1. Fundamentals of Gas Turbines - · PDF file7FA, GE . Combined Cycle Power Plants 1....

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1. Fundamentals of Gas Turbines


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Thermodynamics 53 2

Fundamentals for Gas Turbines 2 1


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Coal

Gas

Oil

Water

Nuclear

Wind

Solar

Geothermal

Biomass

Variety of Fuels Competitive Machine

Effic

iency

Availa

bili

ty

Opera

tin

g

Fle

xib

ility

Em

issio

ns

Co

sts

Power Generation Requirement


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Starter &

gear box

Air inlet Compressor Combustor

Turbine Exhaust

VIGV

Air extraction

ports Diffuser

Transition

piece

Cold section Hot section

A Typical Gas Turbine for Power Generation

7FA, GE


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In a gas turbine, the working fluid for transforming thermal energy into rotating mechanical energy is the hot

combustion gas, hence the term “gas turbine.”

The first power generation gas turbine was introduced by ABB in 1937. It was a standby unit with a thermal

efficiency of 17%.

The gas turbine technology has many applications. The original jet engine technology was first made into a

heavy duty application for mechanical drive purposes.

Pipeline pumping stations, gas compressor plants, and various modes of transportation have successfully

used gas turbines.

While the mechanical drive applications continue to have widespread use, the technology has advanced into

larger gas turbine designs that are coupled to electric generators for power generation applications.

Gas turbine generators are self-contained packaged power plants.

Air compression, fuel delivery, combustion, expansion of combustion gas through a turbine, and electricity

generation are all accomplished in a compact combination of equipment usually provided by a single

supplier under a single contract.

The advantages of the heavy-duty gas turbines are their long life, high availability, and slightly higher overall

efficiencies. The noise level from the heavy-duty gas turbines is considerably less than gas turbines for

aviation.

Gas Turbine


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Idealized Brayton Cycle [1/3]

Compressor

Fuel Combustor

Turbine

Air

Power

Exhaust gas 1

2 4 3

p

2

1

T

(h)

s

qin

3

4 1

2

3

4

qout

win wout

win

wout

qin

qout


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The entering air is compressed to higher pressure.

No heat is added. However, compression raises the air temperature so that the discharged air has

higher temperature and pressure.

The mechanical energy transmitted from the turbine is used to compress the air.

Compression Process (1 2)

Compressed air enters the combustor, where fuel is injected and combustion occurs.

The chemical energy contained in the fuel is converted into thermal energy.

Combustion occurs at constant pressure. However, pressure decreases slightly in the practical process.

Although high local temperatures are reached within the primary combustion zone (approaching

stoichiometric conditions), the combustion system is designed to provide mixing, burning, dilution,

cooling.

Combustion mixture leaves with mixed average temperature.

Combustion Process (2 3)



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The thermal energy contained in the hot gases is converted into mechanical work in the turbine.

This conversion actually takes place in two steps:

• Nozzle: the hot gases are expanded and accelerated, and a portion of the pressure energy is

converted into kinetic energy.

• Bucket: a portion of the kinetic energy is transferred to the rotating buckets and converted into

mechanical work.

Some of the work produced by the turbine is used to drive the compressor, and the remainder is used to

drive load equipment, such as generator, ship propeller, and pump, etc.

Typically, more than 50% of the work produced by the turbine section is used to power the compressor.

Expansion Process (3 4)

Exhaust Process (4 1)

This is a constant-pressure cooling process.

This cooling is done by the atmosphere, which provides fresh, cool air as well.

The actual cycle is an “open” rather than “closed”.



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Variation of Major Parameters

m/s bar C

700 21 2100

600 18 1800

500 15 1500

400 12 1200

300 9 900

200 6 600

100 3 300

0 0 0

Pressure (po)

Temperature (To)

Velocity

http://upload.wikimedia.org/wikipedia/commons/4/4c/Jet_engine.svg


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Terminology Meaning

Combined cycle

• Combined cycle = Brayton cycle (topping cycle) + Rankine cycle (bottoming cycle)

• Combined cycle can be defined as a combination of two thermal cycles in one plant. When

two cycles are combined, the efficiency that can be achieved is higher than that of one cycle

alone.

• Gas turbine + Steam turbine

• Normally the topping and bottoming cycles are coupled in a heat exchanger.

Simple cycle

• The term simple cycle is used to distinguish this configuration from the complex cycles, which

utilizes additional components, such as heat exchanger for regeneration, intercooler, reheating

system, or steam boilers.

Heavy duty gas

turbines

• In general. it means gas turbines for power generation because they differ from aeronautical

designs in that the frames, bearings, and blading are of heavier construction .

Aeroderivative gas

turbines

• The aero-engines transformed into land based gas turbines successfully.

• P&W JT8/FT8, GE J79/LM1500, GE CF6/LM2500, CF6/LM5000, CF6/LM6000

• The LM2500 has been the most commercially successful one.

Mechanical drive

gas turbines

• Sometimes, it includes heavy duty gas turbines, aeroderivative gas turbines, gas (oil) pumping

gas turbines, and gas turbines for marine applications.

• Generally, this means the industrial gas turbines that are used solely for mechanical drive or

used in collaboration with a recovery steam generator differ from power generating sets in that

they are often smaller and feature a "twin" shaft design as opposed to a single shaft. The

power range varies from 1 MW up to 50 MW.

Terminology


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Compressor

Fuel

Combustor

Turbine

Inlet

air

Steam

turbine

G

G

Condenser

Deaerator

Condensate

pump HP boiler feed pump

LP boiler feed pump

HP superheater

HP evaporator

HP economizer

LP superheater

LP evaporator

LP economizer

HP

drum

LP

drum

Exhaust

gas

HRSG

In simple cycle mode, the gas turbine is operated alone, without the benefit of recovering any of energy

in the hot exhaust gases. The exhaust gases are sent directly to the atmosphere.

In combined cycle mode, the gas turbine exhaust gases are sent into HRSG. The HRSG generates

steam that is normally used to power a steam turbine.

Combined Cycle Power Plants [1/11]


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Cycle Diagram for a 3 Pressure Reheat Cycle (F-Class Gas Turbine)


Condenser

G

G

Fuel

Air

Gas turbine

Heat recovery steam

generator

IP steam LP

steam Cold reheat

steam

Hot reheat

steam

Main

steam

Steam turbine

Condensate pump

Steam

Water

Fuel

Air


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Combined cycle power plants have a higher thermal efficiency because of the application of two

complementary thermodynamic cycles

T-s Diagram for a Typical CCPPs


Condenser

(heat out)

T

s

Topping cycle

Bottoming cycle

Combustion

(heat In)

Stack

(heat

out)


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TH

TL

QL

W

QH

Steam turbine

TH

TL

QL

W

QH

Gas turbine

W Steam turbine

HRSG

[ Fossil / Nuclear ] [ Combined cycle]

The Second Law of Thermodynamics



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구분 Topping cycle Bottoming cycle

Main Components GT ST/HRSG

Working Fluid Air Water/Steam

Temperature High Medium/Low

Thermodynamic Cycle Brayton Rankine

Coupling Two Cycles Heat Exchanger

Topping cycle Coupling Bottoming cycle

Cycle Characteristics



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Combined cycle power plant means a gas turbine operated with the Brayton cycle, is combined with a heat

recover steam generator and steam turbine operated with the Rankine cycle, in one plant.

When two cycles are combined, the efficiency increases higher than that of one cycle alone.

Thermal cycles with the same or with different working fluid can be combined.

In general, a combination of cycles with different working fluid has good characteristics because their

advantages can complement one another.

Normally, when two cycles are combined, the cycle operating at the higher temperature level is called as

topping cycle. The waste heat is used for second process that is operated at the lower temperature level,

and is called as bottoming cycle.

The combination used today for commercial power generation is that of a gas topping cycle with a

water/steam bottoming cycle. In this case heat can be introduced at higher temperature and exhausted at

very low temperature.

Temperature of the air used as a working fluid of gas turbines can be increased very high under lower

pressure. Water/steam used as a working fluid can contain very high level of energy at lower temperature

because it has very high specific heat.

Normally the topping and bottoming cycles are coupled in a heat exchanger.

Generals [1/2]



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Air is used as a working fluid in gas turbines having high turbine inlet temperatures because it is easy to get

and has good properties for topping cycle.

Steam/water is an ideal material for bottoming cycle because it is inexpensive, easy to get, non-hazardous,

and suitable for medium and low temperature ranges.

The initial breakthrough of gas-steam cycle onto the commercial power plant market was possible due to

the development of the gas turbine.

In the late 1970s, EGT reached sufficiently high level that can be used for high efficiency combined cycles.

The breakthrough was made easier because gas turbines have been used for power generation as a simple

cycle and steam turbines have been used widely.

For this reason, the combined cycle, which has high efficiency, low installation cost, fast delivery time, had

been developed easily.

