Module-1

Applied Thermo Fluids-II: Module-1 (Thermodynamics of power plant cycles)pp ( y p p y )(Autumn 2014)

Dr.M. Ramgopal, Mechanical Engineering, IIT Kharagpur

Introduction

• Electrical energy is considered to be energy of highest

grade as it can be converted into almost all other forms of

ith hi h ffi ienergy with very high efficiency

• Per capita consumption of electricity is considered to be an

i di i f h d l f hindication of the development of the country

• Per capita consumption of electricity is increasing

i l i I dicontinuously in India.

• However, the per capita electricity consumption in India is

still much smaller than that of most of the developed

countries

Central Electricity Authority, Ministry of Power, 2012

In India, a major part of electricity is generated in coal based thermal power plants. It is

expected that these thermal power plants will continue to dominate the energy sector in the

coming decades also

However, Indian coal has low calorific value and high ash content, as a result, per kWh

consumption of coal is higher in India ( 0.7 kg/kWh) compared to other countries ( 0.45

kg/kWh for US plants)g/ p )

The poor quality of coal affects both the plant’s thermal performance as well as emissions

Advanced and innovative technologies are needed to address these issues

Coal based thermal power plants also dominate the energy sector in many other countries! Hence, proper understanding and improving the overall performance of coal and other fossil fuel based thermal power plants is very important for these countries.

Thermal Power Plants

Th l l i f f l / • Thermal power plants use a variety of fuels/energy sources such as:– Coal– Natural Gas– Various types of petroleum products such as diesel

Nuclear fuels– Nuclear fuels– Solar energy– Geothermal energy– Ocean Thermal Energy etc.

• All the thermal power plants employ a thermodynamic cyclethat continuously converts the thermal energy intothat continuously converts the thermal energy intomechanical or electrical energy

• Hence all these power plants are subjected to thef ffundamental laws of thermodynamics

Basic thermodynamics of thermal power plant cycles

Sign Convention: Heat supplied and work produced are positive

Thermal power plant cycle with two thermal reservoirs

Carnot power cycle

Carnot cycle is a completely reversible but hypothetical cycle thatCarnot cycle is a completely reversible, but hypothetical cycle, thatserves as an ideal for 2-temperature power/refrigeration cycles

Sadi Carnot (1796-1832)

Thermal efficiency of a reversible (e.g. Carnot) cycleCarnot Vapour Power cycle with water as the working fluid

Carnot cycle and practical problems

• Performance of Carnot cycle is a function of temperatures only, and isPerformance of Carnot cycle is a function of temperatures only, and isindependent of working fluid

• Hence, theoretically Carnot cycle can be a vapour cycle or a gas cycleC t g l l t i ibl t d l th i• Carnot gas cycles are almost impossible to develop as they requireisothermal heat addition and heat rejection

• Using the process of phase change, nearly isothermal heat transfer canbe achieved Vapour cycles that resemble Carnot cycle are feasible

• Due to heat transfer and fluid friction, it is not possible achievereversible, adiabatic compression and expansion processes in pumpsreversible, adiabatic compression and expansion processes in pumpsand turbines, respectively.

• A finite temperature difference is required for transferring heat at bothhigh d l t t d C l h t b t ll i iblhigh and low temperature ends Cycle has to be externally irreversible

• Need for avoiding presence of two-phase mixture in turbine and pump,calls for non-isothermal heat transfer

Rankine cycle – Basis for most thermal power plants

William Rankine (1820-1872)

Simple Rankine cycle

Simple Rankine cycle

• The simple Rankine cycle deviates from the Carnot cycle as the heat addition

process in the boiler is no longer isothermal

• This is because, an isothermal heat addition requires, compression/expansion of

two-phase mixture or compression of condensed liquid to very high pressure

followed by non-isobaric heat addition. Both these processes are either not desirable

or extremely difficult to achieve in practice.

• In view of the above, in Rankine cycle a compromise is made between efficiency and

practical problems, which calls for deviation from the ideal Carnot cycle.

Analysis of simple, ideal Rankine cycle

A simple, steady state analysis of the cycle yields useful information related to:p , y y y y

a) Mass flow rate of working fluid for a given power output and operating conditions

(assuming that the working fluid is fixed, i.e., water)

b) Heat transfer rates across boiler and condenser

c) Power output from turbine and power input to pump

d) Cycle efficiency and sources of losses (?)d) Cycle efficiency and sources of losses (?)

e) Effects of working fluid and operating conditions on cycle performance

Simplifying assumptions:

1) The cycle is internally reversible

2) The system is operating in steady state

3) The potential and kinetic energy changes across any component are negligible

compared to work and/or heat transfer across the component

4) The working fluid circulating through the system is a pure fluid (water)4) The working fluid circulating through the system is a pure fluid (water)

Analysis of simple, ideal Rankine cycle (contd.)

Steady State, Steady Flow Energy equation (one inlet and one outlet):

Turbine (process 3-4; assumed to be reversible and adiabatic):

Condenser (process 4-1, assumed to be isobaric):


Pump (process 1-2; assumed to be reversible and adiabatic):

Boiler (process 2-3; assumed to be isobaric):


Overall energy balance for the cycle:

Thermal efficiency of the cycle, th is defined as:


Tm is termed as entropic mean heat addition temperature, and is defined as:

In terms of mean temperature Tm the thermal efficiency of the cycle, is given by:

Since Tm is less than T3, for same maximum and minimum temperatures, the efficiency

Second law or exergetic efficiency of the cycle, 2nd is defined as:

Since Tm is less than T3, for same maximum and minimum temperatures, the efficiency of Rankine cycle is always less than that of Carnot cycle!

