CHAPTER 2 Thermodynamics - Department of Mechanical ...me.emu.edu.tr/haybar/ME446/Chapter2.pdf ·...

Power Plant Engineering Chapter 2 Power Plant Thermodynamics

Chapter 2 – 1

CHAPTER 2

POWER PLANT THERMODYNAMICS

2.1. Thermodynamic Principles ...................................................................... 2

2.2. Steady Flow Engineering Devices and Processes ................................... 4

2.3. Heat Engine and Cycles............................................................................ 8

2.4. Carnot Cycle............................................................................................ 10

2.5. Rankine Cycle.......................................................................................... 10


In a thermal power plant, all processes are based on the fundamentals of

thermodynamics, heat transfer, and fluid mechanics. Fossil-fuel fired power plants, nuclear

power plants, and diesel engines are thermal heat engines.

2.1. Thermodynamic Principles The first and second laws of thermodynamics provide the fundamentals relationships for

a power plant cycle analysis.

In the thermodynamics, there are two types of system: closed system, and open system.

Before discussing the systems, we need to talk on system. A system is the object that we want

to analyze it. In the closed system, there is no mass transfer to the system and from the

system. In an open system there is mass transfer.

Let’s consider an open system (i.e. control volume). The first law is the energy balance

equation and is given by

ControlVolume

Work (W)

Heat (Q)Mass in

Mass out

Figure 2.1. Open System

systemoutin EEE Δ=− (kJ) (2.1)

or in terms of rate this equation will be

tE

EE systemoutin Δ

Δ=− && (kJ/s) or (kW). (2.2)

Energy can transfer to an open system in three ways: heat transfer, work interaction, and

carrying by mass. Energy (E) has components of enthalpy, kinetic energy, and potential

Chapter 2 – 2


energy. If the kinetic and potential energies are omitted from this equation, for an open

system this equation can be written as

ΔtΔ(Mu)

hmhmWWQQ cvoutoutininoutinoutin =−+−+− ∑ ∑ &&&&&& (2.3)

where

inQ& = heat transferred to control volume (kJ/s)

outQ& = heat transferred from control volume (kJ/s)

inW& = work done on the control volume (kJ/s)

outW& = work done by the control volume (kJ/s)

∑ ininhm& = total enthalpy entered to control volume by mass flow (kJ/s)

∑ outout hm& = total enthalpy entered from control volume by mass flow (kJ/s)

Δ(Mu)cv = internal energy change in control volume (kJ)

Similarly, the mass balance equation for control volume will be

∑ ∑ ΔΔ

=−t

Mmm cv

outin)(

&& (2.4)

For steady-state and steady-flow process, there is no mass and energy accumulation in the

control volume. Then the energy and mass balance equations will be

0 hmhmWWQQ outoutininoutinoutin =−+−+− ∑ ∑ &&&&&& (2.5)

and

∑ ∑ =− 0outin mm && (2.6)

Chapter 2 – 3


2.2. Steady Flow Engineering Devices and Processes

Turbine Process (Expansion Process)

Turbine is a device that converts heat energy of working fluid (e.g. steam) to mechanical

energy. If it is assumed that the process is adiabatic (i.e. no heat transfer), and there are no

kinetic energy and potential energy changes, and under steady-state condition, the energy

equation becomes

SuperheatedSteam

Wout

1

2

mPh

1

1

1

mPh

2

2

2 Figure 2.2. Turbine system

outoutininout hmhmW &&& −= (2.7)

Since the steady-state condition m mm outin &&& ≡= then,

outincv

t hhmΔW

w −==&

(kJ/kg) (2.8)

The turbine work (wt) by unit mass of working fluid equals the difference between inlet

enthalpy and exit enthalpy of the turbine. The steam temperature and pressure at the turbine

inlet (hi) determine the inlet enthalpy. To determine the exit enthalpy (he), the turbine internal

efficiency is used. The turbine internal efficiency is defined as

Chapter 2 – 4


s

a

esi

eit w

whhhh

=−−

=η (2.9)

It is the ratio of the actual enthalpy drop to the enthalpy drop that would occur in the

corresponding adiabatic and reversible process.

Figure 2.3 Turbine Expansion Process

Pump Process (Compression Process)

Pump is a device that increases the pressure of liquid fluid, for example water. The pump

process can be considered as a reversed turbine process. Then, the pump efficiency is defined

by

ei

esi

a

sp hh

hhww

−−

==η (2.10)

and the actual pump work for unit mass is

eip hhw −= (2.11)

Isentropic pump process can be written as

)( ieip PPvw −= (2.12)

Chapter 2 – 5


Figure 2.4. Compression process.

