A Tutorial on Power Generation From Thermal Power Plants.docx

8/14/2019 A Tutorial on Power Generation From Thermal Power Plants.docx

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A Tutorial on Power Generation From Thermal Power Plants - TS

Graph, Process, Principles, Turbine Model, Basic Boiler

Schematics

Power Generation from Thermal Power Plant

Introduction

About 70 % of energy used by India is produced in Coal fired thermal power plants. Not just

India, people all over the world heavily rely on thermal power stations. This is because of theabundant availability of coal, reliable cheap power and early advent of steam engine technology.

Though there is a lot of hue and cry over the CO2 emissions and diminishing coal reserves, coal

power continues to dominate the energy sector.

Rankine cycle is the working principle of the plants all over the world. Water is boiled into steamwhich is super heated. This is the phase where the energy of the coal is give to the steam/water. The

high pressure and high temperature steam is allowed to expand in turbines coupled with generators.

Here , a part of energy is given back by the steam. Most of remaining heat is dissipated toatmosphere. More about this will be discussed in the efficiency discussion.

The TS graph for Basic Rankine cycle

For an ideal plant, there are good number of specifications to be satisfied. The power plant must belocated to a coal mine as close as possible. If the plant is dependent on the imported coal it should be

closely located to the sea port. In either cases, dedicated transporation system must exist for

transmission if coal reserves. Another important aspect is the ash disposable facility. Indian Coal has

a higgm amount of ash content which turns out to be around 30 -40 %. This if not disposed properly,

results in health hazards in and around the plant leading to numerous other problems. Presently theash is used for various industries and also used for domestic purposes. In most cases it is stored in

propoer places.Huge quantities of water must be required for condenser, disposal of ash and feed water circuit etc.

It is therefore desirable to locate plant on side of river. For example, VTPS in Vijayawada is located

on the banks of river Krishna.

The Process and Principle


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The basic entities in the power plant are Boiler, Turbine , Condenser , pump. Here, the principle

is explained with the help of Temperature and Entropy (TS) curve.Starting at 1, the water at room temperature is boiled at constant temperature in the boiler. This

process has a T constant for it is the boiling of water which takes at a constant temperature. Here we

are increasing the entropy of by phase change and the energy is sorted in the form of latent heat also.

As you might assume, the temperature is not 1000c because this boiler is at higher pressure and the

boiling point is also high. As shown in the figure the temperature is constant and the line is parallel to

S axis. All this process happens in a boiler. The end product is steam.

TS graph for the power plant operati on

Once you have steam, you cannot immediately pump it to the turbine to extract energy becauseonce it enters turbine and starts condensing forming water droplets without giving much energy. The

point here is, just a phase change wont work out for energy transfer from coal in boiler to turbine.

The steam must be heated to higher temperatures. This phase is called super heater and this phase is

mainly executed in super heater. This super heater will be located in between boiler and the turbine.The source of heat for the super heater is the hot flue gases obtained in the boiler after burning coal.

This explains the phase 2-3 in the T-S curve. Note that , in this process, neither the temperature nor

the entropy remains constant.

Now, in the next process, the super heated steam is allowed to expand in the turbine. As, the highpressure steam is allowed through a small nozzle ,steam acquires kinetic energy. This kinetic energy

of the steam will exert required force on the turbine blades. The turbine is designed well to receive

maximum force from the steam. This process is a constant entropy process. The steam is allowedinside the turbine until water droplets begin to form. In practice, formation of water drops is strictly

prohibited for the water drops will impinge the turbine blades and cause corrosion. Now the ouput of

the turbine is low pressure and low temperature steam. This accounts for the phase 3-4 of the cycle.In this phase of condenser, the heat of steam is exchanged with a heat exchanger, essentially

water. The steam now turns into water and this is processed again and sent into boiler for the next


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cycle. The heat exchanger gets heated up and this needs to be cooled for further use. Hence the heat

of exchanger is dissipated in atmosphere through large cooling towers. A lot of energy from theentire system remains unused in this 4-5 . The analysis can be obtained in the efficiency discussion at

the end of the tutorial.As you have seen throughout the process, water needs to be flown from one part to other. The

necessary draught is created by the pump. The step 5-6 is a pump which is used to circulate water.During this process, a little temperature change can be observed. Finally, the cooled water cannot be

directly sent into boiler. Because the boiler is at higher temperature, it causes irregularly expansion

which results in collapse of the boiler. Hence, the water should be heated to higher temperature. Thisis done in economizer which uses heat from flue gases. Thus this accounts for the 6-1 phase of the

Rankine cycle. The efficiency of the Rankine cycle is given by 1-T2T1. Where T2 is the temperature

of super heated steam and the T1is the temperature of the water entering inside.