Example Problem on Simple Rankine cycle

Given:Boiler Pressure = 163 barCondenser pressure = 0.07 barMax heat addition temp = 538 oCMax. heat addition temp., 538 CNet power output = 500 MW

Results

F d (EES)From property data (EES)

Improving efficiency of Rankine cycle

Rankine cycle efficiency can be increased either by increasing the mean

temperature of heat addition (Tm) and/or decreasing the temperature of heat

rejection (T )rejection (Tc)

Decreasing Tc significantly is not possible due to the constraint imposed by the

available heat sink

Increasing Tm is possible by using either reheat and/or regeneration

In actual power plant cycles, both reheat and regeneration are used to maximize

the efficiency subject to economic constraints

Reheat is also beneficial as it minimizes wet expansion and also provides an

opportunity for increasing the boiler pressureoppo tu ty o c eas g t e bo e p essu e

Effect of increasing boiler pressure

The mean temperature of heat addition (T ) can be increased by increasing theThe mean temperature of heat addition (Tm) can be increased by increasing theboiler pressure Thermal efficiency increases for given heat source temperature

Though the efficiency increases by about 2% for an increase in pressure of 100 bar increasedThough the efficiency increases by about 2%, for an increase in pressure of 100 bar, increasedboiler pressure decreases the dryness fraction at turbine exit Not desirable

Hence operating the cycle at very high pressure in a simple Rankine cycle is not very beneficial

Increased boiler pressure together with reheat results in better performance

Rankine cycle with single reheat

Performance comparison with and without reheat

Given data: Boiler pressure = 163 bar, Condenser pressure = 0.07 barp , pHighest temperature of heat addition (T3) = 538oC

Performance comparison with and without reheat

Given data:

Boiler pressure = 163 bar, Condenser pressure = 0.07 bar

Highest temperature of heat addition (T3) = 538oC

Results show that for given boiler and condenser pressures and heat addition

temperature there is an optimum intermediate pressure at which the efficiencytemperature, there is an optimum intermediate pressure at which the efficiency

reaches a maximum

Possibility of employing superheat and reheat

Whether superheat/reheat is possible or not depends upon the type of external heat

transfer fluid used in the boiler and the boiler pressure

For higher performance, generally a counterflow type arrangement is used in the

boiler of the power plant

The point where the temperature difference between the external fluid and steam

reaches a minimum value is called as a pinch pointreaches a minimum value is called as a pinch point

For a given pinch point temperature difference, theslope of the external fluid temperature depends uponits thermal capacity, i.e.,

Pinch point

its thermal capacity, i.e.,

Pinch pointL

In systems where either the mass flow rate of the externalfluid and/or its specific heat is very large, then the slopeis small.This puts a constraint on the amount of superheat/reheatthat can be employed for a given heat transfer rate.

In a PWR based power plant, due to operational constraints the maximum temperatureof the pressurized water is limited. In addition, since the cp value of water is very high,the temperature variation is small Limited scope for superheat steam at turbineinlet is close to saturationFor the same pinch point temperature difference, in a gas cooled reactor or in aconventional coal based power plant, the temperature gradient is very steep, hence it ispossible to employ superheat/reheat in these systems

Effect of pressure for plants with low external temperature variation in boiler

Worked out example: Steam power plant connected to a PWR

Given:

Wnet = 500 MW

Condenser Pressure = 0.07 bar, boiler pressure = 75 bar

Inlet temperature of heat source (pressurized water) = 318oC

Outlet temperature of heat source (pressurized water) = 289oC

Temperature difference between heat source (inlet) and boiler exit = 18 KTemperature difference between heat source (inlet) and boiler exit = 18 K

Condenser water inlet temperature = 30oC

Condenser water outlet temperature = 35oC

Find:

1) Thermal efficiency of the plant

2) Flow rates of steam, pressurized water and cooling water in condenser

3) Pinch point location and the temperature difference at pinch point

4) Entropy generation (total condenser and boiler)4) Entropy generation (total, condenser and boiler)

5) Carnot efficiency

Property data:Property data:

• Results:

1) Thermal efficiency of the plant = 37 35 %1) Thermal efficiency of the plant = 37.35 %

2) Flow rates:

a) Steam = 506 9 kg/sa) Steam 506.9 kg/s

b) Pressurized water = 8308 kg/s

c) Cooling water in condenser = 40136 kg/s) g g/

3) Temperature difference at pinch point = 10.74 K (at sat. liquid)

4) Entropy generation:

a) Total = 422.3 kW/K Lost work = 129 MW

b) In condenser = 57.9 kW/K

c) In boiler = 364.4 kW/K

5) Carnot efficiency = 47%

The example shows that of the total entropy generation in the power plant, almost

76% is generated in the sub-cooled region of the steam generator itself, even though76% is generated in the sub cooled region of the steam generator itself, even though

the heat transfer rate in this region is about 42% of the total input.

This is obviously due to heat transfer taking place over a very large temperature

difference in this region.

This remains true for all the external heat sources (e.g. PWR or flue gas based)

Temperature profile in steam generatorThe 3 zones in a steam generator

The concept of regenerative feedwater heating

• Analysis of simple Rankine cycle shows that they p y

irreversibility due to heat transfer is very high in the

subcooled liquid region due to the large temperature

difference between the heat source and the working

fluid (feed water)

Id ll thi i ibilit b li i t d if th• Ideally, this irreversibility can be eliminated if the

feedwater enters the boiler at point b, instead of point 2.

