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Energy Conversion
Chapter 3
Internal Combustion Engine
Internal Combustion Engines
Rotary Engine
• Wankel engine
Reciprocating Engine
• Spark Ignition Engine (SIE): gasoline
• Compression Ignition Engine (CIE): diesel
• Dual-cycle engine
Open-cycle Gas turbine
Wankel Engine
Wankel Engine
Reciprocating Engine
Reciprocating Engine
Combustion processes:
1. Intake
2. Compression
3. Power
4. Exhaust
Diagram of a cylinder
as found in 4-stroke
gasoline engines.:
C – crankshaft.
E – exhaust camshaft.
I – inlet camshaft.
P – piston.
R – connecting rod.
S – spark plug.
V – valves.
red: exhaust,
blue: intake.
W – cooling water jacket.
Gray structure – engine
Nomenclature for reciprocating engines
TDC : top dead center
BDC : bottom dead center
Displacement and clearance volumes
of a reciprocating engine
Compression ratio r : r 
Energy Flow
Energy Flow
Energy Flow
Indicated Horsepower ( ihp / Ni )
• The total horsepower actually developed on the
piston in the engine (ICE & AP Edward F. Obert)
 Brake Horsepower ( bhp / Nb )
• The power from an engine
(ICE & AP Edward F. Obert)
 Friction horsepower ( fhp / Nf )
• The power is spent in overcoming friction of the
bearing, pistons, and other mechanical part of
the engine and also in induction of the fuel-air
charge and delivery of the exhaust gas. ( ICE & AP
Edward F. Obert )
ihp = bhp + fhp
Motor efficiency
Theoretical Efficiencies : ηsiklus
• Thermodynamic Efficiency is a function of the
compression ratio and method of combustion.
Since theoretical cycles are based on air as
working substance , their efficiency is also
called “Air-standard Efficiency”.
• Air-standard Otto Cycle :
ηsiklus = 1 - ( 1 / r k-1 )
• Air-standard Diesel Cycle :
ηsiklus = 1- (1/r k-1)(rck-1)/(k(rc-1))
r = Compression ratio
rc = Cutoff ratio
Motor efficiency
 Combustion Efficiency : ηcomb
• Combustion Efficiency designated the ratio of heat
generated to the heat value of fuel .
ηcomb = Qgenerated / HV
 Charge Efficiency : ηch
• Is the ratio of the weight Wch of the actual fresh
charge to the weight of the piston displacement Vs if
it were filled with fresh charge having the outside
pressure and temperature .
ηch = Wch / Vs x ρa
dimana : ρa = pa / R Ta
Motor efficiency
 Volumetric Efficiency : ηv
• Due to the short cycle time and flow restrictions less
than ideal amount of air enters the cylinder.
• Is the ratio of the volume of fresh charge taken in
during the suction stroke to the full piston displacement .
ηv = Vch / Vs
Volumetric efficiency
 Volumetric efficiency (v) = (mass of air actually drawn into
cylinder) / (mass of air that ideally could be drawn into cylinder)
 air (measured)
v 
 airVd N / n
where air is at ambient = Pambient/RTambient and R - 287 J/kgK for air
 Volumetric efficiency indicates how well the engine “breathes” what lowers v below 100%?
• Pressure drops in intake system (e.g. throttling) & intake valves
• Temperature rise due to heating of air as it flows through intake
• Volume occupied by fuel
• Non-ideal valve timing
• “Choking” (air flow reaching speed of sound) in part of intake
system having smallest area (passing intake valves)
 Volumetric efficiency normally around 80% - supercharging and
Engine Geometry
s(q )  a cosq  l  a sin q
1/ 2
Cylinder volume when piston at TC
(s=l+a) defined as the clearance
volume Vc
The cylinder volume at any crank
angle is:
V (q )  Vc 
(l  a  s(q ))
Maximum displacement, or swept,
Vd 
Compression ratio:
For most engines B ~ L
(square engine)
VBC Vc  Vd
rc 
Mean and Instantaneous Piston Speeds
s  a cosq  l  a sin q
1/ 2
Average and instantaneous piston speeds are:
S p  2 LN
Sp 
Where N is the rotational speed of the crank shaft
in units revolutions per second
cos q
 sin q 1 
Sp 2
l / a 2  sin 2 q
1/ 2 
Average piston speed for a standard auto engine
is ~15 m/s. Ultimately limited by material strength.
Therefore engines with large strokes run at lower
speeds those with small strokes can run
at higher speeds.
Engine Torque and Power
Torque is measured using a dynamometer.
Force F
Load cell
The torque exerted by the engine is: T = F b with units: J
The power P delivered by the engine turning at a speed N and
absorbed by the dynamometer is:
P =  T = (2 N) T
w/units: (rad/rev)(rev/s)(J) = Watt
Note: w is the shaft angular velocity with units: rad/s
Indicated Work
Given the cylinder pressure data over the operating
cycle of the engine one can calculate the work done
by the gas on the piston.
