computer simulation of an internal combustion engine

8/11/2019 Computer Simulation of an Internal Combustion Engine

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Faculdade de Engenharia da Universidade do Porto

and

University of Maryland, Baltimore County

Master in Mechanical Engineering

Thermal EnergyProject

Computer Simulation of an

Internal Combustion Engine

Supervisor in UMBC: Dr. Christian von Kerce!

"#visor in $EUP: Pro%. E#uar#o &liveira $ernan#es

E'change "#visor: Dr. (.D. Timmie Topoles!i

"nt)nio Emanuel $igueire#o Costa

*n#Term+ *,,-


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"c!nole#gments

2

/ oul# li!e to e'press my gratitu#e to Dr. Christian von Kerce!

%or his #e#ication an# #evotion %or this project.

/ also oul# li!e to than! my parents %or this li%e time opportunity+

0&1riga#o23


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Contents

Commonly use# sym1ols+ su1scripts+ an# a11reviations 4

"1stract -

&1jectives 5

/ntro#uction 6,

Chapter 67 /nternal Com1ustion Engine 6*

6.6.The Basic /CE Mechanism 6*

6.*.The E8uations o% State o% the 9or!ing ases 6;

6.eat trans%er *6

*.


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Conclusive remar!s 45

Bi1liography ;,

"ppen#i'es ;6

" Mathematical an# thermo#ynamic manipulations ;6

B De%initions =*

C Computer simulations =oever+ heat trans%er+ ,L+ as le%t out hich results somehat arti%icially in an Na#ia1atic

engineN. "lso the com1ustion mo#el use# as 1ase# on a somehat simple %ormulation. /t as

assume# that 1urne# an# un1urne# gases ere homogeneously mi'e# an# 1urning rate as a

constant. Base# on CAK or!+ my or! has a##e# heat trans%er an# a to one com1ustion mo#el

that separates the action o% the 1urne# an# un1urne# gases #uring the com1ustion. The 1oun#ary o%these ones as then #etermine# 1y a tur1ulence %lame spee# mo#el.

/n 1oth o% these cases+ there e'ist ell #evelope# empirical mo#els+ an# the main o1jective o% my

or! as to un#erstan# an# a#just these mo#els an# implement them ithin the theoretical mo#el

an# the computer program #evelope# 1y CAK.

This or! contains a complete #escription o% the theoretical %rameor! employe# 1y CAK as ell

as the mo#i%ications an# implementation o% heat trans%er an# com1ustion mo#el 1y me.

The result o% my project is a computer simulation hich may 1e use# to o1tain some %airly goo#estimates o% engine per%ormance. These estimates are most use%ul %or un#erstan#ing 1asic engine

per%ormance as ell as assessing mo#i%ications as regar#s valve siing+ spar! a#vance an# various

%uels. " particularly use%ul application is to #o a compressortur1ine engine matching %or tur1ocharging.

The report is 1ase# on an# e'ten#s a prior+ in%ormal+ report 1y CAK.

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&1jectives

The main propose o% my or!:

Complete the program ith the heat trans%er mo#el an# insert the correct mo#i%ications to

per%orm a simulation o% a non a#ia1atic engineO "## a ne com1ustion mo#el+ replacing the e'isting one use# in the initial program. The

ne com1ustion mo#el oul# ta!e into account the tur1ulence in the cylin#er an# oul# then

allo the variation o% 1urn #uration hich is %i'e# in the simple mo#el use#L to vary ith

engine spee#.

Despite this+ / also ha# to un#erstan# the e'isting computer simulation implemente# 1y CAK an#

the theoretical concepts 1ehin# it.

9


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/ntro#uction

This report presents the Thermo#ynamics theory #escri1ing the main physical phenomena

occurring insi#e a spar! ignition %our stro!e ?SL internal com1ustion engine /CEL hile it is running at

stea#y spee# constant revolutions per minute+ rpmL. The mathematical %orm o% the Thermo#ynamictheory is #evelope# an# implemente# numerically 1y ay o% a 0Scila13 computer program. The result

is an /CE computer simulation. This computer simulation may 1e use# to o1tain some %airly goo#

estimates o% engine per%ormance in hich the main e%%ects o% compression ratio+ spar!s timing+ some

aspects o% valve timing+ valve siing+ an# %uel types+ over a range o% engine spee#s.

&% course not every #etail o% /CE per%ormance can 1e accounte# %or+ 1ut #epen#ing on the physical

#etails incorporate# an# their relative importance+ many o% the most important per%ormance

characteristics can 1e #etermine# to a reasona1le #egree o% accuracy. This report #oes not #eal ithany structural or mechanical aspects o% an /CE 1eyon# those o% the 1asic geometric %eatures relevant

to the containment an# e'ternal mani%estations o% the Thermo#ynamics processes occurring in the

engine. These thermo#ynamic processes are i#ealie# to a certain #egree in or#er to re#uce the

comple'ity at this stage o% #evelopment o% the engine simulation.

