A Theoretical model showing the effects of the fuel induced gamma effect

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A Theoretical model showing the effects of the fuel

induced gamma effect

Bryan Bordeleau

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A

THEORETICAL MODEL SHOWING THE EFFECTS OF THE

FUEL INDUCED GAMMA EFFECT

Bryan A. Bordeleau

Mechanical Engineering Department

Rochester Institute of Technology

Rochester, NY

A Thesis Submitted in

Partial Fulfillment of the

Requirements for the

Degree of

MASTER OF SCIENCE

In

Mechanical Engineering

Approved by: Professor

_

Dr.

A.

Nye, Thesis Advisor

Professor

-Dr. F. Sciremammano

Industry Sponsor

_

L. Markle

Dr. S. Kandlikar, Dept. Head

Professor

DEPARTMENT OF MECHANICAL

ENGINEERING

COLLEGE OF

ENGINEERING

ROCHESTER

INSTITUTE OF TECHNOLOGY

2000

Copyright Information

This volumeisthe_propertyofthe

Institute,

butthe

literary

rights oftheauthor mustbe

respected. Passages must notbecopied or_closelyparaphrased withoutthe previous

written consent ofthe author. Ifthereader obtains_any assistancefrom_{this volume,}heor

she must give proper creditin hisorherown work.

The

following

persons,whose signatures attesttheiracceptance oftheabove_{restrictions,}

haveusedthis thesis:

PERMISSION TO REPRODUCE

Thesis Title: "A Theoretical Model

Showing

theEffectsoftheFuel Induce Gamma

Effect"

I,

Bryan A.

Bordeleau,

hereby

grant permission totheWallace Memorial

Library

ofthe

Rochester Institute of

Technology

toreproduce _mythesisinwholeorinpart.

Any

reproduction can notbeused_commerciallyorforprofit.

Forward

Ithas beena

long

anddifficultprocesstocompletethis thesis.

Many

long

hours

andlatenights have beenspent_researchingand _writing, anditallhas beenworthit. This

period oftimehasalsobeen difficult forthose around_{me,especially formy friend} and

loving

wife, Carrie. I'd like to thank_{her very}much, for givingme allhersupport,

love,

and

kindness,

andfor

helping

me_{every step}oftheway.

Also Iwouldliketo thank_{my Mom}andDad foralltheirsupport.

They

have

given me _{guidance,encouragement,}and understanding.

They

have instilled inmethe

determinationtosucceedinallthatI do.

Aspecialthanksgoesto_mygrandparents, whohave always supported_{my dreams}

and goals.

Withoutthe

help

andknowledgeofLee Markle andPaul

VanBrocklin,

atDelphi

Automotive

Systems,

thisproject wouldhavenever gotten offtheground.

And

finally,

Iwantto thank"Doc"

Nye,

forallhis

help

and guidance. Without

Nomenclature

Symbols

As

Surface Area

[cm2]

b y-interceptof aline

[cm]

B Bore

[cm]

Bp

Bisection Methodproduct

C,

K Constants

cp Specific heatat constant pressure

[kJ/kg-K]

Cv Specific heatat constant volume

[kJ/kg-K]

E Total

Energy

[kJ]

h _{Specific enthalpy}

[kJ/kg]

or cylinderheight

[cm]

hx

Heattransfercoefficient [kW/m

K]

U

Latent heatof vaporization

[kJ/kg]

m Mass

[kg]

M Molecularweight

[kg]

P Pressure

[kPa]

Q

Heattransfer

[kJ]

Qxy

Heattransferbetween states x and_y

[kJ]

r Radius

[cm]

rv Compressionratio

R Gas constant

[kJ/kg-K]

Ru

Universal gas constant

[kJ/kg-K]

T Temperature

[K]

u Specific internal energy

[kJ/kg]

U _{Internal energy}

[kJ]

V Volume

[cm3]

w Work

[kJ]

x, y Graphicalcoordinates

[cm]

Acronyms BDC CA DI-G FIGE KE LIEF PE TDC

Bottom Dead Center

CrankAngle Degrees

Direct InjectionGasoline

Fuel Induced GammaEffect

Kinetic

Energy

Laser Induced ExciplexFluorescence

Potential

Energy

Greek Letters

A 'Hotto 7

Change

Otto cycle_efficiency Specificheatratio

Subscripts

air _In-cylinderair

ave Average

calc _Calculated

clear Clearance

cyl Cylinder

data Experimental data

f Final

fuel Evaporated fuel

i Initial

loss Loss duetoleaks

max Maximum

min Minimum

resid Residual

s SlopeorSurface

tot Total

TableofContents

COPYRIGHT INFORMATION II

FORWARD IV

NOMENCLATURE V

Symbols v

Acronyms v

Greek Letters vi

Subscripts vi

ABSTRACT X

1. INTRODUCTION 1

2. THE THEORY AND HISTORY OF FUEL INJECTED INTERNAL COMBUSTION ENGINES 3

2.1 Thermodynamic Theory 3

2.1.1 The First Law_ofThermodynamics 3

2.1.2 Ideal Gases 4

2.1.3 Heat Transfer 8

2.1.4 Work 10

2.1.5 The Otto Cycle 11

2.2 Fuel Injection Devices 18

2.2.1 Carburation 18

2.2.2 Port Fuel Injection 19

2.2.3 Direct Injection 20

3. STATE-OF-THE-ART FUEL QUALITY MEASUREMENT TECHNIQUES 22

3.1 Fiber Optic Spark Plug Probe 22

3.2 The Optical Engine 23

3.3 The Argon Ion Laser Technique 23

3.4Laser-Induced Fluorescence 24

3.5 The Fuel Induced Gamma Effect 25

4. DEVELOPING ASIMPLE,INEXPENSIVE TECHNIQUE 26

5. THEEXPERIMENTALSETUPAND PROCEDURE 29

5.1 Setup 29

5.2 Procedure 31

6. DETAILED ANALYSIS OF THE FIGE MODEL 33

6.1 Introductionto theModel 33

6.2 DevelopingandCalibratingtheModel 33

6.2.1 Effective _ClosingAngle 38

6.2.2 Mass Loss 38

6.2.3 HeatTransfer 43

6.2.4Residuals 48

6.2.5_Puttingit AllTogether 49

6.3.1 Fuel InjectionandtheFIGE Process 52

6.3.2

Deriving

theEvaporatedMass Equation 53

7.RESULTS 58

7.1 FIGEDevelopment 58

7.2 FIGECalibration 61

7.3EvaporatedFuel Mass Calculation 64

8. CONCLUSIONSANDRECOMMENDATIONS 68

8.1 TheMotoringCase 69

8.2 The Fuel Injection Case 71

8.3 Evaporated Fuel Mass 72

REFERENCES 76

APPENDIX A. MASSLOSS CALCULATION 77

APPENDIX B. RESIDUAL MASS CALCULATIONS 78

TableofFigures

Figure 2. 1 ApVDiagramof10kg ofAir 7

Figure 2. 2Schematicof aPiston-Cylinder Assembly 15

Figure 2. 3 AFour-StrokeEnginepVDiagram 16

Figure 2. 4 The Otto Cycle 17

T7rnimr.fi ITTTrrn rirmnnrmnrrnnFtnwr)T,.,nn,M M

Figure 6. 2 Mass Lossas aFunctionofIn-CylinderPressure 42

Figure 6. 3 Heat Transfer Coefficientas aFunctionofCrank Angle 47

Figure6. 4 FIGE Process Flow Including Losses 51

Figure 7. 1 apVDiagramofFIGE Motoring Data Without Losses 59

Figure 7. 2 Percent ErrorinPressureas aFunctionofCylinder Volume 60

Figure 7.3 ApVDiagramofFIGEMotoring Data Including Losses 62

Figure 7.4 Percent ErrorinPressureas aFunctionofCylinder Volume Including Losses 63

Figure 7.5 ApVDiagramofFuel Injected FIGE Data 65

Figure7.6 Percent ErrorinPressureas aFunctionofCylinder VolumeforFuel Injection...66

Abstract

The Fuel Induced Gamma Effectuses pressuredatafromasingle-cylinder

direct-injectionengine andinformationaboutthe specificheat_{ratio, gamma,}oftheinjected fuel

topredicttheevaporatedfuelmassin thepiston-cylinder assembly. Thermodynamic

theory

andidealgaslaws are usedtocalculatetheoreticalpressure withinthecylinder

andthispressureis thencomparedtothe actual pressure measuredintheengine. The

difference ingammabetweenthecalculated and actualstates ofthefuel isthen usedto

predicthowmuch fuel hasevaporatedinthe cylinder.

