air standard cycles 9 1.3.2 Further comments on air standard cycles 13 1.4 Basic thermodynamics of real gases 14 1.4.1 Gas properties 14 1.4.2 Combustion 15 1.4.3 Dissociation and reaction kinetics 17 1.5 Real diesel engine cyclic processes 17 1.5.1 Closed period 17 1.5.2 Open period 19 1.6 Detailed cycle analysis methods 21 1.6.1 Closed period 21 1.6.2 Open period (gas exchange process) 22 1.6.3 Completion of calculation sequence 25 References 25

Thetheoryof compression ignition engines5air-fuel ratios well in excess of stoichiometric, is ensured. The1.1Introductionmixing process is crucial to the operation of the Diesel engineand as such has received a great deal of attention which is1.1.1Historicalreflected in a wide variety of combustion systems which mayconvenientlybegrouped intwobroad categories,viz.Although the history of the diesel engine extends back into theclosingyears of the19thcenturywhenDrRudolfDieselbegan(a)DirectInjection (D)Systems asusedinDIengines,inwhichhispioneeringworkonairblastinjectedstationaryengines,andthe fuel is injected directly into a combustion chamber formedinspiteof thedominant position itnowholds in manyapplications,in the clylinderitself,i.e.between a suitably shapednon-stationarye.g.marinepropulsion and landtransport,both road and rail,itpiston crown and a fixed cylinder head in which is mounted theistodaythesubjectof intensivedevelopmentand capableoffuel injector with its single or multiple sprayorifices or nozzles.improvements.These willguaranteethe diesel engineanassured(See Figures 1.I and 1.2.)place as the most efficient liquid fuel burning prime mover yetderivedBefore1914,building ontheworkof DrRudolf Diesel inGermanyandHubertAkroydStuart intheUK,the dieselengineInjectorwasusedprimarilyinstationaryandshippropulsionapplicationsin theformofrelativelylow speed four-stroke normally aspiratedenginesThe1914-18wargave considerableimpetus to thedevelopmentofthehigh speeddieselenginewithits much higher specificoutput,with a viewto extending its application to vehicles.Although the first generation of road transport engines wereundoubtedly of the spark ignition variety,the somewhat laterFigure1.1Quiescentcombustionsystem.Application-Four-strokedevelopment of diesel engines operating on the self or com-andtwo-strokeenginesmostlyabove150mmbore(Bensonandpression ignition principle followed soon after so thatby theWhitehouse)mid 193Os the high speed normally aspirated dieselengine wasfirmlyestablishedasthemostefficientprimemoverfortrucksand buses. At the same time with the increasing use ofturbocharging it began to displace the highly inefficient steamengine in railway locomotives while the impending 1939-45war gave a major impetus to the development of the highlysupercharged diesel engine as a newaero engine,particularlyinGermany.Since the 1939-45 war every major industrial country hasdeveloped its own range of diesel engines.Its greatestmarketpenetration has undoubtedly occurred in thefield of heavyroadtransport where,at any rate in Europe,it is now dominant.It isparticularly in this field where development, in the direction ofturbocharging in its various forms,has been rapid during thelast twenty years,and where much of the current research anddevelopmenteffortis concentratedHowever.a continuousprocess of uprating and refinement has been applied in all itsFigure 1.2High swirl system.Application to virtuallyall truck andfields of application,from the very largest low speed marinebus sized engines, but increasingly also to the high speed passengertwo-stroke engines,throughmedium speed stationary enginescarenginetosmallsinglecylinderenginesforoperationinremoteareaswith minimum attendance.There is littledoubt that it will continueto occupya leadingpositionin thespectrum of reciprocating(b)IndirectInjection(IDDSystemsasused inIDIenginesinprime movers, so long as fossil fuels continue to be availablewhichfuel is injected into aprechamber which communicatesand,provided it can be made less sensitiveto fuel qualitywellwiththe cylinder through a narrow passage.The rapid transferinto the era of synthetic or coal derived fuels.of air from the main cylinder into the prechamber towards topdead centre (TDC)of the firing stroke promotes a veryhighdegreeofairmotionintheprechamberwhichisparticularly1.1.2Classificationsconducive to rapid fuel-air mixing.(See Figure 1.3.The major distinguishing characteristic of the diesel engine is,Combustion systems aredescribed inmoredetail inChapter4 and generally in Chapters 22 to 29 describing engine types.of course,thecompression-ignition principle,i.e.theadoptionA furthermajor subdivision of diesel engines is into two-strokeof a special method of fuel preparation.Instead of relying onand four-stroke engines, according to themanner in which thethepassage of a spark atapredetermined pointtowards the endof thecompression process toigniteapre-mixedand whollygas exchange process is performed.gaseous fuel-airmixture in approximately stoichiometricproportions as inthe appropriatelynamedcategory of spark-1.2Two-strokeandfour-stroke enginesignition (SI)engines,the compression ignition (CI)engineoperateswithaheterogeneouschargeofpreviouslycompressedair and afinelydivided spray of liquid fuel.The latteris injectedAnevenmorefundamental classificationofdieselenginesthanthataccordingto combustion systemis intotwo-strokeor fourintotheengine cylindertowardstheendof compressionwhen,after a suitably intensive mixing process with the air already instrokeengines,althoughthis latterclassification appliesequallythe cylinder,the self ignitionproperties of the fuel causetosparkignitionenginesandcharacterizesthegasexchangcombustiontobe initiatedfrom small nuclei.These spread rapidlyprocesscommontoallairbreathingreciprocatingengines.Thefunctionofthegas exchageprocess,inbothcases,is to effectsothatcompletecombustionofallinjectedfuel,usuallywith

1.1 Introduction 1.1.1 Historical Although the history of the diesel engine extends back into the closing years of the 19th century when Dr Rudolf Diesel began his pioneering work on air blast injected stationary engines, and in spite of the dominant position it now holds in many applications, e.g. marine propulsion and land transport, both road and rail, it is today the subject of intensive development and capable of improvements. These will guarantee the diesel engine an assured place as the most efficient liquid fuel burning prime mover yet derived. Before 1914, building on the work of Dr Rudolf Diesel in Germany and Hubert Akroyd Stuart in the UK, the diesel engine was used primarily in stationary and ship propulsion applications in the form of relatively low speed four-stroke normally aspirated engines. The 1914-18 war gave considerable impetus to the develop￾ment of the high speed diesel engine with its much higher specific output, with a view to extending its application to vehicles. Although the first generation of road transport engines were undoubtedly of the spark ignition variety, the somewhat later development of diesel engines operating on the self or com￾pression ignition principle followed soon after so that by the mid 1930s the high speed normally aspirated diesel engine was firmly established as the most efficient prime mover for trucks and buses. At the same time with the increasing use of turbocharging it began to displace the highly inefficient steam engine in railway locomotives while the impending 1939-45 war gave a major impetus to the development of the highly supercharged diesel engine as a new aero engine, particularly in Germany. Since the 1939-45 war every major industrial country has developed its own range of diesel engines. Its greatest market penetration has undoubtedly occurred in the field of heavy road transport where, at any rate in Europe, it is now dominant. It is particularly in this field where development, in the direction of turbocharging in its various forms, has been rapid during the last twenty years, and where much of the current research and development effort is concentrated. However, a continuous process of uprating and refinement has been applied in all its fields of application, from the very largest low speed marine two-stroke engines, through medium speed stationary engines to small single cylinder engines for operation in remote areas with minimum attendance. There is little doubt that it will continue to occupy a leading position in the spectrum of reciprocating prime movers, so long as fossil fuels continue to be available and, provided it can be made less sensitive to fuel quality, well into the era of synthetic or coal derived fuels. 1.1.2 Classifications The major distinguishing characteristic of the diesel engine is, of course, the compression-ignition principle, i.e. the adoption of a special method of fuel preparation. Instead of relying on the passage of a spark at a predetermined point towards the end of the compression process to ignite a pre-mixed and wholly gaseous fuel-air mixture in approximately stoichiometric proportions as in the appropriately named category of spark￾ignition (SI) engines, the compression ignition (CI) engine operates with a heterogeneous charge of previously compressed air and a finely divided spray of liquid fuel. The latter is injected into the engine cylinder towards the end of compression when, after a suitably intensive mixing process with the air already in the cylinder, the self ignition properties of the fuel cause combustion to be initiated from small nuclei. These spread rapidly so that complete combustion of all injected fuel, usually with air-fuel ratios well in excess of stoichiometric, is ensured. The mixing process is crucial to the operation of the Diesel engine and as such has received a great deal of attention which is reflected in a wide variety of combustion systems which may conveniently be grouped in two broad categories, viz. (a) Direct Injection (DI) Systems as used in DI engines, in which the fuel is injected directly into a combustion chamber formed in the clylinder itself, i.e. between a suitably shaped non-stationary piston crown and a fixed cylinder head in which is mounted the fuel injector with its single or multiple spray orifices or nozzles. (See Figures 1.1 and 7.2.) Figure 1.1 Quiescent combustion system. Application-Four-stroke and two-stroke engines mostly above 150 mm bore (Benson and Whitehouse) Figure 1.2 High swirl system. Application to virtually all truck and bus sized engines, but increasingly also to the high speed passenger car engine (b) Indirect Injection (IDI) Systems as used in IDI engines in which fuel is injected into a prechamber which communicates with the cylinder through a narrow passage. The rapid transfer of air from the main cylinder into the prechamber towards top dead centre (TDC) of the firing stroke promotes a very high degree of air motion in the prechamber which is particularly conducive to rapid fuel-air mixing. (See Figure 1.3.) Combustion systems are described in more detail in Chapter 4 and generally in Chapters 22 to 29 describing engine types. A further major subdivision of diesel engines is into two-stroke and four-stroke engines, according to the manner in which the gas exchange process is performed. 1.2 Two-stroke and four-stroke engines An even more fundamental classification of diesel engines than that according to combustion system is into two-stroke or four￾stroke engines, although this latter classification applies equally to spark ignition engines and characterizes the gas exchange process common to all air breathing reciprocating engines. The function of the gas exchage process, in both cases, is to effect Injector

