ASME_ICES_2006_1444_FIT

1 Copyright 2006 by ASMEProceedings of ICES 06:ASME Internal Combustion Engine Division 2006 Spring Technical ConferenceMay 7-10, 2006, Aachen, GermanyPaper no. ICES2006-1444EXHAUST SYSTEM GAS-DYNAMICS IN INTERNAL COMBUSTION ENGINESR Pearson / Lotus Engineering M Bassett / Lotus EngineeringP Virr / Renault F1 Team S Lever / Renault F1 Team A Early / Renault F1 TeamABSTRACT Thesensitivityofengineperformancetogas-dynamicphenomenaintheexhaustsystemhasbeenknownforaround100yearsbutisstillrelativelypoorlyunderstood.Thenonlinearityofthewave-propagationbehaviourrenderssimpleempiricalapproachesineffective,eveninasingle-cylinderengine.Theadoptionofanalyticaltoolssuchasengine-cycle-simulationcodeshasenabledgreaterunderstandingofthetuningmechanismsbutformulti-cylinderengineshasrequiredthedevelopmentofaccuratemodelsforpipejunctions.Thepresentworkexaminesthepropagationofpressurewavesthrough pipe junctions using shock-tube rigs in order to validateacomputationalmodel.Followingthistheeffectsofexhaust-systemgasdynamicsonengineperformancearediscussedusingtheresultsfromanengine-cycle-simulationprogrambasedontheequationsofone-dimensionalcompressiblefluidflow.NOMENCLATUREa speed of soundc propagation speedp pressureu particle speed ratio of speed heatsSubscripts0 conditions in undisturbed gasINTRODUCTIONLiterature dealing with the effects of gas-dynamic phenomena intheexhaustmanifoldsofinternalcombustionenginesdatesfromthebeginningofthetwentiethcentury[1].Farmer[2],however,mentionsworkundertakenin1893byAtkinsonandCrossleywhichestablishedthattheperformanceofafour-strokeengineissensitivetothelengthofitsexhaustpipe.Farmer[2]clearlydelineatesthebasicmechanismoftuningtheexhaustsystemsoftwo-strokeengines.Inparticularthetuning of the self-induction engine1 is explained where the aimis to size the length of the exhaust pipe such that the rarefactionwave, generated by the reflectionoftheblowdownpulseattheopenendofthepipe,returnstotheexhaustportduringtheintakeandexhaustportoverlapperiod.Thisisalsothebasictuningmechanismforfour-strokeengines.Figure1wasgeneratedusingtheLotusEngineSimulationcycle-simulationprogram,runningthesingle-cylinderengineshownat7000rev/min.Itcanbeseenthat,forthiswell-tunedcase,theblowdownpulsepropagatesdowntheexhaustrunnerfromtheexhaust valve (which is at 0mm) and reflects at the open end (at650mm)toformadeeplow-pressureregionattheexhaustvalve about 180 degrees later in thecycle.Thevariationofthepressure in the exhaust runner as a function of time and positionin the pipe can be seen.Morrison[3,4]discussespressurepulsationsintheexhaustsystemsoffour-strokeenginesandstatesthatengineperformanceismoresensitivetothepressureattheexhaustvalveduringthevalveoverlapperiodthanthelevelofexhaustback-pressure2; manifolds for four- and six-cylinder engines arealsodiscussed.Otherworkersinvestigatedexhaustsystemgasdynamics via measurement techniques [5-7] but, by the1950s,calculation of pressure wave phenomena in exhaust systems wasbeingattempted[8-11].Modellingtechniquesprogressedrapidlyinthe1960sand70s[11-14]andbythelate1980scommercialsoftwarewasbeginningtobeusedforengineperformance prediction, including the effects of exhaust system 1 An engine which does not use an auxiliary air pump.2Exhaustback-pressureisthemeanpressurelevelatapointintheexhaust system in this case in the exhaust port2 Copyright 2006 by ASMEdesign.Todaytheuseofcomputersimulationisaroutinepartof the engine design and development process [15,16].The design of exhaust silencers has a direct effect ontheback-pressure in the exhaust system through pressure-loss effects andthis