CH-4 Thermodynamics Heat Engine Cycles

8/10/2019 CH-4 Thermodynamics Heat Engine Cycles

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INDIABOILER DOT COMTUTORIAL FOR SECOND CLASS BOILER ENGINEERS PROFICIENCY EXAMINATION

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CHAPTER 4

Thermodynamics & Heat Engine Cycles

2.0 Introduction:

Thermodynamics is a branch of technology that deals with energy in all its forms and

the laws governing transformation of energy from one form to another. There are

several forms of energy such as mechanical, thermal or heat, chemical, electrical etc.Thermodynamics deals with the behavior of gases and vapour when subjected to

variations of temperature and pressure and the relationship between heat energy and

mechanical energy. When a substance undergoes a change from one state to anotherin a process, energy transformation may occur. Common processes are:

1). Heating or cooling, (2) Expansion or compression in the cylinder with or without

production or supply of mechanical work (3) Chemical reaction and change of phase

may occur in same processes involving liberation or absorption of heat.

2.1 Thermodynamic Medium or Working Substance

Any thermodynamic process or change involves the use of working substance orthermodynamic medium, Working substances has the ability to receive, store and

give out (or reject) energy as required by the particular process. The medium may be

in any one of the four physical states namely, solid, liquid, vapour and gaseous.

Following are examples of working substances:

1) water vapors ( as used in Steam power generating plant)

2) ammonia or freon ( as used in Refrigerator or ice plant)

Water vapour (steam) is a very suitable medium for power generation process,

because (a) it readily absorbs heat, (b) it flows easily to the engine, (c) it exertspressure on the engine piston and (d) it readily expands in engine cylinder.

Ammonia or freon is a suitable medium far an ice plant, because it boils at atemperature below 0

0C and at a moderate pressure, and absorbs latent heat from water

for such boiling at low temperature thus making it to freeze into ice.

2.2 Entropy: The term entropy means transformation. Entropy is a thermodynamicproperty of a working substance which increases with the addition of heat and

decreases with removal of heat. It is a thermodynamic variable (i.e., it is a parameter

of thermodynamic state like pressure, temperature etc.). It is introduced to facilitatethe study of working fluids (working substances) when they are passing through

reversible cycle (cycle consisting of only reversible operations). The term or propertyis used by engineers, as a means of providing quick solution for problems dealing

with Isentropic Operations.

Entropy is usually represented by the symbol .


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The small increase of entropy d

of a substance upon addition of heat to it is

defined as the ratio of small addition of heat dQ to the absolute temperature T ofthe substances at which the heat is supplied.

Thus, Entropy is a thermodynamic property which is defined as the ratio of heat

supplied or rejected during a reversible process and the absolute mean temperature atwhich the heat is supplied or rejected.

i.e. d = dQ/T or dQ = T . d

The source of heat may be external or internal such as a friction. The heating process,represented on a curve diagram (Fig. 1) having absolute temperature and entropy as

the two co-ordinates is known as T diagram.

Let, a substance be supplied with small amount of heat dQ, during which mean

absolute Temp is T. Then, the area of the shaded strip is given by

T. d = dQ.

Entropy is not a physical property of a substance in the same sense as pressure,

temperature etc. and, therefore, it cannot be measured directly by instruments. It is a

derived thermal property of substance. It depends upon mass of the system and

hence it is an extensive property (i.e., it is not an intrinsic property).The unit of entropy is heat unit per degree Kelvin per kg of substance i.e. KJ/kg

0C.

Perhaps the best way to understand entropy as a driving force in nature is to conducta simple experiment with a new deck of cards. Open the deck, remove the jokers, and

then turn the deck so that you can read the cards. The top card will be the ace of

spades, followed by the two, three, and four

ENTROPY

dT

1

2

TEMPERATURE

d

FIG. 1 Heating process represented on Temp. - Entropy Diagram

T


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of spades, and so on. Now divide the cards in half, shuffle the deck, and note that the

deck becomes more disordered. The more often the deck is shuffled, the more

disordered it becomes. What makes a deck of cards become more disordered whenshuffled? In 1877 Ludwig Boltzmann provided a basis for answering this question

when he introduced the concept of the entropy of a system as a measure of the

amount of disorder in the system. A deck of cards fresh from the manufacturer is

perfectly ordered and the entropy of this system is zero. When the deck is shuffled, theentropy of the system increases as the deck becomes more disordered. There are