Mixing Process in a Mixing Chamber

For the mixing chamber, mass balance and energy balance equations are

∑ = ei mm && and ∑ = eeii mhmh &&

MixingChamber

P =cons.

Cold

Hot

1

2

3

mPh

1

1

1

mPh

2

2

2

mPh

3

3

3

Figure 2.5. Mixing chamber system

Heat Exchange Process in a Heat Exchanger

Heat exchanger is a device that transfers heat energy from hot fluid to cold fluid. Heat

exchangers have to have at least two fluids: hot fluid and cold fluid. The fluids do not mixed,

thus, fluids can be different pressure, can also be different fluids.

Heat exchangers can be classified in terms of flow direction of the fluids as follows:

• Parallel flow (hot fluid and cold fluid flow same direction)

• Counter flow (hot fluid and cold fluid flow opposite direction)

Chapter 2 – 6


• Cross flow (hot fluid and cold fluid flow perpendicular each other).

For example, car radiator is a cross flow heat exchanger in which hot fluid is water and cold

fluid is air.

Since heat exchangers are steady-flow engineering devices, they can be analyzed by the

steady-flow energy balance equation.

Hot Fluid

Cold Fluid

Th,in Th,out

Tc,in Tc,out

mh

mc

Q

Figure 2.6. Turbine system

Energy Balance Equation:

For Hot Fluid (Hot side):

)( ,, outhinhh hhmQ −= & (2.13a)

(2.13b) )( ,,, outhinhhph TTcmQ −= &

For Cold Fluid (Cold side):

)( ,, incoutcc hhmQ −= & (2.14a)

(2.14b) )( ,,, incoutccpc TTcmQ −= &

If heat exchanger is ideally insulated (i.e. nor heat losses), the energy changes for hot fluid

and cold fluid must be equal. Namely,

)()( ,,,, incoutccouthinhh hhmhhm −=− && (2.15)

The temperature distribution of the hot fluid and cold fluid is shown in the following figures.

If there is phase changing process like in condenser and evaporator, there are no temperature

changes in the phase changing side. In that case, the energy equations must be written in

terms of enthalpy, because there is not sensible heat change.

Chapter 2 – 7


Tc,in

Th,in

Th,out

Tc,out

Tc,in

Th,in

Th,outTc,out

ParallelFlow

CounterFlow

Tc,in

Th,in Th,out

Tc,out Tc,in

Th,in

Th,out

Tc,out

CondenserEvaporator

Figure 2.7. Temperature distribution hot and cold fluid

Throttling Process

In the throttling process, pressure will decrease, and the exit enthalpy is equal to the inlet

enthalpy. In another word, the enthalpy of the fluid during this process does not change,

namely

ei hh =

2.3. Heat Engine and Cycles Heat engine is a device that takes thermal energy from the hot reservoir, and converts

part of this energy to work, and dumps the rest of it to the cold reservoir. According to the 2nd

Law of thermodynamics, without two reservoirs, a heat engine cannot be designed. For

example, car engine is a heat engine. The car engine is internal combustion engine which has

Chapter 2 – 8


mainly two thermodynamics cycles: Diesel Cycle (compression cycle), and Otto Cycle (spark

ignition cycle). In a car engine, as a result of fuel combustion, a great amount of thermal

Heat Source (T )H

Sink (T )L

WorkHeatEngine

QL

QH

Figure 2.8. Heat Engine

energy is released which will be as Hot Reservoir of engine. In this case, hot reservoir is

inside the heat engine that’s why called internal combustion engine.

Brayton Cycle is the thermodynamic cycle for gas-turbine cycle engines, and Rankine

Cycle is the thermodynamics cycle for steam-turbine cycle engines.

The energy balance for the heat engines can be written as

(2.16) LH QWQ +=

The main purpose of heat engines is generating mechanical work. This mechanical

energy drives generator, and then electrical energy generated. Generator is a device that

converts mechanical energy to electrical energy.

In the fossil fuel-fired heat engines the fuel is coal, oil, or natural gas; while in nuclear

power plants the fuel is uranium.

Chapter 2 – 9


2.4. Carnot Cycle The Carnot cycle is the most efficient cycle that can operate between two constant

temperature reservoirs. One of them is high temperature reservoir, which is called source, and

the other is low temperature reservoir, which is called sink. The Carnot cycle consists of four

internally reversible processes. Thus, it can be called a reversible cycle.