impacts directly on the engine pumping work, as well as thescavengingprocessinthecylinders.Thedesignoftheexhaustmanifold also impacts upon the pumping work performed by theengine[17,18]viaitsinfluenceonthepressurelevelattheexhaustvalveduringtheexhaustprocess.Inparticularthepumping work is most sensitive to the cylinder pressure aroundthepointofmid-pistonstrokeastherateofchangeofcylindervolume is greatest at this point. This is not the motivation of thepresentwork,whichisconcernedprimarilywithwavepropagationphenomenaandtheireffectonthecylinderscavenging process.Figure 1. Variation of pressure / crank angle withdistance along exhaust pipe at 7000 rev/min.VALIDATION OF JUNCTION MODELSAkeyaspectofthesuccessfulsimulationofhigh-performanceenginesistheabilitytopredictaccuratelythepropagationofpressure wavesthroughpipejunctionsintheexhaustmanifold.Inthissectiontheaccuracyofone-andmulti-dimensionalmodels of pipe junctions is assessed. The angular displacement,withrespecttoeachother,ofthepipesformingthejunctionaffectsthemagnitudeofthetransmittedandreflectedwaveswhich are incident upon it. Other characteristics of the junction,forexamplethewaythepipeendsareprofiledtoformit,alsoaffectthetransmissionandreflectioncharacteristicsbutaregovernedbymulti-dimensionalfeatureswhichcannotberesolved using a one-dimensional model.Three-Pipe JunctionCentral to the rig is the modular junction capable of generatingT- and Y-junctions of various angular orientations, similar tothetypesofpipejunctionfoundintheexhaustandintakesystemsofinternalcombustionengines.Ashockwaveissentdown the rig towards the junction and the pressure time historyisrecordedusingpiezo-resistivetransducers,shownschematically in Figure 2(a). Further details of this rig are givenin[19,20].Figure2(b)showsthemeasuredpressure/timehistory at the three different transducer locations from the sametest (the repeatability of the experiments was extremely good, asdiscussedin[20]).Thedifferentpressurelevelsofthetransmittedwavesthroughthejunctionareimmediatelyapparent.TheincidentshockwavepassestransducerP1andisreflectedasararefactionwavebackintothesamepipe.Thejunction geometry, specifically the different angular dispositionof the pipes, causes the transmitted pressure level at location P3tobesignificantlyhigherthanthetransmittedpressurelevelatlocation P2.Figure2(c)showsacomparisonofmeasuredandpredictedpressure/timehistories.Inthiscasethepredictionsaremadeusingthetwo-dimensionalinviscidmodeldescribedbyBattenetal.[21].Itcanbeseenthatthephaseandamplitudeofthetwo transmitted waves (P2 and P3) and the reflected wave (P1)are well predicted, and the higher frequency components of thepressure variation are also captured. Examination of a sequenceof schlieren images depicting the propagation of the shock frontthroughthisjunction,presentedin[20],showsthatthesehigh-frequencyoscillationsaremostlyduetothepropagationandreflection of the pressure waves perpendicular to the axis of thepipes.Figures2(d)and2(e)showcomparisonsofmeasurementswithpredictionsmadeusingaone-dimensionalmodel(intheworkpresented in this paper this wasLotusEngineSimulation).Itisimmediatelyapparentthatthehigherfrequencycomponentsofthe pressure / time history are not resolved as a one-dimensionalmodelclearlycanonlycharacterisephenomenawhichvaryalongtheaxisofthepipes.Thepurposeofthesemodels,however,issimplytopredictthemeanpressurelevelofthetransmittedandreflectedwaves.ThepredictionsshowninFigure 2(d) were calculated using the constant-pressure modelwhichassumesthattheinstantaneouspressurelevelattheendofeachpipeformingthejunctionisequal[16,22].Thepredicted pressure