Basic Flow Chart of Power Plant

Construction of the plant and parts.

As cited above, the primary parts of the plant are the boiler, turbine, condenser are explained below.

Other numerous parts including pulveriser, water treatment plant, cooling towers etc are alsodiscussed in detail.Boiler :It is used to convert the water into steam where coal is burnt. It is a relatively huge structurewith a typical boiler of a 500 MW plant would be equivalent to 5 storied building. The boiler

material will mostly made of cast iron to with stand high temperature and pressure. The construction

of boiler varies depending upon the heat transfer method used. In a traditional boiler, the boiler hasholes on the lower bottom for the coil powder to enter. The coal enters in such a way that , it creates

a vortex inside the boiler. This is to ensure that coal spends maximum time before settling down and

gets burnt completely. The outer surface of the boiler has thousands of pipes in which water runs

through. This is the process in which heat is exchanged. The flue gases rising out of burning coalpass through the super heater as shown in the figure.

Basic Boiler Schematic


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Turbine:

Steam turbines convert the energy acquired by the steam in to the mechanical energy. These turbines

are couple with the alternators which produce the electrical energy from the mechanical energy. Two

types of turbines are widely prevalent : impulse turbines and reaction turbines.

In the impulse turbines, steam expands at the nozzles and achieved kinetic energy is used to rotatethe blades of the turbine. The blades change the direction of steam but not the pressure. Thus change

in momentum can be accounted for rotation of the rotor. In the reaction turbines, steam is partially

expanded on the nozzles and remaining expansion takes place during the flow over moving blades.Generally there are two or three sets of turbines at one go. All the enrgy stored in the steam cannot

be obtained at one go from a single turbine. So, there are two or three sets of turbines located which

are connected by a shaft. Now the high pressure steam enters into the first turbine, lets call it HPturbine. Once the expansion takes place, the pressure falls. Hence we need to use a turbine designed

for lower pressure appropriate to the out coming steam. So the second turbine will be a medium

pressure turbine (MP turbine).

Further , in some cases a third turbine is also added to make more energy out of steam andthis is called a low pressure turbine. The specifications of turbines are calclcuated during the plant

design and later during operations, same ratings of steam pressure and temperature need to be

maintained for optimum operation. Given below is a figure illustrating the construction of the three

stage turbine. Three turbine model for a plant

Pulverizer:

To generate the massive amount of heat which is required instantaneously , a lot of coal is to be

burnt. If chunks of coal is used, very less surface area of coal is exposed and it takes a lot of space to

burn enough coal chunks for required power. As a result, to overcome this problem, coal ispulverized into powder which is as smooth as talc. Now this powder is blown into the boiler. Thus,

as powder has a very higher surface area compared to chunks of coal, very large amount of coal can

be burnt instantaneously in less volume efficiently. This is the underlying interesting fact for using ofa pulveriser.

Super heater :

The steam is super heated in order to make it hold more energy and transfer it to the turbine. This job

is accomplished by the super heater. Super heater is showed in the boiler schematic. The flue gasescoming out of the boiler are used to super heat the steam.


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Economizer :

The water entering into the boiler must have a temperature compatible with the boiler temperature.So, the heat left with the flue gases after super heater is used to heat the water in the economizer. The

economizer has convoluted tubes in which water flows and the flue gases flow over these tubes in a

closed structure.