Thissimplistic approach also takesinto accountinformation abouttheresidualsin

the cylinder, massloss from_{the system,} andheat losses.

Combining

thesefactorswith

thermodynamic

theory

resultsin a_veryaccurate model which can predicttheevaporation

1. Introduction

Thecost of_{fuel has risen significantly}overthepastfew decades. This has driven

theautomotive

industry

to

develop

cheaper and more efficientinternalcombustion

engines. Onesuchdevelopment isthegasolinedirect-injectioninternal combustion

engine. This

technology

offersimproved fuel economy andfeweremissions.

Also,

the

power outputofthis typeof engine will remainthesame as or_{potentially improveover,}

current portfuel-injectedengines. There are_manyaspects ofthis typeof combustion

technology

thatwill needtobeaddressedinorderfor ittomeetits fullpotential.

Theconcept of_predictingthe amount offuelpresent atthe timeofignition has

beenstudiedinrecent years. A simple,inexpensivetechniquethatisvalidformost

engine configurationshasyettobedeveloped. Thegoal ofthis _{study is} tousetheoretical

equations and asimple engine _setupto

develop

an evaporation profile oftheinjected fuel fromthetimeofinjection untilignitionoccurs.

The Fuel Induced Gamma Effect technique,

FIGE,

was chosenforthis _study

becauseofits simplicityandbecauseothertechniques_onlyprovided subjective results.

The FIGEprocess canbeused todeterminetheevaporation profile offuel injectedinto

anyengine. Itis notinfluenced

by

the_{injection spray}patternor engine configuration.

Previoustechniques used_{costly laser}

imaging

equipment and were _{very difficult}andtime

consumingtoimplement. The FIGEtechniqueis simplebecauseitcanbeused on_any

direct-injectionengine equippedwith a pressuretransducer.

Inthepresentwork,pressuredata fromasingle-cylinderdirect-injectionengine

andinformationaboutthe specificheatratio of

isooctane,

theinjected

fuel,

will beused

predictthein-cylinderpressure at_everycrank angle. The specificheatratiois calculated

attheseconditions and comparedto thecalculated specificheatratiobasedontheengine

testresults. The difference intheseratiosis thenusedtocalculate themass of evaporated

fuelpresentinthe cylinder. Thesecalculations canbeperformedon a crank angle

by

crank anglebasis. Theresultis a graphical representation oftheevaporation profile. The

profile canthenbeusedto predictwhenignition should occur orthe liquidtovapor ratio

ofthefuelatthe timeofignitionif ignition does occur. This informationwill leadto

2.

The

Theory

and

History

ofFuelInjected

Internal

Combustion Engines

2.1

Thermodynamic

Theory

Internalcombustionengines usethecombustion offueltoconvert chemical

energy intomechanicalwork output. To accomplish_this, thechemical_energymustfirst

beconvertedto the_{internal energy}ofthegaseous medium. Thisinternalenergy,in turn,

isconvertedtomechanical work output. Theconversionin thefirststageis dependent

uponthe typeoffuelthatisused and canbequantified_usingabombcalorimeterto

measure the

heating

_value, or_enthalpyofformation. Thermodynamicprocesses canbe

usedtomodelthesecond _{stage; these}processes willbeexplainedin detail.

Furthermore,

once a combustion cycleis modeled_{using thermodynamics, it}can

becomparedtoa real cycle. Ifthe theoreticalmodel_accuratelypredicts real engine

cycles, itcanbeusedtooptimize engine performance parameters. Atheoreticalmodel

willbe discussedtogive abetter understandingoftheprocessesinvolved inthe

combustion cycle.

Parametersimportanttoengineperformanceinclude air/fuelratio,

timing

offuel

enteringthe cylinder,andignitiontiming. Engines haveuseddifferentsystemsto

introduce fuel intothecylinder,

including

carburetors,portfuel

injection,

anddirect fuel

injection. The

history

ofthesesystems will alsobe discussed later inthissection.

2.1.1

The

First Law of

Thermodynamics

A basic knowledgeofthermodynamic

theory

_{is necessary}to_completely

point forthismaterial. The FirstLaw statesthat thetotal changeof_energywithin a

systemisequal tothenet_energytransferredtothe system

by

heattransferminusthenet

workdone

by

thesystem. Thiscanbewrittenin equationformas

AE= Q-W

(2-1)

where

AE=AKE+APE+AU

(2-2)

andAKE is thechangein kineticenergy,APEisthechangeinpotential_energy,AUisthe

changein internalenergy,

Q

is heattransfer to_{the system,} andW is theworkdone

by

the

system.

Thechangeintotal_energyof a_system,

AE,

ismade_upofthree_{contributions,}as

shown above. Thechangein kinetic energy isassociated withthemotion ofthesystem

as a_whole,relativeto an external coordinateframe. Thechangeingravitational potential

energy is associated withtheposition ofthesystem as a wholeintheearth's gravitational

field. Internal energy isan extensive_propertyofthesystem andincludes all other_energy

changes (Moranand

Shapiro,

1995).

2.1.2 Ideal

Gases

Ideal gases areanintegralpart ofthe_studyofthermodynamics andthus_playan

importantroleincombustion enginetheory. An ideal gasisafictitioussubstanceinthe

gaseous phase whose proportionaldependence at constant volume oftemperature on

pressure holds forallpressures (Moran and

Shapiro,

1995). The idealgas equation of

state relatesthesequantities:

pV =_mRT

where

r=r/m

(2-4>

and

Ru

isthe universal gas constant andM isthemolecularweight ofthesubstance.

"The idealgas equation of stateis obeyed_{approximately}

by

a real gas whose pressureis

nottoolarge andwhosetemperatureisnottoolow

-that

is,

adilute gas"

(Moranand

Shapiro,

1995). Inthecontext ofthis paper,allgases

being

studied willbeassumedtobe

idealgases unless otherwise stated.

The ideal gas equation of state allows forthedetermination of one variablein

terms of all others. Since most processes occur with afixedmass of_gas,

knowing

two of

the_remainingthreewilldeterminethe third.

By

_choosingpressure and volume as

independentvariables, the temperaturecanbe determined. These states canbe

represented on a p-Vdiagram. Figure 2.1 shows a p-Vdiagram forair.

Fourtypesofprocesses canbeshown on a p-Vdiagram. Avertical line

representsa constant volume_process, whichis calledisochoric.

Similarly,

ahorizontal

linerepresentsa constant pressure_process,which iscalledisobaric. Thecurve

represented

by

anisothermalprocess (constant_temperature) dependsontheequation of

state ofthesystem. Anadiabatic_process,as will be discussed

later,

is oneinwhichthere

is noheattransfertothesystem. Thecurveitproduces_{is entirely dependent}onthe

system.

Another importantapplication oftheidealgas equation of state is fora constant

mass system. Fora constant mass_{system, the}

following

relationapplies

^

=_C

whereCisconstant. This isusefulin

determining

successive values of_p,

V,

orTina

processbecause

PjVj ₌

PfVf

< CD 90

-1

S 80

1

%

1

% 1 8

1

'

P (T=300

K)

- - _{P (T=600}

K)

70

-1

*

60

1

*

1

*

1

9 50

\

l

1 * 1 * 40 -1

\

V 30 20 -10 -n

*<sm

"*** ^^ SS85Hu msmm "

8 8HS SSS jjjgf j

50 100 150

Volume_(cm3)

200 250

[image:18.545.67.480.77.442.2]

2.1.3

Heat

Transfer

Heattransfer to andfroma system canbecalculatedinseveraldifferentways.