Generals [2/2]



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Gas turbine Steam turbine

Combustion Internal External

Thermodynamic cycle Brayton Rankine

Cycle type Open Closed

Working fluid Air Water/Steam

Max. pressure, bar 23 (40 for Aviation) 350 (5050 psig)

Max. temperature, C(F) 1350 (2462) 630 (1166)

Blade cooling Yes No

Shaft cooling No Yes (USC only)

Max. cycle efficiency, % 40 49 (USC only)

Max. number of reheat 1 2

Power density High Low

Steam conditions of the steam turbines for combined cycle applications are lower than those for

USC steam turbines.

GT vs. ST



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Fuel energy

100%

GT 37.6%

ST 21.7%

Condenser

31.0%

Stack 8.6%

Loss in HRSG

0.3%

Loss

0.5%

Loss

0.3%

Three pressure

reheat cycle Im

pro

ve

d

Heat Balance of CCPPs



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G

Natural gas

G

IP

9

HP

8

LP

10

1

2

3

4

5

6

7

11 12

13

14

15 16

17

18

19 20 1 Dual HP superheater/reheater 2,4,6 HP,IP,LP evaporators 3 HP economizer/IP superheater 5,7 Dual HP/IP economizer 8,9,10 HP,IP,LP drums 11 HP steam turbine 12 IP/LP steam turbine 13,14,15 HP,IP,LP steam bypasses 16 Condenser 17 Condensate pump 18 Deaerator 19,20 IP,HP feedwater pumps

Three Pressure

Reheat Cycle

Flow Diagram of a Typical CCPP



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Three Pressure

Reheat Cycle

Heat Balance Diagram of a Typical CCPP


Air

G

Natural gas

473 MW

G

P 33.7

T 240

P 33.7

T 240

P 33.7

T 240

P bar T C M kg/s X Rel. humidity

Gross output = 280.5 MW

Gross effi. (LHV) = 59.3%

P 1.013 T 15 X 60 %

P 0.045 T 31 M 67

P 28.5 T 565 M 65.1

P 115.2 T 565 M 59.2

P 120 T 568

P 30.0 T 568

P 32.1 T 369 M 5.9 P 4.6

T 150 M 5.4

M 0

M 0

P 5.0 T 152 M 5.4

M 11.3 M 59.2

M 0

M 3.5

P 0.2 T 60

P 1.013 T 103 M 386.7

T 647 M 386.7

178 MW

M 0

102.5 MW


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Simple cycle gas turbines for electricity generation are typically used for standby or peaking capacity and

are generally operated for a limited number of hours per year. Peaking operation is often defined as fewer

than 2,000 hours of operation per year.

In mechanical drive applications, and for some industrial power generation, simple cycle gas turbines are

base-load and operate more than 5,000 hours of operation per year.

Some plants are initially installed as simple cycle plants with provisions for future conversion to combined

cycle.

Gas turbines typically have their own cooling, lubricating, and other service systems needed for simple

cycle operation. This can eliminate the need to tie service systems into the combined cycle addition and will

allow continued operation of the gas turbine during the conversion process and, with proper provisions,

during periods when the combined cycle equipment is out of service.

If future simple cycle is desired, a bypass stack may be included with the connection of the HRSG. A typical

method for providing this connection is to procure a divert damper box at the outlet of the gas turbine.

Simple Cycle

[ with Bypass Stack ] [ without Bypass Stack ]


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Heavy duty gas turbines Aeroderivative gas turbines

• Newly designed for power generation

• High aspect ratio (long, thin) turbine blades with tip

shrouds to dampen vibration and improve blade tip

sealing characteristics

• Single-shaft

• Electrical output of up to 340 MW

• Standardized

• Manufactured on the base of sales forecasts rather

than orders received

• Series of frame sizes

- shorter installation time

- low costs

• Derived from jet engines (lightweight components,

compact design, and high efficiency) and frequently

incorporating a separate power turbine

• Low aspect ratio turbine blades with no shroud

• Two- or three-shaft turbine with a variable speed

compressor (This is an advantage for part-load

efficiency because airflow is reduced at low speeds)

• Higher part load efficiency because of variable

speed

• Two-shaft turbines are usually used for compressor

or pump drives

• The size is limited to 100 MW due to the maximum

size of aircraft

MS7001F, GE LM6000, GE

Heavy Duty vs. Aeroderivative GT [1/3]


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Aero Trent

Trent 60 Gas Turbine (Mechanical Drive)

① New LP compressor replaces fan

② LP bleed added for low speed operation

③ DLN combustor replaces annular aero combustor

④ Last two stages of LPT and exhaust redesigned

⑤ Rear drive added

Aero Trent

MT30



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Both heavy duty and aeroderivative gas turbines are used in combined cycle applications. However, the

majority of the gas turbines used in power generation are heavy duty gas turbines.

The exhaust gas temperatures of heavy duty gas turbines are typically higher than those of aeroderivative

machines.

In addition, the exhaust flow per unit gas turbine output is higher for the heavy duty gas turbines.

In combined cycle mode, this allows more steam with higher superheat temperatures to be generated with

the heavy duty machines, which translates into more electrical output from the steam turbine.

In general, for smaller ratings, the overall heat rate for a heavy duty gas turbine based combined cycle is

slightly higher than that for an aeroderivative based combined cycle plant of similar size.

However, combined cycle power plants with larger heavy duty gas turbines having higher TITs have lower

heat rates compared to aeroderivative based combined cycle plants.

The heavy duty gas turbines are based on more rugged design and can use a much wide range of fuels

than the aeroderivative gas turbines.

Advanced metallurgy and cooling technologies developed for jet engines have enabled heavy duty gas

turbines to achieve higher TIT and efficiency.



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Hot-end drive Cold-end drive

• In the hot-end drive configuration, the output shaft

extends out the rear of the turbine.

• The designer is faced with many constraints, such

as output shaft length, high EGT, exhaust duct

turbulence, pressure drop, and maintenance

accessibility.

• Insufficient attention to any of these details, in the

design process, often results in power loss,

vibration, shaft or coupling failures, and increased

down-time for maintenance.

• This configuration is difficult to service as the

assembly must be fitted through the exhaust duct.

• In the cold-end drive configuration, the output shaft

extends out the front of the compressor.

• The single disadvantage is that the compressor

inlet must be configured to accommodate output

shaft.

• The inlet duct must be turbulent free and provide

uniform, vortex free, flow over the all operating

range.

• Inlet turbulence may induce surge in the

compressor resulting in complete destruction of the

unit.

MS7001E, GE MS7001F, GE

Hot-End Drive vs. Cold-End Drive


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~ ~

Single-shaft Multi-shaft

• Cold-end drive

• Power generation only

• Efficient exhaust

• 50/60 Hz direct drive for large units

• Higher starting power

• Low speed operation is not possible because of

surge

• Hot-end drive

• Both power generation and mechanical drive

• The free power turbine is coupled

aerodynamically with HP turbine

• The speed of the free power turbine is variable

• Optimum solution for emergency power

• The gas turbine is easier to start, especially in

cold weather

• The load does not transmit vibration into the gas

generator

• Less efficient exhaust

• Power turbine over-speed risk at load rejection

Single-Shaft vs. Multi-Shaft [1/2]


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When the operation flexibility is important, such as marine applications, a mechanically independent power

turbine is used.

Compressor and high pressure turbine combination acts as a gas generator for the power turbine.

Fuel flow to the combustor is controlled to achieve variation of power. This will cause a decrease in cycle

pressure ratio and maximum temperature.

At off-design conditions the power output reduces with the result that the thermal efficiency deteriorates

considerably at part loads.

Compressor

Fuel Combustor

LP turbine

(power turbine)

Air

Power

Exhaust gas

HP turbine

Two-Shaft GT

Single-Shaft vs. Multi-Shaft [2/2]


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Base load Intermediate load Peak load

Operating

hours [hr/a] 5000 2000 to 5000 2000

Generating

units

• Nuclear plant

• High-performance steam

turbine plant

• High efficient combined cycle

plant

• Hydropower plant

• Simple steam turbine plant

• Old base-load plant

• Combined gas and steam

plant

• Gas turbine

• Diesel engine

• Pumping-up power plant

• Old simple steam turbine

plant

Characteri-

stics

• Operated at full load as long as

possible during the year

• High efficiency and lowest cost

• Poor load change capability

(take more time to respond load

demand)

• Operated on weekdays and

shutdown at night and on the

weekend

• The efficiency is higher than

that of peak-load plants, but

lower than that of base-load

plants

• Low capital investment, but

highest operating costs

• Ease in startup

• Used as standby or

emergency also

Type of Plants


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2004 2006 2008 2010

Bill

ions o

f d

olla

rs (

20

07

)

3

6

9

12

15

18

Commercial aviation

Electrical generation

Military aviation

Mechanical drive

Marine propulsion

Gas Turbine Production by Sector Source: Davis Franus, Forecast International


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열역학적 성능 향상

온도 향상

압력 향상

유체역학적 성능 향상

2차유동손실 최소화

누설손실 최소화

배기손실 최소화

기타

대형화

Options for Power

Enhancement

USC Steam Turbine H-Gas Turbine

발전설비 성능향상


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A-USC USC SC

(Supercritical) SC

(Subcritical)

TIT, C = 1104 1316 1427 1600

PR = 15 15 20-23 23

th (SC/CC) = 37/55 39/58 --/60 40/61

T, F(C) = 1000(538) 1100(593) 1130(610) 1292(700)

P, psig = 2400 3500 4500 4500

th = 38 44 49 ?