Air pre heater:

The air used for combustion of the coal is also pre heated by the flue gases so as to take maximum

heat from the gases before they diffuse in to the atmosphere. It is also to ensure that the un heated air

should not interfere with proper combustion inside the boiler.Re heater: To improve the efficiencyof the plant, there is something interesting done. The area under curve is the output or work done. If

we could improve the area, we can improve the efficiency of the system. The steam which comes out

of high pressure turbine is taken out and heated using flue gases and this reheated steam is sent into

IP turbine. As a result the new TS graph looks like below.

Improved TS graph after using re heater

Condenser:

As discussed earlier, the job of condenser is to turn the steam from the turbine into water and

thereby reducing the amount of water required for each cycle. There are many types of condensers.

The familiar ones are Jet type and Surface type. In the jet type , the cooling water and the steam aremixed and the resultant steam water mixture is drawn outside. Surface type uses a different circuit

for both and the steam is converted into water and cooling water turns hot. The surface type are the

widely prevalent ones.


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Generators :

The generators also called alternators are coupled with turbines which generate electrical energy. The

output of the generator at 11KV is stepped up to higher voltage of 220KV and transmitted throughthe transmission lines. Here , the interesting area of study is to control the output power of the

generator. As the load on the system continuously vary and as the energy cannot be stored, the output

of generator has to be varied according to load. This aspect will be covered in Power SystemsOperations and Control tutorial.

Overview of a practical power plant

Miscellaneous parts:


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Ash handling plant, Ash precipitators, pumps for draught, turbine governing system etc.

The Efficiency discussion

The efficiency of the thermal powerplant calculated from the Rankine cycle will be around 45% .

But practically efficiencies of 35%-38% only have been achieved so far. This is due to various losses

present in the entire system when put into practice. Out of the losses, energy lost as heat takes a

major chunk. This energy is lost at mainly two points: flue gases entering into atmosphere andcooling of the condensate. The cooling of the condensate is a part and parcel of the cycle and nothing

can be done there to increase the efficiency. Now we can consider decreasing the temperature of flue

gases as much as possible up to room temperatures. But it is also disadvantageous , for, the cooledgases do not flow outside the boiler circuit on their own. They need forced draught to go out if the

temperature is equal to room temperature. So there is a lower limit for temperature of flue gases.

Also note that, high pressure cannot be maintained inside the boiler. It is recommended to maintain

slightly low pressure in the boiler otherwise, the fire will come out from every possible gap in theboiler.

Pollution aspects :

Thermal energy is the most unclean energy. It causes thermal pollution and air pollution apart

from leaving off a lot of ash. The ash can be used for other purposes or should be disposed properly

otherwise during dry season , it mixes with air and makes the surrounding places uncomfortable to

live. The plant also produces thermal pollution ie by adding more and more heat to the atmosphere.But as Nature is a huge sink of heat this doesnt add much trouble. Other pollution from the plant is

due to production of soot, SO x, COx gases and consequent problems. Nowadays, latest technologies

are being implemented to minimize the emission of these gases by designing the boiler in a special

way and adding other compounds so as to neutralize these gases.

Problem : Find out the theoretical efficiency of a power plant whose steam is heated up to a

temperature of 4000Celsius and water temperature at the initial stages is 75

0Celsius.

Efficiency : 1-(75+273)/(400+273) = 1- 0.51 = 0.49 = 49 % efficiency.

8.6 Enhancements of, and Effect of Design Parameters on, Rankine

Cycles

The basic Rankine cycle can be enhanced through processes such assuperheating and reheat. Diagrams for a Rankine cycle with superheating aregiven in Figure8.13.The heat addition is continued past the point of vaporsaturation, in other words the vapor is heated so that its temperature is higher

than the saturation temperature associated with . This doesseveral things. First, it increases the mean temperature at which heat is

added, , thus increasing the efficiency of the cycle. Second is that the qualityof the two-phase mixture during the expansion is higher with superheating, sothat there is less moisture content in the mixture as it flows through the turbine.

(The moisture content at is less than that at .) This is an advantage in termsof decreasing the mechanical deterioration of the blading.
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[ - coordinates] [ - coordinates]

[ - coordinates]

Figure 8.13:Rankine cycle with superheating

The heat exchanges in the superheated cycle are:

Along , which is a constant pressure (isobaric) process: .

Along : , .