The simulation is 1ase# on the stan#ar# con%iguration o% a reciprocating piston in a cylin#er close#

at one en#+ the cylin#er hea#. The piston is connecte# to a cran! 1y ay o% a connecting ro# that

protru#es out the opposite open en# o% the cylin#er an# connects to a cran!. $igure 6 is a schematic#iagram o% one cylin#er o% an /CE. The resulting reciprocating motion o% the piston imparts a rotation to

the cran!. This 1asic sli#er7cran! mechanism the piston 1eing the sli#erL transmits poer generate#

1y a or!ing %lui#+ or gas+ in the space enclose# 1y the piston+ cylin#er an# cylin#er hea#+ to hatever

is connecte# to cran!. The cran! is also geare# to a camsha%t that operates the valves in the cylin#er

hea# that perio#ically open an# close to e'pel or inhale the or!ing gases. Most /CEs have multiple

cylin#ers operating in unison on a common cran!sha%t. The processes that occur are essentially

i#entical %or each cylin#er so that the analysis nee# 1e #one %or only one cylin#er. The /CE

per%ormance is then simply the num1er o% cylin#ers times the inputoutput %or a single cylin#er.

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$igure 6 @ $our stro!e internal com1ustion engine. Q4R

The /CE Thermo#ynamics analysis is 1ase# on the %olloing primary assumptions. "ll

thermo#ynamics processes are assume# to 1e internallyreversi1le. The or!ing me#ium %uel an# air

mi'turesL is assume# to 1e an i#eal gas ith constant speci%ic heats. The e8uations o% state %or the

1urne# an# un1urne# me#ia are #erive# on the 1asis o% e8uili1rium chemistry. The gas e'change

process is 1ase# on 8uasi7stea#y compressi1le %lo through an ori%ice.

$urther secon#ary assumptions an# i#ealiations are #iscusse# in the %ormulation o% the

thermo#ynamics mo#el in the ne't chapters.

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Chapter 67 /nternal Com1ustion Engine

6.6.The Basic /CE Mechanism

The piston cylin#er7cran! mechanism the sli#er7cran!L is shon schematically in $igure *. This%igure in#icates ho the up an# #on motion o% the piston turns the cran!. The space enclose# 1y the

piston an# the cylin#er is the main concern here. This is here the latent energy o% the %uel7air mi'ture

is release# 1y com1ustion o'i#ie#L to pro#uce the sensi1le energy+ hich #rives the piston. The top

o% the cylin#er enclosure contains an inta!e an# e'haust valve hich open an# close at appropriate

moments o% the engine cycle to allo escape o% 1urne# gases an# ingestion o% %resh %uel7air mi'ture.

$igure * 7 " %our7stro!e spar! ignition cycle. Q4R

The 1asic engine per%ormance cycles are controlle# 1y the cran! rotation. The cran! rotation in

turn moves the piston up an# #on+ thus varying the volume V o% the space enclose# 1y the piston

an# cylin#er. This varying volume is the primary controlling %actor o% the se8uence o% thermo#ynamic

events occurring in the piston7cylin#er space. >ence%orth this space ill 1e re%erre# to simply as the

cylin#er.

The cran! rotation is measure# in terms o% the rotation angle F shon in $igure


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$igure < 7 S!etch o% the sli#er cran! mo#el o% piston7cylin#er geometry

"t F, 2n L the piston is at the 1ottom7most point in its travel. This point is calle# 1ottom

center+ BC. The cylin#er volume AFL can 1e shon+ 1y an analysis o% the sli#er7cran! mechanism to

1e+

v =Vm1

rc

1

21

1

rc1cos RcR csin

2 6.6L

/n %ormula 6.6L+ Amis the ma'imumL volume in the cylin#er at BC+ Rc is the ratio o% connecting

ro# length to s + here s=stroke + an# rc is the compression ratioVm

Vc+ here Ac is the

minimumL volume o% the cylin#er at top center TCL or F 2 n1 . Ac is calle# the

clearance volume an# Vd=VmVc is the 0#isplacement3 volume+ the usual measure o% engine

capacity or+ more commonly+ engine sie.

The calculation o% the instantaneous volume e8uation 6.6L is #iscusse# in 0"ppen#i' ".63.