Those important to thecontent ofthispaper willbediscussedhere. Convectionis

describedas

being

the_energytransferbetweena surface and a_{fluid moving}overthe

surface (Incroperaand

Dewitt,

1996). The heattransferrateisproportionalto the

difference intemperaturebetweenthe surface,

Ts,

andthe

fluid,

T,

multiplied

by

the

area,As. The proportionalityconstantistheconvectiveheat_{transfer coefficient,} hj.

Writteninequation

form,

thisis

Q

=

hTAs(Ts-Tj

(2-7)

where

Q

istheheattransfer

by

convectionbetweenthesurface andthefluid.

Inthis study,heattransfer

by

convection occursbetweenthe cylinder andthe

air/fuelmixtureinthecombustion chamber. Asecond mode ofheattransfercanbe

defined

by

a changeintemperatureof a substancedueto the addition ofheatto that

substance. Before startingadiscussiononthis second mode ofheat transfer, it is helpful

todefineseveral parameters.

Thesum of specific_{internal energy}andtheproduct of pressure and specific

volumeisa_quantityoftenrequiredforthermodynamiccalculations. Thisquantity,

h,

is

definedas:

h=_u+pv

(2-8)

andiscalled specificenthalpy. "Thespecificheatof asubstanceis theheatrequiredto

increasethetemperatureof1

kg

ofthesubstance

by

1 K" (Keller,

Gettys,

and

Skove,

1993). Theprocess

by

whicha substance changestemperaturewill

directly

influenceits

constant_pressure,cp, andspecificheatatconstant_volume, cv. For ideal gases,_cp and_cv

aredefinedas follows:

3"

(2-9)

(2-10)

v

dT

dh

Cp~dT~

addition,

Cp~cv=R

(2-11)

Thequantities_cp(T) and_cv(T)are functions oftemperature; ifthevariationis small over

thetemperaturerange

they

canbe assumedtobeconstant. Theconstant value canbe

calculatedas follows:

\cv(T)dT

cv~

Tf

-Tt

h

(T)dT T,

cp-77

~T:

(2-12)

(2-13)

(Moran and

Shapiro,

1995).

The last quantitytobedefined istheratio of specific

heats,

y.

y=-L

(2-14)

v

Anotherpoint worth_{noting in}this section relatestomultiple gases. When several

gases arecombinedinan enclosed_area,theproperties ofthemixtureare acombination

sum ofthepartial pressures oftheindividualgases. As with all otherintensive

properties,thespecific heat isnota simple summation. The

following

formulaapplies:

(2-15)

<t

~

v

i

wherezisthe_propertyinquestion,the subscripttis thecombined valueforthat_property

andthesubscriptiisthe_{property for}eachindividualgas.

When heat istransferred toa substance and causes atemperaturechange,itcanbe

defined usingspecificheats. If heat isadded

during

a constant pressure_{process, the}

amount ofheat is defined

by

Q

=_mcpAT.

(2-16)

Fora constant volume processthedefinitionis

Q

=_mcvAT.

(2-17)

Somereal processes occur so _quicklythata negligible amount ofheatis added.

Thistypeof processis called adiabatic. Thecompression stroke of aninternal

combustion engine canbe approximated as

being

adiabatic.

Keller, Gettys,

andSkove

(1993)

haveshownthatforanadiabaticprocess_using anidealgas

pV7=K

(2-18)

whereKisconstant.

2.1.4 Work

"Work_{is energy} transferredbetween a system anditsenvironment

by

means

independentofthetemperaturedifferencebetweenthem"

this study, the workdonewillbecaused

by

theexpansionofthe_workinggasin a piston

cylinderassembly. Inthiscase workis defined as

' 2

W =

jpdV

(2-19)

The workdone

by

a process _accordingtothisequationisthe area underthecurve on a

p-V diagram. Foranisobaricprocess, theworkwillbeequalto theproduct of pressure and

changeinvolume. The workdone

by

anidealgas

during

an adiabaticprocessis

Wr

PV 1ir

i

7-1

1-'

V.

^"'

V

n

(2-20)

Thesubscripts iand/denotetheinitial andfinal states,respectively.

Workcanbeeither positive or negative.

During

a volume expansion process

work will alwaysbepositive. Fora compression processthe oppositeistrue. As willbe

seen more_{clearly in later}sectionstheworkdone

during

a complete cycleis thearea

betweentheexpansion and compression curves on a p-Vdiagram.

2.1.5

The

Otto

Cycle

Thematerialpresented sofar inthispaperhas beenprovidedtoaidin

developing

thecriteria

forjudging

theperformanceof aninternalcombustion engine. To furtherthis

developmenttheAir-StandardOtto Cyclewillbepresented. TheOttocycleisa

theoretical modelused as abasis forcomparisontoa sparkignition engine.

A_{reciprocating}internalcombustionengineisthesystemmodeled. Figure 2.2 is a

cylinderfittedwith valves and a spark plug. Several importantterms arelabeledonthe

schematic. The bore isthecylinderdiameter. The strokeis thedistance thepistontravels

from bottom deadcenter(maximumcylinder_volume) to

top

dead center(minimum

cylindervolume). Theminimum cylinder volume at

top

deadcenter

(TDC)

iscalledthe

clearance volume. As thepistonmovesfrom bottom dead center

(BDC)

toTDC it

sweeps througha volume whichis known as thedisplacementvolume. Thecompression

ratio oftheengineisthevolume atBDC divided

by

thevolume atTDC. Thecrank

mechanism converts the_{reciprocating}motionofthepiston_{into rotarymotion,} whichis

theuseable work output.

The internalcombustion engines

being

modeled operate withfour distinctstrokes

during

twocomplete revolutions ofthecrankshaft. Some engines run onatwo-stroke

process,butthesewill notbe discussed. Figure 2.3 shows a p-Vdiagram foratypical

four-strokeprocess. The start ofthecyclebegins withthepistonatTDC. The intake

valveopens andthepistonmoves

downward,

drawing

ina combustible charge ofthe

air/fuel_{mixture; this}istheintakeorinductionstroke. Withbothvalves closedthepiston

moves upward_compressingthe_charge, inthecompression stroke. This also raisesthe

temperature. Thecombustion processbegins

by firing

thespark plug. Thecombustion

creates a

high-temperature,

high-pressuregas_mixture, whichexpands andforcesthe

pistondownward. This is definedas thepower stroke. ThepistonmovesbacktoTDC

withtheexhaust valveopen, purgingtheburntgasesfromthecylinder. This is knownas

theexhaust stroke.

TheAir-StandardOtto Cycleattempts tomodel thecompression and power

accurately,aninstantaneousheatadditionprocess _occurring atTDCreplaces the

combustion process. The Ottocycleis shownin Figure 2.4 on a p-Vdiagram. The four

processesshown are asfollows:

1-2 isentropiccompression of airthrough thecompression ratio

2-3 heataddition at constant volume,

Q23

3-4 isentropicexpansionof airto original volume

4-1 heatrejection at constant volume, Q4i.

Efficiency

is definedasthework outputdivided

by

theheataddition

during

the

cycle. Forthe Ottocycle _{the efficiency, rjotto,} is

W

riotto=

(2-21)

FromtheFirst

Law,

AW=

AQ,

neglectingchangesin kinetic and potential energy.

Therefore W=

Q23

-Q41,

so

r)oao=^~

(2-22)

W?23

Since airis

being

considered asanidealgas with constant specific

heats,

Q23=mcv(T3-T2)

e41=/ncv(r4-r1)

(2-23)

Forthe twoisentropic processes, TVrl

isconstant; therefore

Z2-=ZL

=

ry-i

(2-24)

7i

T4

and

r\otto^^

(2-25)

By

specifying thecompression ratio and_using a constant y, the_efficiencyof a real engine

canbeapproximated.

The Otto Cycle has beenpresentedto aidinthe_{understanding}oftheprocesses

usedtomodel an internalcombustion engine. Themodelhelps to _simplifythe_studyof

park_Plug

vaive

TopDeac Center

Stroke

Bottom

Dead Center J,

Reciprocating

J

Motion

Crank

Mechanisi

clearance

Volune

[image:26.545.142.344.59.270.2]

iRotary

Motion

3 w CO 0

[image:27.545.59.524.60.420.2]

Volume

CD

CO CO

CD

[image:28.545.57.512.65.487.2]

Volume

2.2 Fuel Injection Devices

Spark-ignitioninternalcombustionengines create power andtorque.