The thermal efficiency of the ideal Rankine cycle with superheating is

This can be expressed explicitly in terms of turbine work and compression (pump)

work as

Compared to the basic cycle, superheating has increased the turbine work,

increased the mean temperature at which heat is received, , and increased

the cycle efficiency.


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Figure 8.14:Comparison of Rankine cycle with superheating and Carnot cycle

Figure 8.15:Rankine cycle with superheating and reheat for space power application

A comparison of the Carnot cycle and the Rankine cycle with superheating isgiven in Figure8.14.The maximum and minimum temperatures are the same,but the average temperature at which heat is absorbed is lower for the Rankinecycle. To alleviate the problem of having moisture in the turbine, one can heatagain after an initial expansion in a turbine, as shown in Figure8.15,which givesa schematic of a Rankine cycle for space power application. This process isknown as reheat. The main practical advantage of reheat (and of superheating) isthe decrease in moisture content in the turbine because most of the heat additionin the cycle occurs in the vaporization part of the heat addition process.
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Figure 8.16:Effect of exit pressure on Rankine cycle efficiency

We can also examine the effect of variations in design parameters on theRankine cycle. Consider first the changes in cycle output due to a decrease inexit pressure. In terms of the cycle shown in Figure8.16,the exit pressure would

be decreased from to . The original cycle is , and the

modified cycle is . The consequences are that the cycle work,which is the integral of around the cycle, is increased. In addition, as drawn,although the levels of the mean temperature at which the heat is absorbed andrejected both decrease, the largest change is the mean temperature of the heatrejection, so that the thermal efficiency increases.

Figure 8.17:Effect of maximum boiler pressure on Rankine cycle efficiency

Another design parameter is the maximum cycle pressure. Figure8.17 shows a

comparison of two cycles with different maximum pressure but the samemaximum temperature, which is set by material properties. The averagetemperature at which the heat is supplied for the cycle with a higher maximumpressure is increased over the original cycle, so that the efficiency increases.

Muddy Points

Why do we look at the ratio of pump (compression) work to turbine work? We didnot do that for the Brayton cycle. (MP8.10)
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Shouldn't the efficiency of the super/re-heated Rankine cycle be larger becauseits area is greater? (MP8.11)

Why can't we harness the energy in the warm water after condensing the steamin a power plant? (MP8.12)

5.1 Concept and Statements of the Second Law (Why do we need a

second law?)

The unrestrained expansion, or the temperature equilibration of the two bricks,are familiar processes. Suppose you are asked whether you have ever seen thereverse of these processes take place? Do two bricks at a medium temperatureever go to a state where one is hot and one is cold? Will the gas in theunrestrained expansion ever spontaneously return to occupying only the left sideof the volume? Experience hints that the answer is no. However, both theseprocesses, unfamiliar though they may be, are compatible with the first law. In

other words the first law does not prohibit their occurrence. There thus must besome other ``great principle'' that describes the direction of natural processes,that tells us which first law compatible processes will not be observed. This iscontained in the second law. Like the first law, it is a generalization from anenormous amount of observation.

There are several ways in which the second law of thermodynamics can bestated. Listed below are three that are often encountered. As described in class(and as derived in almost every thermodynamics textbook), although the threemay not appear to have much connection with each other, they are equivalent.

1. No process is possible whose soleresult is the absorption of heat from areservoir and the conversion of this heat into work. [Kelvin-Planckstatement of the second law]

Figure 5.1:This is not possible (Kelvin-Planck)

2. No process is possible whose soleresult is the transfer of heat from acooler to a hotter body. [Clausius statement of the second law]
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Figure 5.2:For , this is not possible (Clausius)

3. There exists for every system in equilibrium a property called entropy, ,which is a thermodynamic property of a system. For a reversible process,

changes in this property are given by

The entropy change of any system and its surroundings, consideredtogether, is positive and approaches zero for any process whichapproaches reversibility.

For an isolated system, i.e., a system that has no interaction with thesurroundings, changes in the system have no effect on the surroundings. Inthis case, we need to consider the system only, and the first and secondlaws become:

For an isolated system the total energy

( ) is constant. Theentropy can only increase or, in the limit of a reversible process, remainconstant.