Wi   pdV
The indicated work per cycle is
WA > 0
WB < 0
Indicated Power
Pi = Wi N / nR w/units: (kJ/cycle) (rev/s) / (rev/cycle)
N – crankshaft speed in rev/s
nR – number of crank revolutions per cycle
= 2 for 4-stroke
= 1 for 2-stroke
Power can be increased by increasing:
• the engine size, Vd
• compression ratio, rc
• engine speed, N
Mechanical Efficiency
Some of the power generated in the cylinder is used
to overcome engine friction. The friction power is
used to describe these losses:
Pf = Pi - Pb
Friction power can be measured by motoring the engine.
The mechanical efficiency is defined as:
m = Pb / Pi = 1- (Pf / Pi )
Mechanical efficiency depends on throttle position, engine
design, and engine speed. Typical values for car engines
at WOT are 90% @2000 RPM and 75% @ max speed.
Power and Torque versus Engine Speed
Rated brake power
1 kW = 1.341 hp
Max brake torque
There is a maximum in the brake
power versus engine speed called
the rated brake power.
At higher speeds brake power
decreases as friction power
becomes significant compared
to the indicated power
There is a maximum in the torque
versus speed called maximum
brake torque (MBT).
Brake torque drops off:
• at lower speeds do to heat
• at higher speeds it becomes
more difficult to ingest a full
charge of air.
Mean Effective Pressure (mep)
 The Mean Effective Pressure is the theoretical constant
pressure that , if it acted on the piston during the power
stroke, would produce the same net work as actually
developed in one cycle.
Mean Effective Pressure (mep)
Indicated Mean Effective Pressure (IMEP)
imep is a fictitious constant pressure that would produce the
same work per cycle if it acted on the piston during the power
imep = Wi / Vd = (Pi nR) / (Vd N)
so Pi
= imep Vd N / nR = imep Ap Up / (2 nR)
imep does not depend on engine speed, just like torque.
imep is a better parameter than torque to compare engines for
design and output because it is independent of engine speed,
N, and engine size, Vd.
Mean Effective Pressure (mep)
 Brake Mean Effective Pressure (bmep):
bmep is defined as that theoretical constant pressure
which can be imagined exerted during each power
stroke of the engine to produce power ( or work ) equal
to the brake power ( or work ).
Wb 2  T  nR
bmep 
bmep  Vd
 T
2  nR
Maximum BMEP
Wb 2  T  nR
bmep 
• The maximum bmep is obtained at WOT at a particular
engine speed
• Closing the throttle decreases the bmep
• For a given displacement, a higher maximum bmep means
more torque
• For a given torque, a higher maximum bmep means smaller
• Higher maximum bmep means higher stresses and
temperatures in the
engine hence shorter engine life, or bulkier engine.
• For the same bmep 2-strokes have almost twice the power of
Specific Fuel Consumption
• In engine testing the fuel consumption is measured in
terms of the fuel mass flow rate.
• The specific fuel consumption, sfc, is a measure of how
efficiently the fuel supplied to the engine is used to produce
bsfc = mf / Pb
isfc = mf / Pi
(w/units: g/kW-hr)
• Clearly a low value for sfc is desirable since at a given power
level less fuel will be consumed
Brake Specific Fuel Consumption vs Size
•BSFC decreases with engine size due to reduced heat losses
from gas to cylinder wall.
•Note: cylinder surface to volume ratio increases with bore
cylinder surface area 2rL 1
cylinder volume
r 2 L
Brake Specific Fuel Consumption vs Speed
• There is a minimum in the bsfc versus engine speed curve
• At high speeds the bsfc increases due to increased friction
• At lower speeds the bsfc increases due to increased time for
heat losses from the gas to the cylinder and piston wall
•Bsfc increases with compression ratio due to higher thermal
Performance Maps
Performance map is used to display the bsfc over the engines
full load and speed range. Using a dynamometer to measure
the torque and fuel mass flow rate you can calculate:
bmep = 2 T nR / Vd
Pb = 2 N T
[email protected]
bsfc = mf / Pb
Constant bsfc contours from a
two-liter four cylinder SI engine
Combustion Efficiency
• The time for combustion in the cylinder is very short so
not all the fuel may be consumed or local temperatures
may not support combustion
• A small fraction of the fuel may not react and exits with the
exhaust gas. The combustion efficiency is defined as
actual heat input divided by theoretical heat input:
. .
c = Qin/ (mf QHV) = Qin / (mf QHV)
Where Qin = heat added by combustion per cycle
mf = mass of fuel added to cylinder per cycle
QHV = heating value of the fuel (chemical energy per
unit mass)
Thermal Efficiency
t = work per cycle / heat input per cycle
t = W / Qin = W / (c mf QHV)
or in terms of rates…
t = power out/rate of heat input
t = P/Qin = P/(c mf QHV)
• Thermal efficiencies can be given in terms of brake or
indicated values
• Indicated thermal efficiencies are typically 50% to 60% and
brake thermal efficiencies are usually about 30%
Arbitrary Efficiency
(aka fuel conversion efficiency)
f = Wb / (mf QHV) = Pb / (mf QHV)
Note: hf is very similar to ht, the difference is that ht takes into
account only the actual fuel combusted in the engine.