Introducing

differentamounts of a combustible mixtureintothecylindersoftheengine can regulate

thesequantities. A fuel injectoror a combination of acarburetorandthrottlevalve isused

tocontrol thismixture.

Completecombustionrequiresa stoichiometric mixture offuel and air. This

means thatan exact airtofuelratio isrequiredtoobtain complete combustion ofboth

products. Therearedifferenttypes ofdevicesthataidin obtainingtheproper mixture.

Thesearethecarburetor andthefuel injector. The fuel injectorinjects fueleither

directly

intothecylinder(direct

injection)

orinto aninletmanifold(indirector portfuel injection).

Carburation and portfuel injectionwillbe

briefly

discussedto give general

background information. The detailsofdirect injectionwill alsobe discussedtofurther

the_{understanding}ofthemostdifficultand mostimportantaspect ofthisstudy.

2.2.1 Carburation

Thecarburetorwas one oftheearliestdevicesusedtointroduce fuel intothe

cylinder.

Initially

itwas a mechanical

device,

but has evolved and changedin design sinceitsintroduction.

velocityoftheair

flowing

to thenarrowestsection

increases;

asthecross-section

increases the_{velocity decreases. Due}to theBernoullieffect,the _{increased velocity}

causes a decrease inpressure. Fuel jetssubjectedto thislowerpressure _{supply fuel}tothe

engine. This is dependentupontherate of airflow andtheextent ofthedecreasein

pressure. Thethrottle valve again controlsthese quantities.

Thereare somedisadvantages to _using carburetors. Carburetors_relyon pressure

differences,

yet atmospheric pressureisnot a constant quantity.

Any

variation will cause

differing

supplies offuels for similarthrottleandloadconditions. Another disadvantage

is thatmultiple carburetors areinstalled inordertooptimize aerodynamic performance.

Multiplecarburetorinstallationswillimproveaerodynamic performanceintheinlet

manifold,but thecarburetors thenhavetobe balanced. Eachwillhave toprovidethe

sameflowand mixture strength. Anotherproblem_accordingtoStone

is,

"it isquite usual

forcarburetorstogive 5per cent variationinmixture strengthbetweencylinders, even

forsteady-state

operation"

(1992).

2.2.2 Port Fuel Injection

Fuelinjectors weredesignedtooptimizetheperformanceofinternalcombustion

engines. Thepressure

drop

inthe carburetordecreasespoweroutput andthevolumetric

efficiencyoftheengine. Theoriginalinjector designwas an_entirelymechanicaldevice

with complex two-dimensionalcams. Electroniccircuitshavereplacedthese.

Therearetwo types ofportfuel injection systems:

single-andmulti-point

usedtoinject fuel intothemanifold.

This,

_though, canleadtolowerpower outputthan

themulti-pointinjectionsystem. Themulti-pointinjectionsystemismore_{costly because}

it

typically

hasoneinjectorper engine_cylinder, butthesemultipleinjectors makeitmore

efficient. Althoughthetwo types are quite

different,

the_operatingprinciple_{is very}much

thesame. The differentialpressure acrosstheinjectorcontrolsthefuel flowratethrough

it. The fuel issprayedintotheinletmanifold, whereitcanthenbe introduced intothe

cylinder

during

theinductionprocess.

Thereare_{many benefits}toportfuel injection overcarburation. These are

discussed

by

Newton, Garrett,

andSteeds

(1996)

andinclude elimination oftheventuri

andthrottle

body

heating,

reduction ofadverse effects offuelmovementinthefloat

chamber, lower fuel consumption,higher torque, andincreasedpower output.While

usinga_{carburetor, fuel may}"stick"to thewalls ofthecombustion chamber;thisis called

wall wetting. Thisfuel will notevaporate as _{quickly causing incompletecombustion,}

which causeshigh levels of emissions. Forportfuel injectionwall _{wetting is less}

prevalent. Inportfuel injection fuelenrichment at start_{up is}not_{needed, this too}reduces

emissions.

2.2.3

Direct Injection

Many

automobile makers are

looking

into

developing

gasolinedirect injection

engines toreduce engineemissions,toimproveengineefficiency, andtoincreasepower

output. Thistechniqueuses aninjectionsystemto inject fuel

directly

intothecombustion

engine. This high-pressure injectionresultsinrapid vaporization and smallerfuel droplet

size. Thesetwofactors improvethecombustion_{process, allowing for}more complete

combustion; therefore power outputis increasedand emissions aredecreased.

Although direct injection has been readilyavailablein diesel enginesfor many

years,theconceptofdirect injection ingasoline engines is

fairly

new andhas only been

studiedin depth for ashortperiod oftime. The leadersofthe automotive

industry

have

not yet standardizedthedirect injectionprocess; thereare _manytechniques employedto

accomplishthistypeofinjection. Theelectronic injectorcanbemountedin different

locations

depending

ontheprocesstobeused.

Also,

theinjection

timing

can_vary

depending

ontheprocess andtheloadsonthe engine.

Thereare_many advantagestodirect injection.

According

to

Fan,

etal.,these

include "higherthermal efficiency, highervolumetric_efficiency,lower fuel_consumption,

better

driveability,

andbettercold start

performance"

(1999). The disadvantageof a

direct injectionsystem isthatiftheprocess isnot performed _correctly,hydrocarbon

emissions willincrease.

In summary,it has beenshownthatthebenefits tofuel injection are much greater

thancarburation. Theprocess of

introducing

fuel intothecylinderhas beenchanged and

modifiedthroughoutits history. Fromthe_{early inception}ofthecarburetortothemulti

pointinjectionsystemand nowtodirect

injection,

thefuelsystemhas developedgreatly.

New

technology

has beenand will_continuallyneedtobe developedtomaintain and

3.

State-of-the-Art

Fuel

_{Quality Measurement}

Techniques

Variousstudieshave beenperformedto measure_{fuel spray}characteristicsfora

directinjection sparkignitionengine. Thesestudiesdeterminedthe_{fuel quality}atthe

timeofignition. _{Fuel quality is}theamount offuelvaporized and mixed with airbefore

ignition. The qualityatignition is a majorfactor

influencing

enginedesign.

Varying

this

one parameter canlowerengine_emissions,improve fuel economy, andincreasepower

output.

The state-of-the-arttechniques usedtomeasure fuel qualitywillbeexaminedin

thissection. Thetechniquesincludevapor probe_{measurements,} several_{laser techniques,}

and atechniquethatuses combustion chamber pressuremeasurements. Althoughthese

techniques are_veryuseful,

they

will_{only be discussed in}minordetail inordertogive a

concisebackground forthis study.

3.1 Fiber

Optic

Spark

Plug

Probe

Alger,

et al.

(1999)

used afiberoptic spark_plugprobetomeasure vapor

concentration nearthespark plug.Theprobe consisted oftwochalcogenide optical

fibers,

one used as alight source

input,

theother as an output. These fiberswerefitted intoa

stainless steeltubethatprojectedintothecombustion chamberinplace ofthespark plug.

Insidethecombustionchamberthetubewasfittedwith a mirror. The sides ofthe tube

were machined_away toallowthefuelvaportoflow

freely

throughthedevice.

A lightsourcewas modulated_using a signalchoppertoproduce asquarewave

theoutputfiber. The lightthatreflectedontothesecondfiber wasless intensethan that

comingfromthefirstfiber becausesome oftheradiation fromthelight was absorbed

by

thefuel vaporinthegap. This change couldthenbemeasuredand correlatedtovapor

concentration.

3.2 The Optical Engine

The majorityoftechniques thatused alaser formeasurement ofthe_{fuel quality}at

ignition also used an optical engine. Theseengineshadsome portion removed and

replaced with a quartz window. Indifferent studies,

depending

onthemanufacturer,the

quartz was thecylinderlinerorinthecombustionchamberhead. The designof each

devicewas alsodependent uponthetypeof experiment performed.