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The limit, or , represents the best that can bedone. In thermodynamics, propulsion, and power generation systems weoften compare performance to this limit to measure how close to ideal agiven process is.

All of these statements are equivalent, but3 gives a direct, quantitative measure

of the departure from reversibility.

Entropy is not a familiar concept and it may be helpful to provide some additionalrationale for its appearance. If we look at the first law,

the term on the left is a function of state, while the two terms on the right are not.

For a simple compressible substance, however, we can write the work done in a

reversible process as , so that

Two out of the three terms in this equation are expressed in terms of statevariables. It seems plausible that we ought to be able to express the third termusing state variables as well, but what are the appropriate variables? If so, the

term should perhaps be viewed as analogous to wherethe parentheses denote an intensive state variable and the square bracketsdenote an extensive state variable. The second law tells us that the intensive

variable is the temperature, , and the extensive state variable is theentropy, . The first law for a simple compressible substance in terms of statevariables is thus

(5..1)

Because Eq.5.1 includes the second law, it is referred to as the combined firstand second law. Because it is written in terms of state variables, it is true for allprocesses, not just reversible ones.

We summarize below some attributes of entropy:
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1. Entropy is a function of the state of the system and can be found if any two

properties of the system are known, e.g. or

or .2. is an extensive variable. The entropy per unit mass, or specific entropy,

is .

3. The units of entropy are Joules per degree Kelvin (J/K). The units forspecific entropy are J/K-kg.

4. For a system, , where the numerator is the heat given to thesystem and the denominator is the temperature of the system at thelocation where the heat is received.

5. for pure work transfer.

Muddy Points

Why is always true? (MP5.1)

What makes different than ? (MP5.2)

Thermodynamics and Propulsion

Next:5.4 Entropy Changes in Up:5. The Second Law Previous:5.2 Axiomatic Statements

of Contents Index

5.3 Combined First and Second Law Expressions

The first law, written in a form that is always true:
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15/325

For reversible processes only, work or heat may be rewritten as

Substitution leads to other forms of the first law true for reversible processes only:

(If the substance has other work modes, e.g., stress, strain,

where is a pressure-like quantity, and is a volume-like quantity.)

Substituting for both and in terms of state variables,

The above is always true because it is a relation between properties and is now independent of

process.

In terms of specific quantities:

The combined first and second law expressions are often more usefully written in terms of

the enthalpy, or specific enthalpy, ,


16/325

Or, since ,

In terms of enthalpy (rather than specific enthalpy) the relation is

Next:5.4 Entropy Changes in Up:5. The Second Law Previous:5.2 Axiomatic Statements

of Contents Index

UnifiedTP


Next:3.8 Muddiest points on Up:3. The First Law Previous:3.6 Diesel Cycle Contents Index

Subsections

3.7.1 Work and Efficiency 3.7.2 Gas Turbine Technology and Thermodynamics 3.7.3 Brayton Cycle for Jet Propulsion: the Ideal Ramjet 3.7.4 MIT Cogenerator

3.7 Brayton Cycle

[VW, S & B: 9.8-9.9, 9.12]

The Brayton cycle (or Joule cycle) represents the operation of a gas turbine engine. Thecycle consists of four processes, as shown in Figure3.13 alongside a sketch of an engine:

a - b Adiabatic, quasi-static (or reversible) compression in the inlet and compressor; b - c Constant pressure fuel combustion (idealized as constant pressure heat addition); c - d Adiabatic, quasi-static (or reversible) expansion in the turbine and exhaust nozzle, with

which we1. take some work out of the air and use it to drive the compressor, and
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Figure 3.15:Thermodynamic model of gas turbine engine cycle for power generation

[Open cycle operation] [Closed cycle

operation]

Figure 3.16:Options for operating Brayton cycle gas turbine engines

Muddy Points

Would it be practical to run a Brayton cycle in reverse and use it as refrigerator? (MP 3.10)

3.7.1 Work and Efficiency

The objective now is to find the work done, the heat absorbed, and the thermal efficiency of
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the cycle. Tracing the path shown around the cycle from - - - and back to , thefirst law gives (writing the equation in terms of a unit mass),

Here is zero because is a function of state, and any cycle returns the system to its starting

state3.2.The net work done is therefore

where , are defined as heat received bythe system ( is negative). We thus need to

evaluate the heat transferred in processes - and - .