Using Amas an input varia1le+ some other varia1les such as the Ac+ A# + 1ore 1oL an# stro!e sL

have to 1e calculate# in or#er to procee#. /t as assume# that the 1ore as e8ual to the stro!e in

or#er to simpli%y some e8uations an# to use the minimum ones possi1le+

Vd=4

b2s 6.*L

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Vd

Vc=rc 1 6.


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Aw =vVcbo /8

Ac 6.=L

an#

Ac=bohc2

bo2

6.-L

The operation o% the valves is synchronie# to the motion o% the piston 1y ay o% gear or chain

#rives %rom the cran!sha%t. This is not shon in $igure *. There ill 1e no nee# %or a #escription o% this

mechanism here since it ill not 1e ma#e use o%. $or the present it is only necessary to #escri1e the

valve con%iguration an# actual motion o% the valves as a %unction o% the cran! angle F. This ill 1e

reserve# %or the chapter on the gas e'change process in or#er to !eep the e'position simple at this

stage. The %unction+ o% F+ #escri1ing the motion o% the valves is given as part o% the 1asic engine

speci%ications utilie# in this stu#y. The camsha%t an# valve actuation mechanism must then 1e

#esigne# to realie this valve motion %unction. $or this the rea#er is re%erre# to 1oo!s on engine an#mechanism #esign given in the 1i1liography.

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6.*.The E8uations o% State o% the 9or!ing ases

This gaseous mi'ture is assume# to 1e an i#eal gas+ al1eit ith #i%%erent e8uations o% state in the

un1urne# an# 1urne# states. The e8uations o% state o% the un1urne# su1script uL an# 1urne#

su1script 1L are #erive# on the 1asis o% com1ustion e8uili1rium chemistry an# the coe%%icients o% the

thermo#ynamic properties are given in e%erence 6. These to thermo#ynamic las apply to the

gaseous %uel7air mi'ture in the cylin#er. The linearie# versions o% the e8uations are use# here. $or

illustrative purpose the %uel use# here is C>? ith an e8uivalence ratio o% 6 an# hose properties are

very similar to gasoline. During the process o% com1ustion the cylin#er contains a mi'ture o% the

un1urne# an# 1urne# %uel7air. The mi'ture is 8uanti%ie# 1y the 1urne# to total mass ratio x=mb

m+

here m=mbmu . The e8uations o% state %or %or each o% the gases is

PVu=muRuT 6.5L

an#

uu=CvuThfu 6.6,L

PVb =mbR bT 6.66L

an#

ub=Cv bThfb 6.6*L

then+ i% the gases are homogeneously mi'e#+

PV=mxRb 1xRuT=mRT 6.6


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6.


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dm

d= mi me 6.6=L

dU

d= Q W Hi He 6.6-L

18


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Chapter * 7 Poer Cycle

This chapter presents the thermo#ynamics theory #escri1ing the main physical phenomena

occurring insi#e an /CE.

The thermo#ynamic mo#els o% the %our movements+ or stro!es+ o% the piston 1e%ore the entire

engine %iring se8uence is repeate#+ are #escri1e# in this chapter an# chapter


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%uel ta!es place in a totally enclose# an# nearly constant volumeL vessel. The com1ustion increases

the temperature o% the e'haust gases+ any resi#ual air in the com1ustion cham1er+ an# the

com1ustion cham1er itsel%. $rom the i#eal gas la+ the increase# temperature o% the gases also

pro#uces an increase# pressure in the com1ustion cham1er. The high pressure o% the gases acting

on the %ace o% the piston cause the piston to move to the BC hich pro#uces or!.

Unli!e the compression stro!e+ the hot gas #oes or! on the piston #uring the e'pansion stro!e.

The %orce on the piston is transmitte# 1y the piston ro# to the cran!sha%t+ here the linear motion o%

the piston is converte# to angular motion o% the cran!sha%t. The or! #one on the piston is then use#

to turn the sha%t+ an# to compress the gases in the neigh1oring cylin#ers compression stro!e.

"s the volume increase #uring the e'pansion+ the pressure an# temperature o% the gas ten#s to

#ecrease once the com1ustion is complete#.

*.*.Compression stage

*.*.6 Thermo#ynamic Mo#el o% the compression stage

During this stage+ the energy 1alance on the in7cylin#er gas is+

dU

d= Q W *.6L

"s 1oth valves are close# there is no mass e'change so

dm

d= mi = me=0 *.*L

"%ter the alge1raic manipulation shon in 0"ppen#i' ".*3 e8uation *.6L 1ecomes+

dT

d=

QmA

xRb1x R u T

AV

dV

d

CvT hfA

dx

d *.