6Diesel EngineReferenceBook(a)(D(c)Fiqure1.4Two-strokeengines:(a)Loopscavenqedenqine:(b)Exhaust valve-in-head engine; (c) Opposed piston engine (BensonandWhitehouse)the exhaust ports. As a result the degree of charge purity (i.e. theproportion of trapped air)attheend ofthescavengingprocesstendstobe low.Asecondadversefeatureresultingfromsymmetrical timingFigure1.3Prechambersystem-compressionswirl.Applicationis loss of trapped chargebetween inletandexhaust port closuretraditionallytohigh speedpassengercarenginesbutnow increasinglyand susceptibilityto furtherpollution of the trapped chargereplaced by direct injection enginewith exhaust gas returned to the cylinderby exhaust manifoldpressure wave effects.The great advantage of the system is itsexpulsionoftheproducts of combustion fromtheenginecylinderoutstanding simplicity.and their replacement by a fresh air charge in readiness for thenext working cycle.1.2.1.2Uniflowscavengesinglepistonengines(Figure1.4b)1.2.1Two-strokeengines(Figures1.4a,b,c)In engines of this type admission of air to the cylinder is usuallyeffected bypiston controlledports while theproducts ofIn two-stroke engines combustion occurs in the region of topcombustion are exhausted through a camshaft operatedexhaustdead centre(TDC)of everyrevolution.Consequentlygasvalve.Such systemsare preferable from the standpoint ofexchange also has to be effected once per revolution in theScavenging in thatthe'uniflow'motion ofthe airfromtheinletregionofbottomdeadcentre(BCD)andwithminimumlossofportsupwardsthroughthecylindertendstoleadtophysicalexpansion work of thecylindergasesfollowing combustion.displacement of,rather than mixing with,the products ofThis implies that escape of gas from the cylinder to exhaustcombustion thus giving improved charge purityat the end of theand charging with fresh airfrom the inlet manifold must occurscavengingprocess.Atthesametimeitisnowpossibletoadopunderthemostfavourablepossibleflowconditionsovertheasvmmetricaltimingoftheexhaustandinletprocessesrelativeshortest possible period. In practice the gas exhange orto bottom dead centre (BDC) so that, with exhaust closureSCAVENGINGprocess intwo-strokeengines occupiesbetweenpreceding inletclosure thedanger of escape of fresh charge into100°and 150°ofcrank angle(CA)disposed approximatelytheexhaustmanifoldpresentintheloopscavengesvstemissymmetricallyaboutBDC.completelyeliminated.ThissystemhasbeenadoptedinanumberTwo-stroke engines may be subdivided according to theof stationary and marine two-stroke engines.particular scavenging systemused into thefollowing sub-groups1.2.1.3Uniflow scavengeopposed piston engines1.2.1.1 Loop scavenged engines (Figure 1.4a)(Figure 1.4c)This is the simplest type of two-stroke engine in which bothInenginesofthistypeadmissionofairiseffectedby'airpistoninletand exhaustare controlled byports in conjunction withacontrolledinletports,andrejectionofproductsofcombustionsinglepiston.Inevitablythis arrangementresults in symmetricalby'exhaustpistoncontrolledexhaustports.Themotionofthetiming which from the standpoint of scavenging is not ideal.Intwo sets of pistons is controlled by either two crankshaftsthe first instance the'loop'air motion in the cylinder is apt toconnected through gearing. or by a signle crankshaft with theproduce a high degree of mixing of the incoming air with the'top'bank ofpistonstransmitting their motion tothe singleproductsofcombustion,insteadofphysicaldisplacementthrough

Figure 1.3 Prechamber system-compression swirl. Application￾traditionally to high speed passenger car engines but now increasingly replaced by direct injection engine expulsion of the products of combustion from the engine cylinder and their replacement by a fresh air charge in readiness for the next working cycle. 1.2.1 Two-stroke engines (Figures IAa, b, c) In two-stroke engines combustion occurs in the region of top dead centre (TDC) of every revolution. Consequently gas exchange also has to be effected once per revolution in the region of bottom dead centre (BCD) and with minimum loss of expansion work of the cylinder gases following combustion. This implies that escape of gas from the cylinder to exhaust and charging with fresh air from the inlet manifold must occur under the most favourable possible flow conditions over the shortest possible period. In practice the gas exhange or SC AVENGING process in two-stroke engines occupies between 100° and 150° of crank angle (CA) disposed approximately symmetrically about BDC. Two-stroke engines may be subdivided according to the particular scavenging system used into the following sub-groups. 1.2.Ll Loop scavenged engines (Figure L4a) This is the simplest type of two-stroke engine in which both inlet and exhaust are controlled by ports in conjunction with a single piston. Inevitably this arrangement results in symmetrical timing which from the standpoint of scavenging is not ideal. In the first instance the 'loop' air motion in the cylinder is apt to produce a high degree of mixing of the incoming air with the products of combustion, instead of physical displacement through Figure 1.4 Two-stroke engines: (a) Loop scavenged engine; (b) Exhaust valve-in-head engine; (c) Opposed piston engine (Benson and Whitehouse) the exhaust ports. As a result the degree of charge purity (i.e. the proportion of trapped air) at the end of the scavenging process tends to be low. A second adverse feature resulting from symmetrical timing is loss of trapped charge between inlet and exhaust port closure and susceptibility to further pollution of the trapped charge with exhaust gas returned to the cylinder by exhaust manifold pressure wave effects. The great advantage of the system is its outstanding simplicity. 7.2.7.2 Uniflow scavenge single piston engines (Figure IAb) In engines of this type admission of air to the cylinder is usually effected by piston controlled ports while the products of combustion are exhausted through a camshaft operated exhaust valve. Such systems are preferable from the standpoint of scavenging in that the 'uniflow' motion of the air from the inlet ports upwards through the cylinder tends to lead to physical displacement of, rather than mixing with, the products of combustion thus giving improved charge purity at the end of the scavenging process. At the same time it is now possible to adopt asymmetrical timing of the exhaust and inlet processes relative to bottom dead centre (BDC) so that, with exhaust closure preceding inlet closure the danger of escape of fresh charge into the exhaust manifold present in the loop scavenge system is completely eliminated. This system has been adopted in a number of stationary and marine two-stroke engines. 7.2.7.5 Uniflow scavenge opposed piston engines (Figure IAc) In engines of this type admission of air is effected by 'air piston' controlled inlet ports, and rejection of products of combustion by 'exhaust piston' controlled exhaust ports. The motion of the two sets of pistons is controlled by either two crankshafts connected through gearing, or by a signle crankshaft with the 'top' bank of pistons transmitting their motion to the single