For a constant pressure, quasi-static process the heat exchange per unit mass is

We can see this by writing the first law in terms of enthalpy (see Section 2.3.4)or by

remembering the definition of .

The heat exchange can be expressed in terms of enthalpy differences between the relevantstates. Treating the working fluid as a perfect gas with constant specific heats, for the heataddition from the combustor,

The heat rejected is, similarly,

The net work per unit mass is given by

The thermal efficiency of the Brayton cycle can now be expressed in terms of thetemperatures:

(3..8

)

To proceed further, we need to examine the relationships between the different
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temperatures. We know that points and are on a constant pressure process as are

points and , and ; . The other two legs of the cycle are adiabaticand reversible, so

Therefore , or, finally, . Using this relation in theexpression for thermal efficiency, Eq. (3.8)yields an expression for the thermal efficiency ofa Brayton cycle:

(3..9)

The temperature ratio across the compressor, . In terms of compressortemperature ratio, and using the relation for an adiabatic reversible process we can writethe efficiency in terms of the compressor (and cycle) pressure ratio, which is the parametercommonly used:

(3..10)

Figure 3.17:Gas turbine engine pressures and temperatures
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Figure3.17 shows pressures and temperatures through a gas turbine engine (the PW4000,which powers the 747 and the 767).

Figure 3.18:Gas turbine engine pressure ratio trends (Janes Aeroengines, 1998)
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Figure 3.19:Trend of Brayton cycle thermal efficiency with compressor pressure ratio

Equation (3.10)says that for a high cycle efficiency, the pressure ratio of the cycle shouldbe increased. This trend is plotted in Figure3.19.Figure3.18 shows the history of aircraftengine pressure ratio versus entry into service, and it can be seen that there has been alarge increase in cycle pressure ratio. The thermodynamic concepts apply to the behavior ofreal aerospace devices!

Muddy Points

When flow is accelerated in a nozzle, doesn't that reduce the internal energy of the flow andtherefore the enthalpy? (MP3.11)

Why do we say the combustion in a gas turbine engine is constant pressure? (MP 3.12)

Why is the Brayton cycle less efficient than the Carnot cycle? (MP3.13)

If the gas undergoes constant pressure cooling in the exhaust outside the engine, is thatstill within the system boundary? (MP3.14)

Does it matter what labels we put on the corners of the cycle or not? (MP3.15)

Is the work done in the compressor always equal to the work done in the turbine plus workout (for a Brayton cyle)? (MP3.16)

3.7.2 Gas Turbine Technology and Thermodynamics

The turbine entry temperature, , is fixed by materials technology and cost. (If the temperature is

too high, the blades fail.) Figures3.20 and3.21 show the progression of the turbine entry

temperatures in aeroengines. Figure3.20 is from Rolls Royce and Figure3.21 is from Pratt &

Whitney. Note the relation between the gas temperature coming into the turbine blades and the

blade melting temperature.
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Figure 3.20:Rolls-Royce high temperature technology

Figure 3.21:Turbine blade cooling technology [Pratt & Whitney]

For a given level of turbine technology (in other words given maximum temperature) a

design question is what should the compressor be? What criterion should be used todecide this? Maximum thermal efficiency? Maximum work? We examine this issue below.

Figure 3.22:Efficiency and work of two Brayton cycle engines

The problem is posed in Figure3.22,which shows two Brayton cycles. For maximum
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efficiency we would like as high as possible. This means that the compressor exittemperature approaches the turbine entry temperature. The net work will be less than the

heat received; as the heat received approaches zero and so does the net work.

The net work in the cycle can also be expressed as , evaluated in traversing the

cycle. This is the area enclosed by the curves, which is seen to approach zero as.

The conclusion from either of these arguments is that a cycle designed for maximumthermal efficiency is not very useful in that the work (power) we get out of it is zero.