• This can be done using regenerative feedwater heatersThis can be done using regenerative feedwater heaters

• Conceptually, in regenerative feedwater heating, the feed

water is heated internally by extracting heat from the

expanding steam in the turbine

Ideal, regenerative feed water heating

• Under ideal conditions, the feed water from the

(2) i h d ibl b h hpump (2) is heated reversibly by the steam that

is expanding in the turbine such that it is

saturated at the inlet to the boiler (3) The

economizer is integrated with the turbine!economizer is integrated with the turbine!

• The resulting cycle will have completely

isothermal heat addition and heat rejection

• If there are no other internal or external

irreversibilities, then the efficiency of this cycle

is same as that of a Carnot cycle!

• However, it is impossible in practice to

construct such a system in which there is

reversible heat transfer from the high speed

apo r flo ing thro gh the t rbine blades tovapour flowing through the turbine blades to

the feed water

• In addition, the amount of liquid that forms

d i g th i ill bduring the expansion process will be

unacceptably high!Saturated Rankine cycle with

ideal regeneration

Regenerative feedwater heating

• Since it is not possible to heat the feed water reversibly by direct exchangeSince it is not possible to heat the feed water reversibly by direct exchange

of heat with the expanding steam in the turbine, in practice, separate

feedwater heaters are used in all steam power plants

• Unlike ideal regeneration, use of feedwater heaters does not completely

eliminate the external irreversibility but minimizes it

• Depending upon the type, feedwater heaters can be classified as:p g p yp ,

– Open or direct contact type feedwater heaters

– Closed or indirect contact type feedwater heaters

• Drain cascaded backward

• Drain cascaded forward

I t l l t th f d t i h t d i t ll i g• In actual power plants, the feedwater is heated internally using as many as

5 to 6 feedwater heaters, out of which at least one is an open feedwater

heater.

System with one open or direct contact type feedwater heater

1. No. of pumps required = No. of Open Feedwater heaters + 12. The pressure at the exit of low stage pump P1 (2) cannot be higher than the pressure

at which steam is extracted (7), otherwise there will be reverse flow of condensate water into turbine

3. Mass fraction of extraction steam (y) should be such that the state of the mixture at the exit of the OFW (3) is either saturated or subcooled liquid.

4 If th t ti t fl t i th i d th th ill b4. If the extraction steam flow rate is more than required, then there will be:1. Loss of turbine power, and2. Inlet condition for high stage pump (P2) will be in 2-phase region

From 1st and 2nd law of thermodynamics across each component:

Open Feedwater heater (OFW):

From 1st and 2nd law of thermodynamics across each component:

External irreversibility Internal irreversibility

Open Feedwater heater (OFW):

Worked out example: Steam power plant with an open feedwater heater

Given:

Wnet = 500 MW

Pressures: Condenser = 0.07 bar, Boiler = 75 bar, Feedwater heater = 35 bar , ,

Heat source: Inlet temperature = 318oC, Outlet temperature = 289oC

Temperature difference between heat source (inlet) and boiler exit = 18 Kp ( )

Heat sink: water inlet temperature = 30oC , water outlet temperature = 35oC

Find:

1) Thermal efficiency of the plant

2) Turbine and pump power, heat transfer in boiler and condenser2) Turbine and pump power, heat transfer in boiler and condenser

3) Mass flow rate of steam through boiler and steam extraction fraction

3) Entropy generation (total, condenser, boiler and feedwater heater)3) Entropy generation (total, condenser, boiler and feedwater heater)

Worked out example (contd.)

Worked out example: Results

1. Thermal efficiency, thermal = 39.09 %

(37.35 % without regeneration)

2. Total Turbine output, WTurbine = 505.243 MW

Total Pump input, WPump = 5.243 MW

Boiler input Q = 1279 MWBoiler input, Qboiler = 1279 MW

Condenser heat rejection, Qcond = 779 MW

3. Mass flow rate of steam through boiler = 727.6 kg/sg g/

Fraction of extracted steam, y = 0.3531

4. Entropy generation: Total: 330.9 kW/K (422.3 kW/K without OFW)

Boiler: 62.55 kW

Condenser: 54.44 kW/K

F d t h t 213 9 kW/KFeedwater heater: 213.9 kW/K

Effect of steam extraction pressure

As steam extraction is varied from condenser pressure:

Efficiency increases, reaches a peak and then starts decreasing

Fraction of steam extracted increases Specific turbine work output decreases

Mass flow rate of working fluid (water) increases

It can be shown that the efficiency is maximum when the saturation temperature y p

corresponding to the intermediate pressure is midway between the boiler and

condenser pressures, i.e., tsat(pint) (tboiler+ tcondenser)/2

In general, in conventional power plants, only one open feedwater heater is used, which

also acts as a deaerator

Open feedwater heater inner details

www.crazyengineers.com

System with one closed feedwater heater (drain backward)

1 This is the simplest and most commonly used type of feedwater1. This is the simplest and most commonly used type of feedwater2. This feedwater heater is similar to a shell-and-tube type condenser, wherein the

extracted steam condenses in the shell, while the feedwater flowing through thetubes is sensibly heated

3. Depending upon the condition of extracted steam (6):t3 can be higher or lower than tsat (p6)

4. Only a single feedwater pump is required in this system extracted steamcondensing in the feedwater heater is fed back to the main condenser through acondensing in the feedwater heater is fed back to the main condenser through athrottle valve = Additional internal irreversibility!

5. A desuperheater & drain cooler may be a part of the feedwater heater

Inner details of a closed feedwater heater

(www.levelandflowsolutions.magnetrol.com)( g )

Closed feedwater heater (drain backward) contd.