Thetheory of compression ignition engines7crankshaft through a crosshead-siderod mechanism.By suitable(a) the longer period available for thegas exhange processoffsetting of thecranks controllingtheairand exhaustpistonsand the separation of the exhaust and inlet periods-asymmetrical timing can be achieved.apartfromthecomparativelyshortoverlap-resultingIt is evident that this system displays the same favourablein a purer trapped charge.characteristics as the exhaust valve in head system, but at the(b) the lower thermal loading associated with engines inexpenseofevengreatermechanical complications.Its outstandingwhich pistons, cylinder heads and liners are exposed toadvantage is the high specific output per cylinder associatedthe most severe pressures and temperatures associatedwithtwopistons.However,thesystemisnowretainedonlyinwithcombustiononlyeveryotherrevolution.large low speed marine,and smaller medium speed stationary(c)Easier lubrication conditionsforpistons,ringsand linersandmarineengines,Inhighspeedformitisstillemployedfordue to the absence of ports,and the idie stroke renewingnaval purposes suchas in somefastpatrol vesselsandmineliner lubrication and giving inertia lift off to rings andsearchers, although its use in road vehicles and locomotives issmall and large end bearings.discontinued.These factors make it possible for the four-stroke engine toachieveoutputlevelsof theorderof 75%of equivalenttwo1.2.2Four-stroke engines (Figure 1.5)strokeengines.Inrecentyearsattentionhasfocusedparticularlyon three-cylinder high speed passenger car two-stroke enginesThe vast majority of current diesel engines operate on the four-asapossiblereplacementforconventional four-cylinder,four-stroke principle in which combustion occurs only every otherstroke engines with considerable potential savings in space andrevolution,again in theregion of top dead centre(TDC),andweight.withtheintermediaterevolutionand itsassociatedpistonstrokesgiven over to thegas exchangeprocess, In practice the exhaust1.2.3Evaluation of power output of two-stroke andvalve(s)openwell beforebottomdeadcentre(BDC)followingthe expansion stroke and only close well after the following topfour-strokeengines (Figures 1.6a and b)dead centre (TDC)position is reached.The inlet valve(s) openIn order to determine the power developed within the enginebeforethis latterTDC,giving aperiodof overlapbetween inletcylinderasaresultofgasforcesactingonthepistonasopposedvalve opening (IVO) and exhaust valve closing (EVC) duringto shaft power from the output shaft, it is necessary to have awhich the comparatively small clearance volume is scavengedrecordof thevariationofgas pressure (p)withstrokeorcylinderofmostoftheremainingproductsofcombustion.Followingvolume (V)referredtoasanIndicatorDiagram(orp-VDiagram)completion of the inlet stroke, the inlet valve(s) close well afterThis used to be obtained by mechanical means, but such crudethefollowingbottomdeadcentre(BDC).afterwhichthe‘closedinstrumentationhasnowbeencompletelyreplacedbyelectronicportionofthe cycle,i.e.thesequencecompression, combustion,instrumentsknown as pressure transducers.It is also generallyexpansionleadstothenextcycle,commencingagain withexhaustmore convenient to combine the pressure measurement with avalveopening (EVO)crank angle (CA)measurement,using aposition transducer inThe main advantages of the four-stroke cycle over its two-conjunction with a suitable crank angle marker disc,and subse-stroke counterpart are:quently convert crank angle to stroke values by a simple geometricInletExhausttransformation.valvevalveThe sequenceofevents for the twocycles maybe summarizedas follows:(a)Two-stroke cycle (asymmetrical timing)1-2compression2-3Closed Periodheat release associatedwithcombustionPiston34360°CAexpansion4-5blowdown5-6Open Periodscavenging6-1 supercharge(b)Four-stroke cycle1-2compressionClosed Period2-3heat release associatedwith combustion3-4 expansion720°CATDC4-5blowdown5-6exhaustIVOEVCOpen Period6-7 overlap7-8 induction8-1recompressionIn both cases the cycle divides itself into the closed periodduringwhich poweris beingproduced,and the open or gasexchangeperiodwhichmaymakeasmallpositivecontributionto power production or,inthe case of the four-stroke engine,EVOIVCunder conditions of adverse pressure differences between inletandexhaustmanifold,anegativecontribution.InthecaseoftheBDCfour-stroke engine the area enclosed by the p-V diagram for theFour-stroke engine (turbocharged)Figure1.5gas exchangeprocess,i.e.5-6-7-8,isknown asthepumping

crankshaft through a crosshead-siderod mechanism. By suitable offsetting of the cranks controlling the air and exhaust pistons asymmetrical timing can be achieved. It is evident that this system displays the same favourable characteristics as the exhaust valve in head system, but at the expense of even greater mechanical complications. Its outstanding advantage is the high specific output per cylinder associated with two pistons. However, the system is now retained only in large low speed marine, and smaller medium speed stationary and marine engines. In high speed form it is still employed for naval purposes such as in some fast patrol vessels and mine searchers, although its use in road vehicles and locomotives is discontinued. 1.2.2 Four-stroke engines (Figure 1.5) The vast majority of current diesel engines operate on the four￾stroke principle in which combustion occurs only every other revolution, again in the region of top dead centre (TDC), and with the intermediate revolution and its associated piston strokes given over to the gas exchange process. In practice the exhaust valve(s) open well before bottom dead centre (BDC) following the expansion stroke and only close well after the following top dead centre (TDC) position is reached. The inlet valve(s) open before this latter TDC, giving a period of overlap between inlet valve opening (IVO) and exhaust valve closing (EVC) during which the comparatively small clearance volume is scavenged of most of the remaining products of combustion. Following completion of the inlet stroke, the inlet valve(s) close well after the following bottom dead centre (BDC), after which the 'closed' portion of the cycle, i.e. the sequence compression, combustion, expansion, leads to the next cycle, commencing again with exhaust valve opening (EVO). The main advantages of the four-stroke cycle over its two￾stroke counterpart are: Figure 1.5 Four-stroke engine (turbocharged) (a) the longer period available for the gas exhange process and the separation of the exhaust and inlet periods— apart from the comparatively short overlap—resulting in a purer trapped charge. (b) the lower thermal loading associated with engines in which pistons, cylinder heads and liners are exposed to the most severe pressures and temperatures associated with combustion only every other revolution. (c) Easier lubrication conditions for pistons, rings and liners due to the absence of ports, and the idle stroke renewing liner lubrication and giving inertia lift off to rings and small and large end bearings. These factors make it possible for the four-stroke engine to achieve output levels of the order of 75% of equivalent two￾stroke engines. In recent years attention has focused particularly on three-cylinder high speed passenger car two-stroke engines as a possible replacement for conventional four-cylinder, four￾stroke engines with considerable potential savings in space and weight. 1.2.3 Evaluation of power output of two-stroke and four-stroke engines (Figures 1.6a and b} In order to determine the power developed within the engine cylinder as a result of gas forces acting on the piston as opposed to shaft power from the output shaft, it is necessary to have a record of the variation of gas pressure (/?) with stroke or cylinder volume (V) referred to as an Indicator Diagram (or p'-VDiagram). This used to be obtained by mechanical means, but such crude instrumentation has now been completely replaced by electronic instruments known as pressure transducers. It is also generally more convenient to combine the pressure measurement with a crank angle (CA) measurement, using a position transducer in conjunction with a suitable crank angle marker disc, and subse￾quently convert crank angle to stroke values by a simple geometric transformation. The sequence of events for the two cycles may be summarized as follows: (a) Two-stroke cycle (asymmetrical timing) 1-2 compression 1 2-3 heat release associated > Closed Period with combustion J 3-4 expansion 36O0CA 4-5 blowdown 1 5-6 scavenging f Open Period 6-1 supercharge J (b) Four-stroke cycle 1-2 compression 1 2-3 heat release associated > Closed Period with combustion J 3-4 expansion 72O0CA 4-5 blowdown 5-6 exhaust 6-7 overlap Open Period 7-8 induction 8-1 recompression In both cases the cycle divides itself into the closed period during which power is being produced, and the open or gas exchange period which may make a small positive contribution to power production or, in the case of the four-stroke engine, under conditions of adverse pressure differences between inlet and exhaust manifold, a negative contribution. In the case of the four-stroke engine the area enclosed by the p-V diagram for the gas exchange process, i.e. 5—6—7-8, is known as the pumping Inlet valve Exhaust valve Piston