levels at transducers P2 and P3 are thereforeequal. The pressure level induced by the rarefaction wave at P1isslightlyhigherthanthelevelsatP2andP3.Thisisbecausethetransducerpositionsarenotcoincidentatthepointofthejunction and the velocity levelinducedbytherarefactionwavediffers from that induced by the pressure waves at positionsP2and P3.ThepredictionsshowninFigure2(e)arecalculatedusingthegeneralised pressure-loss junction model described in [22]. Thismodelusesanexpressionderivedfromtheapplicationof3 Copyright 2006 by ASMEmomentumequationstothejunctioninordertoderiveatermforthepressure-lossbetweenanytwopipebrancheswhichisused in the boundary equation. The results from this model giveanexcellentpredictionofthemeanpressurelevelsofthetransmitted waves. The error in the prediction of the level of thereflectedwaveatP1isduetothedifficultyofdefininganequivalentone-dimensionalmodelwhichconsistentlyrepresentstheexpansionratioseenbytheincidentshockwaveat the junction.Figure 2(a). Schematic showing geometry andtransducer locations of the Y-junction.1.0E+051.2E+051.4E+051.6E+051.8E+052.0E+050.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03Time / [s]Pressure / [N/m]P1P2P32(b)1.0E+051.2E+051.4E+051.6E+051.8E+052.0E+050.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03Time / [s]Pressure / [N/m]Measured2D CalculatedP1P2P32(c)1.0E+051.2E+051.4E+051.6E+051.8E+052.0E+050.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03Time / [s]Pressure / [N/m]Measured1D constant pressureP1P2P32(d)1.0E+051.2E+051.4E+051.6E+051.8E+052.0E+050.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03Time / [s]Pressure / [N/m]Measured1D with loss modelP1P2P32(e)Figure 2(b)-(e). Y-junction: comparison of measuredand calculated pressures for different models.Multi-Pipe Junction for Racing EngineTheresultsdiscussedinthissectionweregeneratedfromashock-tube rig using a five-into-onejunction,ofthetypefoundin the exhaust system of a V10 F1 engine. The rig was designedandbuiltbytheauthorsnowaffiliatedtotheRenaultF1TeamEngineDivision.Figure3(a)showsthesideandendviewsofthejunctiontested-theanglebetweentheprimaryandsecondarypipesforthisjunctionis140degrees.Itisapparentthat, in contrast to the junction shown in Figure 2(a), the flow inthisjunctionisthree-dimensionalinnature.Ashockwaveisgenerated by pressurising a short driving tube and then burstinga diaphragm. This wave travels into the junction through one oftheexhaustprimaryrunners(PipeAinFigure3(a))andpropagatesintothesecondarypipe(ortailpipe),seenontheright of the side view of the junction, and into the other exhaustprimaryrunnerswhichhaveclosedends.Thetroughinthepressuretracejustbeyond0.008secondsiscausedbytherarefaction wave reflected at the junction.4 Copyright 2006 by ASMEFigure 3(b) shows a comparison of the measured pressure / timehistoryintheincidentrunnerpipe(PipeA)withresultspredictedusingtheone-dimensionalmodelandathree-dimensionalCFDcode(FLUENT).Bothmodelspredictthephase and amplitude of the pressure wave dynamics well. Thereisaslightdiscrepancyinthephasingoftheone-dimensionalresults,duetothetranslationofthejunctiongeometryintoaone-dimensionalmodel.Thethree-dimensionalCFDmodel,asexpected, gives a more accurate prediction of the detailed formof the pressure variation.Figure3(c)showsacomparisonofmeasuredandpredictedpressurevariationinpipeB,adjacenttothepipeinwhichtheshockwavewasincidentuponthejunction(pipeA).Amuchloweramplitudewavethantheincidentwavepropagatesintopipe B. Again, both the one-dimensional and three-dimensionalmodelsgivegoodpredictionsofthepressurevariation.Thesimplicityoftheformermodelmakesitanextremelyefficientapproachtoincorporatingtheeffectsofthesecomplexcomponents