According

toC. William

Robinson,

thesedevices have beenaround sincethe

1970's attheSandia National Laboratory. "The

top

ofthecombustion chamber was

covered with a window made of quartz orsapphire. This largewindow exposedthe

entire combustion chamber"(1996). The design alsoincludedwindows inthe side ofthe

cylindertoprovide accessforthelaser beams. This _was, and still

is,

the typical_{setup for}

theoptical engine usedincombustion research.

3.3

The Argon Ion Laser

Technique

In 1997 a single cylinderRicardo Hydraoptical engine was used atthe

University

ofWisconsin-Madison toevaluatein-cylinder_spraycharacteristics. Thisengine was

(1997)

used an argonion laserand severalcylindrical lensestocreate alasersheet within

thecombustionchamber. The different lenses were usedtoorientthesheetthrough the

windows ineither ahorizontal orverticalfashion.

Withthelaser inplace, ParrishandFarrell

(1997)

couldtakesnapshots ofthe

injection _{spray using}a sophisticated

imaging

system. These imageswere usedto _study

the_spray characteristics. Theresults ofthe_study centered onthe_{in-cylinder spray}

distribution andin-cylindergasflow.

They

showedthatalthough a_symmetric,

hollow,

cone shaped_spray wouldbe_{optimal, thespray}tendedtobemore asymmetricdueto the

highpressuresandhigh in-cylinder fuel flow velocities.

3. 4

Laser-Induced Fluorescence

A studyperformed

by Wolfgang

Ipp,

et al

(1999)

usedlaser-induced

(exciplex)

fluorescence,

orLIEF.

"By

means ofLIEFmeasurementstheliquid fuelphase andthe

fuelvapor were _{simultaneously}acquired ontotwo separate

images,

sothat theinfluence

of ambient conditions onthefuelvapor phase and _sprayevaporation was visualized".

Thisexperimental _setupwas similar_to,yet more complex_than,theone used

by

Parish

andFarrell. A laserwas usedtoforma _sheet, which causedthefluorescenceofthe fuel.

The_complexitycameintheformof_choosingthecorrectfuel tocausethefluorescenceof

thefuel in boththeliquid and vapor phases. Inthis_studythe_{non-fluorescing base}

fuel,

isooctane dopedwithbenzeneand

triethylamine,

was used.

Theresults showedthat thevapor phase followedthe_{liquid spray}throughout the

injectionprocess. The studyalsoshowedthat

by

_varyingtheinjectiontemperature the

fuelgave a visiblereductionoflarge fuel drops. Althoughthis techniquewas not 100%

effectivein_separating theliquidand vaporphases,it was sufficientfortheevaluationof

the_spraycharacteristics.

3.5 The

Fuel

Induced Gamma

Effect

The finaltechnique tobe discusseduses simple pressuretransducersinsteadof

high-tech measuring devices. The fuel induced gamma effect

(FIGE)

uses thepressure

difference betweenthefueled case andthemotoredcase withoutinjection. "The

techniquerelies onthesignificantdifferenceintheratio ofspecific

heats,

or_gamma, of

fuel fromair or residual

gases"

(Witze,

1999). Witzealso established a parameterto

measurethechangeinpressureduetothevapor-phasefuel:

plGE

fueled

xlQQ P

unfueled

By

collectingpressuredatabeforeand afterinjection for differenttypesof

injection,

Witzequantifiedtheamountof vapor-phasefuel. He utilizeda plot ofthe

FIGEparameterfor different injectiontimingsandopened-_{and closed-valveinjection to}

findtheoptimuminjectiontiming. Theoptimum occurred whereFIGEwas at a

maximum,which wasthepointwhere thefuel vaporizedthemost.

Thesetechniques are all_veryuseful_{in measuring fuel}quality. Some are_very

expensive and require expertiseinthefield. Othersare simple and canbedoneon

standard enginetestsetups withminoradjustments. To

date,

these arethemost_widely

used and mosttechnicallyadvancedtechniques intheautomotive

industry

for_measuring

4. Developinga

Simple,

Inexpensive Technique

Many

techniques thatattempttomeasure theamount of vapor phasefuelpresent

inthecombustion chamberatthe timeofignitionare_costlyanddifficultto implement.

Thegoal ofthis _studyis toresearchand

develop

a_simple,

inexpensive,

theoretical

technique thatwill provide adequate results. This techniquewillbe basedontheFIGE

technique developed

by

Witze. The specificheatratio of air and fuelwillbeusedto

determinetheamountof vapor phasefuel present

during

thecompression stroke andthis

informationwill beusedtopredicttheignitiontiming.

As the

difficulty

of atechnique

increases,

thecostof

implementing

that technique

tends to increase. Asimpletechniquewilluse existing,inexpensivetechnologies to

collectdata. This will allow engineers and scientists moretime to _verifythe_accuracyof

thedataandtofinda solutionto theproblem. Thealternative wouldbe timespent on

developing

newtoolsand equipmentto collectdata.

Thegoalis toprovide adequate results,butwhatdoesthismean? Whatare

adequate results? Inordertodefinethe_adequacyofthe results,it is necessarytoknow

whattheresults willbeusedfor. Theresults ofthis _studywillbeusedtooptimizethe

combustion processin a gasolinedirect-injection spark-ignition engine. This

optimization willimprovefuel economyandincreasepower output while

lowering

the

emissionsfromtheengine.

Injection

timing

willaidinthe improvementandoptimizationofthese three

parameters.

Therefore,

adequate results willdeterminetheinjectiontiming. Themodel

Minoradjustments couldbemade on atestenginetomore_closelyoptimizethe

parameters.

AmodifiedFuel Induced GammaEffecttechniquewillbe introduced inthis

study. There are_manyadvantagesof_using thistechniqueoverthe techniques_previously

studied. Twoimportantbenefits are cost and_accuracyoftheresults. _{For many}ofthe

earlier_studies,itwas _veryexpensiveto

develop

and usethetechniques. Thecost of a

techniquedependson_{many things,}

including

equipment_costs,knowledge

base,

andlabor

costs.

Mostoftheearliertechniques used a_{costly laser for}measurements. Thelaser

also requiredtheresearch anddevelopmentoftheproperlensestofocus thelaser beam

intothe_necessarypattern.

Then,

_{state-of-the-art-imaging}equipment was usedto

photograph animageofthe_spraypattern; this toowas _veryexpensive. The only wayto

take the_necessaryphotographs wasto

design, build,

andtestan optical engine. Itis

evidentthis that thecost of

implementing

thesetechniqueswas _{very high.}

The accuracyoftheprevioustechniques was _adequate, although most ofthe

studies showed resultsthat tended tobesubjective. Thespark_plugprobe_onlygave

resultsinthearea ofthesparkplug. Allofthelasertechniques gave atwo-dimensional

imageofathree-dimensional_spraypattern. These 2Dpatternsweretheninterpretedto

find 3Dresults. In severaloftheexperimentsthe_spraypattern wasimaged usingthree

orthogonal viewstoimproveonthe_accuracyof_{the results,} althoughtherequirementof

laser

lighting

_onlyallowed one viewtobephotographedat atime. Thismeansthatthe

accuracyoftheresults were

highly

dependentuponthe_{repeatability}oftheinjected fuel

There are several usesfora_simple, inexpensivetechniqueto measure vapor phase

fuel in adirect-injectionspark-ignitionengine. Suchatechniquewill providethemeans

to_quicklyand_easily

develop

new engines andto_verifyresults fromprevious studies.

Thiswill_greatlyincreasetheknowledge baseoftheautomotiveindustry.

Thetheoretical nature ofthemodifiedFIGEtechniquewill allowtheinputof

differentvariablesin such a_waythatdifferentengines canbetestedbeforeever

being

built. Iftheresults were _promising,a model couldbe builtto test the_accuracyofthe

designandimprovements couldbemade fromthatpoint. This willbemore cost

effectivethan

designing

and

building

an engine andthen

testing

ittoseeif itwill work.

By

usingtheengine setupsthatweredevelopedfortheother_techniques, the

results of aFIGEmodel canbeverified. The oldertechniques _{may have}given perfect

results,buttherewas no _wayof

knowing

howgoodtheseresults were. Another

verificationmethod will provideabasis for comparingresults.