8Diesel Engine Reference Bookgeometric swept volume Vwepr.In the caseoftwo-strokeengine,43Pwiththegas exchangeperiodoccupyingupto150°CA,(Vswep)em/Vswep may be considerably less than unity whileforfour-strokeengines itvaries between closeto unity and 0.8 (approx.)Similarlythe volumetric compression ratio (CR),whichagainis crucial in air standard cycle calculations,is usually based onEOthe effective swept volume4SO(Vawepc )efr+ Velearmncei.e.(CR)eff=(1.3a)SCVelearanceEC52-rather than the geometric value+BDC116Vswep +Vekewaince(1.3b)(CR)geom2Velearance+V(a)Finally, indicated thermal efficiency n or indicated specificfuel consumption i.s.f.c.areevaluated fromtheexpression4w(eqn (1.2a) or (1.2b)P(1.4a)ni=mr(kg/sec)CV(kJ/kg)where m, is the rate of fuel flow to the engine and CV is thelowercalorificvalueof thefuel andEOAm×3600i.s.f.c. =kg/kWhr(1.4b)W1042IC1.2.4 Other operating parameters8EC(a) Air-fuel ratioInstrokeThe combustion process is governed in large measure by the airfuel ratio in the cylinder, expressed either in actual termsPOut strokema, (kg/sec)(A/F)=i.e.(1.5a)(mr)kg/secV(b)where ma,is the rate of trapped airflow to the engine or relativeFigure 1.6Gas exchange period. p-V diagrams: (a) Two-stroketo the chemically correct or stoichiometric air fuel ratio for the(asymmetrical timing): (b)Four-stroke.(Bensonand Whitehouse)particular fuel, i.e. excess air factor(A/F)actualloopwhichmaycontributepositiveornegativeloopworkto(1.5b)=the work associated with the power loop.Figures .6a and b are(A/F)stoichiometrictypical p-V diagrams of the open or gas exchange period forIn practice,for most hydrocarbon fuelstwo-stroke and four-stroke engines.In both types of engine the cyclic integral expression leads(A/F)soichiomeric = 14.9(1.5c)to the so-called indicated mean effective pressureand, depending on the combustion system used, the limitingJ pdvJawrelative air fuel ratio for smokefree combustion at full load is in(1.1)Pind =VsweptVsweptthe rangewherefdWrepresentsthe cyclic work withthe distinction that1.2<8<1.6the cycleoccupies360°for two-stroke and 720°forfour-strokebeing lower for IDI than for DI engines.engines.The power may then be evaluated from the following(b)Gas exchange parametersexpressions:Fortwo-stroke engines,in particular, it is vitallyimportantmake a distinction berween the trapped rate of airflow mat andWiaoaoke (W)= Pm (bar) eg(m)N (revs)the total rate of airflow supplied to the engine mg.This arises(1.2a)10-2from the fact that the scavenging process in two-stroke enginesis accompaniedby substantial lossofairtoexhaust,partly throughormixing with products of combustion and partly through short-circuiting (see section 1.3.1)and leads to the definition of trappingPinu (bar) Vswept (m)N。(rev/s)nWourstroke (kW)= efficiencyas(1.2b)2 ×10-2(ma)tnu =Forpurposesofcomparison with airstandard cycles (seesection(1.6a)(ma)1.3).itisappropriatetousetheeffectivesweptvolume(Vswepi)effi.e.that associated with the closed period only rather than theor its reciprocal, the scavenge ratio

Figure 1.6 Gas exchange period. p-V diagrams: (a) Two-stroke (asymmetrical timing); (b) Four-stroke. (Benson and Whitehouse) loop which may contribute positive or negative loop work to the work associated with the power loop. Figures 1.6a and b are typical p-V diagrams of the open or gas exchange period for two-stroke and four-stroke engines. In both types of engine the cyclic integral expression leads to the so-called indicated mean effective pressure \pdV JdW Pind= y = y (LI) v swept v swept where J dWrepresents the cyclic work with the distinction that the cycle occupies 360° for two-stroke and 720° for four-stroke engines. The power may then be evaluated from the following expressions: Pmd (bar) K^nt (m3 )7Ve (rev/s)n , rts\\T\ swept v / e v / /1O \ ^two-stroke (kW) = — (1.2a) or Pind (bar) ^ent (m3 )7Ve (rev/s)« TI/ /VYXA ^W CP L v ' c v / OU\ Wfour-stroke (kW) = ~ TTT^ (1.2b) Z, XlU For purposes of comparison with air standard cycles (see section 1.3), it is appropriate to use the effective swept volume (Vswept)eff, i.e. that associated with the closed period only rather than the geometric swept volume Vswept. In the case of two-stroke engine, with the gas exchange period occupying up to 15O0CA, (Vswept)eff/ Vswept may be considerably less than unity while for four-stroke engines it varies between close to unity and 0.8 (approx.). Similarly the volumetric compression ratio (CR), which again is crucial in air standard cycle calculations, is usually based on the effective swept volume /^r> , (^swept )eff + ^clearance ,IO N i.e. (CK)eff = r? (1.3a) ^clearance rather than the geometric value ^swept + ^clearance (^)geom - v (1.3D) ^clearance Finally, indicated thermal efficiency T]1 or indicated specific fuel consumption i.s.f.c. are evaluated from the expression W(eqn(1.2a)or(1.2b)) Tt. — f i 4a) 11 rhf (kg/sec) CV(kJ/kg) v ' ' where mf is the rate of fuel flow to the engine and CV is the lower calorific value of the fuel and i.s.f.c.= ^ X . 360°kg/kWhr (1.4b) W 1.2A Other operating parameters (a) Air-fuel ratio The combustion process is governed in large measure by the air fuel ratio in the cylinder, expressed either in actual terms ma, (kg/sec) - (A/F)=(i^ (A/r ) stoichiometric In practice, for most hydrocarbon fuels (A/F)stoichlometnc =± 14.9 (1.5c) and, depending on the combustion system used, the limiting relative air fuel ratio for smokefree combustion at full load is in the range 1.2 < £ < 1.6 being lower for IDI than for DI engines. (b) Gas exchange parameters For two-stroke engines, in particular, it is vitally important to make a distinction between the trapped rate of airflow mat and the total rate of airflow supplied to the engine ma. This arises from the fact that the scavenging process in two-stroke engines is accompanied by substantial loss of air to exhaust, partly through mixing with products of combustion and partly through short￾circuiting (see section 1.3.1) and leads to the definition of trapping efficiency as (mn )f ^=W c-6a) or its reciprocal, the scavenge ratio In stroke Out stroke

Thetheoryof compression ignition engines93mRsc=(1.6b)P(m,),2Inpractice1.1<Rsc<1.6Forfour-stroke engines,particularly those with small valveoverlap,e.g.in road traction,it is safe to assume that all the airdelivered to the engine is trapped in the cylinder, i.e, n 1.However,due tocharge heating during the gas exchange processand adverse pressure conditions in the cylinder, it is likely thatthe volumetric efficiency nvol defined assweptAOTvolume of air trapped under inletVmanifold conditions(b)↑vol =swept cylinder volumeRT/Vawep=ma(1.7)102p(a)(where T and p are respectively the inlet manifold temperature(°K)and pressure (bar))is considerably less than unity.Clearlyfor the highest specific output, both the relative air fuel ratio eand the volumetric efficiency should be as close to unity aspossible.1.3Air standard cyclesIt will beclearfrom theforegoing sections thatthereal processesin the diesel engine cylinder,particularlythoseoffuel preparation,Vcombustion and gas exchangeare extremely complexandrequire(c)sophisticated computational techniques which are discussed inFigure1.7Air standard cycles:(a)Constant pressure cycle:1,2,3a number of specialisttexts.(b) Constant volume cycle: (c) Dual combustion or composite cycleAir standard cycles which are discussed in most elementarytextbooks,provide a useful basis for comparing actual engine2-3,and theblowdown-gas exchange sequence onceagain byperformance expressed intermsof indicated mean effectiveconstant volume heat rejection 4-1.Again compression 1-2pressure (pind, eqn (1.1) and indicated thermal efficiency (n..and expansion 3-4areisentropic.eqn(1.4a) with corresponding values for highly idealized cycles,Traditionally this is the reference cycle for spark ignitionbased on certain drastic simplifying assumptions as follows:(SI) engines, but it has distinct validity as a reference cycle fordiesel engines,particularlyunder lightload conditions when(a) the mass of working fluid remains constant throughout thethe heat release period is short so that the assumptions of zerocycle, i.e. gas exchange and fuel addition are ignored:heatrelease durationimpliedbythe constantvolumeprocess(b) the working fluid throughout the cycle is pure air treated as2-3 does not introduce excessive errors.a perfect gas;(c)thecombustionandgasexchangeprocessesarereplacedby(c)The‘dual combustion'orcompositecycle(Figure1.7c)external heattransferto or from the working fluid underidealized,This represents a combination of the constantpressure ande.g. constant volume or constant pressure conditions;constant volume cycles and is intended to provide a closer(d)compressionandexpansionprocessesaretreatedasadiabaticapproximation to actual diesel cycles than either of the aboveand reversible,i.e.heattransfer and friction effects are completelyideal cycles. It is particularly appropriate where comparisonsneglected;are to be made with actual diesel cycles on the basis of the(e)atanypoint of theworking cycle,cylinderchargepressuremaximum cylinder pressure Pmax obtained during the heat releaseand temperature are completely uniform,i.e.spatial variationsperiod, i.e.for engines operating in the mid-to full load range.intheir values as for instance during combustion or scavenging,are completely neglected1.3.1Theoretical expressions for air standard cyclesThe most commonly used air-standard cycles are as follows(Figures 1.7a, b and c):In thefollowing derivations it will be assumed that thecompressionratioCRcorrespondstotheeffectivecompression(a)Theconstantpressureordieselcycle(FigureI.7a)ratio (CR)efr of the engine, eqn (1.3a), and that the isentropicHere combustion is simulatedby constant pressure heat additionindex y i.e.the specifc heat ratio for air as a perfect gas, has the(2-3),andblowdown.followedbyscavenge,byconstantvolumeconstant value y= 1.4.heat rejection 4-1.Compression 1-2 and expansion 3-4followthe isentropic state relationships fora perfect gas.This particular1.3.7.1Theconstantpressureordiesel cycle(Figure1.7a)cycle has, in the past, been used as a reference cycle for theFrom basic engineering thermodynamics'classical'Diesel engine with airblast injection giving a ratherlong injection and hence heat release period, corresponding to+p,V,-P2V22-3.It has,however, little relevanceto the modern diesel cycle.compression workwp2 =(i)y-1(b)TheconstantvolumeorOnocycle(FigureI.7b)(note this is negative)Here combustion is simulated by constant volume heat release

