APPLIED THERMODYNAMICS

UNIT II

IC ENGINES AND GAS TURBINES

I C ENGINES AND GAS TURBINES

AIR STANDARD CYCLES

INTRODUCTION

• The ideal cycle is defined as the series of processes occuring in an imaginary

perfect engine

• The actual cycle is defined as the series of processes occuring in an actual

engine.

In internal combustion engines and gas turbines the working fluid remains gas

throughtout the cycle. Plants take in a mixture of air and fuel or air and fuel separately for

combustion and liberate heat energy. The working fluid of the cycle mainly consists of air, so

the properties of working fluid closely follow the properties of air.

AIR STANDARD ASSUMPTIONS

To reduce the analysis to a manageable level, the air standard cycles are based on the

following approximations, commonly known as air standard assumptions.

1. Working fluid is air, throughout the cycle and always behaves as an ideal gas, i.e., it

follows the perfect gas law,

pV = mRT

2. All the processes are internally reversible.

3. Working fluid is homogeneous throughout and at all times and no chemical reaction

takes place.

4. Specific heat of air does not change with temperature.

5. Mass of air in the cycle remains constant.

6. Combustion process which may appear in actual process is replaced by heat addition

process from an external source.

7. Exhaust process is replaced by a heat rejection process and this rejection process is due

to heat transfer alone.

8. Engine operates as a closed cycle so that the working fluid is restored to its initial state

at the end of each cycle. Thus there are no intake and exhaust processes.

Air standard assumptions provide considerable simplification in the cycle analysis

without significant change from the actual cycles. This simplification enables to study

qualitatively the role of major parameters on the performance of the actual engines.

AIR STANDARD EFFICIENCY

Air standard efficiency is defined as the efficiency of an engine using air as the

working fluid. In other words, the thermal efficiency of the ideal air standard cycle is known as

air standard efficiency. This is often called as ideal efficiency.

Work doneAir standard efficiency =Heat supplied

( ) ( )Heat supplied Heat rejected=

Heat supplied−

1 2

1

Q =Qas

Qη

−

Actual efficiency of a cycle is always less than the air standard efficiency of that cycle

under ideal conditions. This is taken into account by introducing the terms relative efficiency

or efficiency ratio which is defined as

Actual thermal efficiencyRelative efficiency =Air standard efficiency

AN OVERVIEW OF RECIPROCATING ENGINE

Basic components of a reciprocating engine are shown in Fig.1. The piston reciprocates

in the cylinder between the two extreme positions of the piston called top dead centre (TDC -

the position of the piston when it forms the smallest volume in the cylinder) and bottom dead

centre (BDC - the position of the piston when it forms the largest volume in the-cylinder).

Fig. 1. Nomenclature of reciprocating engine

The distance between the TDC and BDC is the largest distance that the piston can

travel in one direction and is called as stroke. The diameter of the piston is ca fled the bore.

Minimum volume formed in the cylinder when the piston is at TOC is called as clearance

volume (Va). Similarly, when the piston is at BDC, the fluid will occupy the maximum

volume. The volume displaced by the piston as it moves between TDC and BDC is called

swept volume (V or displacement volume.

Volume of cylinder = (Clearance volume) + (Swept volume)

= Vc + Vs

`Ratio of the cylinder volume to the clearance volume is called the compression ratio

(r) of the engine.

Compression ratio = Cylinder volume/ Clearance volume

Mean effective pressure (m.e.p.) is defined as average pressure which is denoted by Pm

Pm = Work done per cycle / Swept volume

OTTO CYCLE OR CONSTANT VOLUME CYCLE

Figure 2 (a) and (b) show the representation of this cycle on p-V and T-s diagram. It

consists of two adiabatic processes and two constant volume processes.

Fig.2 Otto cycle on p-V and T-s diagrams

Process 1-2

Adiabatic (isentropic) compression of air during which the piston moves from crank end

(BDC) to cover end (TDC).