Asstated_{earlier, the}resultsfound inthis_studywill addto theknowledge baseof

the automotiveindustry. Asthisknowledgebasegrows,theproducts thatare made will

be

increasingly

better.

They

will useless

fuel,

provide morepower,andbe less harmful

5. The

Experimental Setup

and Procedure

This studyrequiredexperimentation anddataacquisitionfortwoimportant

reasons: tocreate a pressure-volume model of an engine cylinder cycle andtoevaluate

thefinal results ofthismodel. The datacollectedhadtoconsist of values pertinentto the

model,most

importantly

pressure as afunctionofcylinder volume. Itwas also_necessary

tocollect several _extra,butnecessary, data

including

initialtemperatureofthesystem

andthemass oftheexhaust gases. All ofthedata forthis _studywas collected atthe

Customer Solutions CenteratTechnical Center

Rochester,

adivisionofDelphi

Automotive Systems. TheteamatDelphiused well-knownprocesses anddatacollection

techniques forthestudy. Thisallowedthemthe_abilitytouse_existingtestsetups with

onlyminor changes. Adetailedexplanationofthe_setupand procedurefollows.

5.1

Setup

All oftheexperiments_necessarytoconductthis_studywere performed on a

Ricardo Single CylinderResearchEngine. Thisenginehada

top

_entryreversetumble

pistonimpingementDirect InjectionGasoline

(DI-G)

combustion chamber. Thevalve

trainconsisted oftwointakevalves andtwoexhaust valves with overhead_{direct acting}

mechanicalbuckets. The Delphi MicroDI-G

injector,

which required 10 MPaoffuel

pressure, was locatedontheside ofthecombustion chamber. Theenginedisplacement

was 0.3225 L. The dimensionsoftheengine'scylinder were74mmand75mmforthe

bore andstroke,respectively. Severalother relevant engine constants are shownin Table

Max Cyl. Surface

Temp

(K)

533

Min Cyl. Surface

Temp (K)

483

Engine Speed

(RPM)

1300

Cylinder Bore

(mm)

74

Piston Head Area

(cm2)

43

ClearanceArea (cm

)

54.97

ClearanceVolume

(cm3)

31.12

Total Volume

(cm3)

356.26

Atmospheric Pressure

(kPa)

101 [image:41.545.116.341.52.213.2]

Injected Fuel Isooctane

Table 5.1 Engine Constants

Theenginewas testedin Delphi'stestcell

#7,

whichhadthe_necessary equipment

for dataacquisition. ACussins

Technology

enginedynamometerwith coolant and oil

temperaturecontrol was used asthe testbed. Thecombustionair _supplywas

thermodynamically

controlled. A30to 122Ftemperaturerange couldbeachieved.

The

humidity

couldbecontrolledbetween and 120F dewpoint. Thepressure was

controlledfrom 70 to 110kPa

(absolute)

with aflowrate of_upto 100 CFM. A5-gallon

Haskel Cartthatcouldbepressurizedfrom 0to 12 MPa

(absolute)

suppliedthefuel.

Emissionsof

N2, NOx, CO, CO2,

and

O2

were measured_usingthe

Peirburg

technique. This techniquetakestheentire exhaust gas fromtheengine anddilutes itwith

airtoprevent chemical reactions andcondensationinthesample. Samplesthatcorrelate

tovarious

driving

conditions andperiodsoftimearetaken and collectedinbags. An

exhaust emissionbenchis usedtocombinethesample analysisdataandthevolumeof

the sample. The resultingcalculation givesthemass of each component emittedfromthe

testengine.

An inline highpressureMicro Motion sensor measuredthefuelpressure. A

pressure. DSP ACAPversion5.0wasusedforhigh-speeddataacquisitionand

combustionchamber analysis.MicrosoftExcel 97andMicrosoft Visual Basic were used

toretrieve and analyzethedata.

Severalfactorsremained constantthroughout the

testing

process. Theengine

speed was setto 1300rpm. Itis importantto notethat theengine speed varied_slightly

throughoutthe

testing

cycle, althoughthevariation was never greaterthan0.5%. The

mean speed remained constant at 1300rpm,and was considered constantthroughout this

study. A loadof330 kPa (netmean effective_pressure)was placed ontheengine. The

coolanttemperaturewaskeptat a constant90Cwiththeinletairtemperatureat25C.

Each dataset consisted of 10enginecyclesinwhich cylinder pressuredatawastakenon

a crank anglebasis. Aspart ofthedataset,thecylinder volume_{corresponding}to the

crank angle was calculated.

5.2 Procedure

Early

injection

timing

was studiedbecausetheevaporation ofthefuelwouldbe

more evident atthisstageofinjection. Asa result oflowertemperatures atthe

beginning

ofcompression,evaporationwould occur more slowly. Thetestprocedure wastostart

theengine and motoritwhile

injecting

fuel until a_steadystate was reached. Atthat

point, fuelinjectioncontinued andtenfour-stokecycles ofdatawere collected. Asingle

injectionoccurred

during

each ofthesecycles. The injectorwas_{then turned off;}

motoringcontinued and a seconddataset_consistingoftencycles wascollected. Thetwo

There were tworeasons for_collectingdata inthis fashion. The firstwasto

minimizetheinitialvalue errorsbetweenthe twodatasets. _{At steadystate, the}initial

cylindertemperaturefor boththe_motoringcase and injectioncase wouldbe nearly

identical,

reducing anyeffects of mismatcheddata.

Also,

the airinthecylinderafter

injection contained residualsfromcombustion.

Any

difference inpressuredata between

the twodatasets caused

by

theseresidual gases was minimized. Thesecond reasonfor

collecting data inthismanner wastominimizetheeffects offalse pressure readings. The

pressure at_everypoint was calculated

by

_eliminatingthehighestandlowestpressure

values ofthe tencycles forthatpoint andthen

taking

the average ofthe_remainingeight

readings. Thisprovided a

"smoothed"

dataset, which couldbemore_accuratelymodeled.

This smoothing would alsotakeinto accountthefactthat

during

motoring,residuals

wouldbecleanedfrom thesystem andthemixture wouldtend tobehave likepure air.

Isooctaneactslikeanidealgasinthevapor_phase,itwas_readilyavailableinthe

test_cell,anditsgammadata iswell

documented;

thereforeitwasthefuel injected into

6.

Detailed

Analysis

of theFIGE Model

6.1

Introduction

to the

Model

Asstatedin Section

4,

thegoalofthis _{study is}tofindaninexpensivetechniqueto

obtainthemass offuelthathas evaporatedinan engine cylinder priortocombustion. In

ordertoaccomplishthis_task,theFuelInducedGamma Effect

(FIGE)

model was created.

Thissection will_{completely describe}theFIGEmodel.

The FIGEmodel uses thespecificheatratio ofthe air andgaseous fuel (isooctane

inthis_study)toextractthemass offuelfrompressure and volumedata. Theoretical

equations for ideal gases are usedtomodelthepressure with respecttocylinder volume.

By

comparingtheexpected pressure valuesfromthemodelto theactual valuesfromthe

experiments, adifference is found.

Taking

into account several otherfactorsthatcause

pressurevariations, themass ofthefuel canbecorrelatedto thedifferences inpressure.

Thecreationofthemodeltookseveral steps.

First,

themodelhadtobecalibrated

tobesurethatitperformedaccurately. Torefinethemodel,factorssuch as mass

loss,

heat transfer,and residualsinthecylinder were added.Then fuelcalculations were

performedtocompletethemodel.

Finally,

themodel wastestedforaccuracy. These

steps willbeexplainedin detailthroughout theremainder ofthis section.

6.2

Developing

and

Calibrating

the Model

TheFIGEmodelis based upon equations2-5 and 2-18. Theseequations relate

the pressure, volume, andtemperatureofthe air/fuelvapor mixtures to theratioof

compression stroke ofthecylinder was needed. Thesevalues weretakenfromthedata

set provided

by

Delphi and remained constantthroughout theentire study. Twoother

datapoints were neededtobeginmodeling; theseweretheinitialpressure and theinitial

temperatureofthegases inthecylinder. The initial pressure,

Pt,

was extractedfromthe

dataset atthe_{correspondingvolume,} V}.

