ME 165
Basic Mechanical Engineering
Internal Combustion Engine
Mantaka Taimullah
Assistant Professor
Department of Mechanical Engineering, BUET.
Being Familiar with IC Engines
An engine is a device that converts heat energy (chemical energy of fuel) into
mechanical energy (usually made available on a rotating output shaft).
The Internal combustion engine (IC Engine) is an engine in which the
combustion of fuel and an oxidizer (typically air) occurs inside a confined
space called a combustion chamber. This exothermic reaction creates gases at
high temperature and pressure, which are permitted to expand inside that
confined chamber. Thrust produced by this expanding gas drives the engine
creating useful work.
Application:
 Mainly used as “prime mover”, i.e., for the propulsion of a vehicle e.g. car, bus,
truck, locomotive, marine vessel, or air plane.
 Other applications includes stationary saws, lawnmowers, bull- dozers, cranes,
electric generators, etc.
Being Familiar with IC Engines
IC Engines: Construction
The three main portions of an IC engine are –
 Head block: Top Part
 Cylinder Block: Middle Part
 Chamber or Sump: Bottom Part
IC Engine: Construction
IC Engine: Terminology
 Piston Cylinder Assembly: It is the assembly for manipulating the
working fluid. The assembly is characterized by a piston moving
inside the confined cylinder.
 Inlet Valve: The valve through which air fuel mixture (in case of SI
engine) or air (in case of CI engine) is introduced inside the
cylinder.
 Exhaust Valve: The valve through which the products of
combustion leave the cylinder.
 Crank Mechanism: Mechanism to convert reciprocating piston
motion to rotary motion.
 Bore: Diameter of Cylinder.
 Top Dead Center (TDC): Position of Piston where
Cylinder Volume is minimum.
 Bottom Dead Center (BDC): Position of Piston where
Cylinder Volume is maximum.
 Stroke: It is the maximum distance that the piston
moves in one direction. It is the distance between TDC
to BDC.
IC Engine: Terminology
 Clearance Volume (Vc): Minimum Cylinder volume
when Piston is at TDC.
 Swept or Displacement Volume (Vs or Vd): Volume
swept out by the piston as it moves from TDC to
BDC.
𝜋
𝑉𝑠 = × 𝑑 2 × 𝑙
4
 Where 𝑑 is the cylinder bore and 𝑙 is the stroke
 Compression Ratio (rv): Ratio of maximum volume
(at BDC) and minimum volume (at TDC).
𝑉 𝑉𝑐 + 𝑉𝑠
𝑟𝑣 = =
𝑉𝑐
𝑉𝑐
 Mean piston speed: the distance traveled by the
piston per unit of time.
2𝑙𝑁
𝑉𝑚 =
𝑚/𝑠
60
 Where 𝑙 is the stroke in meters and N the number
of crankshaft revolution per minute (rpm).
IC Engine: Classification
IC Engine: Classification
Method of Ignition
 Spark ignition (SI): High-voltage electrical discharge between two electrodes ignites
air-fuel mixture in combustion chamber surrounding spark plug
 Compression ignition (CI): Air-fuel mixture self-ignites due to high temperature in
combustion chamber caused by high compression. Diesel engines are CI engines.
Number of strokes per cycle
 Four-stroke: Four piston movements over two engine revolutions for each engine
cycle.
 Two-stroke: Two piston movements over one revolution for each engine cycle.
The cycle of operation
 Otto cycle engine: also known as constant volume cycle engines
 Diesel cycle engine: also known as constant pressure cycle engines,
 Dual combustion cycle engine: also known as semi-diesel cycle engines
IC Engine: Classification
Design
 Reciprocating
 Rotary engine
Number of cylinders
 Single cylinder engines (e.g. lawn-mowers),
 Multi-cylinder engines.
The cooling system
 Air cooled engine
 Water cooled engine
 Evaporative cooling engines
IC Engine: Classification
Arrangement of cylinders:
 In-line or straight engine: cylinders in straight line,
one behind the other in length of crankshaft.
In line
 V engine: two banks of cylinders at an angle with
each other along a single crankshaft, angle typically
60 − 90°
 Flat or opposed cylinder engine: two banks of
cylinders opposite each other on a single crankshaft
(small aircrafts). Basically a V engine with 180° angle.
V
 W engine: three banks of cylinders on same
crankshaft (not very common)
 Opposed piston engine: two pistons in each cylinder,
combustion chamber between pistons
 Radial engine: cylinders positioned radially around
crankshaft.