in an engine-cycle simulation program.Figure4showsacomparisonofmeasuredandpredictedpoweroutputfromaV-10Formula1racingenginefittedwithafive-into-oneexhaustsystem of the type shown in Figure 3(a). The exhaustsystem gas dynamics have a significant effect on theperformanceofthistypeofveryhigh-speedengine.Thequalityofthecorrelationindicatesthattheexhausttuningoftheengineisbeingaccuratelypredicted.Figure 3(a). Five-into-one junction for F1 engine.8.00E+049.00E+041.00E+051.10E+051.20E+051.30E+051.40E+051.50E+051.60E+050.004 0.006 0.008 0.01 0.012 0.014 0.016Time / [s]Pressure / [N/m]Pipe A - measuredPipe A - predicted 3-DPipe A - predicted 1-DFigure 3(b). Five-into-one junction: measured andpredicted pressure variation in pipe A.9.00E+049.50E+041.00E+051.05E+051.10E+051.15E+051.20E+050.004 0.006 0.008 0.01 0.012 0.014 0.016Time / [s]Pressure / [N/m]Pipe B - measuredPipe B - predicted 3-DPipe B - predicted 1-DFigure 3(c). Five-into-one junction: measured andpredicted pressure variation in pipe B.Figure 4. Comparison of measured and predictedpower output for V-10 Formula 1 engine.5 Copyright 2006 by ASMEEMPIRICAL APPROACHES AND THEIR LIMITATIONSItiscommontoattempttocalculatethetunedexhaustrunnerlengthusinganalyticalmethods.Thesimplestoftheseapproaches involves calculating the time required for a pressurewavetopropagatedowntheexhaustrunnerandreturntotheexhaustvalveasararefactionwaveafterbeingreflectedattheend of therunner.Thisapparentlystraightforwardprocedureisfraughtwithdifficultybecausethepropagationspeedofthepressureandrarefactionwavesdifferssignificantlyfromthespeedofsoundinanundisturbedgas.Inadditiontothis,thelarge particle velocity imparted by the pressure wave delays thereturn of the rarefaction wave.Figure5(a)showsthepressure/crankanglehistoryintheexhaust port (point A) of the virtual high-performancesingle-cylinder engine shown in Figure 1, at 7000 rev/min. The lengthoftheexhaustpipeandexhaustvalve-closinganglearewellmatchedsothatalow-pressurelevelisproducedduringthevalveoverlapperiod.Theintakesystemisalsowelltunedatthisspeed.Thehighpressureattheintakevalveopeningpoint(exceedingthecylinderandexhaustportpressures)ensuresthereisnoreverseflowintotheintakesystem.Thehighpressure in the period after bottom-dead-centre of the inductionstrokeextendsthecylinderchargingsothatavolumetricefficiency of 122% is achieved.Simplisticattemptsatdesigningtheexhaustsystemforthisenginewouldusuallyinvolvecalculatingthetimeforthepeakoftheblowdownpulsetoreturntotheexhaustvalveasthetroughoftherarefactionwave.ItcanbeseeninFigure5thatthisperiodisapproximately170degreescrankangle,whichequatesto4.0510-3secondsatanenginespeedof7000rev/min. In this case calculating the time required for a wave topropagate to the end of the pipe and return to the exhaust valve,usingacombinedportandexhaustrunnerlengthof725mmandameanspeedofsoundofabout690ms-1(takenfromthesimulation model), gives 2.10 10-3 seconds. Clearly, if used tocalculate the optimum pipe length for a particular engine speed,this approach would lead to a large discrepancy with the valuespredictedbysolvingthegoverningequationsofone-dimensionalgasdynamicsinthepipes.Thereasonsforthisdiscrepancy are discussed below.Because the waves are nonlinear, the divergences of the speedsof equal amplitude compression and rarefaction waves from themean speed of sound do not cancel each other out. This can beseenbyconsideringtheparticleandwavespeedscreatedbypressureandrarefactionwavespropagatinginanundisturbedgas [16,17,23,24].The particle velocity induced by the passage of a nonlinearwave is given by02100112upp au +]]]]]