• Depending upon the state of the bled

6

3Depending upon the state of the bledsteam, the exit temperature of feedwater is:

1. Greater than the saturation temperature corresponding to the extraction pressure, Case(i): Steam is extracted at

7

2

3

p g p ,or

2. Less than the saturation temperature

high pressure

37 6

Case(ii): Steam is extracted at low pressure

2

2

376

Case(iii): Steam is extracted at low pressure

Closed feedwater heater (drain backward) contd..

Governing equations:Governing equations:

1) Boiler:

2) T bi 2) Turbine:



3) Condenser:

4) Pump:



5) Closed feedwater heater:

6) Throttle valve:



To solve the problem, we need to specify the condition of feedwater (3) and bleed

steam (7) by specifying Terminal Temperature Differences (TTD) = (t7 t3) & (tsat,p6t7)

Worked out example: Closed feedwater heater (drain backward)

Given:

Wnet = 500 MW

Pressures: Condenser = 0.07 bar, Boiler = 75 bar, Feedwater heater = 35 bar , ,

Heat source: Inlet temperature = 318oC, Outlet temperature = 289oC

Temperature difference between heat source (inlet) and boiler exit = 18 Kp ( )

Heat sink: water inlet temperature = 30oC , water outlet temperature = 35oC

Terminal Temperature Difference: Feedwater = 3 K, Drain cooler = 0 K (saturated)p , ( )

Find:

1) Thermal efficiency of the plant1) Thermal efficiency of the plant

2) Turbine and pump power, heat transfer in boiler and condenser

3) Mass flow rate of steam through boiler and steam extraction fraction3) Mass flow rate of steam through boiler and steam extraction fraction

3) Entropy generation (total, condenser, boiler and feedwater heater)

System with one closed feedwater heater (drain forward)

This is also similar in construction to a shell-and-tube type condenser

Throttling losses are eliminated by pumping the drain water to the boiler using a smalldrain water pumpdrain water pump

Since drain water flow rate is smaller compared to condensate water, inlet conditionto boiler (4) is closer to (3)

This system yields slightly better performance compared to drain backward

Internally irreversible Rankine cycle, Heat rate etc.

Further improvements in power plant performance

Thermodynamic analysis shows that thermal efficiency of power plants can be increased by

operating the plant at higher temperatures and pressures.

Studies show that with every 1 % increase in efficiency, the emission levels from the power plants

can be reduced by 2 %.y

R.S. Yadav and Vaibhav Chauhan, Supercritical Technology in Indian Power Sector, National Seminar on Thermal Power Plant Performance Management (NSTPPPM), 2014

The Supercritical Cycle - Concepts

• The temperature at which water canboil is limited by its critical temperature( 374oC)

• When an external heat source p < 221 bar

temperature is much higher than374oC, most of the heating has to takeplace in the superheated zone

Subcritical cycle

p p• The resulting non-uniform temperature

profile, gives rise to a lower meantemperature of heat additiontemperature of heat addition

• Under these conditions, higher meantemperature and hence higherefficiency can be obtained by

p > 221 bar

efficiency can be obtained byoperating the steam generator insupercritical region (pressures higher Supercritical cyclethan, critical pressure of 221 bar)

Supercritical power cycle

• In a supercritical steam generator the properties of water changea supe c t ca stea ge e ato t e p ope t es o ate c a gegradually without undergoing any sudden phase change!

• Thermodynamic analysis is similar to standard Rankine cycle, however, actual,design, operating and performance characteristics etc. are different

Supercritical power cycle – Performance comparisonEffect of boiler pressure

For a given boiler exit temperature (say 700oC), efficiency of SC cycle increases with

boiler pressure howeverboiler pressure, however,

The turbine exit quality decreases as the boiler pressure increases

Hence in actual power plants, reheat is always employed with SC cycle to reduce the

liquid fraction in the turbine

Supercritical power cycle – Performance comparisonEffect of boiler exit temperature

It is seen that for fixed boiler pressures, SC cycle performance exceeds that of a

subcritical Rankine cycle only when the boiler exit temperature is above a certain value

Due to continuous improvement in materials and manufacturing technologies, it is now

possible to operate coal based power plants at much higher pressures and

temperaturesp

Supercritical cycles are becoming, a norm rather than an exception, especially when

the coal is of high quality

Practical Supercritical cycles

To reduce the liquid levels in the turbine, reheat is employed in all practicalSupercritical cycle based power plantsSupercritical cycle based power plants

Often double or triple reheat is used

Due to progressively lower operating pressures, reheat temperature can be higher thanthe boiler exit temperature yielding improved performancethe boiler exit temperature, yielding improved performance

Example problemGiven: Condenser pressure = 0.07 bar

Boiler pressure = 300 bar

1st Reheat pressure = 80 bar

2nd Reheat pressure = 28 bar

Turbine inlet temperature = 600 oC

Find:

Mean temp. of heat addition: 609 K

Turbine work: 391+424+1315 = 2130 kJ/kg

Pump work: 30 kJ/kg

Boiler heat input: 4309 kJ/kg Supercritical cycle with double reheat

Thermal efficiency: 48.73 %

Carnot efficiency: 64.25 %

Binary Vapour Cycles (Topping and bottoming cycles)

• When water is used as the working fluid in a Rankine cycle:

– The boiler pressure is very high at high temperatures (of the order of 100 bar)

– The condenser pressure is very low at low condensing temperatures (of the order of 0.1 bar)

V hi h i b il d l i d• Very high pressure in boiler and very low pressure in condenser are notdesirable due to several practical problems

• When a heat source is available at a high temperatures, it is advantageous touse a working fluid with high boiling point, e.g., Mercury, Sodium, Potassium etc.