Flat
IC Engine: Classification
W
Opposed piston
radial
IC Engine: Problem 1
A four-cylinder SI engine has a bore of 80 mm and stroke of 100 mm and the compression
ratio is 8. If the engine operates at 2000 rpm, calculate the following.
a. Total swept volume/ displacement volume
b. Total clearance volume
c. Average piston speed
Solution:
Given,
The engine bore, B = 80 𝑚𝑚 = 0.08 𝑚
Stroke length, 𝐿 = 100 𝑚𝑚 = 0.1 𝑚
Number of cylinder, 𝑛 = 4
Engine speed, 𝑁 = 2000 𝑟𝑝𝑚
We know,
Swept volume for each cylinder
𝑉𝑠
𝜋
= × 𝐵2 × 𝐿
𝑛
4
Or,
𝑛𝜋
4𝜋 × 0.082 × 0.1 3
2
𝑉𝑠 =
×𝐵 ×𝐿 =
𝑚
4
4
= 2.011 × 10−3 𝑚3
= 2.011 𝐿𝑖𝑡𝑟𝑒 = 2011 𝑐𝑐
Again, the compression ratio
𝑉 𝑉𝑐 + 𝑉𝑠
𝑟𝑣 = =
𝑉𝑐
𝑉𝑐
Or,
𝑉𝑐 + 2.011 × 10−3
8=
𝑉𝑐
Or,
𝑉𝑐 = 2.87 × 10−4 𝑚3
Average piston speed
2𝐿𝑁
2 × 0.1 × 2000
𝑉𝑚 =
𝑚/𝑠 =
𝑚/𝑠
60
60
= 6.67 𝑚/𝑠
IC Engine: Problem 2
A three-liter SI V6 engine that operates on a four-stroke cycle at 3600 RPM. The
compression ratio is 9.5, the engine is square [Bore (B) = Stroke (L)]. Calculate:
a. Cylinder bore
b. Stroke length
c. Average piston speed
d. Clearance volume of one cylinder
Solution:
Given,
Swept volume, 𝑉𝑠 = 3 𝑙𝑖𝑡𝑟𝑒 = 3 × 10−3 𝑚3
Number of cylinder, 𝑛 = 6
Engine speed, 𝑁 = 3600 𝑟𝑝𝑚
The engine bore, B =?
Stroke length, L =?
We know,
Swept volume for each cylinder
𝑉𝑠
𝜋
= × 𝐵2 × 𝐿
𝑛
4
As the engine is square, hence 𝐵 = 𝐿
So,
𝑉𝑠
𝜋
= × 𝐵2 × 𝐵
𝑛
4
𝜋
= × 𝐵3
4
Or,
3
𝐵=
4𝑉𝑠
=
𝜋𝑛
3
4 × 3 × 10−3
𝑚 = 0.086 𝑚
6𝜋
Since 𝐵 = 𝐿
∴ 𝐿 = 0.086 𝑚
IC Engine: Problem 2 (Contd..)
Average piston speed
2𝐿𝑁
2 × 0.086 × 3600
𝑉𝑚 =
𝑚/𝑠 =
𝑚/𝑠
60
60
= 10.32 𝑚/𝑠
The compression ratio
𝑟𝑣 =
𝑉 𝑉𝑐 + 𝑉𝑠
=
𝑉𝑐
𝑉𝑐
Or,
𝑉𝑠
𝑟𝑣 = 1 +
𝑉𝑐
Or,
𝑉𝑠
3 × 10−3 3
𝑉𝑐 =
=
𝑚 = 3.529 × 10−4 𝑚3
𝑟𝑣 − 1
9.5 − 1
Clearance volume of one cylinder,
𝑉𝑐 3.529 × 10−4 𝑚3
=
= 5.88 × 10−5 𝑚3 (= 58.8 𝑐𝑚3 )
𝑛
6
4 Stroke SI and CI Engines
Spark ignition (SI) Engine: High-voltage electrical discharge between two electrodes
ignites air-fuel mixture in combustion chamber surrounding spark plug
Compression ignition (CI) Engine: Air-fuel mixture self-ignites due to high temperature in
combustion chamber caused by high compression. Diesel engines are CI engines.
Four-stroke: The cycle of operation is completed in four strokes of the piston or two
revolution of the crank shaft. Each stroke consists of 180° of crank shaft rotation
In a 4 stroke internal combustion engine, the piston executes four distinct strokes within
the cylinder for every two revolutions of the crankshaft. The four strokes are termed as:
a. Intake Stroke
b. Compression Stroke
c. Power Stroke
d. Exhaust Stroke
4 Stroke SI and CI Engine Operation
4 Stroke SI and CI Engine Operation
First stroke: intake or induction
 Intake valve opens, and exhaust valve remains closed.