The initialtemperature,

7*,-,

was moredifficulttomeasure. Thiswas becausethere

was no convenient_waytoplace athermocouple insidethe cylinder. Theairinthe

cylinder atbottom deadcenter comes_{primarily from}theintake stroke. The intakeair

comes

directly

fromthe atmosphere,orinthiscase the testcell. Thereforetheinitial

temperaturewas assumedtobetheregulatedtestcelltemperature.

Agraphical representation ofthepressure with respecttovolume was_necessary

tocreate themodel andcorrelate thedata. Agraphical model wascreated

by

_calculating

thepressure atincrementalvolume steps (or at_everycrank angle). Foreach_stepthere

was aninitialvalue, orthecurrentvalue of_{the parameter,} as well as afinal _value, orthe

value atthenextstep. Thesewillbe denoted

by

thesubscriptsiand/,respectively.

The_{first step in calculating}thepressure at point

2,

thefinal volume,wasto

assumeafinal temperature,Tf. Forconvenience,thefinal temperaturewas assumedtobe

equaltotheinitial temperature, 7,.

Only

motoring datawas_used; forthedevelopment

and calibration ofthemodelthereforetherewas nofuel inthecylinder.

Knowing

both

7,

and

Tf,

an average specificheatratio, yave,couldbecalculated_usingequations 2-12

through

2-14,

where

C/,(r)=

7.929xl0"14r4

+

9.453xl0~772

-0.00047+1.048

(6-1)

cv(T)=_7.929

xl0~1474

+

9.453xl0~772

Theseequationsforspecificheatof air werederived from Table A.4Thermophysical

PropertiesofGasesatAtmosphericPressure (Incroperaand

Dewitt,

1996)

_usingthe

"LINEST"

functionin Excel.

Then,

by

_rearranging

2-18,

afinalpressure,

F/

couldbe

calculated asfollows:

Ptv7

=PfVj

(6-3a)

rv\Y~

Pf=Pi

v%

(6-3b)

where _yaveisthevalue calculatedfromequation2-14.

This

Pf

was calculated_usingan assumed value of

Tf,

sotherewas_{uncertainty in}

thefinalvalue. Averification of

Tf

was needed. Thiswasdone usingequation 2-6.

Solving

for

Tf,

Tf

=

J T

(6-4)

1

PV

However,

this calculated

7/

_maynot equalthe temperatureassumed atthe

beginning

of

theprocess.

Now,

7/

replacedtheassumedfinaltemperatureandtheprocess was

repeateduntiltheassumedfinaltemperatureandthecalculatedfinaltemperaturewere

equal. ThisistheFIGEprocess. Figure6.1 shows theflow ofthisprocess. The FIGE

processwas continuedforeachcrank angle untilthepiston reachedTDC.

Thisprocessis thebasis forthemodel.

Next,

themodel hadtobecalibratedto

matchthedatacollectedatDelphi. Thecalibration could_{only be done}

by

_matching the

dataon a point

by

pointbasis toseeiftheoverallfitwas sufficient. Themeans of

doing

this wasto findthepercentdeviation fromtheactual value of each calculatedpressure.

%E=

P P

1

calc *data

p 1

data

where

Pcaic

isthecalculated pressure and

Pdata

isthedatapressure. Thestandarddeviation

ofthepercentdeviationwascalculated_using Excel'

s

"STDEV"

function.

By

_adding

variousparameters_{to the model, the}standarddeviation was_{minimized,resulting in} the

best-fitmodel. The

following

sections willdetail theseparameters andhow

they

were

Assume Ta

Calculate

Pf

usingeqn. 6 3b

Calculate

Ta

using

eqn. 6-4

Yes

Goto next

Volume

step

Let

Ta

=

Tf

[image:48.545.137.344.49.399.2]

No

6.2.1 Effective

Closing

Angle

Anengine cycleisacomplex cycleto_{model;many factors have}tobeconsidered

to besurethatthemodel resemblesthephysical cycle. Onesuchfactorthatis important

is thecrank angle at whichthe intakevalve_closes, whichis theeffective_closingangle.

Thisis important becausecompressiondoesnotbeginuntilthisvalve is

fully

closed.

Asthepiston comes to theBDCposition attheend oftheintakestroke, theintake

valve should close. _{In reality}thisdoesnot occurbecauseof

timing delays,

pressurein

the_system, and various otherfactors.

Instead,

the valve closes _shortlyafterBDCand

compressionbegins.

Inorderforthemodeltoperform_{properly, the}pressureattheeffective_closing

anglehadtobeusedastheinitialpressure.Thiscrank angle was usedforthe _starting

point ofthemodel. Theeffective_closinganglehadtobe determinedor calculated. This

turnedouttobea_verysimpletask.

Using

thedatathathad beencollected

it,

was seen

thatafterBDCthepressure remains

fairly

constantfora number of crank angledegrees.

Beyondthispointthepressurebegantoincrease. Althoughnot_{exact, the}effective

closingangle couldbeassumedtobeattheend ofthis constant pressure process. The

effective_closingangleis nota constant value andhadtobe determined foreach

subsequentdataset.

6.2.2 Mass Loss

Arealization was made_{very early in}this _studythat thereare noidealorperfect

inwhich quantitiesof airandfuelwill be lostthroughthe_ringseals aroundthepiston.

There aretwowaystoapproach_calculatingthe_resultingmassloss. The first istousethe

pressuredifferentialsbetweenthecombustionchamber and atmospheric pressure

conditions _alongwithinformationaboutthecross-sectional areathroughwhichtheair

andfuelwill leak. Thesecondis toderiveempirical resultsfromthecollecteddata. The

second_{method, the} simpler ofthetwo,waschosenbecause itwould give adequate results

forthis study. The firstmethod couldbedeveloped into a_{full-scale study}and wouldbe

difficulttopursue.

Several factors hadto beconsideredinorder toderive an equationformassloss.

Thefirstwas a conceptual ideaofhowthe equation shouldbehave. The initialthought

wasthatastheinternalpressure

increased,

whiletheatmospheric pressure remained

constant,thepressuredifferential increasedandthemass losswouldincrease.

However,

thiswas notaccurate and_actuallytheopposite was _true, as will beshown.

As thepressure

increased,

theinternaltemperature alsoincreased. Theresult of

this increasedtemperaturewas anexpansion ofthe

ring

seals.

Combining

thisexpansion

withtheincreased_{pressure, the}areathroughwhich gases could_escape, andthus themass

loss,

decreased. As a_result,asthepressure increasedthemassloss decreasedtoa point

wheretherewas _essentiallyno mass loss.

Theproblemthenwastodeterminethemassloss asafunction of pressure. This

wasderived using boththecollecteddataand a variation oftheFIGEprocessas shown

above. Foreach pressuredatapoint collected a_{corresponding}temperature was

calculated_usingequation6-4:

PfVfTi

Tf

=

J J

(6-4)

PV-Using

thisandtheinitial

temperature,

_yairwas calculated. Thenequation6-3 was usedto

calculatePcaic- Withequation2-3 andthefinal values, mcaicandnidatacouldbecalculated

using

Pcaic

and

Pf,

respectively.

By

_subtractingthedatamassfromthatofthe calculated,

themassloss wasfound. The Visual Basiccodeforthiscalculationis shown in

Appendix A. Figure 6.2 showstheresults ofthiscalculation as afunctionofthedata

pressure.

Excel'

s "LINEST"functionwas usedtogeneratethebest-fitequation to these

results. This isshown here forclarity:

mloss =_-3.75x 10"13

P?

+2.58

xlO-10^

+1.22xl0"7

(6-6)

As canbeseen in Figure

6.2,

_{beyond approximately 1000 kPa}themassloss became

negative. Itwas atthispointthat themassloss wasassumedtobezero.

Atlowerpressuresthemassloss diagramshows order of magnitude variations in

themassloss. Thisis a result of variationsin thedata andthecalculations performed on

thisdata. The ideal dataset would conformto theidealgasequations, but dueto thedata

collectionprocedures andthenatureofthesystemthisdidnothappen. Theprocess,

being

a pointtopointcalculation, wouldover-estimatethemassloss forone point and at

thenext correctforthisextra massand under-estimatethelosses.

