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Engine geometry
AndOperating Characteristics
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engine is really
indicated inside the
work, power, mep etc.
engine is actually
work, power, mep
shaft.
ii- indicated ; is what the
producing, that is
cylinder in terms of
iii- brake ;is what the
delivering, similarly the
measured at the output
power
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inefficiency
iv- the values of the two
parameters is always
given as )indicated l under square )large engines(
d < l over square
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5. Compression ratio r
r =VBDC /VTDC
=) Vd +Vc)/Vc
8 SI 11
12 CI 24
3. Average piston speed
5 Up 15m/s
Up 15 m/s engine high performance automobile
5 Up m/s large diesel engine
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4. Engine speed
200-40012000- higher Up accelerates &decelerates twice in each crankrpm
So N- and t- for each rpmhence, Up- as N -
.Alimit must be set to avoid material strengthfailure in components like piston and con rod.
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.1Clearance volume (Vc)
this is the minimum volume
in the combustion
chamber with the pistonat the TDC
.2 Displacementvolume(Vst)
volume swept by the pistonas it travels through one
stroke
.3Total volume (Vt(
Is the sum of Vc &Vst
Vt =Vc +Vd
.4TDC &BDC
Vc =VTDC
Vt =VBDC
Related volumes
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From which)Vc) can be expressed as:
Compression ratio )Cr(
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P = F/A
P = pressure acting onforce is exerted.
combustion
Pg =gas pressure inside
Work )W) is always the
force )F) exerted over a
distance (x (. When there is no movementof an
object, there will be no work
done,regardless of how much
W =F .X
W =work (kJ/kg(
F =force
x =distance piston moves
But since
F =P .A
A =piston face area
piston face due to
P =Pg Pc
the cylinder due to
combustion process
Pc =pressure in crank case
work
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mass, the expression
Specific work; is the
of AF mixture:
And specific volume is
work )w) is
Sub and rearrangeW =P .A .X For small displacement(dx(
dW =P .A .dx
Where )A. dx =dV) incrementalswept volume
So, dW =P. dV
Therefore;
W =P.dV
Where )P.dV ) is thearea under the PVdiagram
When considering unit
specific is used, i.e
work done per unit mass
w =W/m
v =V/m
Therefore the specific
w =P. dv
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+)ve) whenthegas
expansionstroke(
compressedandthe
**The specificwork is
producingthepressureis
expanding )poweror
**The specificwork is
)- ve) whenthegasis
workisdoneonthegasbytheoutsidesource.
In this equation if )P) is the
pressure inside the cylinder,
then thework is the indicatedwork )w)i.
however, the actual work
delivered by the crank shaft is
the brakework )w)b ,and
)w)i - )w)b ) =w)l
Where )w)l is the specific work
lost
)w)l =] friction +parasitic[
specific workThe units representing work is
)kJ/kg(
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W =mep .Vd
mep =w/Vd =w/ v
TDCBDC
Since )mep) is related to
(w (,
the equation determines the
Due to piston motion andstroke, the pressureinside the cylinder iscontinuously changing
during the cycle, and therefore we can
define )mep) as
the everage pressure
acting on the pistonthrough the power
stroke
So, the work done bymep is:
W =P.dV
Then
v = v -v
then the type of )w) used in
type of (mep.(
Mean effective pressure (mep(
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For SI engines
(w)b bmep(w)i imep(w)pump pmep
(w)frictionfmep if gmep is gross mep and nmep is net mep
nmep =gmep +pmep
bmep =nmep fmepbmep =imep fmep
bmep =m .imep
For typical engines
850kPa bmep 1050kPa
forCI engines
kPa700 bmep 900kPa
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Calculation of engine
power output can be
done in several
methods, since thedefinition of power is
the rate at which
engine is doing work,then power is related
to work and speed.