 Piston travels from TDC (top dead center) to BDC (bottom dead center).
 Volume increases in combustion chamber and creates vacuum.
 Fresh charge is drawn into the cylinder due to suction. For SI engine the charge is a
mixture of fuel and air. For CI engines charge is only air.
Second stroke: compression
 When piston reaches BDC, both intake and exhaust valves close.
 Now piston rises from BDC back to TDC with all valves closed, compresses the charge
raising its temperature and pressure. This stroke requires work input from the piston
to the charge.
 Near the end of compression stroke, combustion of fuel inside the cylinder is initiated.
In SI engines, it is induced by spark plug. In CI engines, combustion is initiated by
injecting fuel into the hot compressed air using fuel injectors.
4 Stroke SI and CI Engine Operation
Third Stroke: Expansion or Power Stroke
 Combustion occurs inside the confined space of engine cylinder.
 Change in composition of gas mixture from air and fuel to exhaust products occurs
due to exothermic blast. Temperature and pressure increase.
 High pressure pushes piston away from TDC. Work is done on the piston as thermal
energy is converted to mechanical energy.
 Piston moves from TDC to BDC, volume increases and pressure and temperature drop.
Fourth Stroke: Exhaust blow down
 Late in power cycle exhaust valve is opened.
 Piston moves from BDC to TDC due to momentum gained.
 Pressure differential pushes hot exhaust gas out of cylinder through exhaust system.
 Exhaust gas carries away high amount of enthalpy, which lowers cycle thermal
efficiency.
 Near end of exhaust stroke before TDC, intake valve starts to open and is fully open by
TDC when intake stroke starts next cycle.
 Near TDC the exhaust valve starts to close and is fully closed some time after TDC.
 Period where both intake valve and exhaust valve are open is called valve overlap
4 Stroke SI and CI Engine: Valve Timing Diagram
TDC: Top dead center
BDC: Bottom dead center
IVO: Inlet/Intake valve opens (10° − 20° before TDC)
IVC: Inlet/Intake valve closes (30° − 40° after BDC)
IGN: Ignition (20° − 30° before TDC)
EVO: Exhaust/Exit valve opens (30° − 50° before BDC)
EVC: Exhaust/Exit valve closes (10° − 15° after TDC)
Valve timing diagram for SI engine
*You may draw the diagram in both the ways showed,
spinning inside or outside
4 Stroke SI and CI Engine: Valve Timing Diagram
TDC: Top dead center
BDC: Bottom dead center
IVO: Inlet/Intake valve opens (10° − 20° before TDC)
IVC: Inlet/Intake valve closes (25° − 40° after BDC)
FVO: Fuel valve opens (10° − 15° before TDC)
FVC: Fuel valve closes (15° − 20° after TDC)
EVO: Exhaust/Exit valve opens (39° − 50° before BDC)
EVC: Exhaust/Exit valve closes (10° − 15° after TDC)
Valve timing diagram for CI engine
SI and CI Engine: Differences
Petrol Engines
Diesel Engines
Draws air-fuel mixture during suction Draws only air during suction stroke
stroke
Pressure at the end of compression Pressure at the end of compression stroke is
stroke is relatively low (about 10 bar)
relatively high (about 35 bar)
Charge is ignited with the help of spark Fuel is injected in the form of fine spray. The
plug
temperature and pressure of the compressed
air is high enough to ignite the fuel
Combustion of fuel takes place Combustion of fuel takes place approximately
approximately at constant volume
at constant pressure
Works on Otto cycle
Works on Diesel cycle
Compression ratio is generally between 6 Compression ratio is high, generally 15 to 25
and 10.
As compression ratio is low, petrol As compression ratio is high, diesel engines
engines are usually lighter and cheaper
are heavier and costlier
Thermal efficiency is lower (about 26%)
Thermal efficiency is higher (about 40%)
Generally employed in light duty vehicles Generally employed in heavy duty vehicles
like scooters, motorcycles and cars
like buses, trucks, earth moving machines etc.
Multicylinder IC Engine: Firing Order
Firing order: In line four cylinder 1-3-4-2
Firing order in a multi-cylinder engine is arranged so that the torsional moment is even
and the load is uniformly distributed on longitudinal direction of the crankshaft. An
even firing order will increase the balance of engine. Successive combustion in the
cylinders that standing side by side should be avoided so that the force transmitted to
the crankshaft does not become one-sided.