Gas Turbine

Steam Turbine

Thermodynamic Improvement

J-class H-class F-class E-class


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Evolution of GE Gas Turbine


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S106B

S107EA

S109E

S106FA

S107FA

S107FB

S109FA

S109FB

S107H S109H

Second Generation • B & E Gas Turbine Technology

• Non-Reheat, 3-Pressure Steam Cycle

Third Generation • F Gas Turbine Technology

• Reheat, 3-Pressure Steam Cycle

Fourth Generation • H Gas Turbine Technology

• Reheat, 3-Pressure Steam Cycle

0 50 100 150 200 250 300 350 400 450 500 550

64

61

60

58

56

54

52

50

48

46

Ne

t E

ffic

ien

cy,

% (

Ba

se

d o

n L

HV

)

Net Plant Output, MW

STAG Product Line Ratings


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Core Technologies

• Materials / coatings

• Cooling / sealing

• 3D aerodynamic designs

• Tools and talent

• Installed base learning

Plant Performance

• Higher efficiency

• Higher output

• Higher reliability

• Lower emissions

• Lower O&M costs

Compressor

Pressure ratio

Combustor

Dry low NOx

Turbine

TIT

Superiority

• Lower cost of electricity

• Higher market share

Why Technology Matters ?


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The gas turbine will continue to play an important role in meeting power generation requirements as

technology advances and as the product and cycle designs respond to changes in fuel economics and

allowable plant emissions.

• Higher efficiency (3D)

• Higher PR

• Larger air flow

• Smaller stages

• Low leakage flow

• Low vibration

• No stall and surge –

variable stators

• Lower emissions

• Low pressure loss

• Higher combustion efficiency

• Less cooling air

• Low vibration / high reliability

• High fuel flexibility

• Uniform outlet temp distribution

• Higher turbine efficiency

• Lower stage loading

• Higher output (larger

enthalpy drop = higher TIT)

• Advanced blade materials

• Coating technologies

• Cooling technologies

• Improved sealing

• Cycle analysis

Required Technologies


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The last 30 years has seen a large growth in gas turbine technologies.

The growth is provided by the increase in compressor pressure ratio, advanced combustion techniques, the

growth of materials technology, new coatings, and new cooling schemes.

The increase in gas turbine efficiency is dependent on two basic parameters, such as pressure ratio and TIT.

The aerospace engines have been the leaders in most of the gas turbine technologies. The design criteria

for these engines was high reliability, high performance, with many starts and flexible operation throughout

the flight envelope.

The industrial gas turbines have always emphasized long life and rugged operation. Therefore, those have

been conservative in pressure ratio and TITs, thus lower efficiency than aerospace ones.

However, this concept has been changed in the last 10 years, and performance gap between these two

types of gas turbines has been reduced greatly.

Currently, axial compressor produces pressure ratio of up to 40:1 in some aerospace applications, and a

pressure ratio of 30:1 in some industrial units.

TITs are similar between these two types of gas turbines, and single crystal materials are used in those two

types of gas turbines.

Gas Turbine Technologies


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Acquire the last proven technology and not the latest. The latest technology contains a high technological

risk.

All possible failure modes are still unknown for the latest generation of gas turbines.

Any operation of the gas turbine outside the ideal operating conditions (base load, ISO conditions)

significantly affects its performance and durability.

Cyclic operation of combined cycles is still vague. (emissions, fuel, part-load, etc.)

Within the lifecycle cost of a combined cycle plant, the maintenance cost is (approximately) twice the initial

cost.

The design of a gas turbine has always being improved.

There is a need for (regulation and) certification of component repair for gas turbine technology.

Approximately between 70-80% of the cost of electricity corresponds to the cost of fuel.

Main technology risks:

• Mechanical component failures: Thermo-mechanic fatigue, creep, …

• Problems due to high TITs: Materials & coating life, cooling effectiveness,...

• Rotor & blading integrity: Rotor assembly, vibrational/rotordynamic integrity, …

• Combustion process: Flame instability, NOx control, etc.

Users Point of View


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Increased pressure ratio

• Higher engine efficiency requires higher engine pressure ratio.

• Higher pressure ratios will also increase the number of stages and potentially longer rotors.

• The number of turbine stage has been changed from three to four as the pressure ratio increases.

• Variable stator has adopted to control compressor stall and to increase efficiency during part load

operation.

Increased specific flow

• Specific flow will continue to increase and approach aero-engine technology.

• Siemens: 820 kg/s (latest 50 Hz engine); MHI: 860 kg/s (J-class)

• GE: 745 kg/s (9FB.05), 440 kg/s (7FA), 558 kg/s (7H)

• The absolute maximum of today is around 1000 kg/s@3000 rpm, but this can be achieved only with mul

ti-spools.

• GE and Alstom have upgraded compressor with aero-engine technology.

All major OEMs have on-line compressor vibration measurements and associated protection system.

Developmental Trends

Compressor [1/7]


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Previous Designs New Designs Risk

2D double circular arc or NACA 65 profiles 3D or Controlled Diffusion-shaped Airfoil

(CDA) profiles

Large number of airfoils Reduced airfoils

Repeating stages Stages unique

Shorter chords Longer chords

Low/modest aspect ratios High aspect ratios

Large clearances Small clearances

Low/modest pressure ratios Much high pressure ratios

Low/modest blade loading per stage High blade loading per stage

Wider operating margin Narrow operating margin

Thicker leading edges Thinner leading edges

Dry operation Wet operation

Lower costs Higher costs


Compressor [2/7]


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Pressure Ratio P

ressure

ratio

7E/9E

501ATS

7EA/9EC

V84.2/V94.2

7H/9H

V84.3A/

V94.3A

V84.3

501F/701F

7F/9F

7FA/9FA

GT24/GT26

GT13E2

GT11N2

501G/701G

35

30

25

20

15

10

5

80 78 84 82 88 86 92 90 96 94 00 98

501D5A

/701D

GE

Siemens

Alstom

WH/MHI

Compressor [3/7]


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10

Pre

ssu

re r

atio

8

66 70 78 74 86 82 98 94 90 02

14

12

18

16

22

20

24

MS9001E

MS5001M

MS7001H

MS6001B

MS9001H

MS7001EF MS9001F MS7001EA

MS9001B

MS7001C

MS7001B MS7001A

MS5001P

MS7001E

MS5001N

MS9001FA

Pressure Ratio - GE

Compressor [4/7]


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200

0

66 70 78 74 86 82 98 94 90 02

600

400

1000

800

1400

1200

1600

MS9001E

MS5001M/R

MS7001H

MS6001B MS6001A

MS9001H

MS7001EF

MS7001FA

MS9001FA

MS7001EA

MS9001B

MS7001C

MS7001B

MS7001A

MS5002A MS5001P MS5002B

MS5001N

Air flo

w, lb

/se

c

MS7001E

Air Flow - GE

Compressor [5/7]


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200

0

1940 1950 1970 1960 1990 1980 2010 2000

600

400

1000

800

1400

1200

Air m

ass flo

w, kg

/se

c

TIT

, C

TIT

Air mass flow

Historical Development of Maximum Air Flows and TITs

Compressor [6/7]


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High Pressure Packing

Sealing became an important issue

as the pressure ratio increases

Brush seals

• Minimize air leakage

• Tolerant of misalignments

• More durable than labyrinth seals

Compressor [7/7]


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The TIT defines the technology level of the gas turbine. The primary objective of increasing the TIT is to

allow for higher power output for a given engine size. Due to the improvements in material science and

blade cooling techniques, the allowable TIT has steadily increased by 10 K every year over the last few

decades and there is hope that this trend will continue. Unfortunately, however, the life of the turbine blade

is halved by each 15 K rise in temperature, hence new technologies are always being sought to suppress

creep, thermal fatigue and oxidation which are the primary mechanisms that limit blade life.

Considerable effort has also been made in developing efficient cooling techniques and surface coating, so

that TITs can be increased.

The TIT will increase to 1600C to get higher combined cycle efficiency.

It seems that the engines have TIT higher than 1600C will little market penetration because of the

necessity of steam cooling. Steam cooling engines will not meet user’s requirements for rapid startup and

steep ramp rates.

The fact that 60 percent efficiency could be obtained only by employment of steam cooling has definitely

proven false.

Higher TITs force the steam turbine throttle temperature above 600C.

The number of turbine stage increased to four as the pressure ratio increase. There is an efficiency gain

associated with the fourth stage because the stage loading will be reduced and larger exhaust area.

Siemens H-class machines have reverted back to DS blades instead of SC blades because of cost

problems.

Recent research activities have been focused in the area of new materials that can withstand higher

temperatures and higher stresses at the same time. This would enable improvement in cycle efficiencies,

decrease the number of turbine stages.