,`

.|(1)where 0a and 0u arethespeedofsoundandtheparticlevelocityintheundisturbedgas,respectively.Thepropagationspeed, c, of a point on the wave at pressure p isthesumofthelocal gas velocity and the local speed of sound and is given by( )0210012112upp ac +]]]]]

,`

.| +(2)Itcanbeseenfromequation(2)thatthepropagationspeedofpointsinawaveincreaseasthepressureincreases;thiswillresultintheformofthewavedistortingasthehigh-pressureregionstravelfasterthanthelow-pressureregions.Forairthevalueoftheratioofspecificheats,,is7/5andequations(1)-(2) become:07 / 1001 5 uppa u +]]]]

,`

.| ;07 / 1005 6 uppa c +]]]]

,`

.| (3,4)Forapointonanon-linearpressurewavewhere(p/p0)=1.6(commonlyencounteredinbothintakeandexhaustmanifolds)equations (3) and (4) give0 0347 . 0 u a u + and0 0417 . 1 u a c + ,showingthatthewavepropagatesintoanundisturbedgas(u0=0) at a speed which is 42 per cent higher than thespeedofsound based on the undisturbed gas temperature. The passing ofthe wave imparts a velocity to the gas molecules of about 35 percent of the undisturbed speed of sound.Forapointonararefactionwavewherep/p0=0.4(i.e.0.6barbelow an ambient pressure of 1 bar) equations (3) and (4) give0 0613 . 0 u a u + and0 0264 . 0 u a c + ,showingthatthewavepropagatesataspeedwhichisonly26percentofthespeedofsoundbasedontheundisturbedgastemperature.Thepassingofthewaveimpartsanegativevelocityonthegasmoleculesofabout61percentoftheundisturbed speed of sound.When(p/p0)=0.2791thepropagationspeedfornon-linearwaves(equation(4))iszero(inair,=1.4).Thepropagationspeedbecomesnegativeatpressureratioslessthanthisvalueduetothenegativeparticlevelocitybeinggreaterthanthepositive propagation speed relative to the gas. In the case of thestationary wave, the gas speed in the backwards direction is justequal to the local speed of sound [23].HavingestablishedtheseprinciplesofnonlinearwavepropagationthepredictedresultsshowninFigure2fromthesingle-cylinderenginecanbere-examined,withaviewtodiscoveringwhythepressurewaveintheexhaustsystemtakesmuchlongertotraversetheexhaustsystemthanasimplecalculationwouldsuggest.ItispossibletodecomposetheresultantpressurevariationshowninFigure5(a)into6 Copyright 2006 by ASMEcomponentpressurewaveswhichtravelinoppositedirections[16]. The variation of these component waves during an enginecyclehasbeenplottedinFigures5(b)and5(c)atlocationsAand B in the exhaust system (see Figure 1). In Figure 5(b) it canbeseenthattheforward-travellingwave(fromtheexhaustvalve to the open end of the pipe) takes about 30 degrees crankangle to travel from point A to point B, shown in Figure 1. Thereverse-travellingwave,showninFigure5(c),takesapproximately 140 degrees crank angle to travel from point B topoint A, due to the disproportionatelylowerpropagationspeedoftherarefactionwavediscussedabove.Thisillustratesthedifficultyofusinganaveragespeedofsoundinordertoevaluateexhaustsystemtuningeffectsasadvocatedbysomeworkers [17].Figure 5(a). Single-cylinder engine: variation ofresultant pressure with crank angle at exhaust valve(point A) - 7000 rev/min.Figure 5(b). Single-cylinder engine: forward-travellingcomponent pressure wave at each end of exhaustpipe 7000 rev/min.Figure 5(c). Single-cylinder engine: reverse-travellingcomponent pressure wave at each end of exhaustpipe 7000 rev/min.SINGLE-CYLINDER ENGINEThebasictuningofahigh-performancesingle-cylinderenginehasbeenpreviouslydiscussed[25].Inthepresentwork,onlytheeffectsoftheexhaustsystemwillbediscussed.Figure6showsthevolumetricefficiency/speedcurveforthehypotheticalsingle-cylinderengineshowninFigure1withvarious