Process 2-3

The piston is at rest for a moment at TDC, the addition of heat (Q1) at constant volume takes

place.

Process 3-4

The fluid expands adiabatically (isentropically) and the work is done by the system, i.e., the

piston moves from TOC to BDC by the expansion of gases.

Process 4-1

The piston is at rest for a moment at BOC, the hut rejection (Q2) at constant volume takes

place.

The air standard efficiency of the Otto cycle can be calculated as follows:

Consider 1 kg of air flowing through the cycle and it is a closed system.

Heat supplied at constant volume (Q1) during process 2 3

Heat rejected at constant volume (Q2) during process 4 1

Q2 = m Cv T

Work done = (Heat supplied) - (Heat rejected)

This expression is known as the air standard efficiency of the Otto cycle which states

that the efficiency increases with the increase in the value of r. Due to practical difficulties the

r value is limited to about 7.

Mean Effective Pressure for Otto cycle Let Pm be the mean effective pressure (m.e.p)

.

Condition for Maximum Work Done

Work done is given by

Finally we obtain,

DIESEL CYCLE OR CONSTANT PRESSURE CYCLE

The cycle consists of two isentropic (adiabatic) processes, one constant pressure and

one constant volume process. Figure 3(a) and (b) show the representation of Diesel cycle on

p - V and T- s diagram.

Process 1-2

Isentropic compression of air during which the piston moves from BDC to TDC raising

pressure and temperature.

Process 2-3

At constant pressure the heat is supplied to the compressed air from an external source.

At point 3 the heat addition is stopped and the volume ratio V3/V2 is called the cut-off ratio.

Process 3-4

Isentropic expansion of air till the piston reaches BDC by which the work is done.

Process 4-1

At constant volume the heat is rejected to an external sink till the air restores initial

state.

Fig.3 Diesel cycle on p - V and T - s diagrams

Compression ratio, r = (V1/V2)

Cut-off ratio, = (V3/V2)

DUAL CYCLE OR COMPOSITE CYCLE

Combination of Otto cycle and Diesel cycle is called as Dual cycle. In this cycle the

combustion of fuel oil is carried out partly at constant volume and partly at constant pressure.

Semi-diesel engines work on this cycle. Figure 4 (a) and (b) show the representation of Dual

cycle on p-V and T-s diagrams.

Fig. 4. Dual cycle on p - V and T - s diagrams

Process 1-2 represents the isentropic compression of air

Process 2-3 represents the combustion of fuel at constant volume

Process 3-4 represents the combustion of fuel at constant pressure

Process 4-5 represents the isentropic expansion during which work is done by the system

Process 5-1 represents the heat rejection at constant volume.

Considering 1 kg of air flowing through the cycle,

Heat supplied, Q = (Heat addition during constant volume process) +

(Heat addition during constant pressure process)

Substituting the values of T2, T3, T4 and T5 the efficiency becomes

JOULE CYCLE OR BRAYTON CYCLE

The air standard Brayton cycle or Joule Cycle or constant pressure cycle is an idealised

cycle on which a gas turbine works. Figure 5 shows the representation of the Brayton cycle on

the p-v and T-s diagram. The cycle employs an air compressor, combustion chamber and a gas

turbine.

Fig. 5 Brayton cycle on p-V and T-s diagrams

Process 1 - 2

Air is compressed adiabatically in a compressor entropy constant process 2-3

Compressed air is heated at constant pressure

Process 3-4

Air expands adiabatically in a turbine and its pressure reaches the initial pressure.

Process 4-1

Heat rejection process in which the air at 4 is passed through a heat exchanger where it

is cooled to its initial condition 1.

These sequences of operations are for a closed cycle, but most of the gas turbine plants

in actual practice operate on open cycle.

The efficiency of the cycle increases with the rise in pressure ratio. But the rate of

increase in efficiency decreases with rise in pressure ratio.