Recall that sfc = mf / Pb
Thus f = 1 / (sfc QHV)
Volumetric Efficiency
• Due to the short cycle time and flow restrictions less
than ideal amount of air enters the cylinder.
• The effectiveness of an engine to induct air into the
cylinders is measured by the volumetric efficiency which
is the ratio of actual air inducted divided by the
theoretical air inducted:
v = ma / (a Vd) = nR ma / (a Vd N)
where ra is the density of air at atmospheric conditions Po, To
for an ideal gas ra =Po / RaTo and Ra = 0.287 kJ/kg-K (at
standard conditions ra= 1.181 kg/m3)
• Typical values for WOT are in the range 75%-90%, and
lower when the throttle is closed
Air-Fuel Ratio
• For combustion to take place, the proper ratio of
air and fuel must be present in the cylinder.
•The air-fuel ratio is defined as
. .
AF = ma / mf = ma / mf
• The ideal AF is about 15:1, with homogenous combustion
possible in the range of 6 to 19.
• For a SI engine the AF is in the range of 12 to 18
depending on the operating conditions.
• For a CI engine, where the mixture is highly nonhomogeneous and the AF is in the range of 18 to 70.
Fuel-Air Equivalence Ratio
Actual Fuel- Air Ratio :
m fuel
  
 A  act m air,act
Stoichiometric Fuel- Air Ratio :
Fuel Air Equivalence Ratio:
m fuel
  
 A  sto m air, sto
 
   A  act
 
 A  sto
Fuel properties
Heating value,
QR (J/kg)
f at stoichiometric
(f=Fuel mass fraction in mixture (---))
43 x 106
50 x 106
20 x 106
27 x 106
34 x 106
17 x 106
Fruit Loops
16 x 106
Probably about the same as paper
120 x 106
U235 fission
82,000,000 x
Example Problem
Calculating performance
Other performance parameter
 Heating Value / Calorific Value
 kJ/kg.fuel ; kcal/kg.fuel ; Btu/lbm.fuel
 Higher Heating Value (HHV):
 The higher heating value (also known as gross calorific value or gross
energy) of a fuel is defined as the amount of heat released by a
specified quantity (initially at 25°C) once it is combusted and the
products have returned to a temperature of 25°C, which takes into
account the latent heat of vaporization of water in the combustion
 Lower Heating Value (LHV):
 The lower heating value (also known as net calorific value) of a fuel is
defined as the amount of heat released by combusting a specified
quantity (initially at 25°C) and returning the temperature of the
combustion products to 150°C, which assumes the latent heat of
vaporization of water in the reaction products is not recovered.
Spark Ignition Engine
Four-stroke engine
Two-stroke engine
Four-stroke SIE
Two-stroke SIE
Two-stroke SIE
Theoretical Otto Cycle
Actual Otto Cycle
Combustion stages in SIE
Flame Propagation in SI Engine
After intake the fuel-air mixture is compressed and then ignited by a
spark plug just before the piston reaches top center.
The turbulent flame spreads away from the spark discharge location.
N = 1400 rpm
Pi = 0.5 atm
Flame Development
Mass fraction burned
Flame development angle Dqd – crank angle interval during
which flame kernal develops after spark ignition.
Rapid burning angle Dqb – crank angle required to burn most of
Overall burning angle - sum of flame development and rapid
burning angles
Mixture Burn Time vs Engine Speed
How does the flame burn all the mixture in the cylinder at high
engine speeds?
The piston speed is directly proportional to the engine speed, up ~ N
Recall the turbulent intensity increases with piston speed, ut = ½ up
Recall the turbulent burning velocity is proportional to the turbulent
St ~ ut, so at higher engine speeds the turbulent flame velocity is also
higher and as a result need less time to burn the entire mixture
Combustion duration in crank angles (40-60 degrees) only increases
a small amount with increasing engine speed.
 = 1.0
Pi =0.54 atm
Spark 30o BTC
Heat Losses During Burn
During combustion the cylinder volume is very narrow.
Heat loss to the piston and cylinder head is very important
In order to reduce the heat loss want burn time to be small (high
flame velocity) accomplished by either increasing
a) laminar burning velocity, or
b) turbulence intensity.