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gases are homogeneously mi'e#+ here x=mr

m. Thus e8uations 6.6eat trans%er

>eat trans%er plays an important role insi#e an /CE 1ecause it a%%ects the engine per%ormance+

e%%iciency+ an# emissions.

0The pea! 1urne# gas temperature in the cylin#er o% an internal com1ustion engine is o% or#er

*4,,K. Ma'imum metal temperatures %or the insi#e o% the com1ustion cham1er space are limite# to

much loer values 1y a num1er o% consi#erations+ an# cooling %or the cylin#er hea#+ cylin#er+ an#

piston must there%ore 1e provi#e#. These con#itions lea# to heat %lu'es to the cham1er alls that can

reach as high as 6, M9m*#uring the com1ustion perio#.3Q6R

/n regions o% high heat trans%er+ it is necessary to estimate it in or#er to avoi# thermal stresses that

oul# cause %atigue crac!ing in the engines materials 0temperatures must 1e less than a1out ?,,C

%or cast iron an# eat

trans%er #ue to the %riction is negligi1le.

0The ma'imum heat %lu' through the engine components occurs at %ully open throttle an# at

ma'imum spee#. Pea! heat %lu'es are on the or#er o% 6 to 6, M9m *. The heat %lu' increases ith

increasing engine loa# an# spee#. The heat %lu' is largest in the center o% the cylin#er hea#+ the

e'haust valve seat an# the center o% the piston. "1out 4, o% the heat %lo to the engine coolant is

through the engine hea# an# valve seats+


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There%ore+ heat trans%er is a very important parameter in an engine 1ecause it is re8uire# %or a

num1er o% important reasons+ inclu#ing engines per%ormance an# e%%iciency+ material temperature

limits+ lu1ri%icant per%ormance limits+ emissions+ an# !noc! see appen#i' B.6L.

aL >eat trans%er mo#eling

/n the previes e8uations+ the #i%%erential heat trans%er is represente# 1y Q .

The #i%%erential heat trans%er Q to the cylin#er alls can 1e calculate# i% the instantaneous

average cylin#er heat trans%er coe%%icient hgFL an# engine spee# rpmL are !non.

The average heat trans%er rate at any cran! angle F to the e'pose# cylin#er all at an engine

spee# is #etermine# ith a etonian convection e8uation:

Q=h!Aw TTw /" *.?L

The cylin#er all temperature Tis the area7eighte# mean o% the temperatures o% the e'pose#

cylin#er all+ the hea#+ an# the piston cron. The heat trans%er coe%%icient hgFL is the instantaneous

average# heat trans%er coe%%icient. "t this stage+ the e'pose# cylin#er area "FL is the sum o% the

cylin#er 1ore area+ the cylin#er hea# area an# the piston cron area+ assuming a %lat cylin#er hea#.

1L >eat trans%er coe%%icient

The instantaneous heat trans%er coe%%icient+ h! #uring the poer cycle #epen#s on the gas

spee# an# cylin#er pressure+ hich change signi%icantly #uring the com1ustion process.

There are to correlations that are use# to get the heat trans%er coe%%icient+ the "nnan# an# the

9oschni correlation. >oever+ to compute the heat trans%er coe%%icient it as use# an empirical

%ormula %or a spar! ignition engine given in >an et al.655=L+

h!=687P0.75

U0.75

bo0.25

T0.465

*.4L

22


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ith some slightly mo#i%ications.

The units o% hg+ P+ U+ 1 an# T are 9m*K+ !Pa+ ms+ m an# K+ respectively.

The heat trans%er coe%%icient can also 1e o1taine# using the average# heat trans%er coe%%icient

correlation o% C. $. Taylor NThe /nternal Com1ustion Engine in Theory an# PracticeN+ M/T Press+

65-4L+

hb

k=10.4m

3 /4 U b

V

3 /4

*.;L

here ! is gas thermal con#uctivity an# the gas !inematic con#uctivity.

>oever+ this %ormula can 1e manipulate# into the %orm+

h!=C #P0.75

U0.75

bo0.25

T0.75

*.=L

$ormula *.4L #i%%ers %rom this only 1y the coe%%icient C an# the poer o% T. 9e have %oun# that the

value o% C


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means. Since the coe%%icient o% this term is very small+ e le%t it out.

*.


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oever+ in this stu#y e are mainly intereste# in overall per%ormance an#

not in #etaile# com1ustion cham1er #esign. >ence e ill use a simpli%ie# mo#el o% the com1ustion

cham1er an# %lame %ront.

aL Engine com1ustion Cham1er Design

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There are a large num1er o% options %or the /CE cham1er #esign hich inclu#es cylin#er hea# an#

piston cron shape+ spar! plug location+ sie an# num1er o% valves+ an# inta!e port #esign. The

#esign o% these important parts o% the /CE revolves aroun# issues such as cham1er compactness+

sur%acevolume ratio+ %lame travel length+ the %uel mi'ture motion an# more important the 1urning

velocity.