8.066 x 1067

different ways of organizing a deck of cards. The probability of obtaining

any particular sequence of cards when the deck is shuffled is therefore 1 part in 8.066x 10

67. In theory, it is possible to shuffle a deck of cards until the cards fall into

perfect order. But it isn't very likely! Boltzmann proposed the following equation to

describe the relationship between entropy and the amount of disorder in a system. S= k ln W

In this equation, S is the entropy of the system, k is a proportionality constant equal tothe ideal gas constant divided by Avogadro's constant, ln represents a logarithm to the

base e, and W is the number of equivalent ways of describing the state of the system.

According to this equation, the entropy of a system increases as the number of

equivalent ways of describing the state of the system increases.

2.3 Zeroth Laws of Thermodynamics: This Law known as Zeroth Law, states that If

two bodies are each in thermal equilibrium with a third body, they are also in thermal

equilibrium with each other. If we take two bodies A and B, one hotter than theother, and bring them in to contact with each other, the heat energy will be transferred

from body at higher temperature to the body at lower temperature and after some time

when there is no further heat transferred between them, then the bodies are said to bein thermal equilibrium with each other now if a third body C is brought in contact

with the two bodies (let us take thermometer as a third body). Now suppose there is

no change in mercury level of the thermometer (body C) then we can say that thebodies A and B are each in thermal equilibrium with the third body C

(thermometer).

2.3.1 First Law of Thermodynamics: This law states that energy can neither be creatednor destroyed, if mass is conserved. The sum total of the energy in the universe is

constant; however, it can be converted from one form into another.

A machine cannot create work from nothing nor it can deliver more work than theenergy it receives.

In a thermal power generating plant, the chemical energy of the fuel is converted intoheat energy in the boiler, which in turn is converted into mechanical energy in the

steam engine or steam turbine. If the turbine is coupled to a generator the mechanical

energy is converted into electrical energy. If the generated electrical energy is

supplied to drive electric motor, the electrical energy is again converted into


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mechanical energy. If the electrical energy is supplied to heaters, it is converted to

heat.

It was established by Joule that Heat and mechanical energies are mutuallyconvertible. Joule established experimentally that there is a numerical relation

between the unit of heat and the unit of work. This relation is known as Joulesequivalent or mechanical equivalent of heat according to this relation

1 kcal = 427 kg m

2.3.2 General Energy Equation: According to the 1stLaw of Thermodynamic or the Law

of Conservation of Energy, when heat energy is supplied to a body, it is used, (i) As

an increase in internal energy i.e. increase in kinetic energy and potential energy ofgas molecules and (ii) in doing external work.

In stating the above as a general energy equation,

Let, Q = Amount of heat added to a body in kJ,

E = that part of Q that is used in increasing the store of internal energy i.e.

kinetic energy and potential energy of the gas molecules in kJ,W = that part of Q that is used in doing external work in kJ.

Then we have Q = E + W.

If Q is negative, it would be interpreted as heat rejected by the gas. If Q is positive,it denotes that heat is absorbed by the gas.

2.3.3 Second Law of Thermodynamics: This law states that It is impossible for self

acting machine, unaided by any external agency, to convey heat from a body at lowertemperature to a body at a higher temperature i.e., heat cannot, by itself, pass from a

colder body to a hotter body. Heat can be forced to pass to a higher temperature as in

the action of a refrigeration machine but only by applying an external agency to drive

the machine.

2.3.4 Reversible and Irreversible Processes: A process of a system, in which reverse or

back movement of system restoring the system as well as surrounding along the same

path is possible, is called a Reversible Process. In a Reversible Process all means ofenergy dissipation (due to friction, viscosity, electric resistance, magnetic hysterisis,

plastic deformation etc) are absent. In a reversible process, a system must be in

thermodynamic equilibrium at all states.