intake pipe lengths. The heavy line shows the results fortheenginefittedwitha650mmexhaustpipe(with50mmdiameter)anda225mmintakepipe.TheresultantandcomponentpressurevariationshowninFigures5(b)-5(d)corresponds to this intake and exhaust system geometry. Figure6showsthattheunderlyingshapeofthecurveisdictatedmainly by the intake system whilst Figure 7 shows that the localpeaksandtroughsareinfluencedbythedesignoftheexhaustsystem but that the underlying performance characteristic is notaffected.Thecauseofthepeakat7000rev/minhasalreadybeendiscussed and the pressure / time history at the exhaust valve isre-plottedinFigure8forthecaseofthe650mmexhaustpipe.Thepressurevariationattheexhaustvalveatenginespeedsof4500rev/minand2500rev/minarealsoshowninFigure8.Itcanbeseenthat,atthelowerenginespeeds,ahighpressurelevelprevailsattheexhaustvalveduringthevalveoverlapperiod,whichexceedstheamplitudeofthepressureinthecylinder and the intake pipe (not shown), causing a reverse flowof residual gas into the intake system. The consequent reductioninthemassoffreshchargethecylinderisabletoingestgivesrise to a trough in the volumetric efficiency curve.Performanceoptimisationisaniterativeprocessinwhichtheinteractionofmanyparametersisexamined.Aspartofthisprocesstheeffectsoflengthoftheexhaustpipeelementsandthetimingoftheexhaustvalveeventsneedtobeanalysedtogether.Figure9showshowthevolumetricefficiencyoftheenginevarieswithbothexhaustrunnerlengthandexhaust-valve-closing (EVC) timing at 2500 rev/min. It is apparentthat7 Copyright 2006 by ASMEmaximumvolumetricefficiencyatthisspeedisachievedwithan exhaust runner length of about 500mm and an exhaust-valve-closingtimingof70degreescrankangleaftertop-dead-centre.Atotherenginespeedstheoptimumcombinationsofexhaustpipe length and EVC timing differ.Figure 6. Single-cylinder engine: variation ofvolumetric efficiency with engine speed for variousintake pipe lengths.Figure 7. Single-cylinder engine: variation ofvolumetric efficiency with engine speed for variousexhaust pipe lengths.Figure 8. Single-cylinder engine: variation of resultantpressure with crank angle at exhaust valve(pointA) for various engine speeds.Figure 9. Single-cylinder engine: volumetric efficiencycontours as a function of exhaust runner length andexhaust valve closing timing.TWIN-CYLINDER ENGINEThe tuning mechanisms in exhaust manifolds for multi-cylinderenginesaremoredifficulttounderstandbecauseoftheincreasednumberofsitesforgeneratingwavereflections.Inthissectionatwin-cylinderengineisconsideredinordertoprovidethesimplesttypeofmulti-cylindermanifold.Figure10(a)showsamodelofatwin-cylinderenginebasedonthevirtualsingle-cylinderenginediscussedinSection4.Thefiringintervalbetweenthetwocylindersis360degreescrankangle.Inthismodeltheexhaustprimaryrunnerpipesareidenticaltothatusedinthesingle-cylinderenginemodeltogeneratetheresultsshownFigure5(i.e.650mmlong,50mmdiameter). These pipes have been joined together to form a 170degree-Y-junctionwithasecondarypipeof60mmdiameter.Figure10(b)showsthesensitivityoftheenginevolumetricefficiencytothelengthofthesecondaryexhaustpipe.Inthiscase,increasingthesecondarypipeslengthgenerallydecreasesthe performance of the peak volumetric efficiency of the enginebutgivesbenefitsatparticularpointsfurtherdownthespeedrange.Thepressure/timehistoryattheexhaustvalveat7000and4500rev/minareshowninFigures11(a)and11(b)forsecondarypipelengthsof100mmand800mm.Thepressure/time history for the single-cylinder model discussed in Section 