IC ENGINESINTRODUCTION

Heat engine is a device which transforms the chemical energy of a fuel Into thermal

energy; utilize this thermal energy to perform useful work. Thus, thermal energy is converted

to mechanical energy. Heat engines can be broadly classified into two categories:

1. Internal Combustion Engines (IC Engines)

2. External Combustion Engines (EC Engines)

In external combustion engines the combustion takes place external to the cylinder,

e.g., steam engines.

In internal combustion engines the combustion takes place inside the cylinder, e.g.,

petrol, diesel, gas engines.

The main advantages of internal combustion engines over external combustion engines

are greater mechanical simplicity, lower ratio of weight. A bulk output due to absence of

auxiliary apparatus like boiler and condenser. The cost is lower, higher overall efficiency and

lesser requirement of water for dissipation of energy through cooling system.

CLASSIFICATION OF IC ENGINES

Internal combustion engines are classified as follows:

1. Number of stroke per cycle

• Four stroke engine

• Two stroke engine

2. Type of Ignition used

• Spark ignition (SI) engine

• Compression ignition (CI) engine

3. Types of fuel used

• Petrol or Gasoline engine

• Diesel engine

• Gas engine

4. Type of cooling system

• Air cooled engine

• Water cooled engine

5. Arrangement of cylinder

• Vertical engine

• Horizontal engine

• Radial engine

• V-engine

• Opposed cylinder engine

• Opposed piston engine

6. Applications

• Stationary engine

• Automotive engine

• Marine engine

• Aircraft engine

• Locomotive engine

WORKING PRINCIPLE OF FOUR STROKE CYCLE IC ENGINE

The working cycle of the engine is completed in four strokes or in two revolutions of

crank and petrol or diesel is used as fuel.

Suction or Induction Stroke [6(a)]

During this stroke inlet valve stays open and the exhaust valve is closed. The piston

moves downward from top dead centre (TOC) by means of crank shaft which involving by the

momentum of the flywheel or by power generated by the electric start motor. This movement

increases the size of combustion space thereby reducing the pressure in it, with the result that

the higher pressure of outside atmosphere forces the air into the combustion space.

In petrol engines a carburetor is put in the passage of incoming air which supplies a

metered quantity of fuel to this air. This air fuel mixture thus comes into the engine cylinder.

In diesel engines air alone comes into the engine cylinder.

Fig. 6 (a) Suction stroke, (b) Compression stroke, (c) Working stroke, (d) Exhaust stroke

Compression Stroke [6(b)]

The sucked in substance during the suction stroke is compressed during the next

upward stroke. The compression forces the fuel into closer combination with air. The heat

produced during this compression stroke aids the combustion of fuel just a little before the end

of compression stroke. Both the inlet and exhaust valves remain closed during this stroke.

In petrol engines, the fuel d air mixture is ignited by a spark produced by spark plug. In

diesel engines, fuel injector injects the fuel in atomized form and the combustion takes place

by means of high pressure and temperature of air.

Expansion Stroke [6(c)]

During this stroke both inlet and exhaust valves remain closed. The fuel and air which

burn at the end of the compression stroke expands due to the heat of combustion.

Exhaust Stroke [6(d)]

During this stroke, the inlet and fuel valves remain closed and exhaust valve remains

open. The piston moves up in the cylinder and pushes out the burned gases. The piston reaches

the TDC and completes the exhaust stroke and becomes ready for the next cycle.

VALVE TIMING DIAGRAM OF FOUR STROKE CYCLE ENGINE

The actual valve timing diagram of a four stroke cycle engine is shown in Fig. 7. The

inlet valve opens 100 to 25° in advance of top dead centre position (TDC) and 25° to 50° after

the bottom dead centre (BDC) position. Exhaust valve opens 30° to 50° in advance of BDC

position and closes at 10° - 15° after the TDC position. The fuel injection takes place at 50° to

10° after the TDC position. The inlet valve remains open for 25°+ 80°+35° = 240°.