#sc - 7?V (L6b) Oa )t In practice 1.1 < Rsc < 1.6. For four-stroke engines, particularly those with small valve overlap, e.g. in road traction, it is safe to assume that all the air delivered to the engine is trapped in the cylinder, i.e. T] tr = 1. However, due to charge heating during the gas exchange process and adverse pressure conditions in the cylinder, it is likely that the volumetric efficiency T]vol defined as volume of air trapped under inlet manifold conditions vo1 swept cylinder volume PT I = Wa T^T-/Vswept (1-7) 10-P/ (where Tandp are respectively the inlet manifold temperature ( 0K) and pressure (bar)) is considerably less than unity. Clearly for the highest specific output, both the relative air fuel ratio £ and the volumetric efficiency should be as close to unity as possible. 1.3 Air standard cycles It will be clear from the foregoing sections that the real processes in the diesel engine cylinder, particularly those of fuel preparation, combustion and gas exchange are extremely complex and require sophisticated computational techniques which are discussed in a number of specialist texts.1 ' 2 ' 3 Air standard cycles which are discussed in most elementary textbooks, provide a useful basis for comparing actual engine performance expressed in terms of indicated mean effective pressure (pind, eqn (1.1) and indicated thermal efficiency (T]1, eqn (1.4a) with corresponding values for highly idealized cycles, based on certain drastic simplifying assumptions as follows: (a) the mass of working fluid remains constant throughout the cycle, i.e. gas exchange and fuel addition are ignored; (b) the working fluid throughout the cycle is pure air treated as a perfect gas; (c) the combustion and gas exchange processes are replaced by external heat transfer to or from the working fluid under idealized, e.g. constant volume or constant pressure conditions; (d) compression and expansion processes are treated as adiabatic and reversible, i.e. heat transfer and friction effects are completely neglected; (e) at any point of the working cycle, cylinder charge pressure and temperature are completely uniform, i.e. spatial variations in their values as for instance during combustion or scavenging, are completely neglected. The most commonly used air-standard cycles are as follows (Figures 1.7'a, b and c): (a) The constant pressure or diesel cycle (Figure 1.7a) Here combustion is simulated by constant pressure heat addition (2-3), and blowdown, followed by scavenge, by constant volume heat rejection 4-1. Compression 1-2 and expansion 3-4 follow the isentropic state relationships for a perfect gas. This particular cycle has, in the past, been used as a reference cycle for the 'classical' Diesel engine with air blast injection giving a rather long injection and hence heat release period, corresponding to 2-3. It has, however, little relevance to the modern diesel cycle. (b) The constant volume or Otto cycle (Figure 1.7b) Here combustion is simulated by constant volume heat release (C) Figure 1.7 Air standard cycles: (a) Constant pressure cycle; (b) Constant volume cycle; (c) Dual combustion or composite cycle 2-3, and the blowdown-gas exchange sequence once again by constant volume heat rejection 4-1. Again compression 1-2 and expansion 3-4 are isentropic. Traditionally this is the reference cycle for spark ignition (SI) engines, but it has distinct validity as a reference cycle for diesel engines, particularly under light load conditions when the heat release period is short so that the assumptions of zero heat release duration implied by the constant volume process 2-3 does not introduce excessive errors. (c) The 'dual combustion' or composite cycle (Figure 1.7c) This represents a combination of the constant pressure and constant volume cycles and is intended to provide a closer approximation to actual diesel cycles than either of the above ideal cycles. It is particularly appropriate where comparisons are to be made with actual diesel cycles on the basis of the maximum cylinder pressure /?max obtained during the heat release period, i.e. for engines operating in the mid-to full load range. 1.3.1 Theoretical expressions for air standard cycles In the following derivations it will be assumed that the compression ratio CR corresponds to the effective compression ratio (CR)eff of the engine, eqn (1.3a), and that the isentropic index y, i.e. the specifc heat ratio for air as a perfect gas, has the constant value J= 1.4. 1.3.1.1 The constant pressure or diesel cycle (Figure Ua) From basic engineering thermodynamics: + P1Vi - p2 V2 compression work W\2 = ; (i) (note this is negative) swept volume

10DieselEngineReferenceBook0.7Welt(vii)(n;)cp=Q23CR=200.6(vii)eventually reduces to18-BY-11(n:)cp = I (1.8)16Limiting air-fuel ratio14.(CR)y-JY(β-)0.5(equation 1.9)12The volume ratio βis an indication of the air-fuel ratio A/F at10NeNDwhich the engine is operating,since to a firstapproximation0.48CR=6Q23= mCp(T3- T2)= P2V2(β-1)0.3= m(CV)(vili)where m is the mass of fuel burnt0.2P,V,But mair=m, =(ix)RT,0.1Y(β- 1)PaV2P,Vy-1whence A/F=RT,(CV)10213A567Cut-off ratio βCVFigure 1.81Constant pressure cycle. Indicated efficiency vs cut-off(1.9)ratio (eqn 1.8)RTCRY(β-1)y-1constant pressure workAssuming that the limiting air-fuel ratio is the stoichiometricW23=P2 (V-V2) =P2V2(β- 1)(ii)ratio (A/F)stoich eqn (1.5c),it is possible to find a limiting valueofthevolumeratioβforanygivencompressionratioCRfromVeqn (1.9).This is shown inFigure1.8 indicating the behaviourwhere β= volume ratioV2ofeqn(1.8)withdifferentvaluesof compressionratioCRand'cut off'ratioβ,including theposition of the"limiting line'forconstantpressureheattransferstoichiometric combustion.Indicated efficiency (n,)cp is seen to increase rapidly withQ23 = mCp(T3 - T2)volumetric compression ratio CR andtodecrease with increasingvalues of the cut off ratio β, i.e.with decreasing air-fuel ratio,(beinga minimum,for any valueof CR on the limit line,and amaximumfora cut offratioβ=1.Efficiency is not the only consideration appertaining to cycles.Specific output also hastobe taken into account so thatthe=P2V2β-11(iii)relationship between indicated efficiency,specific output andcompression ratio is equallyimportant.The specific outputisbest measured in terms of the mean effectivepressure definedexpansion work Wy=DV-_Vβ-pM(iv)by eqn (1.1) relative to the trapped pressure pi.The calculationy-1Y-Iis as follows:nettworkWne=W12+W23+W34For any assumed value of the cut-off ratio β the equivalent air-fuel ratio A/F may be calculated from eqn (1.9).giving theheat=PiV-p2V2+PaVeB-p4viinput to the cycle as-1y-1PIVCVCV(i)+ p2V2(β- 1)(v)Qin=mA/FRTA/FbutWith indicated efficiency (n)cp from eqn (1.8),the indicatedworkoutputofthecycle isgivenby= PI(CR)Y. V2 =P2 = p3 =CRJdW=Qm(n)cp(ii)() =p()and the mean effective pressure,from eqn (1.1)becomesP4 = p3[=P2(vi)Tp,VCV(ni)cpJawJdwRT,A/FSubstituting from (vi) for p2,V and p4 in (v) and (ii) andPind =writing for the ideal efficiency of the constantpressure (CP)VsweptV(1-v.(1-cycle:CRCR