A more useful criterion is that of maximum work per unit mass (maximum power per unitmass flow). This leads to compact propulsion devices. The work per unit mass is given by:

where is the maximum turbine inlet temperature (a design constraint) and is atmospheric

temperature. The design variable is the compressor exit temperature, , and to find the maximum

as this is varied, we differentiate the expression for work with respect to :

The first and the fourth terms on the right hand side of the above equation are both zero(the turbine entry temperature is fixed, as is the atmospheric temperature). The maximum

work occurs where the derivative of work with respect to is zero:

(3..11)

To use Eq. (3.11), we need to relate and . We know that

Hence,
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Plugging this expression for the derivative into Eq. (3.11)gives the compressor exit

temperature for maximum work as . In terms of temperature ratio,

The condition for maximum work in a Brayton cycle is different than that for maximumefficiency. The role of the temperature ratio can be seen if we examine the work per unitmass which is delivered at this condition:

Ratioing all temperatures to the engine inlet temperature,

To find the power the engine can produce, we need to multiply the work per unit mass bythe mass flow rate:

(3..12

)

The trend of work output vs. compressor pressure ratio, for different temperature

ratios , is shown in Figure3.23.
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Figure 3.23:Trend of cycle work with compressor pressure ratio, for different temperature

ratios

[Gas turbine engine core] [Core power vs. turbine entry

temperature]

Figure 3.24:Aeroengine core power [Koff/Meese, 1995]

Figure3.24 shows the expression for power of an ideal cycle compared with data from
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actual jet engines. Figure3.24(a) shows the gas turbine engine layout including the core(compressor, burner, and turbine). Figure3.24(b) shows the core power for a number ofdifferent engines as a function of the turbine rotor entry temperature. The equation in thefigure for horsepower (HP) is the same as that which we just derived, except for theconversion factors. The analysis not only shows the qualitative trend very well but capturesmuch of the quantitative behavior too.

A final comment (for this section) on Brayton cycles concerns the value of the thermal

efficiency. The Brayton cycle thermal efficiency contains the ratio of the compressor exittemperature to atmospheric temperature, so that the ratio is not based on the highesttemperature in the cycle, as the Carnot efficiency is. For a given maximum cycletemperature, the Brayton cycle is therefore less efficient than a Carnot cycle.

Muddy Points

What are the units of in ? (MP3.17)

Question about the assumptions made in the Brayton cycle for maximum efficiency andmaximum work (MP3.18)

You said that for a gas turbine engine modeled as a Brayton cycle the work done

is , where is the heat added and is the heat rejected. Does thissuggest that the work that you get out of the engine doesn't depend on how good your

compressor and turbine are? since the compression and expansion were modeled as

adiabatic. (MP3.19)

3.7.3 Brayton Cycle for Jet Propulsion: the Ideal Ramjet

A schematic of a ramjet is given in Figure3.25.

Figure 3.25:Ideal ramjet [J. L. Kerrebrock, Aircraft Engines and Gas Turbines]

In the ramjet there are ``no moving parts.'' The processes that occur in this propulsion
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device are:

: Isentropic diffusion (slowing down) and compression, with a decrease in Mach

number, .

: Constant pressure combustion.

: Isentropic expansion through the nozzle.

The ramjet thermodynamic cycle efficiency can be written in terms of flight Mach

number, , as follows:

and

so

See also Section11.6.3 for other figures of merit.

Muddy Points

Why don't we like the numbers 1 and 2 for the stations? Why do we go 0-3? (MP3.20)

For the Brayton cycle efficiency, why does ? (MP3.21)

3.7.4 MIT CogeneratorMIT operates a Brayton cycle power generator on campus. For more information, see thewebsite athttps://cogen.mit.edu/ctg.cfm .

Next:3.8 Muddiest points on Up:3. The First Law Previous:3.6 Diesel Cycle Contents Index
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3. At state the system is brought in contact with a heat reservoir at temperature . It is

then compressed to state , rejecting heat in the process.

4. Finally, the system is compressed adiabatically back to the initial state . The heat

exchange .