Any process that is not reversible is known as an irreversible process. All naturally

occurring i.e. spontaneous process are irreversible

2.4 Heat engine cycle.

A heat engine cycle is a series of thermodynamic process through which a workingfluid or substance (steam in a steam engine) is passing in a certain sequence. At the

completion of the cycle the working fluid returns to its original thermodynamic state

i.e., the working fluid at the end of the cycle has the same pressure, volume,temperature and internal energy that it had at the beginning of the cycle. Somewhere

during every cycle, heat energy is received by the working fluid. It is then the object

of the heat engine cycle to convert as much of this heat energy as possible into useful


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work. The heat energy, which is thus not converted, is rejected by the working fluid

during some process of cycle.

Any machine designed to carry out a thermodynamic cycle that converts heat energysupplied to it into mechanical energy, is called Heat Engine. Hence the cycle on

which it operates is known as a Heat Engine Cycle.Engineers have developed many methods of producing work from heat. Some of

these Heat Engine Cycles are.

Name of ideal cycle Use Fuel

Carnot Concept (Ideal) Any

Stirling Research Any

Otto Cycle Petrol engines Petrol

Diesel Cycle Diesel Engine Diesel (DERV)Brayton Cycle Jet Engines Kerosene

Brayton Cycle Gas turbines Gas/Oil

Rankine Cycle Coal power station Coal

Rankine Cycle Nuclear power statio Radioactive material

2.4.1 Available Energy: The amount of heat energy, which is converted into mechanical

energy, by a heat engine, is known as available energy.

The available energy can be calculated by subtracting the heat rejected during the

cycle from the total heat produced by the combustion of the fuel during the cycle.

Let Q1= Total heat produced by the combustion of the fuel per cycle and

Q2= Heat rejected during the cycle.

Then available energy = Q1 Q2

2.4.2 Thermal Efficiency:

The ratio of work done to the heat supplied during the cycle is known as ThermalEfficiency of cycle.

The work done during the cycle can be calculated by subtracting the heat rejected

from the total heat supplied during the cycle.That is, Work done during the Cycle = Heat Supplied Heat rejected.

W = Q1 - Q2

W = Work done during the cycle

Q1= Heat supplied during the cycle

Q2= Heat rejected during the cycle

Therefore Thermal efficiency = (Q1 Q2)/Q1


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This thermal efficiency does not take into consideration the actual or practical losses

during cycle of operation. Therefore, this is known as thermal efficiency of the cycle.

2.5 Carnot CycleAir as Working Medium:Carnot Cycle consists of Four Operations, Two Isothermal and Two frictionless

Adiabatic as shown in Fig. 2& Fig. 3 on T- & P-V diagram respectively.

Heat is supplied at constant Temperature T1 (Operation ab) & Rejected at constanttemperature T2(Operation cd). Frictionless Adiabatic Expansion is carried out during

operation bcand Frictionless Adiabatic compression is carried out during operation

da.

Heat Supplied = T1( b a)Heat Rejected = T2( c d) = T2( b a)

Work Done = Heat Supplied Heat Rejected = T1( b a) - T2( b a).= (T1 T2) (b a)

Efficiency = Work Done/Heat Supplied = (T1 T2) (b a) / T1(b a)= (T1 T2) / T1

Thus efficiency of the Carnot Cycle depends on two temperatures T1& T2. For higher

efficiency T1should be highest possible and T2 should be minimum possible.

The Carnot cycle gives highest possible efficiency but practically no Engine isconstructed operating on it as Isothermal process needs very slow speed of the Piston

T

T2

a b

d c

T1

Entropy

Temperature

Fig. 2 T- Diagram

Isothermal Compression

P

Pressure

a

d

V

c

b

Volume

Isothermal Expansion

Adiabatic Compression

Adiabatic Expansion

Fig. 3 P-V Diagram

Carnot Cycle Working Fluid is Air


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where as Isentropic process needs very fast Piston speed. Moreover it is clear from P-

V diagram that cycle is very narrow as compared to its length. That means very small

amount of useful Work is obtained which increases size of the Plant for the requiredoutput. Therefore Carnot Cycle remains a theoretical cycle and serves as a yard stick

for the comparison purpose.