Turbine [1/6]


HIoPE

Turbine Inlet Temperature T

urb

ine

In

let Te

mp

era

ture

, C

7E/9E

501ATS

7EA/9EC

V84.2/V94.2

7H/9H

V84.3A/V94.3A

V84.3

GT11N2

501F/701F

7F/9F

7FA/9FA

GT24/GT26 GT13E2

501G/701G

1600

1500

1400

1300

1200

1100

1000

80 78 84 82 88 86 92 90 96 94 00 98

501D5A/701D

GE

Siemens

Alstom

WH/MHI

Turbine [2/6]

EGT increases with TIT. The HRSG efficiency increases with EGT.


HIoPE

Advanced Vortex Blades

Turbine [3/6]


HIoPE

Precision Casting

• Equi-axial material

• Directional solidification

• Single crystal

Coating

• Oxidation resistance

• Corrosion resistance

• Thermal barrier

Heat Resistance Alloy

Forging

Production Technologies

Turbine [4/6]


HIoPE

Cooling Technologies

Turbine [5/6]

Te

mp

era

ture

, C

1500

1965

Allowable Gas

Temperature Film Cooling

Closed-loop

Cooling

U700

IN738 IN939

IN92DS

1st Gen. SX

2nd Gen. SX

Maximum Material

Temperature 1000

700

TBC; Thermal Barrier Coating

DS; Directional Solidification

SX; Single Crystal

1975 1985 1995 2005 2015

Benefits of

Cooling


HIoPE

Advanced Seal Systems

Turbine [6/6]


HIoPE

Gas Turbine Steam Turbine Remarks

2차유동손실

최소화

배기손실

최소화

• GT: 1) Hot-End Drive

Cold End Drive

2) TBN: 3 4 stages

(large exhaust area)

• ST: 1) Advanced LP exhaust

hood

2) longer LSB

누설손실

최소화

• 작동압력 증가에 따라 누설

제어 중요

• Brush seal 적용

내열소재 Single Crystal

Cooling Technology Ni-alloy Creep 특성 향상

Mechanical Improvement


HIoPE

Thermodynamics 2

Fundamentals for Gas Turbines 1


HIoPE

Turbomachinery Research Development Design Manufacturing Maintenance

Fluid Mechanics

Thermodynamics

Heat Transfer

Solid Mechanics

Vibration

Rotor Dynamics

Material Science

Acoustics

Manufacturing Engineering

Mathematics

Numerical Analysis

Control System

Electrical Engineering

Turbomachinery research, analysis, design, computation, and development involve the interaction of

various subjects. A large turbomachinery company will have experts and groups in most of areas

indicated in this figure.

It would be useful to review some basic concepts and equations in both thermodynamics and fluid

dynamics that are useful for better understanding of turbomachinery.

Which Subject ?


HIoPE

발전설비는 가장 대표적인 열기관

열기관은 열에너지를 기계적인 에너지로 변환시키는 기계장치

열기관에서의 에너지 변환은 열역학 및 유체역학을 이용 분석 (발전설비는 가장 대표적인 열유체기계)

발전설비의 효율 극대화를 위해 극단적인 열 및 유동 조건 적용

• Thermodynamics: the higher maximum cycle temperature and pressure, the greater specific power output and thermal efficiency (A-USC coal-fired power plants, & H-class GTs)

• Fluid dynamics: supersonic flow, stall, surge, choking, cooling

• Materials: heat resistant materials (creep), erosion, corrosion, coating

• Others: reliability/availability

A Typical Gas Turbine for Power

Generation

A Typical Steam Turbine for

Power Generation

Heat Engines

1. Change of State


HIoPE

열역학은 일(work)과 열(heat)을 다루는 과학

• 일: 어떤 물체를 힘을 가해서 이동시켰을 때, 힘과 변위의 곱으로 주어지는 물리량

• 열: 온도차가 존재하는 경우에 계의 경계를 넘어서 이동하는 에너지

• 일과 열은 열역학적 상태량이 아니라 물질의 에너지 상태 및 열역학적 상태량을 달라지게 하는 열역학적인 양(thermodynamic quantities)으로서 일과 열은 에너지 전달이다

일은 쉽게 열로 변환 가능

열 또한 일로 변환 가능. 그러나 열을 일로 바꾸는 것은 쉽지 않음. 이는 일을 하기 위해서는 힘이 필요한데 열 속에는 힘의 요소가 없기 때문에 열을 직접적으로 일로 바꾸기 힘들며, 열을 일로 변환시키기 위해서는 반드시 열기관 필요

열기관은 열에너지를 이용해서 동력을 얻는 장치로서 공기 또는 증기와 같은 물질의 압력 및 온도가 쉽게 변하는 성질을 이용하여 열을 일로 변환시키는 기계적 장치

공기나 증기와 같은 물질을 작동유체(working fluid)라 함

즉, 작동유체는 계 내부를 채우고 있거나 계를 통과하여 흘러가는 유체로서 열에너지를 저장(보관)할 수 있는 능력을 가지고 있으며, 이는 작동유체의 열역학적 상태변화를 통해서 확인 가능

따라서 열기관을 해석하기 위해서 작동유체의 상태변화를 이해하는 것이 매우 중요

열기관에서 작동유체의 상태변화는 여러 가지 과정(process)으로 나타남

대표적인 열역학적 상태량: 온도, 압력, 비체적, 내부에너지, 엔탈피, 엔트로피 등

1. Change of State


HIoPE

Working

Fluids

Water Steam Combustion

Gas

Hydraulic Turbine Steam Turbine Gas Turbine

Air

Wind Turbine

작동유체 종류에 따른 터빈 분류

1. Change of State


HIoPE

상 (phase): 기체, 액체, 고체처럼 화학적 성질과 분자식은 같지만 분자가 모여있는 구조가 다르며, 상질도 약간 다른 모습이 존재하는 것을 말한다. 얼음, 물, 증기의 경우 분자식은 H2O로 같지만 얼음의 경우 분자는 가깝게 모여있고, 액체인 물의 경우 조금 더 떨어져 있고, 증기의 경우에는 훨씬 더 떨어져 있다.

상태 (state): 계를 구성하는 작동유체(working fluid)의 물리적화학적 특성

상태량: 물질의 존재 방식을 나타내는 양

• 대표적 상태량: 온도, 압력, 체적, 질량, 밀도 등

• 추상적 상태량: 내부에너지, 엔트로피 등

• 거시적 상태량: 물질이 다수의 분자로 이루어짐에 따라 이들 양의 조합에 의해 물질의 상태를 나타낼 수 있을 때 이들 양을 거시적 상태량이라 함 (밀도, 온도, 압력 등)

• 미시적 상태량: 분자 수준의 상태로 나타낼 수 있는 양 (질량, 운동량, 에너지 등)

상태변화: 계를 구성하는 작동유체가 열(heat)이나 일(work)에 의하여 한 상태에서 다른 상태로 변화되는 것 (예: 계의 온도나 압력의 변화)

p

1

2

1. Change of State


HIoPE

열역학은 에너지(energy)와 평형(equilibrium)을 다루는 과학

어떤 한 물질(substance)의 열역학적 상태는 에너지를 나타낼 수 있는 상태량(properties)과 평형상태에 이르게 하는 에너지 전달에 의하여 기술

A

B C

비체적 (specific volume): 단위질량당 체적 (종량성 상태량인 체적을 강도성 상태량으로 나타내기 위함)

= V /m [m3/kg]

밀도 (density): 단위체적당 질량

= m /V [kg/m3] ( = 1 / )

상태량 [Properties]

강도성 상태량 종량성 상태량

• 물질의 질량과 관계 없음

• 압력, 온도, 밀도,

• 비체적, 비엔탈피, 비엔트로피, 비내부에너지

• 열역학에서 주로 사용하며, 소문자로

표시

• 물질의 질량에 정비례하여 변함

• 질량, 체적, 엔탈피, 엔트로피, 내부에너지

• 대문자로 표시

1. Change of State


HIoPE

과정(process): 상태가 변해가는 연속적인 경로(path)

과정 종류: 정압과정, 정적과정, 등온과정, 단열과정, 등엔트로피과정, 폴리트로픽과정

가역과정 (reversible process): 어떤 진행된 과정을 거꾸로 진행시켰을 경우 계 및 주위가 최초 상태로 되돌려질 수 있는 과정. 마찰손실을 수반하지 않는 과정 (유체마찰과 열전달이 없는 경우 가역과정이 가능하지만 유체가 흘러가는 동안 마찰과 열전달이 필수적으로 수반되기 때문에 가역과정은 실질적으로 불가능)

비가역과정 (irreversible process): 과정이 진행되는 동안 마찰손실을 수반하는 과정

p

1 2

[ 정압과정 ] [ 정적과정 ] [ 등온과정 ] [ 단열과정 ]

T 1 2

s

T

1

2

s

p

1

2

과정 [Process]

1. Change of State


HIoPE

2. Heat and Work

Heat Work Work Heat

pA

피스톤 운동

dx

W

W

2

1

2

1

2

112 pddxFww

[ 밀폐계에서의 절대일 ]

일(work) = 힘 거리

일은 경로함수(path function) – 불완전미분 (미분기호 “ ” 사용)

m

온도계

낙하추

교반기

액체

[ 줄의 실험장치 ]

줄(Joule)은 단열용기에 물을 채운 상태에서 낙하추를 떨어뜨리는 실험을 통하여 다음 사항을 확인함.