Fig. 7. Valve timing diagram for a four stroke cycle engine

In diesel engines, fuel injection takes place at 5° to 10° before TDC position and

continues up to 15° to 25° after TDC position.

Thus the exhaust valve remains open for 40° + 180° + 15° = 235°. In petrol engines,

spark is produced through spark plug 30° to 40° before the TDC during the compression

stroke. The angle through which the spark is given earlier is called ignition advance or angle of

advance.

WORKING PRINCIPLE OF TWO STROKE CYCLE ENGINE

• Two stroke cycle engines require two strokes of the piston or one revolution of the

crank shaft to complete the cycle. In two stroke engines, ports are used instead of

valves.

• The exhaust gases are expelled out from the engine cylinder by the fresh charge of the

fuel entering the cylinder. In this engine the suction and exhaust strokes are eliminated.

• In case of two stroke cycle engine, the mixture of air and petrol is ignited by means of

an electric spark produced at the spark plug.

• The two strokes of the engine are First stroke and Second stroke.

Fig. 8. Working principle of two stroke petrol engine

First Stroke

• During first stroke, the piston moves upwards from bottom dead centre to top dead

centre. It closes the transfer port and the exhaust port.

• The charged air-petrol mixture which is already there in the cylinder is compressed.

• Due to upward movement of the piston, a partial vacuum is created in the crank case

and a fresh charge is drawl into the crank case through the uncovered inlet port.

• At the end of this stroke, the pistol reaches the TDC position.

Second Stroke

• The compressed charge is ignited in the combustion chamber by means of an electric

spark produced by the spark plug, slightly before the completion of the compression

stroke.

• Due to combustion of the air-petrol mixture, the piston is acted by a large force and is

pushed in the downward direction producing the useful power.

• During this stroke, the inlet port is covered by the piston and the fresh charge is

compressed in the crank case.

• Further downward movement of the piston uncovers the exhaust port and then the

transfer port. The expanded gases start escaping through the exhaust port and at the

same time fresh charge which is already compressed in the crank case is forced into the

cylinder through the transfer port.

• The charge strikes the deflector on the piston crown, rises to the top of the cylinder and

pushes out most of the exhaust gases.

Fig 9. Port timing diagram of two stroke petrol engine.

ENGINE POWER AND DIFFERENT EFFICIENCIES

Indicated Mean Effective Pressure (Pm):

The indicated mean effective pressure of an engine is obtained from the indicator

diagram with the help of an engine indicator

Where is area of diagram of rectangle in m2, s is scale of pressure, i.e., scale of indicator

spring kN/m2 per m and l is length of the diagram in m.

Indicator Horse power (IHP):

Indicated horse power is the power actually developed by the engine cycle.

where pm is actual mean effective pressure as obtained from the indicator diagram in kN/m2,

L is length of stroke in meters; A is area of the piston in m2,

N is speed of the engine in rpm,

n is number of working strokes/mm, n = N/60 (for two stroke cycle) and n = N/2 × 60 (for four

stroke cycle).

Brake Horse Power (BHP):

• Brake horse power is the power available at the crank shaft.

• The brake horse power of an IC engine is usually measured by means of a brake

mechanism (Proney brake or rope brake).

Brake power of the engine

where W is dead load in kg, S is spring balance reading in kg, D is diameter of brake drum in

meters, d is Diameter of the rope in meter, N is rpm of the engine

Efficiency of IC Engine

It is the ratio of work done to the energy supplied to an engine.

Mechanical Efficiency:

It is the ratio of brake power (BP) to the indicated power (IP).

Mechanical efficiency, m = B.P / I.P

Indicated Thermal Efficiency:

It is also called thermal efficiency. It is defined as the ratio of the heat equivalent of

indicated power to the heat energy supplied in fuel.

indicated = (Heat equivalent of IP / sec) / (Heat supplied in

fuel /sec)

= B.P / (F.C × C.V)

Air Standard Efficiency

Air standard efficiency of an IC engine may also be obtained from the general

expression for the standard efficiency

Relative Efficiency

It is also known as efficiency ratio. The relative efficiency of an IC engine is the ratio

of indicated thermal efficiency to the air standard efficiency.