IC Engine: Subsystems
 Air Intake System
 Cooling System
 Ignition System
 Lubrication System
 Starting System
 Fuel supply system
 And many more…
Subsystems: Air intake System
 Job of air intake system is to take fresh air from the atmosphere to be mixed with
fuel for combustion. It usually consist of air cleaner/filter and ducts
Subsystems: Air intake System
 Normally Aspirated Intake:
 Air flows through an air-filter naturally and directly into the cylinders.
Movement of vehicle assists this intake process. Most cars are normally
aspirated.
 Turbocharged & Supercharged Intake:
 Air coming into the engine is first compressed so that much air can be
squeezed into each cylinder. This process increases performance of IC
engine as much air can burn much fuel and produce much power.
 A turbocharger uses the energy from exhaust gas and drives a small turbine
attached which makes the compressor shaft rotate and thus compress the
incoming air stream.
 A supercharger takes energy from engine to spin the compressor and thus
compress the incoming air stream.
Subsystems: Ignition System
 The ignition system produces a high-voltage electrical charge and transmits it to the
spark plugs via ignition wires. The change in electric flow in primary winding of
transformer created by a contact breaker. High voltage (22000 V) from secondary
winding of transformer flows to a distributor. The distributor has connected to four,
six, or eight wires (depending on the number of cylinders). These ignition wires send
the charge to each spark plug.
Spark plugs
Distributor
Contact Breaker
(CB)
Battery
(12 V)
Transformer
Subsystems: Lubrication System
 The lubrication system is necessary to ensure the proper movement of every engine
part. The two main parts that need lubrication are the pistons that move inside the
cylinders and bearings that carry shafts to rotate freely.
 Process: Oil is sucked out of the oil pan by the oil pump, run through the oil filter
to remove any grit, and then squirted under high pressure onto bearings and the
cylinder walls. The oil then trickles down due to gravity into the sump, where it is
collected again and the cycle repeats.
Functions
 Reduce wear of mating
components
 Reduce frictional power losses
 Serve as a cooling agent
 Serve as a cleaning agent
 Better sealing
 Better cushion at bearings
Subsystems: Cooling System
Cooling system in an IC engine can be classified as :
 Air Cooled: Atmospheric air flows around the fins attached with the engine and
causes cooling.
 Water Cooled: Clean water flows through the water jackets around the hot engine
cylinders. Hot water is then collected and cooled by means of a radiator.
Air Cooled Engine
Water Cooled Engine
Subsystems: Starting System
An engine is started by spinning the engine (or cranking) using energy from some
source other than burning of fuel. The combustion of starts due to the spinning of
engine. The engine is spun by external energy until energy from fuel burning retains the
spinning of engine.
There are various ways of engine cranking. Some of them are:
 Manual hand cranking: The engine is spun by means of energy from muscles. Usually
motorcycle engines have this provision.
 Electric Motor: The starting system consists of an electric starter motor. When the
ignition key is turned, the starter motor spins the engine a few revolutions so that
the combustion process can start.
 There are other ways too.
IC Engine Analysis: Air Standard Cycles
The accurate study and analysis of I.C.E. processes is very complicated. To simplify the
theoretical study "Air Standard Cycles" are introduced.
Assumptions of air–standard cycles
 Cylinder contains constant amount of air treated as ideal gas. No change in
composition throughout the full cycle.
 The specific heats and other physical and chemical properties remain unchanged at
their ambient temperature values during the cycle. (cold air-standard).
 The process of heat generation by combustion is represented by heat transfer from
external heat source.
 The process of heat removal in the exhaust gases is represented by heat transfer from
the cycle to external heat sink.
 All the processes are reversible i.e. there is no friction or heat loss.
 There is no Intake and Exhaust Strokes like an actual engine.
As Air-Standard Cycle analysis simplifies the study of internal combustion engines
considerably, the values of different parameters (pressure, temperature) calculated on
this basis may depart significantly from those of actual engines. So, Air-Standard analysis
allows internal combustion engines to be examined only qualitatively. Thermodynamic
cycles that adhere to air-standard assumptions are –
 Otto Cycle of Petrol Cycle (for SI Engines)
 Diesel Cycle (for CI Engines)
Air Standard Otto Cycle
The air-standard Otto
cycle or petrol cycle
assumes the heat
addition to occur
instantaneously while
the piston is at TDC.
Therefore in petrol
cycle, heat addition will
take place at constant
volume. Thus this cycle
is also known as
constant volume cycle.