4isalsoshown(labelledasindividualprimarypipesastheresultisobviouslytheequivalentofmodellingatwin-cylinderenginewiththesameexhaustmanifoldgeometryasthesingle-cylinderengine).Itcanbeseenthatconnectingthecylinderstogetherwiththe100mmsecondarypipegivesremarkablysimilarpressurevariationat7000rev/minbetween90and450degreescrankangle(i.e.fortheentireopeningdurationoftheexhaust valve) to that obtained from the single-cylinder engine.At 4500 rev/min the phasing and amplitude of the waves differssomewhatmoreacrossthecyclebetweenthesingle-cylinderengine and the twin-cylinder engine fitted with a 100mm8 Copyright 2006 by ASMEsecondary pipe but the timing of the peakofthepressurewaveandthereturningrarefactionwaveisverysimilar.Forthesereasonsthevolumetricefficiencycharacteristicofthetwin-cylinder engine with the 100mm secondary exhaust pipe and thesingle-cylinder engine are similar.Figure 10(a). Cycle simulation model of twin-cylinderengine.Figure 10(b). Twin-cylinder engine: variation ofvolumetric with engine speed for various secondaryexhaust pipe lengths.Figure 11(a). Twin-cylinder engine: variation ofresultant pressure at the exhaust valve (point A) withcrank angle for various secondary pipe lengths 7000 rev/min.Figure 11(b). Twin-cylinder engine: variation ofresultant pressure at the exhaust valve (point A) withcrank angle for various secondary pipe lengths 4500 rev/min.Figure 12(a). Twin-cylinder engine: variation offorward-travelling component pressure waves withcrank angle for a secondary pipe length of 800mm 4500 rev/min.Figure 12(b). Twin-cylinder engine: variation ofreverse-travelling component pressure waves withcrank angle for a secondary pipe length of 800mm 4500 rev/min.9 Copyright 2006 by ASMEWhenthe800mmsecondarypipeisfittedtothetwin-cylinderenginethevolumetricefficiencyoftheenginedifferssignificantlyfromthatofthesingle-cylinderengine.At7000rev/min the 800mm secondary pipe produces a high pressure atthe exhaust valve in the valve overlap period this reduces thevolumetric efficiency by about nine percentage points. At 4500rev/minthevolumetricefficiencyofthetwin-cylinderenginefittedwiththe800mmsecondarypipeisaboutninepercentagepoints higher than the single-cylinder engine and ten percentagepointshigherthanthetwin-cylinderfittedwiththe100mmsecondary pipe. The low volumetric efficiency levels are causedby the presence of a high- pressure level at the exhaust valve atthestartofthevalve-overlapperiod.Withthe800mmsecondary pipe a second rarefaction wave arrives to prolong thelowpressurecreatedbythereflectedblowdownpulseintothevalve overlap period.Theoriginofthissecondrarefactionwavecanbedeterminedby considering the component pressure waves shown in Figures12(a)and12(b).Forward-travelling(lefttoright)component-pressure waves are shown in Figure 12(a) at points A, B, and CinFigure10(a).Itisclearthattheforward-travellingwavesinitiatedattheexhaustvalvesAandB,atabout200and560degreescrankangle,causethetwopeaksintheforward-travellingwavesatpointCoccurringatabout220and580degreescrankangle.Thereverse-travelling(righttoleft)componentpressurewavesshowninFigure12(b)indicatethatthe extension of the low-pressure region in Figure 11(b), for the800mmsecondarypipe,isduetothepropagationoftherarefaction wave, created at the end of the secondary pipe, backupstreamtotheexhaustvalvethroughthejunction.Itisthismechanismwhichenhancesthevolumetricefficiencyat4500rev/minwiththelongsecondarypipe.Afurthereffectcausedbythesecondarypipeisthat,bypropagatingandreflectingwaveswithinitself,itmodifiesthedownstreamboundarycondition for the wave reflection process at the primary pipe.FOUR-CYLINDER ENGINEAfour-cylinderversionofthevirtualsingle-cylinderenginediscussedinSection4isconsideredinthissection.Againthelengthoftheexhaustprimaryrunnerpipesis650mm.Thesepipes