Volumetric Efficiency

It is the ratio of actual volume of charge admitted during the suction stroke a NTP to

the swept volume of the piston.

APPLICATIONS OF IC ENGINES

Petrol Engine(i) Four-stroke petrol engine

Light vehicles such as cars, jeeps, aero planes and small generating sets

(ii) Two-stroke petrol engine

Very light vehicle such as motorcycles, scooters, three wheelers and par table crop

sprayers, etc.

Diesel engine(i) Four-stroke diesel engine

Diesel power plants, heavy vehicles such as buses, road - rollers, tractors, diesel

locomotives and water pumps.

(ii) Two-stroke diesel engine

Mainly used in marine engines where lesser weight is the ma consideration.

COMBUSTIONCombustion of fuels can be represented by chemical equation, both qualitatively and

quantitatively. The smallest quantity of a gas which can exist alone is a molecule, hence a

quantity of separate gas in a chemical equation must be stated as O2, H2, N2 etc., Table 1 gives

the approximate atomic and molecular masses of the substances which will be necessary, for

calculation work in problems on combustion of fuels.

Table 1: Approximate atomic and molecular masses of some substances

JAYAM COLLEGE OF ENGINEERING AND TECHNOLOGY

DHARMAPURIDEPARTMENT : EEE

YEAR / SEM : SECOND/ THIRD

SUBJECT : ME1211 / APPLIED THERMODYNAMICS

ASSIGNMENT NO 2

Unit 2 - IC Engines and Gas Turbines

PART A

1. What is thermodynamic cycle?

2. What are the assumptions made for air standard cycle analysis?

3. Mention the various process of diesel cycle.

4. Mention the various process of dual cycle.

5. Mention the various process of Brayton cycle.

6. Sketch Otto cycle on p-V diagram and name all the process.

7. Plot the Diesel cycle on p-V & T-s diagram.

8. Define mean effective pressure as applied to gas power cycle. How it is related to

indicate power of an I.C. engine?

9. Comparison between the S.I engine and C.I engine.

10. What is meant by octane number and cetane number?

11. What is meant by Ignition lag?

12. What is meant by auto ignition?

13. What is meant by Knocking?

14. What are the effects of Knocking?

15. Define the following terms. 1) Compression ratio 2) cut off ratio 3) Expansion ratio

16. Name the factors that affect air standard efficiency of Diesel cycle?

17. For the same compression ratio and heat supplied, state the order of decreasing air

standard efficiency of Otto, diesel and duel cycle.

18. What is the range of compression ratio for Otto and Diesel cycle?

19. Write an expression for mean effective pressure for an Otto cycle interns of

compression ratio and other parameters.

20. Different between the auto cycle, diesel cycle, duel cycle.

PART B

1. An engine on Otto cycle has a compression ratio of 8.5. The temperature and pressure

at the beginning of compression are 93º C and 0.93 bar. The maximum pressure in the

cycle is 38 bar. Determine the pressure and temperature at salient points and find the

air standard efficiency.

2. Sketch the Brayton cycle. Air enters the compressor of the cycle at 1 bar and 25º C.

Pressure after compression is 3 bar. Temperature at turbine inlet is 650º C. determine

per kg of air the cycle efficiency, heat supplied to air, work available, heat rejected in

the cooler and temperature of air leaving the turbine.

3. An oil engine working on theoretical diesel cycle has a bore of 200 mm and a stroke of

300 mm. Compression ratio is 16. Cutoff takes place at 10% of stroke. Find clearance

volume, cutoff ratio, and expansion ratio and air standard efficiency.

4. Sketch the p-v and T-s diagram for the Diesel cycle and obtain an expression for its air

standard efficiency.

5. Sketch the p-v and T-s diagram for the Duel cycle and obtain an expression for its air

standard efficiency.