Cut-off ratio ft Figure 1.8 Constant pressure cycle. Indicated efficiency vs cut-off ratio (eqn 1.8) constant pressure work W23 = P2 (V3 - V2 ) = P2V2 (P - 1) (ii) V3 where /3 = volume ratio —— constant pressure heat transfer Q23 = mCp (T3 - T2 ) P2V2 ( 7 .YV3 = \ -KfT [T^T *}{v; - 1 J^ = p2v2 ^-I1J(JS-O №) P3V3 -P4V4 P2V2 I-P4Vi expansion work Vr34 = —: = — (iv) nett work Wnett = W12+ W23 + W34 = PiVi -P2V2 P2V2 I-P4Vi 7-1 7-1 + P2V2OS-I) (v) but A » 2 =P3=P,(£)r ^1(CK)', V 2 = (^) ( v3 y f/?v2 y fjs y P4=P3 ^_J =P2^_ J = p2^_J (v,) Substituting from (vi) for p2, V2 and p4 in (v) and (iii) and writing for the ideal efficiency of the constant pressure (CP) cycle: W (Hi ) CP = ^ (ViO (vii) eventually reduces to (l" )CT = I - bM W^) (L8) The volume ratio /3 is an indication of the air-fuel ratio A/F at which the engine is operating, since to a first approximation Q23 = mCp(T3 - T2) =P2V2~ (ft - O = mf(CV) (viii) where mf is the mass of fuel burnt But mair = m, = ^L (ix) ^ 1V1 /IPM^P-V whence A/F= ^i-/ L_ My-'oi i (19) ICK J «*£<,_„ Assuming that the limiting air-fuel ratio is the stoichiometric ratio (A/F)stoich eqn (1.5c), it is possible to find a limiting value of the volume ratio /3 for any given compression ratio CR from eqn (1.9). This is shown in Figure 1.8 indicating the behaviour of eqn (1.8) with different values of compression ratio CR and 'cut off ratio j3, including the position of the 'limiting line' for stoichiometric combustion. Indicated efficiency (r/^cp is seen to increase rapidly with volumetric compression ratio CR and to decrease with increasing values of the cut off ratio /3, i.e. with decreasing air-fuel ratio, being a minimum, for any value of CR on the limit line, and a maximum for a cut off ratio j8 = 1. Efficiency is not the only consideration appertaining to cycles. Specific output also has to be taken into account so that the relationship between indicated efficiency, specific output and compression ratio is equally important. The specific output is best measured in terms of the mean effective pressure defined by eqn (1.1) relative to the trapped pressure ^1. The calculation is as follows: For any assumed value of the cut-off ratio ft the equivalent air￾fuel ratio A/F may be calculated from eqn (1.9), giving the heat input to the cycle as O -m CV _ PiV, CV m ^ in " m ~A/F ~ ~RT]~ ~A/F (l) With indicated efficiency (T]J)CP from eqn (1.8), the indicated work output of the cycle is given by JdW=Gi n (Tj 1 ) C P (H) and the mean effective pressure, from eqn (1.1) becomes PiVi CV (n . _ IdW _ IdW RT, A/F(7?i)cp ^ ind ~ V f \ \~ ( \ \ Vswept y f j _ J_ y I I _ _L 1 I CR) 1 I CR j HIND Limiting air-fuel ratio (equation 1.9)

Thetheoryof compressionignition engines11Substituting from (ii) in (i) and (ii) and writing for the ideal20efficiencyof the constantvolume(CV)cycle18CR = 20Wert16Limiting air-fuel(iv)(ni)cv=ratio (equation 1.9)14Q231512(iv)eventuallyreducesto10(ni)cy=/-(1.11)CRRPnd10PEquation (I.11)demonstrates that the efficiency of the constantvolumecycleisa functionofcompressionratioCRonly,andCR=6unlike the constant pressure cycle,independent of the level ofheat addition, as expressed by the pressure ratio p/p2=T,/T2=α (seeFigure 1.10).5It is generally quoted in support of arguments to raisecompression ratio in spark ignition (SD) engines.-D1.3.1.3Thedualcombustionorcompositecycle234567(Figure 1.7c)Cut-off ratio βAs already stated, this cycle tends to approximate more closelyFigure1.9Constant pressure cycle.Indicatedmean effective pressureto actual diesel cycles than either the pure constant pressure orvs cut-off ratio (eqn 1.10)constant volume cycles as described above. It lends itselfparticularly well to the representation of limited maximumCVcylinderpressure,as expressedbythepressureratioα=ps/p1AVF(n)cPoften specified in real diesel cycles, and to assessment of theRT.Piador(1.10)effectof increased orretarded heat release,asexpressed mainlyp1CP1-bythevolumeratioβ=V/V,CRThe evaluation of cycle efficiencyfollows a similar patternto that adopted above:Equation(1.10)isrepresentedbyFigure1.9andshowsthat,forany given compression ratio CR, efficiency decreases withnett cycle work =W2+W34 +W45increasing specific output,with a minimum valueagain onthelimit line. PiVi-P2Va2+p3Vs(β-1)+P3V4-psVsFigure 1.9 may be used both for naturally aspirated engines(i)y-1Y-1forwhichthetrappedpressureP,is approximatelyequaltoatmosphericpressurep.as well asfor supercharged enginesConstantvolume heattransferwitha supercharge (orboost)pressureratio given approximatelybyR= (p//pa) (>1).0.71.3.1.2TheconstantvolumeorOttocycle(Figure1.7b)As already stated this cycle has only limited applicability to0.6diesel engines,mainly under part loadconditions.Heat transfernowoccurs under constant volume conditions,both for the'combustion process2-3andthegas exchangeprocess 4-1.0.5Nett cycle work( aae eWner = Wi2 + W34P,V-paV40.4PV-P2V2(i)Y-1-1constant volumeheattransfer0.3Q23 =mC,(T, -T2)= PaV_RRT-T0.2P2V(α-1)(ii)Y-10.1whereα=PP2Vi1110But p2 =pI(CR), V2 == V3048121620CRCompression ratio (CR)Figure 1.10Constantvolume cycle.Indicated efficiency vs(ili)P4=p=piα=p2(CRChcompression ratio

Cut-off ratio /3 Figure 1.9 Constant pressure cycle. Indicated mean effective pressure vs cut-off ratio (eqn 1.10) CV 1 „ (a^ _W^f^' ( ">° ('-£) Equation (1.10) is represented by Figure 1.9 and shows that, for any given compression ratio CR, efficiency decreases with increasing specific output, with a minimum value again on the limit line. Figure 1.9 may be used both for naturally aspirated engines for which the trapped pressure p\ is approximately equal to atmospheric pressure pa as well as for supercharged engines with a supercharge (or boost) pressure ratio given approximately by RE = (Pi/Pa) (> O. 1.3.1.2 The constant volume or Otto cycle (Figure 1.7b) As already stated this cycle has only limited applicability to diesel engines, mainly under part load conditions. Heat transfer now occurs under constant volume conditions, both for the 'combustion' process 2-3 and the 'gas exchange' process 4-1. Nett cycle work HU = Wl 2 + W34 = P1V1 -P2 ^ 2 P3V3 -P4V4 (n y- 1 7-1 constant volume heat transfer Q23=mC^-T2}-^^-l)T2 = frj(a-l> («) ft-, where a = -^- Pi But p2 = p} (CR)Y, V2 = ^ = V3 p< = P*(ZR) = ^a (^) =*<* (ill) Substituting from (iii) in (i) and (ii) and writing for the ideal efficiency of the constant volume (CV) cycle w (Hi)CV = ^ Ql3 W (iv) eventually reduces to (TJi)CV = I -(c^)7 O- 1 1 ) Equation (1.11) demonstrates that the efficiency of the constant volume cycle is a function of compression ratio CR only, and unlike the constant pressure cycle, independent of the level of heat addition, as expressed by the pressure ratio p-Jpi - T3/T2 - a (see Figure 1.10). It is generally quoted in support of arguments to raise compression ratio in spark ignition (SI) engines. 13.13 The 'dual combustion or composite cycle (Figure Uc) As already stated, this cycle tends to approximate more closely to actual diesel cycles than either the pure constant pressure or constant volume cycles as described above. It lends itself particularly well to the representation of limited maximum cylinder pressure, as expressed by the pressure ratio a = p$lp2 often specified in real diesel cycles, and to assessment of the effect of increased or retarded heat release, as expressed mainly by the volume ratio ft = V4IV3,. The evaluation of cycle efficiency follows a similar pattern to that adopted above: nett cycle work = W12 + W34 + W45 = ^^+P3v3 (/M)+^^ (1) Constant volume heat transfer Compression ratio (CR) Figure 1.10 Constant volume cycle. Indicated efficiency vs compression ratio Limiting air-fuel ratio (equation 1.9) Thermal efficiency (77,) Pjnd Pl