/t is !non+ that the com1ustion cham1er #esign hich increases the 1urning velocity+ %avors the

engine per%ormance. 9hen the %uel 1urning process ta!es place %aster + occupies a shorter cran!

angle interval at a given engine spee#+ pro#uces less heat trans%er #ue to loer 1urne# gas

temperaturesL an# increases e%%iciency.

/llustrations o% each o% the most commons e'amples /CE cham1er shapes hich pro#uces a 0%ast

1urn3 ill 1e given ne't $igure 4L+

$igure 4 @ E'ample o% common internal com1ustion engine cham1ers: aL hemispherical cham1erO 1L e#ge

shape# cham1erO cL 1athtu1 cham1erO #L 1ol W piston ith %lathea# on the right. Q;R

26

(a) (b) (c)

(d)


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/n the scila1s program it as assume# that the com1ustion cham1er as the simplest possi1le+ so

the piston is %lat on top+ the location o% the spar! plug is in the mi##le o% the cylin#er 1eteen the

valves an# the com1ustion cham1er has a cylin#rical geometry. Using this shape an# !noing that the

com1ustion reaction is so 8uic!+ it is possi1le to assume that the mean 1urne# gas %ront can also 1e

appro'imate# 1y a cylin#er instea# 1y a sphere ithout committing signi%icant errors as regar#s

overall per%ormance

1L Com1ustion cham1er consi#erations

"ssuming that the 1urne# one is a cylin#er o% height+ h an# ra#ius+ r at any instant o% F an#

using the mo#el hich consists in a to one analysis o% the com1ustion cham1er hich contains an

un1urne# an# 1urne# gas region separate# 1y a tur1ulent %lame %ront $igure ;L+

$igure ; @ S!etch o% the %ront shape o% the com1ustion cham1er

/t is possi1le to pre#ict ho the ra#ius+ r is going to change #uring the %lame travel+ assuming a

linear #istri1ution as it ill 1e e'plaine# ne't.

The variation o% the 1urne# ra#ius #ue to the change o% the cran! angle can 1e e'presse# 1y theappro'imation $igure =L+

27

Bore

Unburned zoneBurned zone

r(F)


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$igure = 7 Schematic o% 1urne# ra#ius as a %unction o% the cran! angle

here R=bo

2+ an# d is the angle at hich the 1urne# gas cylin#er reaches the engine

cylin#er all. d is #etermine# 1y the %lame spee# Vf in terms o% angular ratesL+

Then+

r=dr

d=0 %or s

r= Vfs an#dr

d= Vf %or sd

r=R an#dr

d=0 %or d

The %lame spee# Vf

is given 1y the tur1ulence mo#el. See 0"ppen#i' ".?3 %or r mathematical

#evelopment.

Being h=h the height %rom piston+ at any instant o% F+ to the top o% the cylin#er+ comes

h= v

R2

*.6?L

here v is the total volume o% the cylin#er.

The 1urne# an# un1urne# volume an# mass are easy to pre#ict+ no that r an# h are!non.

The 1urne# volume is+

Vb=hr2

*.64L

so

28

(2.13)


29/96

Vb =1

R2vr

2

*.6;L

an# its #erivative

dVb

d=

1

R2r

2 dv

d

2vr

R2

dv

d *.6=L

the un1urne# volume comes+

Vu=vVb *.6-L

$inally+ assuming that mb is proportional to Vb + it is possi1le to say+

mb

m=

Vb

v *.65L

then+ the 1urne# mass is

mb=m

v Vb *.*,L

its #erivative

dmb

d=m

1

v

dVb

d

Vb

v2

dv

d *.*6L

an# the un1urne# mass is

mu =mmb *.**L

an# its #erivative

dmu

d=

dmbd

*.*


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heredmu

dt = &u= &b +

&u is the mass trans%er rate to the un1urne# one an# &b is the

mass trans%er rate to the 1urne# oneO Qu is the heat trans%er rate %rom the un1urne# one to the

allsO P is the pressure in the cylin#erO Vu the un1urne# volumeO an# Uu is the total internal

energy in the un1urne# one.

"%ter the alge1raic manipulation e'plaine# in 0"ppen#i' ".43 this e8uation 1ecomes+

&uCvudTu

dt = Q uP

dVu

dt &bCv uC$uTu *.*4L

The energy 1alance %or the 1urne# one is

dUb

dt =QbP'dVb

dt &bhu *.*;L

heredmb

dt = &b O here

Qb is the heat trans%er rate %rom the 1urne# one to the allsO Vb

an# Ub are the volume an# internal energy o% the 1urne# one. The mass 1alances are

&b=d&b

dt *.*=L

an#

&u=d&b

dt *.*-L

here &b an# &u are the one masses.