Power ((
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1. Related to work
= W . (N/n)W : work (kJ/kg)
N : engine speed (rpm x 1/60) rps
n = 2 for 4 stroke engine
= 1 for 2 stroke engine
= power output (kW)
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The conversion factor )C (
C =4500 for )metrichp(
C =6120 for (kW(
2c. Related to (mep(
=k[PLAN/n] /CWhere:
C =conversion factork =number of cylinders
=power output )kW, metric hp(P =mep )kgf/cm (
L =piston stroke )m)A =piston cross section area (cm (N =engine speed (rpm(
n =rev/cycle
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get
3. Related to mean Up
= [PLAN/n] / CSince
L= stroke (S)N= engine speed
And
Up = 2LN = 2SN
ThenUp/2 = LN
Sub in equation to
=] P. A.Up] /n C
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swept volume (m (
)N/60n) :rev/s
a =is the air mass rate
a =v .Vd .a .) N/60n(
a : air mass rate kg/s
v : volumetric efficiency
Vd =/ 4d l
a =Pin/(Rg.Tin)
inlet air density
Pin (kPa (
Rg =0.287 kJ/kg.k
Tin )deg. K(
4. Related to combustion
=f .CV .th.i
Also since
FA =f/a
or AF =a /f
then f =FA. a
)=FA.a) CV .th.i
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From above equation, we can notice the followings:
If either )mf) or )AF) is given then, the power can be evaluated
engine geometry is known.
Considering the term )CV .th.i(
if
CV - is the fuel calorific value which is the fuel heating
value (Q).
- is the thermal efficiency of the engine cycle, which
means the fraction of heat liberated from fuel(CV . th.i ) that could be converted to mechanical
energy.
th.i
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In general power output =heat energy in fuel x abilityof conversion
What is the engine ability of conversion
In this respect, ability of conversion is best looked at through terms of efficiencies:
c -combustionefficiency, which is the ability of how much of the fuel that can really
be burned.
f - fuel conversion efficiency, which is the ability of how much heat energy canreally be converted to power.
So [f . CV] determines the total heat that can possibly be produced by combustionprocess.
Using the above efficiencies :Heat input to the engine
Qin= f . CV . c
Poweroutput from engine
=f .CV. f
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th = f .CV. f /f. CV . c
Heat input to the engine
Qin =f .CV . c Power output from
engine
=f .CV. f
th. -is the thermalefficiency
th = /Qin
th =f / c
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From all of the previous equations, power
correlation can be summarized as follows:
1. =W .) N/n(
2. =] PLAN/n] /C
3. =] P. A.Up] /n C
4. =f
.CV .th.
5. =2 N
summary
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2 =W/nAnd
obtain torque-powercorrelation
Torque is a force acting ata distance, measured in(N.m.(
Or more specifically
torque is a force that ,when applied, results in
twisting an object rather
than its physical
movement .Analytically, torque is
2 = W/n =bmep.Vd/n =bmep.Vd/ 2 n
Since =W ) .N/n(
Using the common factor )W)to
=2 N
Engine Torque
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correlation depends on the power used
i.e
units(gm/kW.hr(
sfc =fuel mass rate /engine power
sfc =f/The indicated or brake (sfc) in this
isfc =f / i
bsfc =f
/bThe )sfc) is usually measured in the
Specific fuel consumption
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are more commonly used, i.e
AF =a /f )mass rates kg/s(
Fuel/air ratio =fuel/air =FA
FA =mf /ma )mass kg()combustion) safe and
rates are set in such a values
Oxygen, from ambient air, isneeded in the engine cylinder
to chemically react with fuel
HC constituents.
In order to control suchchemical reaction
)combustion), there must be a
limit set upon both reactants
to keep the reaction
economical.
Therefore air and fuel mass
that satisfy such requirements
The ratios of both mass rates
Air/fuel ratio =air/fuel =AF
AF =ma /mf )mass kg(
FA =f /a )mass rates kg/s(
It is useful to acknowledge that
AF =1/ FAand
FA =1/ AF
Air /fuel mixture
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process (AF)a differ from
(to be discussed later).the engine to completely react
appears called the
stoichiometric)AF)stor )FA)st .
) =FA)a /) FA)st
In actual combustion
)AF)st due to many causes
So new expressionequivalence ratio
) =AF)st ) /AF)a
=1 stoichiometric >1 lean )O2 in exh(.