The pressure inside the
cylinder rises rapidly
during the combustion
period as soon as
ignition of air-fuel
mixture is started by a
spark plug.
Air Standard Otto Cycle
Process 1-2:
Process 2-3:
Process 3-4:
Process 4-1:
Isentropic Compression. Piston: BDC → TDC
Constant Volume Heat Addition. Piston: at TDC
Isentropic Expansion (Power Stroke). Piston: TDC→ BDC
Constant Volume Heat Rejection. Piston: at BDC
The three relations of an isentropic process for ideal gases with constant specific heats in
compact form are
𝑃𝑉 𝑘 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑇𝑉 𝑘−1 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
1−𝑘
𝑇𝑃 𝑘
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Where,
𝑘 = specific heat ratio
𝐶𝑃
𝑘 =
= (1.4 for air as ideal gas)
𝐶𝑉
𝐶𝑃 = specific heat at constant pressure (1.005 𝑘𝐽/𝑘𝑔 for air as ideal gas)
𝐶𝑉 = specific heat at constant volume (0.718 𝑘𝐽/𝑘𝑔 for air as ideal gas)
Air Standard Otto Cycle
Process 1-2: Isentropic Compression:
𝑃1 𝑉1 𝑘 = 𝑃2 𝑉2 𝑘
𝑇1 𝑉1 𝑘−1 = 𝑇2 𝑉2 𝑘−1
or
𝑃2
𝑉1
=
𝑃1
𝑉2
or
𝑇2
𝑉1
=
𝑇1
𝑉2
1−𝑘
𝑇1 𝑃1 𝑘
=
𝑘
= 𝑟𝑘
𝑘−1
= 𝑟 𝑘−1
1−𝑘
𝑇2 𝑃2 𝑘
Where,
𝑟 = compression ratio (Sometimes written as 𝑟𝑣 )
=
Total Cylinder Volume 𝑉1 𝑉4
=
=
Clearance Volume
𝑉2 𝑉3
Process 2 – 3: Reversible heat addition at constant volume:
𝑄23 = 𝐶𝑉 𝑇3 − 𝑇2 𝑘𝐽/𝑘𝑔
Air Standard Otto Cycle
Process 3 -4: Isentropic expansion:
𝑘−1
𝑇3
𝑉4
=
= 𝑟 𝑘−1
𝑇4
𝑉3
𝑄34 = 0
Process 4 – 1: reversible constant volume cooling:
𝑄41 = 𝐶𝑉 𝑇4 − 𝑇1 𝑘𝐽/𝑘𝑔
Work output Otto Cycle = Heat Supplied − Heat Rejected = 𝑄23 − 𝑄41
Heat Supplied − Heat Rejected
Thermal efficiency, 𝜂𝑡ℎ =
Heat Supplied
𝑚𝐶𝑉 𝑇3 − 𝑇2 − 𝑚𝐶𝑉 𝑇4 − 𝑇1
=
𝑚𝐶𝑉 𝑇3 − 𝑇2
𝑇4
𝑇
1
𝑇4 − 𝑇1
𝑇1
1
𝑇1 − 1
=1−
=1−
= 1 − = 1 − 𝑘−1
𝑇3
𝑇3 − 𝑇2
𝑇2
𝑟
𝑇2 𝑇 − 1
2
1
∴ 𝜂𝑂𝑡𝑡𝑜 = 1 − 𝑘−1
𝑟
Air Standard Diesel Cycle
Air standard Diesel Cycle assumes the heat addition occurs during a constant pressure
process that starts with the piston at TDC. Thus this cycle is also known as constant
pressure cycle.
Process 1-2: Isentropic Compression. Piston: BDC → TDC
Process 2-3: Constant Pressure Heat Addition (1st part of Power Stroke). Piston: TDC → BDC
Process 3-4: Isentropic Expansion (Remainder of Power Stroke). Piston: TDC → BDC
Process 4-1: Constant Volume Heat Rejection. Piston: at BDC
This cycle is the theoretical cycle for compression-ignition or diesel engine.