By

_applyingabest-fit

curveto thecalculated mass

loss,

the errors wouldbeaveraged andthe_resultingcurve

wouldgive abetterapproximationofthemassloss.

Thisequation, althoughderivedwith_{motoring dataonly,} was usedforall

subsequentcalculations. There may have beenminimal errorsintroducedbecauseof_this,

buttheireffect wouldbe slightbecause the totalmasslosswas smallcomparedto the

Asecond part ofthemasslossproblem washowto calculatethefuelmassloss.

Thesolution was

fairly

simpleand relied on several assumptionsthatheldtrue

throughout thisstudy. The firstwasthat the_{only loss}came fromvapor; thereforeno

liquid fuel leftthesystem.

Secondly,

whenthefuelevaporatedit

instantaneously

mixed

withtheairinthe_{system, making}ahomogeneousmixture.

Using

these assumptions, the

masslosscouldbecalculated. Inthecase of_motoringthecalculation_{is simply}

mair=mi-mloss

(6"7)

When injectionoccurred, thecalculationbecame more complicatedbecause_mioss

wasthe totalmass loss fromthesystem. Thelossneededtobe divided into two

constituents, namely fueland air. Sincethemixture was assumedtobe

homogeneous,

themasslossof each substance wouldbeproportionaltoitspercentage ofthe totalmass.

So,

rmx^

ymtot _j

(6-8)

wherethe subscript xdenotesthesubstance andmtotisthe totalmass ofthe vaporinthe

1.5

?.*?

0.5

?? ?

-? ?

?-? Mass Loss

Poly. (Mass

Loss)

E,

CO CO

OB

16100

-1

[image:53.545.51.517.118.478.2]

J-Pressure

(kPa)

6.2.3

Heat Transfer

Another factorthatwouldinfluencethe behaviorofthesystemistheheat

transferredbetweenthepiston-cylinder_assemblyandthemixture ofliquid fueland

vapor. This heattransferwould cause a changeintemperature ofthe mixture,whichis

animportantparameterintheFIGEprocess. This heattransferproblem was complexfor

tworeasons. Calculationoftheheattransfercoefficientforthecylinder-_{vaporinterface}

was thefirstcomplexity. The second was thatthesystem wasdynamic andthesurface

area was always changing.

The Engineers atDelphi madethecalculationoftheheattransfercoefficient

muchless complex.

They

evaluatedthisparameterfora similar enginein a previous

study and providedtheresults. Figure 6.3 showsthe results, ortheheattransfer

coefficient with respectto thecrank angle oftheengine. Excelwas usedtocalculate

equation

6-9,

abest-fitapproximation ofthe

data;

thiswillbeusedin theremainder of

the study.

hT

=

0.09,

CA<240

hT

=

2.32X10"7CA3

- 0.00017

CA2

+0.041752CA-

3.39289,

(6-9)

CA>240

whereCA is definedasthecrank anglein degrees.

Before

looking

intothedynamicnature of_{the system,}itwas_necessarytoknow

theparameters neededtosolvetheheattransferproblem. Equations2-7 and2-16show

everythingneededto evaluatethechangein temperatureofthefuelvapormixture.

Q

=

hTAs(Ts-Tj

(2-7)

The

following

equationistheresult of_combiningtheseequations and_solving for A7:

AT=hTAATs-T)

(6io)

mcp

Thetwounknownfactors werethesurface_area,

As,

andthe surfacetemperatures, 7*. The

calculation ofthese variables wasdifficult becauseofthedynamicsofthe system.

Thesurface areaconsistedofthreeregions,two of which were static whilethe

thirdwasdynamic. The area ofthepistonheadwas measuredto_{be approximately 43}

cm . Thesecondconstant area region was that_ofthe_{area above}the

top

ofthestrokein

theclearance volume region. The surface areainthisregion was_{approximately 55}cm2.

Thesevalues were measured and provided

by

the testengineers atDelphi.

Thefinal surface area wasthatofthe walls ofthecylinder. As thevolume ofthe

cylinder_{changed, this}surface area also changed. In ordertocalculatethis surface area

some basicgeometric equations of a cylinder were needed. These were:

V=7tr2h

(6-11)

As

=2nrh

(6-12)

where Visthecylindervolume, ris thecylinder_radius,h is theheightofthecylinder and

As

isthelateral surface area ofthecylinder. Alsonotethatthevolumeintheengine

cylinder, that

is,

thevolumeassociated withthecylinder wall surface area,is

V

cyl =Vi~Vclear

(6-13)

where

V,

is theknowntotalvolume ofthesystem and

Vciear

istheclearance volume.

By

relating equations6-11 and6-12totheengineand

letting

Bequaltheboreof

the engine,itwas clearthat

B r=

Theseequations werecombinedto get

Vt

~Vclear =

As

^

(6-15)

Solving

for As:

A AWi_^clear)

(6_16)

B

So,

with _anygiven_volume,thesurface area couldbecalculated.

Eachsurface areathenhadtobeassociated with atemperature. Forthestatic

areasthetemperature was _easyto

find;

theengine couldbeprobed withthermocouples in

theseareas. Delphiprovidedthesereadings. Thepistonheadareatemperaturewas483

Kandthecylinderheadareatemperaturewas 533 K.

Twoassumptionshadtobemadetocalculatethewalltemperature. The firstwas

that the abovetwo temperatureswere theminimum and maximumincylinder surface

temperatures,respectively. Thesecond assumption was that the temperaturevaried

linearly

from theminimumtothemaximum_alongthewall. Fromtheseassumptions,the

surfacetemperatureequation wasderived.

Using

thebasicequation of a

line,

y=_mx+b

(6-17)

surfacetemperature with respecttovolume couldbecalculated asfollows:

Ts=msV{+b

(6-18)

providedthattheslope ofthe

line,

_ms,andthe temperature

intercept,

b,

wereknown.The

slope varied

linearly

fromtheminimumtemperature atthe totalvolumeto themaximum

?max

?min

(619)

V , -V

clear rtot

Using

thiscalculated slopetheinterceptcouldbecalculated:

b=

Tm^-{msVclear)

(6-20)

Therefore,

theminimum cylinder walltemperaturecouldbecalculated asafunctionof

volume.

Sincethetemperaturevaried

linearly

_{alongthe wall, the} average walltemperature

was

(mvV,+fc)+7max

Combining

theseequations with equation

6-10,

the value of A7 couldbe foundat each

volumeincrement. Thentheinitial temperaturewas calculatedasfollows:

0.5

0.45

0.4

* 0.35

E

5

_> _0.3

c o

O 0.2b

h-0)

+

CO c m 0.2

i_

H

CO

X 0.15

0.1

0.05

175 195 215 235 255 275 295

Crank Angle

(degrees)

315 335 355 375

6.2.4 Residuals

Once again, thesystem usedinthis _studywas notanidealsystem. Ifitwere,

completecombustionofthefuelwould occur. Duetothenature ofthe system,only

partialcombustionoccurred and exhaust and residual gases were expelledfromthe

engine.

Unfortunately,

all oftheseresiduals were not purgedfromtheengine

during

the

exhaust stroke. Theresult was a mixture of air and residual gasesinthecylinder. This

hadtobecompensatedfor intheFIGEmodel calculations.

The first step in calculatingtheresidual gases wastomeasurethe amountof

residualsintheexhaust. Thiswasaccomplished

by

_usingthe

Pierburg

process

during

the

proceduretocollect theemissions fromtheengine. Theresult ofthisprocess was the

mass of each residualfortheentiretestcycle. Inordertoreachthefinal goal of

calculatingthespecificheatratioforthe residuals, thepercentage ofthe totalresidual

mass was calculatedforeach residual gas. Theseincluded

N2, NO, CO, CO2,

andO2.

Thespecificheatratio of a substance at a giventemperaturewascalculated_using

thespecificheatvalues ofthesubstanceatthat temperature.

So,

a percentage oftotal

mass was knownforeach residual _{gas; this}percentage was assumedtoremainconstant

throughout thestudy.

Therefore,

by knowing

the totalmass of residuals withinthe

cylinder, the specificheatratiofortheresi