2.6 Carnot CycleSteam as Working Medium:

When Steam is used as a Working medium the P-V & T- diagram of the Carnot

cycle are as shown in the fig. 4 and Fig. 5. Here heat is supplied at constanttemperature T1and constant pressure P1and rejected at constant temperature T2and

constant pressure P2.

Expansion and Compression of Steam are carried out isentropically. Referring to T-

diagram Fig. 4 Heat Supplied = T1( b a)

Heat Rejected = T2( c d) = T2( b a)

Work Done = Heat Supplied Heat Rejected = T1(b a) - T2(b a).= (T1 T2) ( b a)

Efficiency = Work Done/Heat Supplied = (T1 T2) (b a) / T1( b a)

= (T1 T2) / T1

It is also difficult to operate on this Cycle due to followings:

1. Heat rejection must be stopped at state d so that subsequent Compression

restores the fluid to its original State a. This is difficult.

2. If Superheated Steam is used, Cycle would be still more difficult owing tosupplying the steam at constant temperature.

These operations were modified by the Rankine to realize practical steam cycles. Heatrejection continues till all the vapour is converted to water. Addition and Rejection of

Heat is carried out at constant pressure instead of constant temperature.


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ba1 c

a

p

v

e

f

d

Volume V

Pressure

Fig. 6 P-V Diagram

Entropy

a

a1

Temperature

b

d

c

Fig. 7 T- Diagram

T

Rankine Cycle

Carnot Cycle- Working Fluid is Steam

Saturated

water line

a b

cT2

Entropy

Temperature

a,d b, c

T1

d

Saturatedsteam line

Fig. 4 T- Diagram

e f

T

Volume

P

b

c

a

d

Va Vb

Vc

Vd

P1

P2

Pressure

Fig. 5 P-V Diagram

V


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2.7 Rankine Cycle:

In steam plant, the supply of heat and rejection of heat is more easily performed atconstant pressure than at constant temperature. Therefore in Rankine Cycle heat

supply and rejection is carried out at constant pressures and the rejection of heat is

continued till the vapour is totally converted to water..

Hence Rankine cycle is a modified Carnot cycle.

Rankine cycle is represented by the closed figure abcd on P-V and T- diagramsin FIG. 6andFig. 7. The FIG. 8shows the schematic diagram of a steam engine orturbine plant. The various processes of the Rankine cycle are as follows.

aa: The point arepresents the water at condenser pressure and feed Pump, raises its

pressure to boiler pressure by adiabatic compression aa. During this process there isslight rise in temperature.

ab and bc: Heat is supplied to the boiler at constant pressure and the point b is

reached, which is the saturation temperature corresponding to the boiler pressure. Inp-v diagram point b nearly coincide with a as increase in volume is negligible.

Further addition of heat evaporates the water and the process is represented by bc.The final condition of steam may be wet, dry or superheated depending upon the

quantity of heat supplied.

cd: The steam is now expanded adiabatically to do work in a steam engine or aturbine.

Condensate

Extraction Pump

Boiler

Cooling

Water

Feed Pump

Engin

eOr

Fig. 8

Schematic Diagram of Steam Engine or Turbine Plant


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da: The exhaust from steam engine or the turbine is led into a condenser, where theLatent heat of the exhaust steam is removed by circulating water at constant pressure.

The process is represented by da.

In the P-V diagram, work done by the pump in increasing to pressure of water from

condenser pressure to boiler, is represented by the area aafe.This is however, verysmall at Low pressure and is, therefore, generally neglected.

The modified P-V and T-S diagrams representing the Rankine cycle neglecting feed

pump work are shown in FIG-6.10

Let hf2= enthalpy of water at point a,

h1= enthalpy of Steam at point c,

h2= enthalpy of Steam at point d,

Heat supplied during the process aband bc=h1hf2

Heat rejected during the process = h2- hf2

Work done = h1 h2

(h1 h2) is known as heat drop in engine / Turbine

Efficiency of the Rankine cycle = (Work done)/(Heat supplied)

= (h1-h2)(h1-hf)

From the T - diagram it can be seen that with superheating, the amount of increaseof work done is comparatively greater than the amount of increase of heat supplied.