1 kcal = 427 kgf‧m (낙하추 일 마찰열+유체 교란)

p

d

1 2


HIoPE

2. Heat and Work

열역학적 상태량은 상태변화가 일어난 경로(path)에 좌우되어 그 변화량이 결정되는 상태량이 있는 반면에 경로에는 무관하게 최초상태와 최종상태에 의해서만 상태변화량이 결정되는 상태량이 있다.

예를 들면, 열과 일은 상태변화가 일어난 경로에 따라 상태변화량 크기가 달라지는 경로함수(path function)이며, 상태변화량은 수학적으로 불완전미분을 이용해서 구해진다.

이에 반해서 내부에너지의 상태변화량 크기는 상태변화가 일어난 경로에 무관하고 최초상태와 최종상태에 의해서만 상태변화량이 결정되는 점함수(point function)이며, 상태변화량은 수학적으로 완전미분을 이용해서 구해진다.

열역학에서 완전미분에 대해서는 미분기호 d , 불완전미분에 대한 미분기호는 를 사용한다.

완전미분과 불완전미분을 통해서 구해진 상태변화량 크기를 서로 구분하기 위하여 각각 다음과 같이 표현한다.

2

112ww

Path Function vs. Point Function

2

112 hhdh

p 2

1

1 2

b

a

d


HIoPE

[ 열과 일에 대한 방향성 ]

System

Win () Wout (+)

Qout ()

Qin (+)

경계

• The rotor changes the stagnation

enthalpy, kinetic energy, stagnation

of the working fluid.

• In a compressor, the energy is

imparted to the working fluid by a

rotor.

• In a turbine, the energy is

extracted from the fluid.

일의 방향

There are two types of fluid machines, power-

producing and power-absorbing machine. In both

power-producing and power-absorbing machines,

energy transfer takes place between a fluid and a

moving machine part.

The representative power-producing machines are

steam and gas turbines, which extract energy from

fluid.

The representative power-absorbing machines are

compressors and pumps, which transfer energy to

fluid.

2. Heat and Work


HIoPE

Heat

2. Heat and Work

열역학적으로 평형에 도달하는 과정에서 열은 고온체로부터 저온체로 흘러가며, 열평형에 도달한 후에 열은 더 이상 전달되지 않는다.

즉, 열 (heat)은 계와 주위 또는 다른 계와의 온도차에 의하여 이동하는 에너지로서 Q로 표시.

열에 의한 에너지 전달은 다음 식으로 표현한다.

(or )

비열(c)은 단위 질량을 가지는 물질의 온도를 1℃ 상승시키는 데 필요한 열량을 의미한다.

TmcQ mcdTQ

한편, 단위질량당 전달된 열량을 나타내기 위하여 소문자 ‘q'를 사용한다.

열역학적 계에서 전달된 열이 없는 경우 단열(adiabatic)이라 한다.

열은 부호를 가지며, 계로 유입되는 열을 양(+)의 열, 계를 빠져나가는 열을 음(-)의 열이라 한다.

일과 마찬가지로 열도 에너지 전달이다. 그러나 일이 거시적으로 조직화된 에너지 전달인 반면에 열은 미시적으로 비조직화된 에너지 전달이다.

이에 대한 이해를 돕기 위하여 기체로 채워진 밀봉된 용기를 가열하는 경우를 살펴보기로 한다. 이 경우 열역학적 상태량인 온도와 압력을 조사하면 비록 가해진 일이 없더라도 기체의 에너지 상태가 바뀌었다는 것을 알 수 있다. 열역학적 개념에서 열은 이런 에너지 전달을 나타내는 것이다. 그러나 계가 일단 평형상태에 도달하면 에너지가 열에 의해서 전달되었는지 아니면 일에 의해서 전달되었는지 확인하기 어렵다.


HIoPE

열의 방향

Fuel in =

qin (+)

Fuel in =

qin (+)

Exhaust gas =

qout ()

Exhaust gas =

qout ()

Exhaust gas =

qout ()

Fuel in =

qin (+)

2. Heat and Work

http://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&docid=8WEB_QKPWuCp8M&tbnid=Zs1f0f_uaQ2u_M:&ved=0CAUQjRw&url=http://www.epamact.tennessee.edu/rice/riceTour5.shtml&ei=S4DHU8vCOsaE8gWepICwBQ&bvm=bv.71198958,d.dGc&psig=AFQjCNEwdoSzpDOZu8hXnJcc_qwAADRDDQ&ust=1405669719544001


HIoPE

1 kcal = 물 1 kg의 온도를 1℃ (14.5℃15.5℃)상승시키는데 필요한 열량

1 Btu = 물 1 lbm의 온도를 1℉(63℉ 64℉) 상승시키는데 필요한 열량

1 kcal = 4.185 kJ

1 Btu = 0.252 kcal = 1.055 kJ

일의 단위: J(Joule) = N‧m (일 = 힘 거리)

열의 단위:

1) 국제단위계: J

2) 공학단위계: kcal or Btu,

일과 열의 관계: 1 kcal = 427 kgf‧m = 4.185 kJ (Joule’ experiment)

열과 일의 단위

2. Heat and Work


HIoPE

단위계

2. Heat and Work

대부분의 국가에서 국제단위계 사용

단위계 국제단위계 공학단위계 단위 환산

기본단위 길이 (m) 질량 (kg) 시간 (sec)

길이 (m) 힘 (kgf)

시간 (sec)

질량 kg kgfs2/m

힘 N (Newton) kgf 1 kgf = 9.81 N

압력 Pa (=N/m2) kgf/m2 1 kgf/cm2 = 98,069 Pa

일(에너지) J (Joule) kgfm 1 kgfm = 9.81 J

열량 J (Joule) kcal or Btu 1 kcal = 427 kgfm = 4.185 kJ

1 Btu = 778 lbfft = 1.055 kJ

동력 W (Watt) PS 1 PS = 75 kgfm/s = 735.5 W


HIoPE

열역학 제1법칙 = 에너지 보존법칙

국제단위계: Q = W [kJ]

공학단위계: Q = AW [kcal], JQ = W [kgf‧m] (1 kcal = 427 kgf‧m or 1 Btu = 778 lbf‧ft)

A: 일의 열당량 (A = 1/427 kcal/kgf‧m)

J: 열의 일당량 (J = 427 kgf‧m/kcal)

열역학 제1법칙에 대한 표현:

1) 열은 에너지의 한 형태로서 일을 열로 변환시키는 것과 역으로 열을 일로 변환시키는 것이 가능

2) 열을 일로 변환시킬 때 혹은 일을 열로 변환시킬 때 에너지 총량은 변화하지 않고 일정

3) 에너지를 소비하지 않고 계속해서 일을 발생시키는 기계인 제1종 영구기관을 만드는 것은 불가능

3. The First Law of Thermodynamics

754 MJ/s (100%)

205 MW (27.2%) 203 160 119 MW = 482 MW (63.9%)

277 MW (Net Output = 36.7%)

272 MJ/s (36.1%)

가스터빈에서 열과 일의 변화 (국제단위계)


HIoPE


c1

c2 q

w z1

z2

1

2

q w

[ Closed system ]

[ Open system ]

wdeq

계에 가해진 열량은 일부가 일로 변화되고 나머지 일부는 에너지 변환으로 나타남

기계공학(열유체기계) 계에 관계된 에너지는 내부에너지, 유동에너지, 운동에너지, 위치에너지

PEKEFEue

1212

2

1

2

2112212122

1wzzgccppuuq

1212

2

1

2

212122

1wzzgcchhq

일반식:

밀폐계:

개방계:

121212 wuuq

1212

2

1

2

2112212122

1WzzgccppuumQ

wPEdKEdFEdduq )()()(

12

2

11

2

22122

1

2

1wchchq

121212 whhq

wdhq

121,2,12 whhq oo (ho: stagnation enthalpy)

(If KE is small)


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Flow energy (flow work) is the work associated with the masses crossing the control surface.

The term p11 represents the work done by the fluid in the flow channel just upstream of the inlet to move

the fluid ahead of it into the system (control volume), and it thus represents energy flow into the system.

Similarly, p22 is the flow work done by the fluid inside the system to move the fluid ahead of it out of the

system. It represents energy transfer as work leaving the system.

pdmpmddVpdlApFE

Flow Energy [유동에너지]

c1

c2 q

w z1

z2

1

2

[ Open system ]



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wduq 밀폐계에 대한 열역학 제1법칙:

밀폐계 정압과정에 대한 일의 크기는,

따라서 다음과 같은 관계식 성립

결론적으로, 밀폐계 정압과정에서 가열한 열량의 크기는 최종상

태와 초기상태 사이의 (u + p) 상태량 변화와 같아졌으며, 이를

특별한 열역학적 상태량인 엔탈피라한다.