Process 1-2: Isentropic Compression:
𝑃2
𝑉1
𝑘
𝑘
𝑃1 𝑉1 = 𝑃2 𝑉2
or
=
𝑃1
𝑉2
𝑇1 𝑉1 𝑘−1 = 𝑇2 𝑉2 𝑘−1
or
1−𝑘
𝑇1 𝑃1 𝑘
=
𝑇2
𝑉1
=
𝑇1
𝑉2
𝑘
= 𝑟𝑘
𝑘−1
= 𝑟 𝑘−1
1−𝑘
𝑇2 𝑃2 𝑘
Where, 𝑟 = compression ratio (Sometimes written as 𝑟𝑣 )
=
Total Cylinder Volume 𝑉1 𝑉4
=
≠
Clearance Volume
𝑉2 𝑉3
Air Standard Diesel Cycle
Process 2-3: Constant pressure heat addition
𝑃2 𝑉2 𝑃3 𝑉3
=
𝑇2
𝑇3
𝑜𝑟
𝑇3 𝑉3
=
= 𝑟𝑐 ;
𝑇2 𝑉2
𝑟𝑐 = cut − off ratio
𝑄23 = 𝐶𝑃 𝑇3 − 𝑇2 𝑘𝐽/𝑘𝑔
Process 3 -4: Isentropic expansion:
𝑘−1
𝑇3
𝑉4
=
𝑇4
𝑉3
𝑄34 = 0
Process 4 – 1: reversible constant volume cooling:
𝑄41 = 𝐶𝑉 𝑇4 − 𝑇1 𝑘𝐽/𝑘𝑔
Cut-off ratio is defined as the ratio of combustion chamber volume at the end of fuel
injection/combustion to the combustion chamber volume at the beginning of fuel
injection/combustion.
Air Standard Diesel Cycle
Thermal efficiency, 𝜂𝑡ℎ
Heat Supplied − Heat Rejected
=
Heat Supplied
Now,
𝑇1
1
𝑇3
= 𝑘−1 𝑎𝑛𝑑
= 𝑟𝑐
𝑇2 𝑟𝑣
𝑇2
𝑇
To get the value of 𝑇4:
1
𝑚𝐶𝑃 𝑇3 − 𝑇2 − 𝑚𝐶𝑉 𝑇4 − 𝑇1
=
𝑚𝐶𝑃 𝑇3 − 𝑇2
=1−
𝑉3
𝑇4 = 𝑇3 ×
𝑉4
𝑘−1
𝐶𝑉 𝑇4 − 𝑇1
𝐶𝑃 𝑇3 − 𝑇2
𝑇
𝑇1 𝑇4 − 1
1
=1−
𝑇
𝑇2 𝑘 𝑇3 − 1
2
𝑇1
=1−
𝑇2
𝑇4
1
𝑇1 − 1
× ×
𝑇3
𝑘
𝑇2 − 1
∴ 𝜂𝐷𝑖𝑒𝑠𝑒𝑙
𝑟𝑐 𝑘 − 1
= 1 − 𝑘−1
𝑟𝑣
𝑘 𝑟𝑐 − 1
= 1−
1
𝑟𝑣 𝑘−1
(𝑟𝑐 𝑘 −1)
𝑘 𝑟𝑐 − 1
Air Standard Cycles: η vs. r
 For each cycle, thermal efficiency increases with the increase of compression ratio.
 The thermal efficiency of the Otto cycle is higher than Diesel cycle for the same
compression ratio.
 In reality, diesel engines have much higher compression ratio than petrol engines; so
they become more efficient.
Air Standard Cycles: MEP
Mean Effective Pressure (MEP):
It is a theoretical parameter used to measure the performance of an internal
combustion engine (ICE). The mean effective pressure can be regarded as an average
pressure in the cylinder for a complete engine cycle. By definition, mean effective
pressure is the ratio between the work and engine displacement:
𝑀𝐸𝑃 =
𝑊𝑛𝑒𝑡
[𝑃𝑎]
𝑉𝑑
𝑊𝑛𝑒𝑡 𝐽 : Work performed in a complete engine cycle
𝑉𝑑 𝑚3 : Displacement/Swept volume of engine
𝑊𝑛𝑒𝑡 = 𝑀𝐸𝑃 × 𝑃𝑖𝑠𝑡𝑜𝑛 𝑎𝑟𝑒𝑎 × 𝑆𝑡𝑟𝑜𝑘𝑒 = 𝑀𝐸𝑃 × 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑉𝑜𝑙𝑢𝑚𝑒
The MEP can be used as a parameter to compare the performance of reciprocating
engines of equal size. The engine with a larger MEP delivers more net work per cycle
and thus better performance.
IC Engine: Problem 3
In an air standard Otto cycle, the compression begins at 35℃ and 0.1 MPa and the
compression ratio is 7. The maximum temperature of the cycle is 1100°C. Find:
a. The pressure after compression
b. The temperatures at various points of the cycle,
c. The heat supplied per kg of air,
d. work done per kg of air,
e. the cycle efficiency and
f. the MEP of the cycle.