– e.g. at 600oC, Mercury has saturation pressure of about 12 bar!

• Similarly when a heat sink is available at a low temperatures it is advantageous• Similarly when a heat sink is available at a low temperatures, it is advantageousto use a working fluid with low boiling point, e.g., ammonia

– e.g. at 40oC, Ammonia has saturation pressure of 15.6 bar, while it is 0.07 bar for water

• The above facts, give rise to the concept of topping and bottoming cycles, inwhich a high boiling point temperature is used in the topping cycle and a lowboiling point fluid is used as working fluid in the bottoming cycle

A binary (Topping) vapour cycle with mercury (www.expertsmind.com)

Combined gas-vapour cycles

Introduction to gas cycles

• In gas cycles the working fluid does not undergo any phase change allthe heat transfer processes are sensible processes, and hence are non-isothermalisothermal

• Among the gas cycles, the Brayton cycle is most widely used in manyapplications including for large scale power generation

• Since Brayton cycle employs a gas turbine for generating power, Braytoncycle is also called as a “gas turbine” cycle

• All commercial aircraft systems are based on the gas turbine cycle

• Gas turbines are also used in various industries for driving mechanical andelectrical equipment such as compressors pumps etcelectrical equipment such as compressors, pumps etc

• Due to their high power-to-weight ratios, gas turbines were also used insome of the racing cars and there are efforts to use them in railways also!

Chrysler gas turbine car

Close view of a gas turbine car

Introduction to gas turbines (contd.)

• Compared to steam power plants gas turbine based power plants offer• Compared to steam power plants, gas turbine based power plants offer

several advantages:

1 For the same output they are smaller in size and lighter in weight1. For the same output, they are smaller in size and lighter in weight

2. For the same output, they also cost less

3 Th t k l ti t i t ll d i i3. They take less time to procure, install and commission

4. They are quick-starting and run smoothly

5. They can use a wide variety of liquid or gaseous fuels, e.g. natural gas,

fuel oil, syngas, naphtha, crude oil etc.

6. Environmentally, they can provide better emissions with fewer

restrictions


• However gas turbines do suffer from some major disadvantages:• However, gas turbines do suffer from some major disadvantages:

• For the same maximum and minimum temperatures, their

efficiency is much lower compared to a vapour cycle

• They are not preferred for continuous, stand-alone power

generation applications

• They are not compatible with solid fuels such as coal

However, using gasification, solid fuels can be converted into

gaseous fuels (e.g. syngas) and used in gas turbine plants,gaseous fuels (e.g. syngas) and used in gas turbine plants,

e.g. integrated gasification combined cycle (IGCC)


• Considering the low initial cost but low efficiency of gas turbine as• Considering the low initial cost, but low efficiency of gas turbine as

compared to high initial cost and high efficiency of steam power plants,

it would be advantageous to develop systems wherein:it would be advantageous to develop systems, wherein:

– Steam power plant would be operating continuously at base loads with high load

factor and high efficiency

– while the gas turbine plant would be put into operation, only during peak loads

• Alternately, since due to improved material and manufacturing

techniques, it is possible to operate gas turbines at very high

temperatures (as high as 1600oC) with high efficiency, they can be used

as:

– topping cycles in steam power plants, thus improving the overall plant efficiency

tremendously!tremendously!


• Depending upon the arrangement for heat supply and heatDepending upon the arrangement for heat supply and heatrejection, gas turbine cycles can be classified into:

1. Direct open gas turbine cycle1. Direct open gas turbine cycle

2. Direct closed gas turbine cycle

3 Indirect open gas turbine cycle3. Indirect open gas turbine cycle

4. Indirect closed gas turbine cycle

• Depending upon how they are coupled to the load they can• Depending upon how they are coupled to the load, they canalso be classified into:

1 Single shaft model or1. Single shaft model, or

2. Two shaft model


1. Gas enters the compressor (C) at point 1p ( ) p

2. Gas is compressed to point 2

3. Compressed gas enters the combustion chamber (CC)

t th b t i t 22 3

or reactor, as the case may be at point 2

4. Compressed gas is heated to point 3

5. Hot compressed gas at point 3 enters the turbine and

expands to a lower pressure at point 4

6. Exhaust gas from turbine at point 4 is expelled into the

atmosphereDirect, open gas turbine cycle

1 4

p

Note:

a) Since this is an open cycle, only air can be used as the

orking fl idworking fluid

b) The pressure at point 1 and point 4 have to be

atmospheric

c) Used in air crafts


1. Gas enters the compressor (C) at point 1


3. Compressed gas enters the combustion chamber (CC)

or reactor, as the case may be at point 2

2 3



expands to a lower pressure at point 4

1 1

Direct, closed gas turbine cycle(Ideal Brayton cycle)

p p p

6. Exhaust gas from turbine at point 4 is cooled in the

heat exchanger (HR) to initial condition 1

Note: (Ideal Brayton cycle)Note:

a) This is a theoretical cycle, since in practice, mass

balance cannot be maintained with continuous addition of

fuel unless heat is directly added by some other wayfuel, unless heat is directly added by some other way.