여기서 p를 유동에너지(또는 유동일)라고 한다. 그러므로 엔탈

피는 내부에너지와 유동에너지의 합이다.

2

1112212 pppdww

11122212 pupuq

puh

pA

피스톤 운동

dx

W

W

[ 정압 가열과정]

1212 hhq

Enthalpy


[Exercise 1.1]

1) 발전설비에서 정압가열이 중요한 이유를 설명하시오.

2) 발전설비에서 정압가열 후 가장 중요하게 취급되는 열역학적 상태량은 무엇인가?


HIoPE

Cycle


Cycle: 계를 구성하는 작동유체가 일련의 과정을 거쳐서 최초의 상태로 다시 돌아왔을 경우 사이클(cycle)을 이루었다고 함

Brayton Cycle - Open System Otto Cycle - Closed System

흡입 압축 연소 배기

p

2

1

3

4

2

1

3

4

p


HIoPE

2

1

3

2

4

3

1

4qqqqqqcycle

열역학 제1법칙은 사이클을 겪는 계에 대해서도 성립

WQ

41342312 qqqq

2

1

3

2

4

3

1

4wwwwwwcycle

41342312 wwww

Cycle Integration


[ Otto Cycle ]

[ Sabathe Cycle ]

2

1

3

4

p

1

5

2

3 4

p


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wdhq

개방계에서의 열역학 제1법칙과 열역학

제2기초식을 비교하면,

dpdhq

2

112 dpw

다음과 같은 공업일을 구할 수 있다.

p

2

1

p2

dp

p1

펌프(비압축성유체)인 경우 :

12112 ppw

4. 공업일 (Technical Work)


HIoPE


p

2

1

dp

1

2

0

2 1

p1

p2

1 2

과정 11:

• 흡입과정

• 일의 크기 = p11

과정 12:

• 팽창과정

• 일의 크기 = 면적 1-2-2-1-1

과정 22:

• 배기과정

• 일의 크기= -p22

과정 21:

• 공급압력 상승

• 일의 크기= 0

유동가스가 한 공업일의 크기 =

2

1dp


HIoPE

p

2

1

1 2

b

a

d

절대일 (absolute work) 공업일 (technical work)

p

2

1

p2

dp

p1

밀폐계에서의 일 개방계에서의 일

절대일 vs. 공업일



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Brayton Cycle


p

2

1

3

4

win

(a)

p

2

1

3

4

wout

(b)

p

2

1

3

4

wsys

(c)


HIoPE

cdTq dT

qc

dT

dh

dT

qc

p

p

dT

du

dT

qc

dTcdh p

dTcdu

(열역학 제2기초식 참조)

(열역학 제1기초식 참조)

mcdTQ

c

cp : Specific heat ratio

단원자 가스 : = 5/3 (= 1.67)

2원자 가스 : = 7/5 (= 1.40)

다원자 가스 : = 4/3 (= 1.33)

5. Specific Heat

[ Exercise 1.2 ]

Solid materials have one specific heat. However, all gases

have two different specific heats. Discuss for this.

W

pA

dx

W


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물: 지구상에 존재하는 물질 가운데 비열이 가장 크다.

물이 풍부한 지방이 온화; 겨울 동안 공기(cp=1004.7 J/kgK) 온도가 내려감에 따라 물에서 공기로 열이 전달되기 때문에 공기 온도 증가. 미국 서해안에는 겨울 동안에 동풍이 불기 때문에 동쪽의 육지로 따뜻한 공기가 유입. 따라서 미국의 경우 겨울엔 기후가 온화한 서해안 선호.

Substance J/kgK kcal/kgK

Aluminium 900 0.215

Beryllium 1,820 0.436

Cadmium 230 0.055

Copper 387 0.0924

Germanium 322 0.077

Gold 129 0.0308

Iron 448 0.107

Lead 128 0.0305

Silicon 703 0.168

Silver 234 0.056

Glass 837 0.20

Ice (-5C) 2,090 0.50

Wood 1,700 0.41

Alcohol (ethyl) 2,400 0.58

Mercury 140 0.033

Water (15C) 4,186 1.00

Steam (100C) 2,010 0.48

Specific Heats of Some Substances at 25C and

Atmospheric Pressure

해변에서 공기의 순환

한여름 더운 낮에 모래 위의 차가운 공기는 물 위에 있는 공기보다 더 빨리 가열. 따뜻해진 공기가 부력에 의해 상승하면 물 위의 차가운 공기가 모래사장 쪽으로 유입.

5. Specific Heat


HIoPE

기체의 비열은 각종 엔진의 성능을 계산하는데 필수적으로 사용되는 매우 중요한 물리량 임. 따라서 비열은 매우 정확하게 구해야 함

가스터빈엔진에 있어서 통상적으로 다음과 같은 비열 값과 비열비가 사용

Cold end gas properties: cp = 1004.7 J/kg-K, = 1.4

Hot end gas properties: cp = 1156.9 J/kg-K, = 1.33

이는 Cold end gas는 공기(2원자 가스)이며, Hot end gas는 CO2, H2O, NOx 등과 같은 다원자 가스이기 때문임

그러나 이렇게 일정한 값을 가진다고 가정하여 성능을 계산하는 경우 최대 5% 정도의 오차를 보이는 것으로 알려져 있음

한편, 비열에 대한 정확한 값을 계산하기 위해서는 연료 종류 및 연소 생성물 등을 고려하여 계산해야 함

5. Specific Heat


HIoPE

c

cp (1.4 for air)

Rc1

1

Rcp1

puh

Specific Heat for Ideal Gases

RTuh

RdT

du

dT

dh

Rccp

An ideal gas model assumes that internal energy is only a function of temperature u=u(T). Therefore,

shows that enthalpy is also a function of temperature only.

From this equation and the ratio of specific heat, we can get

RTuh

5. Specific Heat


HIoPE

T1

(hot)

T2

(cold)

q

Heat transfer

There exists a useful thermodynamic variable called entropy (s).

A natural process that starts in one equilibrium state and ends

in another will go in the direction that causes the entropy of the

system plus the environment to increase for an irreversible

process and to remain constant for a reversible process.

T

qds

Entropy = Energy + Tropy

Tropy = Transformation (in Greek)

엔트로피 물질의 열적 상태를 나타내는 물리량 (1865년 Clausius가 제안)

전통적으로 엔트로피라는 물리량은 신비에 싸여 있음 엔트로피가 다른 물리량들에 비해 훨씬 덜 명확함

이는 엔트로피는 그 절대적인 값보다는 그 변화량에 관심을 두기 때문임

압축과정이나 팽창과정에서 엔트로피가 증가된다는 것은 열에너지(thermal energy)가 유용한 일(useful work)로 사용할 수 없는 마찰로 손실된다는 것을 의미

6. Entropy


HIoPE

A

uA

sA

B

uB

sB

A

B

q

,uss

ds

duu

sds

u

pdduTds

Tdsq

Gibbs Equation

pdduq

(Gibb’s equation)

(The first law of thermodynamics)

T

s

2

1

s2 s1 ds

2

112 Tdsq

Tdsq

revT

qds

(for a simple compressible substance)

6. Entropy


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정량적 계산

From Gibbs’ equation and first law of thermodynamics,

and integrating. This gives

Entropy is assigned the value zero at the reference state, Tref = 0 K and pref = 1 atm. The value of entropy at

temperature T and pressure p is then calculated from

p

dpR

T

dTcds

dpdhTds

p

1

21122 ln,,

12

p

pR

T

dTTc

T

dTTcpTspTs

T

Tp

T

Tp

refref

ref

T

Tp

p

pR

T

dTTcpTs

ref

ln,

6. Entropy


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All engine cycles are illustrated schematically by both p- and T-s diagram.

The amount of work produced or supplied can be predicted by p- diagram.

Similarly, the amount of heat supplied or exhausted can be predicted by T-s diagram.

2

112 pdvw

p

2

1

1 2 d

2

112 Tdsq

T

s

2

1

s2 s1 ds

q=Tds

Why we need T-s diagram ?

6. Entropy


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Rankine Cycle

T

s

1

2

3

4

qout

T

s

2

3

qin

1

4

T

s

1 2

3

4

qsys

(a) (b) (c)

T-s diagram

6. Entropy


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Otto Cycle / Diesel Cycle / Brayton Cycle

과정의 s-축에 대한 투영면적이 계로 공급되거나 계를 빠져나간 열량을 나타냄

엔트로피가 증가하면 계 내부로 열량 공급, 엔트로피가 감소하면 계 외부로 열량 배출 의미

(a) (b) (c)

T

s

2

1

3

4

qin

T

s

2

1

3

4

qout

T

s

2

1

3

4 qsys

T-s diagram

6. Entropy


HIoPE

p

p = const.

adiabatic

T

s

=

const.

T = const.

T = const.

s =

co

nst.