Solution:
Given,
𝑇1 = 35℃ = 308 𝐾
𝑃1 = 0.1 𝑀𝑃𝑎 = 100𝑘𝑃𝑎
𝑇3 = 1100℃ = 1373 𝐾
𝑉1
𝑟=
=7
𝑉2
Since the compression process(1-2) is isentropic
𝑘
𝑃2
𝑉1
=
= 71.4 = 15.24
𝑜𝑟, 𝑃2 = 15.24 × 100 𝑘𝑃𝑎 = 1524𝑘𝑃𝑎
𝑃1
𝑉2
𝑇2
𝑉1
=
𝑇1
𝑉2
𝑘−1
= 71.4−1 = 2.178
𝑜𝑟, 𝑇2 = 2.178 × 308 𝐾 = 670.8 𝐾
IC Engine: Problem 3 (Contd..)
Since the expansion process (3-4) is isentropic
𝑘−1
𝑇3
𝑉4
1373
=
= 71.4−1 = 2.178
𝑜𝑟, 𝑇4 =
𝐾 = 630.4 𝐾
𝑇4
𝑉3
2.178
Heat input:
𝑄𝑖𝑛 = 𝐶𝑉 𝑇3 − 𝑇2 = 0.718 × 1373 − 670.8 𝑘𝐽/𝑘𝑔 = 504.18 𝑘𝐽/𝑘𝑔
Heat rejected:
𝑄𝑜𝑢𝑡 = 𝐶𝑉 𝑇4 − 𝑇1 = 0.718 × 630.4 − 308 𝑘𝐽/𝑘𝑔 = 231.48 𝑘𝐽/𝑘𝑔
𝑁𝑒𝑡 𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 = 504.18 − 231.48 𝑘𝐽/𝑘𝑔 = 272.7 𝑘𝐽/𝑘𝑔
Thermal efficiency:
1
1
𝜂𝑂𝑡𝑡𝑜 = 1 − 𝑘−1 = 1 − 1.4−1 = 0.54 = 54%
𝑟
7
Could also be determined from,
𝑊𝑜𝑟𝑘 𝑂𝑢𝑡𝑝𝑢𝑡
272.7
𝜂𝑡ℎ =
=
= 54%
𝐻𝑒𝑎𝑡 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑑 504.18
MEP:
𝑅𝑇1 287 × 308 3
𝑣1 =
=
𝑚 /𝑘𝑔 = 0.884𝑚3 /𝑘𝑔
𝑃1
100000
𝑊𝑛𝑒𝑡
𝑊𝑛𝑒𝑡
272.7
𝑀𝐸𝑃 =
=
=
𝑘𝑃𝑎 = 359.9 𝑘𝑃𝑎
𝑉𝑑
𝑣1 − 𝑣2 0.884 − 0.884
7
IC Engine: Problem 4
In a Diesel cycle, Compression begins at 0.1 MPa, 40°C and the compression ratio is 15.
The heat added is 1.675 MJ/kg. Find:
a. Temperature after compression
b. The maximum temperature in the cycle c. The cut-off ratio
d. The temperature at the end of the isentropic expansion
e. Work done per kg of air f. The cycle efficiency
g. The MEP of the cycle
Solution:
Given,
𝑇1 = 40℃ = 313 𝐾
𝑃1 = 0.1 𝑀𝑃𝑎 = 100𝑘𝑃𝑎
𝑄𝑖𝑛 = 1.675 𝑀𝐽/𝑘𝑔 = 1675 𝑘𝐽/𝑘𝑔
𝑟𝑣 = 15
𝑅𝑇1 287 × 313 3
𝑣1 0.898 3
=
𝑚 /𝑘𝑔 = 0.898𝑚3 /𝑘𝑔 ∴ 𝑣2 =
=
𝑚 /𝑘𝑔 = 0.060𝑚3 /𝑘𝑔
𝑃1
10000
𝑟
15
Since the compression process(1-2) is isentropic
𝑘−1
𝑇2
𝑣1
=
= 151.4−1 = 2.954
𝑜𝑟, 𝑇2 = 2.954 × 313 𝐾 = 924.66 𝐾
𝑇1
𝑣2
𝑄𝑖𝑛
1675
𝑄𝑖𝑛 = 𝐶𝑃 𝑇3 − 𝑇2
∴ 𝑇3 =
+ 𝑇2 =
+ 924.66 = 2591.33 𝐾
𝐶𝑃
1.005
𝑣1 =
IC Engine: Problem 4 (Contd..)