"%ter the alge1raic manipulation e'plaine# in 0"ppen#i' ".;3 e8uation *.*;L 1ecomes++

&bCv bdTb

dt =QbP

dVb

dt &bC$ uTu Cv bTbhfuhfb *.*5L


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r=R

/% the en# o% the com1ustion process is progressively #elaye# 1y retar#ing the spar! timing+ or

#ecreasing the %lame spee# 1y #ecreasing the piston spee#+ the pea! cylin#er pressure occurs later in

the e'pansion stro!e an# is re#uce# in magnitu#e. These change re#uce the e'pansion stro!e or!

trans%er %rom the cylin#er gases to the piston.

*.


32/96

%unctions o%d&c

dt.

The term P is the tur1ulence energy pro#uction rate per unit mass an# is mo#ele# 1y+

P=+$

Aw

v U3

2

3k

1

v

dv

dt *.


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an# dt=1

wd comes+

dr

d=

Vf

w *.


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The e'pose# 1urne# area varies in %unction o% the 1urne# ra#ius+

Awb=r2

*.?6L

the e'pose# un1urne# area comes+

Awu=AwAwb *.?*L

$inally+ the heat trans%er e8uation %or the the 1urne# one is+

Qwb=h!A wbTbTw/" *.?


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*.?.6 Thermo#ynamic e8uation o% 1urne# gas e'pansion

During this stage+ the energy 1alance on the in7cylin#er gas is+

dUd =

QW *.?=L

"s 1oth valves are close# there is no mass e'change so

dm

d= mi = me=0 *.?-L

"%ter the alge1raic manipulation shon in 0"ppen#i' ".=3 comes+

dT

d=

QmCv

RbT

CvVdV

d *.?5L

*.?.* >eat Trans%er

"t this stage+ the heat release rate at any cran! angle F to the e'pose# cylin#er all at an enginespee# is #etermine# ith a etonian convection e8uation+

Q=h!Aw TTw /" *.4,L

The heat trans%er coe%%icient hgFL is the instantaneous average# heat trans%er coe%%icient an#

Aw is the e'pose# cylin#er area.

The instantaneous heat trans%er coe%%icient #uring the e'pansion stage is estimate# in the same

ay as the heat trans%er coe%%icient in the compression stage.

h!=300P0.75U

0.75bo0.25Tb

0.465/1000 *.46L

35


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here the units o% hg+ P+ U+ 1 an# T are !9m*K+ !Pa+ ms+ m an# K+ respectively. The piston spee#+ U

is given 1y e8uations *.5L an# *.6,L.

36


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Chapter < @ as e'change cycle

This cycle #eals ith the %un#amentals o% the gas e'change process+ inta!e an# e'haust an# the

valves mechanism in a %our stro!e internal com1ustion engine+ calle# the gas e'change cycle . &nly a

1rie% e'planation a1out the thermo#ynamics state an# gas %lo rate ill 1e given.

This cycle is calle# the gas e'change cycle 1ecause it is here the 1urne# gases %rom the

e'pansion stro!e are e'pelle# e'haust stro!e+ =evo2 to F


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Curt-in -re-=(.


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$igure 6, @ /sentropic %lo through an ori%ice

$or an i#eal gas+

o= Po

RTo eat that is le%t

over %rom the poer stro!e is no trans%ere# to the ater in the ater jac!et until the pressure

approaches atmospheric pressure. The e'haust valve is then opene# 1y the cam on the roc!er arm to

1egin the e'haust stro!e.

The purpose o% the e'haust stro!e is to clear the cylin#er o% the spent e'haust in preparation %or

40


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h!=300P0.75U

0.75bo0.25Tb

0.465/1000


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44/96

"s it as sai#+ the computer simulation as implemente# 1y ay o% 0Scila13 computer program.

0Scila13 is a scienti%ic so%tare %or numerical computations+ an# it is currently use# in e#ucational

an# in#ustrial environments aroun# the orl#. This program can 1e %oun# %reely in the %olloing

e1site: http:.scila1.org

The /CE computer simulation #evelope# is calle# CycleComC see appen#i' C.6L an# the

original one #evelope# 1y CAK is calle# CycleCom see appen#i' C.*L.

CycleComC /nputs

The values o% the input parameters use# in this simulation can 1e %oun# in the ta1les 1elo.