b) Since this is closed cycle, any gas can be used as the

working fluid

) Th t i t 1 ( d i t 4) b hi hc) The pressure at point 1 (and point 4) can be higher

than atmospheric pressure Dense gas cycles




3. Compressed gas enters the high temperature heat

exchanger (HHX) at point 2

HHX



expands to a lower pressure at point 4p p p

6. Exhaust gas from turbine at point 4 is expelled into the

atmosphere

Note:Note:

a) Used in applications that prevent direct heating of air,

e.g. in nuclear power stations

b) Since this is an open cycle only air can be used as the

Indirect, open gas turbine cycle

b) Since this is an open cycle, only air can be used as the

working fluid

c) The pressure at point 1 (and point 4) is same as

t h iatmospheric pressure




3. Compressed gas enters the high temperature heat

exchanger (HHX) at point 2



expands to a lower pressure at point 4p p p

6. Exhaust gas from turbine at point 4 is cooled in the low

temperature heat exchanger CHX

Note:Note:

a) Used in applications that prevent direct heating of air,

e.g. in nuclear power stations

b) Since this is an open cycle any gas can be used as the

Indirect, closed gas turbine cycle

b) Since this is an open cycle, any gas can be used as the

working fluid

c) The pressure at point 1 (and point 4) can be higher

th th t h ithan the atmospheric pressure


Single shaft, open gas turbine cycle Two shaft, open gas turbine cycle

In single shaft systems, the rotational speed of gas turbine and the external load aresame, as they are mounted on the same shaft

In a two shaft system, the speed at which the gas turbine and load operate can bedifferent. This is done by splitting the turbine into two parts – HT and LT

The high pressure turbine (HT) called as gas generator is connected to thecompressor and drives the compressor

The low pressure turbine (LT) connected to the load can operate at variable speed

Analysis of an Ideal Brayton cycle

Air

2 3

1 4

Ideal Brayton cycle

Assumptions: Cold Air Standard Cycle Analysis

1. The working fluid is a pure fluid that circulates through the closed system withoutundergoing any change in its composition

2. The working fluid receives heat from an external source (in CC) and rejects heat to anexternal sink (in HR)

3. All the internal processes are reversible

4. The specific heat of the working fluid (cp) is constant

5. The system operates at steady state

6. Kinetic and potential changes across the components are negligible


3

Air

Qin

1

2 3

4

Ideal Brayton cycle

1 4

Qout

Applying steady flow energy balance across each component:

1 Compressor (Process 1-2: reversible and adiabatic compression) 1. Compressor (Process 1-2: reversible and adiabatic compression)


3

Air

Qin

1

2 3

4

Ideal Brayton cycle

1 4

Qout

2. High temperature heat exchanger, CC (Process 2‐3: Isobaric heat addition):

3 Low temperature heat exchanger (Process 4 1: Isobaric heat rejection):3. Low temperature heat exchanger (Process 4-1: Isobaric heat rejection):


3

Air

Qin

1

2 3

4

Ideal Brayton cycle

1 4

Qout

4. Turbine (Process 3-4: reversible and adiabatic expansion):


3

Air

Qin

1

2 3

4

Ideal Brayton cycle

1 4

Qout

From overall energy balance:

Since there is no pressure drop during heat addition (2-3) and heat rejection (4-1);

Therefore, the net power output is given by:


3

Air

Qin

1

2 3

4

Ideal Brayton cycle

1 4

Qout

The thermal efficiency th is given by:

From the above equations it is clear that for a given working fluid (fixed ) the thermal

efficiency of a simple, ideal Brayton cycle is independent of the minimum and

maximum temperatures (T1 and T3) and depends only on the pressure ratio rp, andp ( 1 3) p y p p,

increases continuously with rp.

Variation of thermal efficiency of a simple Brayton cycle with pressure ratio


However, it can be shown that the net specific power output (kJ/kg) depends on T1 and T3 as well as and rp. 3 p

The above equation shows that:

•For a given minimum and maximum temperatures (T and T ) the net specific work•For a given minimum and maximum temperatures (T1 and T3) the net specific workoutput increases as:

1. cp increases, and/or,

2. increases and/or,

3. Pressure ratio rp increases

•For a given gas (fixed values of c and ) and fixed pressure ratio r the net specific work•For a given gas (fixed values of cp and ) and fixed pressure ratio rp, the net specific workoutput increases as:

1.maximum temperature T3 increases and/or

2.minimum temperature T1 decreases


Higher the net specific work output, more compact T3

will be the system as the mass flow rate of the gas for

the same net power output will be lower

The maximum temperature T is limited by the

T 1

2

3

The maximum temperature T3 is limited by the

metallurgical considerations, while the minimum

temperature is limited by the available heat sink T1

2

From the expression for net specific power output it can be shown that for a given gas the

swnet,2 > wnet,1, wnet,3

net specific power output reaches a maximum when:


Effect of working fluid and pressure ratio on wnet and th

The above figure shows that:

1. Compared to other gases, Helium offers very high specific power output as well asp g , y g p p p

thermal efficiency due to high values of cp and

2. The pressure ratio at which the net specific power output reaches a maximum is

much lower for helium compared to other gases

Actual Brayton cycles

• In actual systems based on Brayton cycle:• In actual systems based on Brayton cycle:

1. Compression and expansion processes are non-isentropic

2 H t dditi d h t j ti i b i2. Heat addition and heat rejection are non-isobaric

3. Mechanical losses in bearings etc. reduce the useful net power output

4. Properties of the working fluid vary along the cycle due to variation in

gas composition and operating conditions

As a result of the above, the performance characteristics of the actual

Bratyon cycles differ from that of an ideal cycleBratyon cycles differ from that of an ideal cycle


Non-isentropic compression and expansion:

The compressor power input is given by:



The turbine power output is given by:


The net power output is given by:

In terms of the maximum and minimum temperatures and pressure ratios, the net power output is given by:


The heat input is given by:p g y


The thermal efficiency is given by:

Non-isentropic compression and expansion

Evaluation of an actual Brayton cycle

• Given:

a) Mass flow rate of air = 1 kg/s

b) Max. temperature of heat addition = 1200 K

c) Min temperature of heat rejection = 323 Kc) Min. temperature of heat rejection = 323 K

d) Isentropic efficiency of turbine = 90 %

e) Isentropic efficiency of compressor = 87 %

f) Pressure ratio = 12

• Find:

a) Temperature at the exit of compressor and turbine (706.9 K, 651 K)

b) Turbine power output and compressor power input (606.7 kW and 424.2 kW)

c) Thermal efficiency of the cycle (33 49 %)c) Thermal efficiency of the cycle (33.49 %)

d) Total entropy generation (0.668 kW/K)

e) Lost work (215.8 kW)

Evaluation of an actual Brayton cycle

The above results show that:

a) Maximum entropy generation is in low temperature heat exchanger (LT HX)) py g p g ( )

followed by the high temperature heat exchanger (HT HX)

This is due to the large temperature difference over which heat transfer takes

place in the heat exchangers

b) To improve efficiency entropy generation in HXs should be minimized

Modified Brayton cycle

f f f• Performance of Brayton cycle can be improved significantly by:

1. Regeneration

2. Intercooling between compression processes

3. Reheating between expansion processes

4. Water injection after compression

Out of the above,

• Regeneration is useful for low to medium pressure ratios

• Intercooling and reheating are useful for high pressure ratios

• Water injection (after compression and before regeneration) improves

power output but has a marginal effect on efficiency

Regeneration

Regeneration

Heat transfer rate in regenerator (R):

Effectiveness of regenerator (R):

Evaluation of Brayton cycle with regeneration

• Given:



c) Min temperature of heat rejection = 323 Kc) Min. temperature of heat rejection = 323 K



f) Pressure ratio = 12

g) Effectiveness of regenerator = 0.90

• Find:

a) Temperature at the exit of compressor and turbine

b) Turbine power output and compressor power inputb) Turbine power output and compressor power input

c) Thermal efficiency of the cycle

d) Entropy generation and Lost work in each component

Comparison between simple and regenerative Brayton cycles

0.5

0.3

0.4

th

th,simpleth,simple

0.1

0.2

T 323 K T 1200 K 0 87 0 9 0 9

th,regenerativeth,regenerative

Results show that for a given maximum heat addition and minimum heat rejection

5 10 15 20 25 300

rp

T1 = 323 K, T4 = 1200 K, C = 0.87, T = 0.9, R = 0.9

Results show that for a given maximum heat addition and minimum heat rejection

temperatures and non-ideal compressor and turbine,

a) The efficiency of the regenerative Brayton cycle reaches a maximum at a particular a) The efficiency of the regenerative Brayton cycle reaches a maximum at a particular

pressure ratio, which is much less than that of a simple cycle

b) Beyond a certain high pressure ratio, the efficiency of simple Brayton cycle is better

than a regenerative Brayton cycle

System with water injection

In a simple Brayton cycle,

1. Liquid water is injected into the air stream after compressionq j p

2. The injection rate should be such that all the liquid water evaporates in the injectorand the moist air that leaves the injector (3) does not contain any liquid water

3. Due to evaporation of water (assumed to be adiabatic), the temperature of moist airp ( ), pdecreases (T3 < T2)and its specific volume increases due to presence of water vapour

4. The heat input required in the combustion chamber increases. However, the net workoutput also increases (main reason for injecting water!)

5. The thermal efficiency may increase or decrease depending upon the operatingconditions. However, the NOx formation decreases due to lower temperatures.

Analysis of a simple Brayton cycle with water injection

Typical results

Open Brayton cycle with regeneration and water injection• Given:



c) Min. temperature of heat rejection (compressor inlet) = 323 K) p j ( p )



f) Pressure ratio = 12 (Pressure at compressor inlet = 1 atm.)

g) Effectiveness of regenerator = 0.90

h) Relative humidity of air at compressor inlet = 40%) y p

i) Relative humidity at the exit of water injector = 100 %

• Find:

a) Rate of water injection (kg/s)

b) Temperatures at all the state points

c) Turbine power output and compressor power input (in kW)

d) Thermal efficiency of the cycle

Other modifications to gas turbine cycles

• Evaporative cooling:Evaporative cooling:

– The air at the inlet to the compressor is cooled by making it pass through an

evaporative cooler

– Since the compressor and turbine in gas turbine plants are typically,

constant volume flow components, the lower temperature air at the inlet to

the compressor increases the mass flow rate and hence the power output

• Steam Injected Gas Turbine (STIG):

– Injection of steam into the compressed air increases both the power output

and efficiency

M i l d i i l h i h i j i i– Mainly used in cogeneration plants, wherein the steam injection rate is

increased when the requirement for process steam is low.

Combined gas-vapour cycles

• The large amount of energy available at the exit of the turbine in a gas turbinepower plant can be used as heat input for a steam power plantpower plant can be used as heat input for a steam power plant

• Such a system which combines a gas turbine cycle with a steam power plantcycle is called as a combined cycle power plants

• Combined cycle power plants offer very high overall efficiency of the order of• Combined cycle power plants offer very high overall efficiency of the order of50% or more, in addition to other environmental benefits

• These plants are simpler compared to steam power plants due to the absencef l h dli g it bb t Th i t t i l f tof coal handling units, scrubbers etc. Their start-up is also very fast.