(ad

iab

atic)

= const.

p = const.

p- and T-s Diagrams

6. Entropy


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Isentropic Efficiency & Loss

6. Entropy

Ava

ilab

le e

ne

rgy

Use

ful e

ne

rgy

A

B C

D

pi

po

Loss ds

Reduction in useful energy

(Performance degradation)

Increase in entropy due to aging

AB : Isentropic expansion line

AC : Original expansion line

AD : New expansion line due to aging

pi : Pressure at the inlet of turbine

po : Pressure at the outlet of turbine

ds : Increase of entropy due to the loss

h

s

th = Useful energy

Available energy


HIoPE

dT

qds

= entropy increase by heat transfer

= entropy increase due to internal irreversibility, such as friction

T

q

d

T

LWd

= lost work LW

Friction is ignored in thermodynamics, thus this equation is not used generally. However, isentropic

process can be expressed very clearly by this equation.

The Second Law of Thermodynamics

6. Entropy


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12

12

12

12

TT

TT

hh

hh ssC

ss

TTT

TT

hh

hh

43

43

43

43

Efficiency of compressor (or pump)

Efficiency of turbine

Efficiency

6. Entropy

T

s

1

2 2s

3

4s 4

[ Brayton cycle T-s diagram ]


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① 보일러(HRSG)급수펌프에서 다양한 손실 발생 – 펌프 자체효율 존재

② 보일러는 보일러 배관에서 발생하는 마찰손실, 외벽을 통해 빠져나가는 열손실, 연도가스 통로 압력손실, 굴뚝으로 빠져나가는 열손실, 보일러 자체의 열전달 효율이 존재 - 보일러 자체효율 존재

③ 가스터빈/증기터빈에서 다양한 손실 발생 – 가스터빈/증기터빈 자체효율 존재

④ 복수기 손실 발생

⑤ 기계적 손실 발생 – 가스터빈/증기터빈에서 생산된 동력이 발전기에 전달되면서 베어링에서 기계적 손실 발생

⑥ 발전기 자체효율(대개 98~99%) 존재 – 전기적 손실 및 기계적 손실

⑦ 발전소 보조기기(오일펌프, 팬 등)에 사용되는 전력 존재

복합발전에서 Heat Rate를 사용하는 이유

Heat rate는 열입력을 발전기 출력으로 나눈 값

Heat rate는 열효율과 역수 관계

실질적으로 다양한 손실을 반영하여 정확하게 효율을 계산

하기 어려움

7. Heat Rate


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1 kcal = 물(water) 1 kg의 온도를 1C 상승시키는데 필요한 열량

1 Btu = 물(water) 1 lb의 온도를 1F 상승시키는데 필요한 열량

1 kcal = 427 kgfm = 427 kg 9.81 m/s2 m = 4185 Nm = 4.185 kJ

1 Btu = 1 kcal 1/2.204619 5/9 = 0.252 kcal = 1.055 kJ

양변을 시간 h로 나누면,

1 Btu/h = 1.055 kJ/3600 s = 1.055/3600 kW

1 kWh = 3600/1.055 Btu = 3412.14 Btu

따라서 이상적인 경우(열효율 100%)에 1 kWh의 전기를 생산하기 위해서는 3412.14 Btu의 열량이

필요. 그러나 실제적으로는 다양한 손실로 인하여 1 kWh의 전기를 생산하기 위해서는 이상적인

경우보다 더 많은 열량이 요구.

]kJ/kWhorBtu/kWh,[outputgenerator

inputheatrateheat

발전설비 열효율은 각 구성품에서 발생하는 비가역성으로 인하여 계산하기 어렵다. 따라서 열효율 대신에 열입력을 발전기 출력으로 나누어준 열율을 많이 사용

]kJ/kWh[

3600

]Btu/kWh[

14.3412

rateheatrateheatth 열율과 열효율 관계:

7. Heat Rate


HIoPE

The net plant efficiency is affected by three main components, such as net turbine heat rate (NTHR), boiler

efficiency, and auxiliary power consumption.

The net plant efficiency or its reciprocal term net plant heat rate (NPHR) is a key evaluation parameter for

the cost of electricity.

In the US, the net plant efficiency is defined as the ratio of net generated electric energy by the fuel energy,

on a higher heating value (HHV) basis.

NPHR = NTHR/ ((Blr/100) (100%AP)/100) [kJ/kWh (Btu/kWh)]

Where, NTHR = net turbine heat rate, Btu/kWh, input heat by steam divided by net generator output

power.

Blr = boiler fuel efficiency, %, this is the fuel higher heating value energy input to steam.

%AP = percent auxiliary power in % of gross power generation.

Boiler fuel efficiency is the percent of fuel input heat absorbed by the steam.

Boiler efficiency is typically in a range from about 85 to 92%.

Net Plant Efficiency

7. Heat Rate


HIoPE

C + O2 = CO2 + 33.9 MJ/kg

H2 + 1/2O2 = H2O(water) + 143.0 MJ/kg (HHV)

H2 + 1/2O2 = H2O(vapor) + 120.6 MJ/kg (LHV)

S + O2 = SO2 + 9.28 MJ/kg

Combustion

7. Heat Rate


HIoPE

The heat rate will be different by the type of heating value.

In the US, the standard is HHV, whereas in Europe the practice is to use LHV.

The fuel HHV is obtained by laboratory analysis in an oxygen bomb calorimeter.

The LHV of the fuel is computed by subtracting the latent heat of vaporization for water produced by fuel

hydrogen combustion and fuel moisture content.

LHV = HHV – Hfg (M + 8.94H2)/100

where, M is fuel moisture % by weight, Hfg is water latent heat at reference temperature 25C, H2 is fuel

hydrogen % by weight.

The lower heating value of the gas is one in which the H2O in the products has not condensed. The lower

heating value is equal to the higher heating value minus the latent heat of the condensed water vapor.

Heating Value [1/2]

7. Heat Rate


HIoPE

[Exercise 1.3]

어떤 발전소 열효율이 HHV를 기준으로 45%이다. 이 발전소의 열효율을 LHV를 기준으로 계산하시오. 이 발전소에 사용하는 석탄의 HHV는 12540 Btu/lb이며, 석탄은 5.2%의 수분과 4.83%의 수소를 포함하고 있다.

[Solution]

Heat rate를 구하면 다음과 같다.

th,HHV = 3412.14/HRHHV = 0.45 HRHHV = 7,582.5 Btu/kWh

LHV를 계산한다.

LHV = HHV – Hfg (M + 8.94H2)/100 = 12540 – 1049.7 (5.2 + 8.94 4.83)/100

= 12032.15 Btu/lb

LHV/HHV를 계산한다.

LHV/HHV = 12032.15/12540 = 0.9595

따라서 LHV를 기준했을 때 heat rate는 다음과 같다.

HRLHV = HRHHV 0.9595 = 7275.41 Btu/kWh

th,LHV = 3412.14/HRLHV = 3412.14/7275.41 = 46.9%

Heating Value [2/2]

7. Heat Rate


HIoPE

8. Cycle Analysis

p

2

1

3

4

2 1 3

T

s

1 2

3 4 TH

TL

qout ()

qin (+)

s2 s1

The Carnot cycle is the most efficient cycle that can operate between two constant temperature

reservoirs. This is because its processes are reversible.

The Carnot cycle is very useful to compare with other power producing cycles.

The Carnot cycle is an ideal cycle that could not be attained in practice.

Isothermal

compressor

Isentropic

compressor

Isothermal

turbine

Isentropic

turbine

q q

Carnot Cycle


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Process Work Heat

12 Compression at constant temp. w12 = RT1 ln(1/2) (= win) q12 = w12 = T1(s1s2) (= qout)

23 Adiabatic compression w23 = (u3u2) = c(T3T2) (= win) q23 = 0

34 Expansion at constant temp. w34 = RT3 ln(4/3) (= wout) q34 = w34 = T3(s4s3) (= qin)

41 Adiabatic expansion w41 = u4u1 = c(T4T1) (= wout) q41 = 0

wduq

in

out

in

outin

in

sys

in

sys

thq

q

q

qq

q

q

q

w

input

output

1

H

LCarnotth

T

T

T

T

ssT

ssT

111

3

1

343

211,

8. Cycle Analysis

Carnot Cycle

41342312 wwwwwwOutput sys

[Exercise 1.4]

카르노사이클 열효율 향상방법 두 가지를 제시하시오. 1) 2)

121212 wuuq


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T

s

1

2

3

4 qC

wT qB

qB

qB

wP

a

Process Component Heat Work Process

12 Pump q12 = qP = 0 w12 = wP = (h2h1) Power in (adiabatic compression)

23 Boiler q23 = qB = h3h2 w23 = wB = 0 Heat addition at constant pressure

34 Turbine q34 = qT = 0 w34 = wT = h3h4 Power out (adiabatic expansion)

41 Condenser q41 = qC = (h4h1) w41 = wC = 0 Heat release at constant temperature

1212

2

1

2

212122

1wzzgcchhq

Rankine Cycle

8. Cycle Analysis


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Process Component Heat Work Process

12 Compressor q12 = qC = 0 w12 = wC = (h2h1) Power in (adiabatic compression)

23 Combustor q23 = qB = h3h2 w23 = wB = 0 Heat addition at constant pressure

34 Turbine q34 = qT = 0 w34 = wT = h3h4 Power out (adiabatic expansion)

41 Exhaust q41 = qE = (h4h1) w41 = wE = 0 Heat release at constant pressure

1212

2

1

2

212122

1wzzgcchhq

p

2

1

T

(h)

s

qin

3

4 1

2

3

4

qout

win

wout

win

wout

qin

qout

Brayton Cycle

8. Cycle Analysis


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Steam is used in more of today’s power plants than any other working fluid.