12Diesel EngineReferenceBookP2V2(α-)(-)Q23+Q4==mr(CV)Q23 = mC,(T, - T)=(α-1)(ii)(vi)y-1y-1y-1(see constant volume cycle,above)where m,is the mass of fuel burnt, i.e.Constant pressureheat transfermi-pVimair-LA/F(vii)mf=A/F.A/FRT-(β-1)Qu=mC,(T+-T3)= p,V2(iii)Y-Substitutingfor m,from (vii)in (vi)provides an explicitsolution(see constant pressure cycle,above).forβ,aalreadybeingknownfrom (v)interms of the stipulatedmax.pressure Pmax=P,resulting eventually inVButP:=P)(CR) V2=R=V3,P=4=p2α=p(CR)α1Y~/- 1CVA/F =(1.13a)CRRT, (α-1)+y(β-1)VV =Vsβ=(iv)β,Ps=p4=P3CRCR(7-1VyY-1CV(1.13b)Substituting from (iv) in (i), (ii)and (ii) and writing for the(PR)RT, (α- 1)+ y0(β-1)ideal efficiency of the dual combustion cycleAs before, the concept of the limiting air-fuel ratio may beWetapplied, with A/F = (A/F)stoichiometric, to give a limiting value of(n:)DC=(v)Q23+ Q34β for anygiven value of CR.Finally,with mean effective pressure given by (pind )pceqn (v) eventually reduces to=J dW/Vwepland applying similar arguments to thosefortheαβr_1(1.12)(n)Dc=diesel cycle(α-1)+ yα(β-1)CV1Inspection of eqn (1.12) shows that with β= 1, characteristic of(ni)DcRT,A/FPindthe constant volume cycle, the efficiency reduces to thatgiven(1.14)Pbyeqn(1.11)forthatcycle,becomingafunctionofcompressionCRratio CR only,while with α= 1 characteristic of the constantpressure cycle,the efficiency reducesto thatgiven byeqn (1.8)Equations(1.12),(1.13)and (1.14)have been combined in Figureforthat particularcycle.Thedual combustioncyclemaytherefore1.1l to give a single representation of indicated efficiency andbe regarded as embracing, at the same time, those other idealmean indicatedpressureasafunctionofcompressionratio(CR)cycles.the upper limit of mean effective pressure being set by theAs in the case of the diesel cycle,itis of interest to establishlimiting air-fuel ratio.The assumed value pmax/p,has been setthe relationship between specific output, represented by theat 68 corresponding toamax.cylinderpressureof 68barforamean effective pressure rationaturally aspirated engine or136barfor a supercharged engineoperating with a boost ratio of 2:l.The relationshipbetweenPindcompressionratio CR,the pressure ratioPIthe efficiency (n,)pc and compression ratio CR. A maximumP3 = PmaxPmax=αfor=68 and thecut-off ratioBpressure ratioP2P2PIPmarP (Figure 1.7c)0.70pIpIhas to befixed,in thefirstinstance.This in conjunction with theCR=200.6518.compression ratio CRwill yield thepressureratio14.1612Q=P3100.60p28fromIND 0.55Limiting constantvolume cycieαP2α(CR)=PRPmaxCR=6(v)piPI0.50SubstitutingforCRintermsofPRfromeqn(v)intheefficiency0.45expression eqn (1.12)leadsto the altemative expression,inLimiting air-fuelratio (equation1.13)terms of the pressure ratio PR0.40ty-1/yαβr-15010152025(1.12a)(ni)Dc:-PR(α - 1) + yx(β- I)PindPThe equivalent air-fuel ratio A/F may also be determined by aprocedure equivalent to that adopted for the diesel cycles fromFigure 1.11.Dualcombustioncycle.Indicatedefficiency(eqn1.12)(ii) and (iii) abovevs indicated mean.Effective pressure (eqn 1.14) Pmax/P, =68

Q23 =mCv (T3 -T2) = -^j(a- 1) (ii) (see constant volume cycle, above). Constant pressure heat transfer Q34=mCp (T4-T3) = p3v2^ (P-I) (in) (see constant pressure cycle, above). ButP2=P1 (CRy, V2= -^-= V3, p3=p4=p2 a = Pl(CRya C/v V4 = V3P = ^ ft, P5 = P4 [^]" =P3 (A J (1V) Substituting from (iv) in (i), (ii) and (iii) and writing for the ideal efficiency of the dual combustion cycle Wvc = n W Tn (v) (^23 + C^34 eqn (v) eventually reduces to f 1 \J ~ l C(B7 - 1 ( ^ c = 1-fe) (a- I) + 7^-I) (U2) Inspection of eqn (1.12) shows that with ft = 1, characteristic of the constant volume cycle, the efficiency reduces to that given by eqn (1.11) for that cycle, becoming a function of compression ratio CR only, while with cc = 1 characteristic of the constant pressure cycle, the efficiency reduces to that given by eqn (1.8) for that particular cycle. The dual combustion cycle may therefore be regarded as embracing, at the same time, those other ideal cycles. As in the case of the diesel cycle, it is of interest to establish the relationship between specific output, represented by the mean effective pressure ratio Pmd Pl the efficiency (T]J)DC and compression ratio CR. A maximum pressure ratio Pr^L = PL (Figure Uc) Pi Pi has to be fixed, in the first instance. This in conjunction with the compression ratio CR will yield the pressure ratio a= ^- P2 from EJ^L = ^L a(CRy =pR (v) Pi Pi Substituting for CR in terms of PR from eqn (v) in the efficiency expression eqn (1.12) leads to the alternative expression, in terms of the pressure ratio PR •"'-•'-(arv.?,'/.-., "•-' The equivalent air-fuel ratio A/F may also be determined by a procedure equivalent to that adopted for the diesel cycles from (ii) and (iii) above Q23 + Q34 = e&F^1 + "3 T*"0 - m< (CV) /— i /— i W) where mf is the mass of fuel burnt, i.e. —&-•&-'%-/"' Substituting for mf from (vii) in (vi) provides an explicit solution for /3, a already being known from (v) in terms of the stipulated max. pressure /?max = p3 resulting eventually in A/F = MY-' cv T^i (113a) ™* (CR) RT1 (a-l) + ya(p-\) ( } = (_cL\ (7' V}' 7 CV 7-1 (] nh) (PR) RT1 (a-.\) + ya(p- 1) ( ' } As before, the concept of the limiting air-fuel ratio may be applied, with A/F = (A/F)stoichiometric, to give a limiting value of /3 for any given value of CR. Finally, with mean effective pressure given by (pm(i)vc = J dWVswept and applying similar arguments to those for the diesel cycle CV 1 fn . / «^ \ UT A /J7 Wi'DC 1 = *r. UF (M4) V 7I JDC [i _ J_l ( CR) Equations (1.12), (1.13) and (1.14) have been combined in Figure 1.11 to give a single representation of indicated efficiency and mean indicated pressure as a function of compression ratio (CR) the upper limit of mean effective pressure being set by the limiting air-fuel ratio. The assumed value pmax/p\ has been set at 68 corresponding to a max. cylinder pressure of 68 bar for a naturally aspirated engine or 136 bar for a supercharged engine operating with a boost ratio of 2:1. The relationship between compression ratio CR, the pressure ratio £3_ = Pn^ = afor ^ma^ = ^ ^ ^ cm_off ^0 ^ P2 P2 Pl P\nd P^ Figure 1.11 Dual combustion cycle. Indicated efficiency (eqn 1.12) vs indicated mean. Effective pressure (eqn 1.14) Pmax/Pi = 68 ^IND Limiting constant volume cycle CR= 6 Limiting air-fuel ratio (equation 1.13)