Highest laminar burning velocity is achieved for slightly rich
mixtures (for isooctane maximum Sl = 26.3 cm/s at   1.13)
Optimum F/A Composition
Maximum power is obtained for a F/A that is about 1.1 since this
gives the highest burning velocity and thus minimum heat loss.
Best fuel economy is obtained for a F/A that is less than 1.0
Spark Timing
Spark timing relative to TC affects the pressure development and
thus the imep and power of the engine.
Want to ignite the gas before TC so as to center the combustion
around TC.
The overall burning angle is typically between 40 to 60o,
depending on engine speed.
Engine at WOT, constant
engine speed and A/F
WOT=Wide open throttle
Maximum Brake Torque Timing
If start of combustion is too early work is done against piston and if
too late then peak pressure is reduced.
The optimum spark timing which gives the maximum brake torque,
called MBT timing occurs when these two opposite factors cancel.
Engine at WOT, constant
engine speed and A/F
MBT=maximum brake torque
Effect of Engine Speed on Spark Timing
Recall the overall burn angle (90% burn) increases with engine speed,
to accommodated this you need a larger spark advance.
Brake Torque
Fixed spark advance
2600 rpm
Fuel-air Ratio
Performance curve SIE
Variable Speed Test of Automotive SIE at Full Throttle (CR = 9)
Power and mep SIE
Efficiency and sfc SIE
Example: Eff and sfc SIE
Gross indicated, brake, and friction power (Pi, Pb, Pf), indicated,
brake, and friction mep, indicated and brake SFC, and hm for 3.8dm3 six cylinder automotive SIE at wide-open throttle. Bore = 96.8
mm, stroke = 86 mm, rc = 8.6.
Abnormal Combustion in SI Engine
Knock is the term used to describe a pinging noise emitted from a
SI engine undergoing abnormal combustion.
The noise is generated by shock waves produced in the cylinder
when unburned gas ahead of the flame auto-ignites.
Knock cycle
Exhaust valve
Spark plug
Normal cycle
Intake valve
Observation window
for photography
As the flame propagates away from the spark plug the
pressure and temperature of the unburned gas increases.
Under certain conditions the end-gas can autoignite and burn
very rapidly producing a shock wave
The end-gas autoignites after a certain induction time which is
dictated by the chemical kinetics of the fuel-air mixture.
If the flame burns all the fresh gas before autoignition in the
end-gas can occur then knock is avoided.
Knock is a potential problem when the burn time is long.
Parameters Influencing Knock
i) Compression ratio – at high compression ratios, even before
spark ignition, the fuel-air mixture is compressed to a high
pressure and temperature which promotes autoignition
ii) Engine speed – At low engine speeds the flame velocity is
slow and thus the burn time is long, this results in more
time for autoignition
- However at high engine speeds there is less heat loss so
the unburned gas temperature is higher which promotes
autoignition. Some engines show an increase in propensity
to knock at high speeds while others don’t.
iii) Spark timing – maximum compression from the piston
advance occurs at TC, increasing the spark advance makes
the end of combustion crank angle approach TC and thus
get higher pressure and temperature in the unburned gas
just before burnout.
Oktane number
Cetane number
Cooperative Fuel Research (CFR)
Fuel Knock Scale
Octane number: a standard measure of a fuel’s ability to resist
knock. The octane number determines whether or not a fuel will
knock in a given engine under given operating conditions.
The higher the octane number, the higher the resistance to
Normal heptane (n-C7H16) has an octane value of zero and
isooctane (C8H18) has a value of 100.
Blends of these two hydrocarbons define the knock resistance of
intermediate octane numbers: e.g., a blend of 10% n-heptane
and 90% isooctane has an octane number of 90.
A fuel’s octane number is determined by measuring what blend
of these two hydrocarbons matches the test fuel’s knock
Cooperative Fuel Research (CFR) Engine
Two methods have been
developed to measure ON
using a standardized
single-cylinder engine
developed under the
auspices of the
Cooperative Fuel Research
Committee in 1931.
The CFR engine is 4-stroke
with 3.25” bore and 4.5”
stroke, compression ratio
can be varied from 3 to 30.
Cooperative Fuel Research (CFR) Engine
Two methods: RON and MON
Note the motor octane number is always higher because it
uses more severe operating conditions: higher inlet
temperature and more spark advance.
Octane Number Measurement
Testing procedure:
• Run the CFR engine on the test fuel at both research
and motor conditions.
• Slowly increase the compression ratio until a standard amount of
knock occurs as measured by a magnetostriction knock
• At that compression ratio run the engines on blends of nhepatane and isooctane.
• ON is the % by volume of octane in the blend that produces the
The antiknock index which is displayed at the fuel pump :
Antiknock index 
Fuel Additives
Chemical additives are used to raise the octane number of
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