Therefore, the efficiency of the Rankine cycle increases with superheating.

2.7.1 Modified Rankine Cycle:

In steam engines the expansion is not continued up to the point of d, as the workobtained is very small at the tail end as can be seen from FIG. 10In fact it is not even

sufficient to overcome the work lost in friction in tail end part of the stroke.Therefore, in actual practice, release is allowed to take place before the expansion is

complete at some point e by opening the exhaust port.

This causes a sudden pressure drop ef at constant volume due to steam

communicating with the outside atmosphere. This considerably reduces the stroke

length without any appreciable change in the work done. The cycle is then known as

modified Rankine cycle.

Work done in modified Rankine cycle = Area gbce+ Area gefa


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2.7.2 Effect of pressure and Temperature on Rankine cycle

2.7.2.1 Effect of exhaust pressure and Temperature: Let the exhaust pressure be loweredfrom P2to P2. The temperature at which the heat is rejected is also correspondingly

lowered. From the T-diagram shown in FIG. 10it is clear that the net increase inwork is represented by area ecce. At the same time the heat transferred to steam is

also increased by area eegf. As these two areas are approximately equal, therefore

the efficiency of the Rankine cycle is increased. It should be noted that although the

efficiency of the cycle increases with decreases in exhaust pressure and temperature,

the moisture content in the exhaust steam increases, which is not desirable

TP2P2

a b

c

c1

e

e1

f g h

Entropy

Temperature

Fig. 10: EFFECT OF EXHAUST PRESSURE & TEMP. ON RANKINE CYCLE

Pressur

e

Volume

V

a

P

b c

d

g e

j

1

2

3

Entropy

Temperat

ure

Work Lost

Constant volume

Work Lost

b

T

a

c

d

e

f

Fig. 9 The Modified Rankine Cycle


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2.7.2.2 Effect of supply pressure and temperature:Let the supply pressure be increasedfrom P1 to P1 with the corresponding increase in the temperature (saturation

temperature). The temperature of the superheated steam is kept constant. (Fig. 11).

Figure shows that increase in Pressure increases Work by an area abea, but

decreases in Work by an area ebcc. These two areas are approximately equals.Therefore there is no effect on the work output on the Cycle. However increase in

Pressure causes reduction in heat rejection by an area cchg. Hence the efficiency of

the Rankine Cycle increases with increase in supply pressure. But the increase in

supply pressure increases moisture content in the exhaust steam. This causes erosionof the later stages of the Turbine blades.

a1

b1

e

d

b

g hEntropy

Temperature

Fig-11: EFFECT OF SUPPLY PRESSURE & TEMPERATURE

a

T1

T1

Ts

T

cc1

Condense

Boiler

Cooli

Feed

C.W

IN

C.W

OUT

h3(1-M kg)

2

21

1

3

h2 M kg

1 kg

hf2 hf3

4

1 kg h3

1-

1 k

1-M

M k

2

4

3

2

1

Entro

T

Fig. 12 Actual Regenerative Cycle


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2.8 Regenerative Cycle:

The efficiency of Rankine cycle is less than Carnot cycle because in the Rankine

cycle all the heat is not added at highest temperature. The temperature is raised by

reversible interchange of heat before water enters the Boiler. This is shown in Fig. 12.The feed water is heated by bleeding small amount of steam from the Turbine.

The cycle in which an infinite number of such bleedings are assumed to take placebetween the points where the steam becomes dry saturated and it is finally exhausted

to the condenser, is known as Regenerative cycle.

[Bleeding is extraction of steam from any section of the turbine, before it has

completely expanded to the final temperature, for heating feed water.]

2.9 Ideal Regenerative Cycle:

The layout and the T- diagram of an Ideal regenerating cycle is shown in FIG. 13The steam enters the turbine, dry saturated, at temperature T1 and expands

adiabatically to temperature T2. The condensate from the condenser is pumped backthrough an annular space in the turbine casing and the feed water is heated by the

steam in a reversible manner, the temperature of steam and feed water being same at

any section.