𝑃2 𝑣2 𝑃3 𝑣3
=
𝑇2
𝑇3
𝑜𝑟
𝑇3 𝑣3
=
= 𝑟𝑐
𝑇2 𝑣2
∴ 𝑟𝑐 =
𝑇3 2591.33
=
= 2.80
𝑇2
924.66
𝑣3 = 𝑟𝑐 × 𝑣2 = 2.80 × 0.060 = 0.168 𝑚3 /𝑘𝑔
Since the expansion process (3-4) is isentropic
𝑘−1
𝑘−1
𝑇3
𝑣4
𝑣3
𝑣3
=
𝑜𝑟, 𝑇4 = 𝑇3
= 𝑇3
𝑇4
𝑣3
𝑣4
𝑣1
𝑘−1
0.168
= 2591.33
0.898
1.4−1
Heat rejected:
𝑄𝑜𝑢𝑡 = 𝐶𝑉 𝑇4 − 𝑇1 = 0.718 × 1325.37 − 313 𝑘𝐽/𝑘𝑔 = 726.88 𝑘𝐽/𝑘𝑔
Net work output = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 = 1675 − 726.88 𝑘𝐽/𝑘𝑔 = 948.12 𝑘𝐽/𝑘𝑔
Thermal efficiency:
𝑊𝑜𝑟𝑘 𝑂𝑢𝑡𝑝𝑢𝑡
948.12
𝜂𝑡ℎ =
=
= 56.6%
𝐻𝑒𝑎𝑡 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑑
1675
𝑀𝐸𝑃 =
𝑊𝑛𝑒𝑡
𝑊𝑛𝑒𝑡
948.12
=
=
𝑘𝑃𝑎 = 1131.4 𝑘𝑃𝑎
𝑉𝑑
𝑉1 − 𝑉2 0.898 − 0.898
15
= 1325.37 𝐾
IC Engine: Problem 4 (Alternative Soln)
Since the compression process(1-2) is isentropic
𝑘−1
𝑇2
𝑉1
=
= 151.4−1 = 2.954
𝑜𝑟, 𝑇2 = 2.954 × 313 𝐾 = 924.66 𝐾
𝑇1
𝑉2
𝑄𝑖𝑛
1675
𝑄𝑖𝑛 = 𝐶𝑃 𝑇3 − 𝑇2
∴ 𝑇3 =
+ 𝑇2 =
+ 924.66 = 2591.33 𝐾
𝐶𝑃
1.005
𝑃2 𝑉2 𝑃3 𝑉3
𝑇3 𝑉3
𝑇3 2591.33
=
𝑜𝑟
=
= 𝑟𝑐
∴ 𝑟𝑐 =
=
= 2.8
𝑇2
𝑇3
𝑇2 𝑉2
𝑇2
924.66
Since the expansion process (3-4) is isentropic
𝑘−1
𝑘−1
𝑘−1
𝑘−1
𝑇3
𝑉4
𝑉3
𝑉3
𝑟𝑐 𝑉2
2.8
=
𝑜𝑟, 𝑇4 = 𝑇3
= 𝑇3
= 𝑇3
= 2591.33
𝑇4
𝑉3
𝑉4
𝑉1
𝑟𝑐 𝑉2
15
= 1324.56 𝐾
Heat rejected:
𝑄𝑜𝑢𝑡 = 𝐶𝑉 𝑇4 − 𝑇1 = 0.718 × 1324.56 − 313 𝑘𝐽/𝑘𝑔 = 726.30 𝑘𝐽/𝑘𝑔
Net work output = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 = 1675 − 726.3 𝑘𝐽/𝑘𝑔 = 948.7 𝑘𝐽/𝑘𝑔
Thermal efficiency:
𝑊𝑜𝑟𝑘 𝑂𝑢𝑡𝑝𝑢𝑡
948.7
𝜂𝑡ℎ =
=
= 56.6%
𝐻𝑒𝑎𝑡 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑑 1675
𝑅𝑇1 287 × 313 3
𝑣1 =
=
𝑚 /𝑘𝑔 = 0.898𝑚3 /𝑘𝑔
𝑃1
10000
𝑊𝑛𝑒𝑡
𝑊𝑛𝑒𝑡
948.7
𝑀𝐸𝑃 =
=
=
𝑘𝑃𝑎 = 1131.4 𝑘𝑃𝑎
𝑉𝑑
𝑣1 − 𝑣2 0.898 − 0.898
15
1.4−1
46