• Sometimes a Supplementary Firing (SF) equipment may be used to boost up theoutput from the steam turbine

Comparison between steam, gas turbine and combined cycles

St di h th t f t t l t f ti i t f iStudies show that from total cost of operation point of view:

1. Gas turbine plants are good for peak load operations, while

2. Steam turbine plants are good for base load operation

3. Combined power plants are good a compromise between gas turbine and steam

power plants

Combined cycle power plant concepts (Alex Lezuo, Siemens, Taylor & Francis, 2007)

Characteristics of different types of Combined Cycle (CC) plants

1. Natural gas fired CC power plant:1 Highest possible efficiency (+)1. Highest possible efficiency (+)2. Simplest and lowest specific investment cost (+)3. Only natural gas can be used with high efficiency ()4 Most commonly used arrangement4. Most commonly used arrangement

2. Parallel powered CC power plant:1. Simple system for improving the heat rate of existing coal fired power

plants with minimum investment and minimum lead time (+)plants with minimum investment and minimum lead time (+)

2. Offers excellent part-load performance ()

3. In stead of generating steam, the gas turbine exhaust gases can also beused for heating the feedwater thus eliminating the bleed stem fromused for heating the feedwater, thus eliminating the bleed stem fromsteam turbine, thereby improving the output of the steam turbine ()

3. Integrated Gasification Combined Cycle (IGCC) plant:1. Can be used with fuels other natural gas, e.g. coal (+)1. Can be used with fuels other natural gas, e.g. coal ( )2. Permits use of lower cost fuels such as coal in an environment friendly

manner (+)3. Very complex system and suitability depends upon relative costs of coal

and NG ()

Cogeneration

• Cogeneration refers to the simultaneous generation of electricity andheat or steam (or hot water)

• It has long been used in industries and by municipalities that need bothelectricity and steam (say for house heating in winter)electricity and steam (say for house heating in winter)

• Cogeneration is beneficial only if it results in saving of primary energywhen compared to separate production of electricity and steam by twodiff t tdifferent systems

• The cogeneration plant efficiency is given by:

• Where: • co = cogeneration plant efficiency• PE = Electrical power generated (MWh)• Qu = Useful heat supplied from the plant (MWh)• Q = Heat added to the plant through the fuel (MWh)• Qin = Heat added to the plant through the fuel (MWh)

Cogeneration (contd.)

If electricity and steam are generated individually, then the amount of heat tobe added per unit total energy (electrical + heat) output is given by:be added per unit total energy (electrical + heat) output is given by:

Where:E = Fraction of electrical energy of the total energy output;E Fraction of electrical energy of the total energy output;

E = Efficiency of electrical power generation of a stand‐alone power plantQ= Efficiency of heat generation of the heat/steam generatorQ Efficiency of heat generation of the heat/steam generator

Therefore, the combined efficiency for individual plants for electricity and heat is given by:

Hence, cogeneration is beneficial, if:

A basic cogeneration plant with extraction-condensation turbine

Practical example of a large combined cycle CHP Plant(Operating in The Hague, Netherlands)

Assignment on the large combined cycle CHP Plant(Data from the plant operating in The Hague, Netherlands

• Given Data: • Given Data: • Steam turbine:

– Power output (net): 25 MW;

– Steam supply to turbine: 30 bar 450oC Steam supply to turbine: 30 bar, 450 C,

– pressure of bleed steam to SWH: 2 bar,

– mass flow rate of bleed steam to SWH: 17 kg/s,

– Isentropic eff.: Turbine: 80%, Condenser sat. temp: 25oC, Isentropic eff.: Turbine: 80%, Condenser sat. temp: 25 C,

– no subcooling in condenser

– Electric generators: 95 % efficiency

– District heating: Supply temp: 115oC, return temperature: 75oCDistrict heating: Supply temp: 115 C, return temperature: 75 C

• Gas Turbines (2 in number): – Power output (net): 25 MW each;

– Pressure ratio: 12; ;

– Maximum cycle temperature: 1013oC

– Exhaust gas temperature: 83oC;

– Isentropic eff.: Turbine: 85%, Compressor: 83%, Combustion Eff.: 0.98p p

– Cp of gas = 1.11 kJ/kg.K, = 1.333

Assignment on the large combined cycle CHP Plant(Data from the plant operating in The Hague, Netherlands

• To find: • To find:

1. Overall efficiency of the system: (ans. 68.9%)

2 Mass flow rate of water for district water heating: (ans 331 5 kg/s)2. Mass flow rate of water for district water heating: (ans. 331.5 kg/s)

3. Air flow through each gas turbine: (ans. 131 kg/s)

4 St fl t (t t l) ( 35 39 kg/ )4. Steam flow rate (total): (ans. 35.39 kg/s)

5. Heating output (water heating): (ans. 55.69 MW (total))

Tri-generation• Tri-generation is the production of electricity, heat and cooling in a

single power plant (steam or gas turbine)single power plant (steam or gas turbine)

• Steam from the boiler or gas from a gas turbine is used for:– Production of electricity in the steam turbine-generator (PE)

P d i f h /h f h i (Q )– Production of heat or process steam/hot water for heating purposes (Qu)

– Production of refrigeration/air conditioning using an absorption chiller (Qr)

• The ratio of electricity (PE), heat (Qu) and refrigeration (Qr) can varyd di g th i tdepending upon the requirements

(Qr)

(Qu)

(PE)

Concept of tri-generation

Tri-generation

A typical gas turbine based tri-generation plant (Dusan Medved 2011)A typical, gas turbine based tri generation plant (Dusan Medved, 2011)

Module-1

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