The water enters the boiler in a saturated condition at 4. The heat gained by feedwater during 3-4, (area 3 4 b a), is equal to the heat given by the steam during 1 2,

S

BoilerCondenser

Pump

Turbine

1 2

3

4

Temperature

Entropya

b

T2

T1 4

3

31

c

d

221

1

T

Fig. 13 Ideal Regenerative Cycle


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(area 1d c2). It can be shown that the efficiency of this ideal regenerative cycle is

equal to that of cannot cycle.

Heat Supplied = area under 41 = 41 d b

Heat rejected = area under 21

d b 31

The above expressions are same as in Carnot cycle.

The advantage of regeneration is explained by the fact that in Rankine cycle moreLatent heat is thrown in condenser than in regenerative cycle.

The ideal regenerative cycle cannot be followed in actual practice. Even if we could

practically approach it, it would not be used because of the Low dryness fraction of

the steam in the latter stages of the turbine. Therefore in actual Practice advantage istaken of the principle of regeneration by bleeding a part of the steam flowing at

certain stages of expansion for feed water heating so that the dryness fraction of the

remaining part is not greatly reduced.

The Fig. 12shows the actual regenerative cycle.

2.10 Reheat Cycle:

The efficiency of the ordinary Ranking cycle can be improved by increasing thepressure and Temperature of the steam entering into the turbine.

As the initial pressure increases, the expansion ratio in the turbine also increases andthe steam becomes quite wet at the end of expansion. This is not desirable because the

increased moisture contents of the steam causes corrosion & erosion of the turbine

blades and increases the losses. This reduces the nozzle and blade efficiency.

In reheat cycle, the steam is extracted from a suitable point in the turbine and is

heated with the help of gases in the boiler furnace as shown in Fig. 14 & Fig. 15

shows Reheat cycle on H-& T-diagram.


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The dryness fraction of steam coming out of turbine should not fall below 0.88.

By using the reheat cycle, the specific steam consumption decreases and thermal

efficiency also increases.

Boiler

3

Superheater 2

2NDStage

Turbine

1stStage

Turbine

1

4

5

Condenser

Reheater

Pump

Enthalpy

P2= P3

P3

P42

1

4

3

Entropy

H

P42

P1T

P21

3

Temperature

4

Entropy

Fig. 14 Reheat Cycle

Fig. 15 Reheat Cycle on H- & T- Diagram


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The increase in thermal efficiency due to reheat depends upon the ratio of reheat

pressure to original pressure of steam ( i.e. P2/P1)

The reheat pressure is generally kept within 20% of the initial pressure of the

steam.

In reheater, the steam is generally heated to its initial temp. of steam. The efficiency of the reheat cycle may be less than the Rankine efficiency if the

reheat is used at low pressures.

The reheat cycle is only preferred for high capacity plants (above 50 MW and

when pressure of steam is as high as 100 kg/cm2ab)

It is not preferred for low capacity plants as the cost of the reheater is notjustified.

2.10.1 Advantages of Reheat cycle:

1.

There is a limit to the degree of superheat due to metallurgical conditions;therefore, it is not possible to get all superheat in one stage. The inevitable effectof use of higher pressure in modern power plants is that, the saturation line is

reached earlier during isentropic. Expansion as shown in Fig. 15, T- dia. H-diagram. Therefore most of the turbine stages operate in saturated steam region

which is highly undesirable. There is heavy blade erosion due to the impact of

water particles carried with the steam. Therefore, the reheating is essential in highpressure Modern power plants to increases the life of the plant.

2. The reheating reduces 4 to 5% fuel consumption with a corresponding reduction

in fuel handling.

3. The reheat cycle reduces the steam flow of 15 to 17% which corresponding

reduction in boiler, turbine and feed heating equipments capacities. This alsoreduces the pumping power in that proportion.

4. The wetness of the exhaust steam with reheat cycle is reduced to 50% of Rankine

cycle with a corresponding reduction in exhaust blade erosion.

5. Lower steam pressure and temperature and less costly material can be used toobtain the required thermal performance.

6. A reduction in steam volume and heat to the condenser is reduced by 7 to 8%.Therefore, the condenser size and cooling water requirement are also reduced by

the same percentages.

7. The size of the LP turbine blades is reduced because specific volume is reduced

by 7 to 8%.