Process 1-2 : reversible, isothermal heat addition

Process 2-3 : reversible, adiabatic

Process 3-4 : reversible, isothermal heat rejection

Process 4-1 : reversible, adiabatic

Since the processes are reversible, the Carnot cycle offers maximum thermal efficiency

attainable between two constant temperature reservoirs. The cycle thermal efficiency is

generally defined as

η th =work produced by the cycleheat supplied to the cycle

(2.17)

For the Carnot cycle the thermal efficiency becomes

H

L

H

LH

H

outth Q

QQ

QQQW

−=−

== 1η (2.18)

or

ηthH L

H

L

H

T TT

TT

=−

= −1 (Note that all temperature must be in Kelvin.) (2.19)

2.5. Rankine Cycle

Simple Ideal Rankine Cycle

The Rankine cycle is similar to the Carnot cycle with one exception in the condensation

process. In the Rankine cycle the condensation process terminates at the saturated liquid state.

The processes of a Rankine cycle are following:

Chapter 2 – 10


Process 1-2 : Isentropic compression process in pump

Process 2-3 : Constant pressure heat addition in boiler

Process 3-4 : Isentropic expansion process in turbine

Process 4-1 : Constant pressure heat rejection in condenser.

Boiler

Turbine

Condenser

Pump

Wt,out

CoolingWater

Qout

Qin

SaturatedLiquid

SuperheatedSteam

Steam

CompressedLiquid

Figure 2.9. Simple ideal Rankine cycle

It is evident that in the T-s diagram that the Rankine cycle is less efficient than a Carnot cycle

for the same maximum and minimum temperatures.

T

S

1

2

3

4

Qin

Qout

Wt,out

Wp,in

P =P1 4

P =P2 3

BoilerPressure

CondenserPressure

Chapter 2 – 11


Figure 2.10. T-s Diagram of Simple ideal Rankine cycle.

The thermal efficiency of the cycle can written as

in

outnetth Q

W ,=η and inpouttoutnet WWW ,,, −= or outinoutnet QQW −=,

As it is given above, there are four steady state processes:

Process 1-2: Pump Process 12, hhw inp −= or

( )121, PPvw inp −= for isentropic pump

Process 2-3: Boiler Process 23 hhqin −=

Process 3-4: Turbine Process 43, hhw outt −=

Process 4-1: Condenser Process 14 hhqout −=

Now we can ask why we have to use condenser. According to the 2nd Law of

Thermodynamics, without two reservoirs we cannot design a heat engine, so condenser

needed in cycle to damp some heat to sink. Another reason is that we use condenser is that the

work needed for compressing liquid is much less than that of vapor. Thus, always at the inlet

of pumps we need saturated liquid.

The Figure 2.11 shows the deviation of the actually Rankine cycle form the ideal one.

The efficiency of the Rankine cycle can be increased by

lowering the condenser pressure

increasing turbine inlet temperature

increasing boiler pressure

increasing boiler inlet temperature.

Chapter 2 – 12


Chapter 2 – 13

Figure 2.11 (a) Deviation of actual vapor power cycle from the ideal Rankine cycle. (b) The

effect of pump and turbine irreversibilities on the ideal Rankine cycle.

Lowering the Condenser Pressure:

The work produces in the Rankine cycle can be increased by lowering the condenser pressure.

However, it does not mean the condenser pressure should be reduced infinitely. Lowering the

condenser pressure can cause an increase in the moisture content in the turbine exhaust end.

These will affect adversely the turbine internal efficiency, and erosion of turbine blades. Also,

a low condenser pressure will result in an increase in condenser size and cooling water flow

rate.

Increasing Turbine Inlet Temperature:

Increasing the steam temperature also result in an increase of heat supplied in the boiler.

Increasing the steam temperature not only improves the cycle efficiency, but also reduces the

moisture content at the turbine exhaust end.

Increasing Boiler Pressure:

The maximum steam temperature and the condenser pressure are held constant. It is seen that

the steam pressure increases, the net work tends to remain unchanged.

Increasing Boiler Inlet Temperature:


If the boiler inlet temperature is increased, the amount of heat supplied in the boiler will

decrease.

Figure 2.12. The effect of lowering the condenser pressure on the ideal Rankine cycle.

Figure 2.13. The effect of superheating the steam to higher temperatures on the ideal

Rankine cycle.

Chapter 2 – 14


Figure 2.14. The effect of increasing the boiler pressure on the ideal Rankine cycle.

The Ideal Reheat Rankine Cycle

In this design, the idea is to increase turbine inlet temperature. The use of reheating is very

common in steam power plants. Reheating process may not improve the cycle efficiency, but

it does reduce the moisture content in the steam leaving the turbine. This may improve the

turbine internal efficiency and thus increase the cycle performance.

Chapter 2 – 15


Chapter 2 – 16

Figure 2.15 The ideal reheat Rankine cycle.