have been joined together to form a 170 degree four-into-onejunction,showninFigure13,withasecondarypipeof70mmdiameter.ThesimulationmodelisalsoshowninFigure13.Figure14showshowthevolumetricefficiencyoftheengine varies with the length of the secondary pipe. In this casethesecondarypipeappearstohavelittleimpactonthepeakvolumetricefficiencyoftheengine.Thisisbecausetheresultant pressure variation at the exhaust port is similar to thatofthesingle-cylindermodel(casewithindividualprimaryrunners) fortherangeofsecondarypipelengthsconsidered,asshowninFigure15.Thisbehaviourdiffersfromthatofthetwin-cylinderenginewherethesecondarypipelengthimpactstheenginevolumetricefficiencyacrossthespeedrange.Withthefour-into-oneexhaustmanifoldthesecondarypipelengthcan be chosen to improve the volumetric efficiency at several ofthelow-speedoperatingpoints(withsomeoptionsalsogivingsmallimprovementsatthehighestenginespeeds)withoutcompromising the peak level.170Figure 13. Models of four-cylinder engine: four-into-one exhaust manifold.Figure 14. Four-cylinder engine with four-into-oneexhaust manifold: variation of volumetric with enginespeed for various secondary exhaust pipe lengths.Figure 15. Four-cylinder engine with four-into-oneexhaust manifold: variation of pressure with crankangle at the exhaust valve for various secondaryexhaust pipe lengths.10 Copyright 2006 by ASMECONCLUSIONSGasdynamicsintheexhaustsystemofinternalcombustionengineshaveasignificanteffectontheirperformance.Apressure-loss-junctionmodel,developedbyBassett[20],hasbeenvalidatedforthepropagationofpressurewavesthroughboth simple Y-junctions and a five-into-one junction of the typeused in V10 Formula 1 engines. Simple empirical approaches todesigningexhaustsystemsneglectthelargedifferenceinpropagationspeedoftheforward-andreverse-travellingcomponentpressurewavesthatcanleadtolargeerrorsinthecalculationoftunedlengths.Theprimaryexhaustsystemtuningmechanisminvolvesproducingalow-pressureregionduringthevalve-overlapperiod.Thisisachievedbyutilisingthereflectionoftheexhaustblowdownpulseattheendoftheprimarypipewhichreturnstothevalveasararefactionwave.In multi-cylinder engines the duration and amplitude of the low-pressureregionproducedbythisrarefactionwavecanbeincreasedbythearrivalattheexhaustvalveofararefactionwave that has been created by a reflection process at the end ofthe secondary pipe. This effect can remove or ameliorate dips inthe volumetric efficiency / speed curveandproducebenefitsinthemid-speedrangecomparedwithfittingindividualpipestothe cylinders.REFERENCES1.Koester, E.W. Luftkompressoran. ZVDI, 48, pp. 109-118, 1904.2.Farmer, H.O. Exhaust systems of two-stroke engines. Proc. Instn.Mech. Engrs., 138, pp. 367-390, 1938.3.Morrison,J.C.Theproblemofexhaustsilencingandengineefficiency. Proc. Instn. Auto. Engrs., 27, pp. 614-647, 1932-3.4.Morrison, J.C. Exhaust systems for four and six-cylinder engines,with notes on induction and exhaust gas phenomena. Proc. Instn.Auto. Engrs., 34, pp. 211-252, 1939-40.5.Mucklow,G.F.Exhaust-pipeeffectsinasingle-cylinderfour-stroke engine. Proc. Instn. Mech. Engrs., 143, pp. 109-127, 1940.6.Schweitzer,P.H.Improvingengineperformancebyexhaustpipetuning. J. American Soc. Naval Engnrs., 56, pp. 185-212, 1944.7.Williams,T.J.Exhaustarrangementsandtheirinfluenceonthepower output of internal-combustion engines. Proc. Instn. Mech.Engrs., 168, pp. 947-955, 1954.8.Wallace,F.J.,andMitchell,R.W.S.Waveactionfollowingthesudden release of air through an engine port system. Proc. Instn.Mech. 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