Engine #ata:

E'haust valve #ata:

44

Connecting ro#stro!e length ratio *

Compression ratio 66

Ma'imum cylin#er volume ,.,,,44

/gnition onset ra#

Burn #uration ra#

Burning en# ra#

Engine rpm rpm ;,,, rpm

Cylin#er all temperature ?,, K

c

rc

Am mence the amount o% inta!e gases is

re#uce#. "lso the or! re8uire# %or pumping o% the inta!e an# e'haust+ especially e'haust is greatly

increase#.

49

$or a non7a#ia1atic engine

PM Poer !9L E%%iciency L 9or! !VL


50/96

The results %rom the last version o% the CycleComC are the %olloings+

$igure 6; @ Aariation o% the poer+ e%%iciency+or! an# heat loss ith the engine spee# rpmL %or a non7a#ia1atic engine

Comparing this values %or the %inal program ith the ones o1taine# in heat trans%er mo#el+ e

conclu#e that the values %or the e%%iciency are to high. $or ;,,,rpm+ the e%%iciency result o1taine# %or

this %inal simulation #oing , is ==. This cannot 1e correct 1ecause it e'cee#s Carnot e%%iciency

hich is only appro'imately ;,. This con%irms that something is rong ith the 1asic to one

mo#el e have #evelope#. >oever+ e ill sho the results o1taine# 1y this mo#el.

50

PM Poer !9L E%%iciency L t !9L 9or! !VL !9ra#L

*,,, -.5, ?,., 76,.;, ,.4


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$igure 6= @ Poer as a %unction o% engine spee# rpmL

"s e'pecte#+ the poer rises an# %alls ith rpm+ 1ut the pea! occurs %or -4,,rpm hich is much

too high. "lso the pea! poer is much too large.

9hen e have heat loss in an engine+ occurs a re#uction in its temperature an# pressure hich

represents or! that cannot 1e #one lea#ing to loer values o% poer.

$igure 6- @ E%%iciency as a %unction o% engine spee# rpmL

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"nalising the %igure 6- an# the e%%iciency values o1taine# %or an non7a#ia1atic engine %igure 6;L+

e see that the com1ustion mo#el is not correct in the simulation program. /n %act+ as e'pecte# the

e%%iciency #rops %or a non7a#ia1atic engine. >oever+ an# as it as sai#+ %or an a#ia1atic engine

running at ;,,,rpm the e%%iciency is == hich is impossi1le to occur 1ecause even the Carnot Cycle

#oes not have so high e%%iciency.

"%ter some e'periences ith the program+ CAK an# / conclu#e that something is rong ith the

pressure calculation hich is lea#ing to high values o% or! an# e%%iciency.

$igure 65 @ Total heat trans%er as a %unction o% engine spee# rpmL

$rom %igure 65 e can say that the pea! o% total heat trans%er occur %or 5,,,rpm. "s the engine

spee# is increasing the heat trans%er also increase 1ecause the temperature an# pressure in the

cham1er are also increasing. >oever+ a%ter 5,,,rpm+ the heat trans%er start to #ecrease #ue to the

#ecrease o% the temperature in the cham1er 1ecause the amount o% %resh gas #ecreases #ue to

restricte# gas e'change process as e'plaine# 1e%ore.

ote as the engine spee# increases+ the heat loss per cycle an# the or! #rops o%% 1ecause the

amount o% gas 1urne# goes #on. "s it as sai#+ at high engine spee# the gas e'change process is

more an# more restricte#.

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$igure *, 7 Temperature vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

$igure *6 @ "verage temperature vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

"s it as e'pecte#+ the temperature pea! occurs %or the com1ustion stage+ hen the spar! goes

o%%. (oo!ing to the average temperature curve+ the temperature pea! occurs %or ? ra#+ 1ut this is #ue

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to the %act that in the un1urne# curve there is a small glitch hen the un1urne# mass goes to ero the

temperature increase hich in a real engine is rongL. This pro1lem is occurring #ue to some

restrictions that ere implemente# %or the com1ustion stage.

$igure ** @ P7A #iagram %or a %our stro!e engine running at ;,,,rpm

The pressure increases ith the movement o% the piston %rom the BC position to the TC position.

The pea! pressure occurs hen the piston is in the TC position. /n this position+ the spar! alrea#y

ent o%% an# e are in the mi##le o% the com1ustion stage. The pressure starts to #rop hen the

piston start the #escen#ing movement to the BC position+ here the e'haust valve ill open. ote that

ith the increase o% the piston spee#+ the pea! pressure gets smaller.

9e can see that the pressure pea! here is consi#era1ly higher 4*,,!PaL than the ?*,,!Pa o% the

single one mo#el ith heat trans%er %igure 6*L. The single one mo#el is much more realistic %or

typical engines. This shos that the appro'imation e have ma#e %or the pressure calculation is not

accurate.