In this cycle,

reheaterboilerin QQQ += and LPTHPToutt WWW +=,

so ∑ −= inpouttoutnet WWW ,,,

In the analysis of the system given in Figure 2.15, we can write

The Ideal Regenerative Rankine Cycle

The main idea in this process is to increase boiler inlet temperature, namely to preheat the

feedwater before entering to the boiler using the waste energy of the turbine. The average

temperature for heat addition in the Rankine cycle us usually lower than maximum

temperature. It is only due to the liquid heating in the boiler. If this liquid heating could be

eliminated from the boiler, the average temperature for heat addition would be greatly

increased and equal to the maximum cycle temperature in the liquid case.

Analysis:

Boiler Process 45 hhqin −=

Condenser Process ( )( )171 hhyqout −−=

Turbine Process ( ) ( )( )7665, 1 hhyhhw outt −−+−=

Pump Process ( ) inpinpinp wwyw ,2,1, 1 +−=


Figure 2.16. The ideal regenerative Rankine cycle with an open feedwater heater.

Figure 2.17. The ideal regenerative Rankine cycle with a closed feedwater heater.

Feedwater Heaters

As it is mentioned above, there are two types of feed water heaters: Open feed water heater

(OFWH), and closed feed water heater (CFWH).

Open Feedwater Heater (Direct-Contact Heater):

Chapter 2 – 17


Open Feedwater Heaters (OFH) are called Direct-Contact Feedwater Heaters as well. They

are mixing chamber. In OFH the extraction steam is mixed directly with the incoming

sucooled feedwater to produce saturated water at the extraction steam pressure. Every

Rankine cycle power plant has at least one OFWH to remove non-condensable gases from the

system. The condensate water (saturated water) leaves the condenser is pumped to a pressure

equal to that of the extraction steam pressure from the turbine. The subcooled water after

pumping process and wet steam, which comes from the turbine, mix in the OFH to produce

saturated water. Thus the amount of bled steam (from the turbine) is essentially equal to that

would saturate the subcooled feedwater.

Closed Feedwater Heater (Surface Heater):

Closed Feedwater Heaters (CFH) are heat exchanger. This type of feedwater heater, though it

results in a greater loss of availability than the open type, is the simples and most commonly

used type in power plants. The closed feed water heaters are a shell-and-tube type heat

exchanger. In a closed feedwater heater, the feedwater (i.e. cold fluid) flows in the tubes, and

the bled steam (i.e. hot fluid), which is superheated steam or saturated steam, flows in the

shell side, and it passes its energy to the feedwater, and it condenses. Thus, they are small

condensers. Because the feedwater goes through the tubes in successive closed feedwater

heaters, it does not mix with the bled steam and therefore can be pressurized only once by the

first condensate pump, which then doubles as a boiler feed pump. Another boiler feed water

pump is required and placed after the open feedwater heater (i.e. deaerating) if one used in the

power plant.

Feedwater (cold)

Steam(superheatedor saturated) 1

2

34TxTy

Tdrain

Tsat

In the design of closed feed water heaters, there are two approaches:

Chapter 2 – 18


• Terminal Temperature Difference (TTD) ysat TTTTD −=

• Drain Cooler Temperature Difference (DCTD) xdrain TTDCTD −=

The value of TTD varies with heater pressure. In the case of low-pressure heaters, which

receive wet or at most saturated bled steam, the TTD is positive and often of order of 5°C.

This difference is obtained by proper heat-transfer design of the heater. Too small a value,

although good for plant efficiency, would require a larger heater than can be justified

economically. Too large a value would effect cycle efficiency. In the drain cooler, the drain

(i.e. condensate) is slightly sobcooled. The low-pressure feedwater heater receives saturated

or wet steam can have a drain cooler and thus physically composed of a condensing section

and a drain cooler section. The high-pressure feedwater heater receives superheated steam

bled form the turbine has desuperheating section and condensing section.

Thus, there are four physical possibilities of closed feedwater heaters composed of the

following section:

1. Condenser

2. Condenser, drain cooler

3. Desuperheater, condenser, drain cooler

4. Desuperheater, condenser.

DC CT

L

TTD

DCTD

DC C DST

L

TTD

DCTD

C DST

L

TTD

CT

L

TTD

Chapter 2 – 19


Figure 2.20. Temperature distribution of (a) Condenser, (b) Condenser and drain

cooler, (c) Desuperheater, condenser, and drain cooler, (d) Desuperheater and

condenser.

There are two types of connection of closed feedwater heaters: forward connection,

backward connection. For the forward connection a pump is needed to increase pressure. For

the backward connection, a throttling valve is needed to decrease pressure.

Feedwater (cold)

Steam (hot)

Forward

Pump

Feedwater (cold)

Steam (hot)

Backward

Throttling Valve

Chapter 2 – 20

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