8. The advantages claimed for the reheat cycle are higher thermal efficiency,

reduced feed pump power, smaller condenser, smaller boiler, long life of turbine

and less handling of fuel and firing equipment.


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2.10.2 Disadvantages of Reheat cycle:

1) The cost of extra pipes and equipments and controls makes this cycle more

expensive than ordinary Rankine cycle. There fore, the minimum capacity of theplant must be 50 MW for the adoption of reheat cycle.

2)

The greater floor space is required to accommodate the larger turbine(multicylinder) and reheat piping.

3) The complexity of operation and control increases with the adoption of reheatcycle.

Other Heat Engine Gas Cycles:

2.11 Otto Cycle- Internal Combustion Engine:Otto cycle is the prototype of the actual cycle used in engines with spark ignition i.e.

automobiles, aircraft etc.

Proces Nature of process Heat inpu Work outpu

12

23

34

41

Compression Stroke. Adiabatic compression of gas fuel

mixture in the cylinder.

Ignition of gas fuel mixture. Take place rapidly at top of tcompression stroke while the volume is essentially consta

Expansion Stroke. Adiabatic, isentropic expansion of gas

in the cylinder after fuel mixture is ignited. This is the parof the cycle that does positive work

Exhaust of the spent gases and the intake of a new fuel

mixture into the cylinder. The volume is the same at

beginning and ending of the exhaust and intake stroke.

0

Cv(T3-T2)

0

Cv(T1-T4)

- Cv(T2-T1)

0

- Cv(T4-T3)

0

T

V

P

1

2

3

4

V=0

1

2

3

4

V=0=0

=0

Otto CycleFig. 16


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Efficiency =

2.12 Diesel Cycle:In Diesel cycle heat is added at constant pressure. This cycle (Fig. 17) is typical ofheavy fuel engines referred to as diesel engines.

Proces Nature of process Heat inpu Work outpu

12

23

34

41

Compression Stroke. Adiabatic compression of gas fuel

mixture in the cylinder.

Ignition of gas fuel mixture. Fuel is ignited by high

temperature due to a large compression. Burning takes

places while the pressure is essentially constant.

Expansion Stroke. Adiabatic, isentropic expansion of gas

This is the part of the cycle that does positive work.

Exhaust of the spent gases and the intake of a new fuel

mixture into the cylinder. The volume is the same at

beginning and ending of the exhaust and intake stroke.

0

Cp(T3-T2)

0

Cv(T1-T4)

- Cp(T2-T1)

0

- Cp(T4-T3)

0

Efficiency =

(T4 T1)

(T3 T2)1

(T4 T1)

(T3 T2)1

Cv

Cp

(T4 T1)

(T3 T2)1

1

=

P

1

2

3

4

1

4

=0

2 3 P=0

T

V

=0

V=0

Diesel Cycle Fig. 17


19/19


LP/BOE-II/ 4- 01092001

D - 19

2.13 Brayton cycle:This cycle is used in gas turbine. Here the various processes take place in separate

steady flow machines such as compressor, turbine, heater and cooler. The workingmedia medium may be air or some other gas

Proces Nature of process Heat input Work outp

12

23

34

41

Isentropic-compression of the intake air into the combustisection of the engine.

Constant-pressure combustion of fuel injected into

combustion chamber.

Isentropic-expansion through the turbine section. This is t

part of the cycle that does positive work.

Constant-pressure heat is exhausting into the air.

0

Cp(T3-T2)

0

- Cp(T4-T1)

- Cv(T2-T1)

R(T3-T2)

- Cv(T4-T3)

R(T1-T4)

Efficiency

Let rpbe the pressure ratio as the process of compression and expansion are adiabatic, then

Efficiency = 1 -

2 3

4

1

2

1

3

4

P T

V

Adiabatic

P=0

P=0

Brayton cycle Fig. 18

1

2 3

4

Heater

Cooler

TurbineCompressor

Flow diagram Fig. 19

1rp

( )

-1

(T4 T1)

(T3 T2) 1 =

CH-4 Thermodynamics Heat Engine Cycles

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Transcript of CH-4 Thermodynamics Heat Engine Cycles