The thermal efficiency of the cycle is given by the definition

(3..4)

In this equation, there is a sign convention implied. The quantities , as defined are

the magnitudes of the heat absorbed and rejected. The quantities , on the otherhand are defined with reference to heat received by the system. In this example, the formeris negative and the latter is positive. The heat absorbed and rejected by the system takesplace during isothermal processes and we already know what their values are from Eq.(3.1):

The efficiency can now be written in terms of the volumes at the different states as

(3..5)

The path from states to and from to are both adiabatic and reversible. For a

reversible adiabatic process we know that . Using the ideal gas equation

of state, we have . Along curve - , therefore, .

Along the curve - , . Thus,
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Comparing the expression for thermal efficiency Eq. (3.4)with Eq. (3.5)shows twoconsequences. First, the heats received and rejected are related to the temperatures of theisothermal parts of the cycle by

(3..6)

Second, the efficiency of a Carnot cycle is given compactly by

(3..7)

The efficiency can be 100% only if the temperature at which the heat is rejected is zero.The heat and work transfers to and from the system are shown schematically in Figure 3.5.

Figure 3.5:Work and heat transfers in a Carnot cycle between two heat reservoirs

Muddy Points

Since , looking at the - graph, does that mean the farther apart

the , isotherms are, the greater efficiency? And that if they were very close, it would
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be very inefficient? (MP3.2)

In the Carnot cycle, why are we only dealing with volume changes and not pressurechanges on the adiabats and isotherms? (MP3.3)

Is there a physical application for the Carnot cycle? Can we design a Carnot engine for apropulsion device? (MP3.4)

How do we know which cycles to use as models for real processes? (MP3.5)

Next:3.4 Refrigerators and Heat Up:3. The First Law Previous:3.2 Generalized Representation

of Contents Index

UnifiedTP


Next:8.8 Some Overall Comments Up:8. Power Cycles with Previous:8.6 Enhancements of

Rankine Contents Index

8.7 Combined Cycles in Stationary Gas Turbine for Power Production

The turbine entry temperature in a gas turbine (Brayton) cycle is considerably higher thanthe peak steam temperature. Depending on the compression ratio of the gas turbine, theturbine exhaust temperature may be high enough to permit efficient generation of steamusing the ``waste heat'' from the gas turbine. A configuration such as this is known as a gasturbine-steam combined cycle power plant. The cycle is illustrated in Figure8.18.
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e139.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node5.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node23.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node21.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node25.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node67.html#fig6:CombinedCyclehttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node139.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node5.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node66.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node66.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node60.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node68.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/notes.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node139.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node5.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node23.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node23.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node21.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node25.htmlhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node29.html#mud1:RealCyclesRealProcesseshttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node29.html#mud1:CarnotPhysicalApplicationhttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node29.html#mud1:CarnotVolumeChangeshttp://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node29.html#mud1:IsothermSeparationAndEfficiency


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Figure 8.18:Gas turbine-steam combined cycle [Kerrebrock,Aircraft Engines and Gas Turbines]

Figure 8.19:Schematic of combined cycle using gas turbine (Brayton cycle) and steam turbine (Rankine

cycle) [Langston]

The heat input to the combined cycle is the same as that for the gas turbine, but the workoutput is larger (by the work of the Rankine cycle steam turbine). A schematic of the overallheat engine, which can be thought of as composed of an upper and a lower heat engine inseries, is given in Figure8.19.The upper engine is the gas turbine (Brayton cycle) whichexpels heat to the lower engine, the steam turbine (Rankine cycle).

The overall efficiency of the combined cycle can be derived as follows. We denote the heat

received by the gas turbine as and the heat rejected to the atmosphere as . The

heat out of the gas turbine is denoted as . The hot exhaust gases from the gas turbinepass through a heat exchanger where they are used as the heat source for the two-phase

Rankine cycle, so that is also the heat input to the steam cycle. The overall combinedcycle efficiency is

where the subscripts refer to combined cycle (CC), Brayton cycle (B) and Rankine cycle (R)

respectively.

From the first law, the overall efficiency can be expressed in terms of the heat inputs and

heat rejections of the two cycles as (using the quantity to denote the magnitudeofthe heat transferred):
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The first square bracket term on the right hand side is the Brayton cycle efficiency, , the second

is the Rankine cycle efficiency, , and the term in parentheses is . The combined

cycle efficiency can thus be written as

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