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$igure *< 7 9or! vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

"s e can see %rom %igure *


56/96

$igure *? 7 >eat trans%er coe%%icient vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

$igure *4 @ >eat trans%er vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

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$igures *? an# *4 represent the results %rom the heat trans%er mo#el. "s e ere e'pecting in 1oth

curves the pea!s occur %or the com1ustion stage in hich the temperature hits the higher values. ote

that the values %or the heat trans%er are negative 1ecause this heat represents the heat losses in the

engine.

$igure *; @ Tur1ulence vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

$igure *= @ $lame spee# vs cran! angle #iagram %or a %our stro!e engine running at ;,,,rpm

$igures *; an# *= represent the results %rom the com1ustion mo#el in hich is ta!en into account

the tur1ulence in the cylin#er.

The main o1jective o% this mo#el as to atch the variation o% 1urn #uration ith the engine spee#.

/n real engines+ the mi'ture 1urning an# the %lame spee# are strongly in%luence# 1y engine spee#.

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9hen the engine spee# increases+ the %lame spee# also increases. >oever+ the 1urning rate

throughout the com1ustion process increases+ thought not 8uite+ as rapi#ly as engine spee# lea#ing to

higher cran! angle intervals.

/n the CycleComC+ the o1jective as to implement one tur1ulence mo#el that represent this

variation+ hoever the results ere not 8uite the ones e'pecte#. "s e can see %rom the %igures *;

an# *= the variation o% the tur1ulence is proportional to the piston spee#. $rom this e can conclu#e+

that the tur1ulence mo#el use# ere not the most accurate. The increase in the engine spee# lea#s to

a proportional increase in the %lame spee# an# the com1ustion #uration stays constant. The net e%%ect

is not much #i%%erent %rom CvKs essentially constant 1urning rate. The tur1ulence mo#el use# as

appro'imate# %rom (umleys mo#el. This shoul# 1e correcte# in a %uture e%%ort.

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Conclu#ing remar!s

The %un#amentals principles hich govern internal com1ustion engine #esign an# operations ere

ell #evelope# an# implemente# using the 0Scila13 computer program. "ll the o1jectives propose#

ere achieve#. $or the heat trans%er mo#el the results o1taine# ere 8uite goo#. >oever+ the resultso1taine# %rom the last simulation here it as a##e# the heat trans%er mo#el plus the com1ustion

mo#el ere not the ones e'pecte#. "s mentione# previously+ the mo#el use# as oversimpli%ie#+ thus

lea#ing to 8uantitatively erroneous results although the results ere 8ualitatively correct.

9e can conclu#e that treating the com1ustion mo#el CAK #evelope# is simpler than the one

#evelope# #uring this project an# lea#s to the goo# results. >oever+ the CycleComC is more

realistic 1ecause it presents a non7a#ia1atic engine+ an# the to one mo#el insi#e the com1ustion

cham1er hich ta!es into account the tur1ulence insi#e it. >oever+ some o% the #etails nee# to 1e

improve# in or#er to give 8uantitatively more accurate results.9e have conclu#e# that the main #i%%iculty is the pressure appro'imation. /t is %elt that ith a little

more time the pressure calculation can 1e improve# 1y a ne mo#el that e have #evelope#.

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Bi1liography

Q6R V. B. >eyoo#. /nternal Com1ustion Engine $un#amentals. Mcra7>ill+ /nc.+ 65--.

Q*R V. (. (umley. Engines "n /ntro#uction. Cam1ri#ge University Press+ Cam1ri#ge+ UK+ 6555.

Qill+ /nc.+

e Yor!+ Y+ *,,-.

Q4Rhttp:.1ritannica.com

Q;Rhttp:.secon#chancegarage.com

60
http://student.britannica.com/http://student.britannica.com/http://www.secondchancegarage.com/http://www.secondchancegarage.com/http://student.britannica.com/http://www.secondchancegarage.com/


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"ppen#i' "

Mathematical an# thermo#ynamic manipulations

".6. E8uation 6.6

$igure *< 7 S!etch o% the sli#er cran! mo#el o% piston7cylin#er geometry

9hen

=0 / 0 =.s

2

= / 0 =.s

2

0 =.coss

2cos

.sin s

2sin sin =

s

2 .sin

an#

cos=1sin2

comes+

cos =1 s

2 .2

sin2

so

0 =.1 s

2 .2

sin2

s

2cos

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62/96

$inally+

V=4

bo20 .

s

2

".*. E8uation *.

computer simulation of an internal combustion engine

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