Thetheoryofcompression ignition engines 13the latter for limiting air-fuel ratio, is summarized in Table I.1.Likewise the values of ideal efficiency based on Table I.1and eqns (1.12)and (1.14), showing that with the limiting air-fuel ratio a value of 0.570 (57%) is reached for the highestTable1.1compressionratioof 20:1whenoperatingon thedual combustioncycle, while for the pure constant volume cycle and for the12CR6810IA161820same compression ratio,but withzerofuelling,thecorresponding5.533.712.711.021.111.691.401.19aefficiency is 0.696 (69.5%),are clearly far above practicallyBin1.351.732.122.502.913.313.734.16realizablevalues.Nevertheless indicatedefficiencies approaching46%havebeenachieved inpracticeandmaywell beexceededFigure 1.11 dispels the widespread misconception that theinfuture,withcontinuing improvementsin suppressionofheatloss to coolantt,fuel injection equipment and turbochargingconstantvolumecycleforwhichβ=1 is themostefficientpossibleair standard cycle.For agiven maximum pressure ratioarrangementsPR and a given indicated mean effective pressure ratio1.3.2.2Other theoretical cycles and representationsPindpt(a)The modified Arkinson cycle (FigureI.12)It has already been indicated that maximum cylinder pressureFigure I.ll shows clearly that the constant volume cycle is theis an important limiting factor in improving diesel engineleast efficient,and thatcycle efficiencyincreases progressivelyperformance.In practice values of Pmux in excess of 150 bar areasthe constantpressurecycle is approachedrarelypermissibleformechanicalreasons.InspectionofFigure1.ll shows that the more thetrapped'pressurepi(approximatelyequal to the boostpressure)is raised to raise output, the more1.3.2Further comments on air standard cyclesthevolumetriccompressionratioCRwillhavetobereducedif1.3.2.1 Interpretation of results so farthe limiting value of pmax is not to be exceeded. Equation (1.12)and Figure 1.l1 indicate that this inevitably has an adverseThe three reference cycles described above, i.eeffect on efficiency.The Atkinson cycle seeks to redress this(a)the'classical'constant pressure diesel cycle;effectpartiallybyoperating withanexpansion ratioERwell in(b)theconstantvolumeOttocycle;excess of the compression ratio CR.In practice this isachieved(c)thedualcombustion'cyclenot by lengthening the stroke of the piston,but by early inlethave been, and are still, widely used as useful reference cyclesclosingand lateexhaustopening (Figure1.12)the latterbeingfor the assessment of the actual performance of diesel engines.delayed until the cylinder gases have fully expanded to theTheirlimitations.resultingmainlyfromthedrasticidealizationstrapped pressure pr.involvedintheirformulationhavealreadvbeenstated.ActualItmaybe shown,returningtothenotation adopted fortheperformance will therefore inevitablyfallfar short ofthatpredicteddual combustioncycle,withCRdenotingcompressionratioasbyair standard cycletheory,the quantitativeeffects of the manydepartures from ideal conditions being the subject of a laterβα = 1.5 [section of this chapter.Nevertheless,FigureI.ll inparticular.1.61.4forthedual combustioncycle.provides someextremelyvaluable1.20.8insight into the limits of performance of high output diesel1.0enginesIt is clear that limiting indicated mean effective pressures,βirrespective ofcompression ratio,are of the order of 22 barfor1.00.7anaturally aspirated engine,with proportionallyhighervalues1.2for supercharged engines,assuming that the trapped cylinder1.4temperaturecanbemaintainedconstantbyaftercooling.Typical1.6high output engines now operate at boost pressure ratiosapproaching3:Iandwithverygenerous aftercooling,suggesting0.6a theoretical limiting IMEP of the order of 66 bar.This figureoeeehastobedrasticallyreducedtoaccountforα=1.5(a) the need to operate with actual air-fuel ratios of the order of22:I instead of the assumed limiting air-fuel ratio (A/F)stoic =0.514.9(b)therealeffectsof(i)pumping and heat losses duringthegas exchange process;(i) heat losses during the closed period,particularly during theperiodofhighestcylinder temperatures,i.e.combustionand theearlyphasesofexpansion;(ii)inevitable irreversibilities during combustion;Dual combustioncycle(v)variable specific heats a function of temperature and0.3composition.Modified Atkinson cycleHence one would expect to achieve a limiting IMEP of ratherless than half the theoretical value,i.e.30 bar in a highly developedfour-stroke diesel engine operating at a boost ratio of 3:l,and110.2even less in a two-stroke engine due to its generally shorter4.08.012.016.020.0effective stroke and the need for even more generous air-fuelCRratiostoensuresatisfactory scavenging andfreedomfrom thermalFigure 1.12 Atkinson cycle (Benson and Whitehouse)overloading

the latter for limiting air-fuel ratio, is summarized in Table Ll. Table 1.1 Figure 1.11 dispels the widespread misconception that the constant volume cycle for which /3 = 1 is the most efficient possible air standard cycle. For a given maximum pressure ratio PR and a given indicated mean effective pressure ratio Pind P 1 Figure 1.11 shows clearly that the constant volume cycle is the least efficient, and that cycle efficiency increases progressively as the constant pressure cycle is approached. 1.3.2 Further comments on air standard cycles 1.3.2.1 Interpretation of results so far The three reference cycles described above, i.e. (a) the 'classical' constant pressure diesel cycle; (b) the constant volume Otto cycle; (c) the 'dual combustion' cycle. have been, and are still, widely used as useful reference cycles for the assessment of the actual performance of diesel engines. Their limitations, resulting mainly from the drastic idealizations involved in their formulation have already been stated. Actual performance will therefore inevitably fall far short of that predicted by air standard cycle theory, the quantitative effects of the many departures from ideal conditions being the subject of a later section of this chapter. Nevertheless, Figure 1.11 in particular, for the dual combustion cycle, provides some extremely valuable insight into the limits of performance of high output diesel engines. It is clear that limiting indicated mean effective pressures, irrespective of compression ratio, are of the order of 22 bar for a naturally aspirated engine, with proportionally higher values for supercharged engines, assuming that the trapped cylinder temperature can be maintained constant by aftercooling. Typical high output engines now operate at boost pressure ratios approaching 3:1 and with very generous aftercooling, suggesting a theoretical limiting IMEP of the order of 66 bar. This figure has to be drastically reduced to account for (a) the need to operate with actual air-fuel ratios of the order of 22:1 instead of the assumed limiting air-fuel ratio (A/F)stoic = 14.9 (b) the real effects of (i) pumping and heat losses during the gas exchange process; (ii) heat losses during the closed period, particularly during the period of highest cylinder temperatures, i.e. combustion and the early phases of expansion; (iii) inevitable irreversibilities during combustion; (v) variable specific heats a function of temperature and composition. Hence one would expect to achieve a limiting IMEP of rather less than half the theoretical value, i.e. 30 bar in a highly developed four-stroke diesel engine operating at a boost ratio of 3:1, and even less in a two-stroke engine due to its generally shorter effective stroke and the need for even more generous air-fuel ratios to ensure satisfactory scavenging and freedom from thermal overloading. Likewise the values of ideal efficiency based on Table 1.1 and eqns (1.12) and (1.14), showing that with the limiting air￾fuel ratio a value of 0.570 (57%) is reached for the highest compression ratio of 20:1 when operating on the dual combustion cycle, while for the pure constant volume cycle and for the same compression ratio, but with zero fuelling, the corresponding efficiency is 0.696 (69.5%), are clearly far above practically realizable values. Nevertheless indicated efficiencies approaching 46% have been achieved in practice and may well be exceeded in future, with continuing improvements in suppression of heat loss to coolant4 , fuel injection equipment and turbocharging arrangements. 1.3.2.2 Other theoretical cycles and representations (a) The modified Atkinson cycle (Figure 1.12) It has already been indicated that maximum cylinder pressure is an important limiting factor in improving diesel engine performance. In practice values of /?max in excess of 150 bar are rarely permissible for mechanical reasons. Inspection of Figure 1.11 shows that the more the 'trapped' pressurep} (approximately equal to the boost pressure) is raised to raise output, the more the volumetric compression ratio CR will have to be reduced if the limiting value of /?max is not to be exceeded. Equation (1.12) and Figure 1.11 indicate that this inevitably has an adverse effect on efficiency. The Atkinson cycle seeks to redress this effect partially by operating with an expansion ratio ER well in excess of the compression ratio CR. In practice this is achieved not by lengthening the stroke of the piston, but by early inlet closing, and late exhaust opening (Figure 1.12) the latter being delayed until the cylinder gases have fully expanded to the trapped pressure p\. It may be shown, returning to the notation adopted for the dual combustion cycle, with CR denoting compression ratio as CR Figure 1.12 Atkinson cycle (Benson and Whitehouse) Dual combustion cycle Modified Atkinson cycle Thermal efficiency CR a Aim 6 5.53 1.35 8 3.71 1.73 10 2.71 2.12 12 1.11 2.50 14 1.69 2.91 16 1.40 3.31 18 1.19 3.73 20 1.02 4.16