The physical properties of steam are complex because any one steam property is changed, such as

pressure, temperature, specific volume, energy or moisture, all the other properties will also change.

The Mollier diagram has been developed to show this interrelationship of steam properties, and how they all

fit together.

The vertical axis is enthalpy(kJ/kg or BTU/lb) which is defined as internal energy plus flow energy of the

working fluid, and the horizontal axis is entropy(kJ/kg-K or BTU/lb-F) representing energy loss.

Mollier diagram shows lines of constant pressure, constant temperature, constant moisture, and the steam

saturation line (below which the steam is wet, and above which the steam is dry and superheated.

h-s Diagram [Mollier Diagram]

8. Cycle Analysis

h-s 선도는 이상기체와 다른 성질을 가지는 실재기체의 상태변화를 실험을 통하여 확인하여 표와 선도로 나타낸 것이다.

h-s 선도는 1906년 R. Mollier가 개발

h를 종축, s를 횡축으로 설정하여 증기의 상태(p, , T, x)를 나타낸 선도.

증기의 상태량(T, p, , x, h, s) 가운데 2개를 알면, h-s 선도로부터 다른 상태량을 알 수 있다.

주로 연소기체나 수증기를 대상으로 하기 때문에 가스터빈 및 증기터빈의 사이클 해석에 이용된다.

압축수의 엔탈피는 파악하기 어렵다.


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8. Cycle Analysis


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Wilson line

T

(h)

s

1

2

3

4

win

wout

qin

qout


8. Cycle Analysis

[Exercise 1.5]

작동유체가 공기(이상기체)인 경우 T-s 선도와 h-s 선도가 동일한 형상을 가지는 이유에 대해서 설명하시오.


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s

h

Turbine

Efficiency 0%

25%

75%

1

h2 at 25%

h2 at 50%

h2 at 75%

h2 at 100%

50%

100%

h2 = h1 at 0%

Turbine efficiency decreases as

the entropy increases during

expansion process.


8. Cycle Analysis


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9. Throttling Process

유체가 노즐이나 오리피스와 같이 갑자기 유로가 좁아지는 곳을 통과하면 외부와 열량이나 일의 교환 없이

도 압력이 감소하는 교축과정(throttling process) 발생

교축과정이 발생하면 와류가 생성되어 에너지가 손실되면서 압력손실 발생

작동유체가 액체인 경우 교축과정이 일어나서 압력이 액체의 포화압력보다 낮아지면 액체의 일부가 증발하

며, 증발에 필요한 열을 액체 자신으로부터 흡수하기 때문에 액체 온도 감소

Pre

ssu

re

p

1 2


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열역학 제1법칙:

단순유동에서 교축과정이 일어나면, 벽면에서의 열전달이 없으며, 이루어진 일이나 공급된 일도

없으며, 위치에너지 변화량도 무시할 수 있으므로,

속도가 40m/s 이하인 경우 운동에너지는 엔탈피 크기에 비해 매우 작다.

교축과정은 발전설비에서 자주 일어나는 과정인데, 특히 증기가 밸브를 통과할 때 교축과정이 발

생하며, 이때 압력강하가 발생한다.

12 hh (교축과정 = 등엔탈피 과정)

1212

2

1

2

212122

1wzzgcchhq

02

1 2

1

2

212 cchh



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작동유체가 이상기체인 경우 교축과정이 발생한 후에 엔탈피는 일정하게 유지됨

엔탈피는 온도만의 함수이므로 교축과정 발생 후에 온도변화 없음

그러나 작동유체가 증기인 경우에는 교축과정이 발생하면 압력과 온도가 떨어져서 에너지 수준이 낮아짐.

주울-톰슨 효과(Joule-Thomson effect)

증기터빈 버켓커버 상부에는 증기누설을 방지하기 위해서 seal을 설치하여 증기누설 방지

Seal을 통해서 누설되는 증기는 seal strips을 통과하면서 교축과정이 발생하기 때문에 실을 빠져나온 증기

는 온도와 압력이 떨어져서 엔탈피가 낮아짐

따라서 누설증기가 다음 단에서 주유동과 합류하더라도 주유동의 에너지 수준을 높이지 못하기 때문에 손실

발생 누설손실

즉 누설증기가 실을 빠져나오면서 에너지를 잃지 않았다면 다음 단에서 사용할 수 있지만 이미 잃어버렸기

때문에 손실 발생

증기 특성



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[Exercise 1.6] Compare the velocity at 2

그림에서 A와 B는 동일한 규격의 도관이다. 도관 B에 오리피스를 설치하였다. 그리고 도관 B 입구압력은

도관 A와 동일하게 유지시킨 상태에서 질량유량을 절반으로 줄였다. 그리고 이때 도관 B의 하류 2에서

압력을 측정하였더니 입구 압력의 절반이었다. 이때 오리피스 하류 2에서 유속을 비교하시오.

1 2

A

1 2

B



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[Solution]

문제에서 주어진 조건은 다음과 같다.

(1)

그리고

교축과정이 일어나면 온도는 변하지 않는다. 따라서 이상기체라고 가정하면 다음 관계식이 성립한다.

그러므로 다음 관계식이 성립한다.

and , therefore, (2)

유동 단면적이 일정하기 때문에 식 (1)은 다음과 같이 된다.

(3)

식 (2)와 식 (3)을 결합하면 다음과 같은 식을 얻는다.

따라서 질량유량이 달라지더라도 압력을 조절하여 하류에서 일정한 속도를 얻을 수 있다.

2,2,2,2,

2

1

2

1ABAB VAVAmm

1,1,2,2

1

2

1ABB ppp

2,2,1,1, BBBB pp

2,1,2 BB

2,2,2,2,2

1AABB VV

2,1,1, AAB 2,2,2 BA

2,2, AB VV



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A turbine has different expansion lines as the load is

decreased.

But the part load expansion lines are generally parallel

to the full load expansion line.

This means that the internal efficiency under part load

conditions is very close to that under full load

conditions. That is, design efficiency of the turbine

blades is maintained during part load operations by

using the control valve.

However, the cycle efficiency is reduced under part

load conditions.

p1

Ava

ilab

le E

ne

rgy

pc

p0

T0

h

s

Partial-flow expansion line

Expansion lines are

essentially parallel

Design-flow expansion line

p1’

p0: Inlet pressure

p1: Throttle pressure 1 1′

2′

2

U 100% load

Nozzle Row

25% load

100%

25%

Bucket Row

U

75% load

50% load

[ Effect of Throttling on Non-Reheat

Steam Turbine Expansion Line ]

[ Velocity Diagram at Various Loads ]



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Load, % 30 40 50 60 70 80 90 100

65

60

75

70

85

80

95

90

100

49.0

48.3

47.6

46.9

46.2

45.5

44.8

44.1

43.4

42.7

42.0 45 50 55 60 65 70 75 80 85 90 95 100

200

500

470

440

410

380

350

320

290

260

230

Load, %

Eff

icie

ncy,

%

Po

we

r, M

W

Power

Efficiency


Comparison of Part Load Efficiency

[ Gas Turbine] [ Steam Turbine]


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Pulverizers

Coal Piping

Coal Burners

교축과정 적용 예 – Coal Pipe Arrangement



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The steam has an initial pressure P1 at the entry to the seal

assembly.

After expanding past the first constriction, the pressure will

have been reduced to condition Xo, with pressure P2.

In the chamber formed between the first and second seal

strips, the kinetic energy of the steam is destroyed and

reconverted at constant pressure P2 to condition X.

From point X, there is then a further expansion of the steam

past the second constriction, with the pressure falling to P3 at

condition Yo.

The kinetic energy is again reconverted in the chamber

between the second and third seal strips, raising the thermal

energy level from Yo to Y at constant pressure P3.

This process of expansion and kinetic energy reconversion is

continued throughout the series of seal strips until the final

expansion takes the steam to condition Qo at pressure P5.

The locus of the points Xo….Qo is called the Fanno curve.

h

s

T1

P1 P2 P3 P4

P5

Xo Yo Zo

Qo

X Y Z

Leakage

Flow

P1 P2 P3 P4 P5

X Y Z

Rotation Side

Principle of Labyrinth Seal



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질의 및 응답

작성자: 이 병 은 (공학박사) 작성일: 2015.02.11 (Ver.5) 연락처: [email protected]

Mobile: 010-3122-2262 저서: 실무 발전설비 열역학/증기터빈 열유체기술

1. Fundamentals of Gas Turbines - · PDF file7FA, GE . Combined Cycle Power Plants 1....

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